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Refrigerator

A refrigerator, colloquially fridge, is a commercial and home appliance consisting of a thermally insulated compartment and a heat pump (mechanical, electronic or chemical) that transfers heat from its inside to its external environment so that its inside is cooled to a temperature below the room temperature. Refrigeration is an essential food storage technique around the world. The low temperature lowers the reproduction rate of bacteria, so the refrigerator reduces the rate of spoilage. A refrigerator maintains a temperature a few degrees above the freezing point of water. The optimal temperature range for perishable food storage is 3 to 5 C. A freezer is a specialized refrigerator, or portion of a refrigerator, that maintains its contents’ temperature below the freezing point of water. The refrigerator replaced the icebox, which had been a common household appliance for almost a century and a half. The United States Food and Drug Administration recommends that the refrigerator be kept at or below 40 °F and that the freezer be regulated at 0 °F.

The first cooling systems for food involved ice. Artificial refrigeration began in the mid-1750s, and developed in the early 1800s. In 1834, the first working vapor-compression refrigeration, using the same technology seen in air conditioners, system was built. The first commercial ice-making machine was invented in 1854. In 1913, refrigerators for home use were invented. In 1923 Frigidaire introduced the first self-contained unit. The introduction of Freon in the 1920s expanded the refrigerator market during the 1930s. Home freezers as separate compartments (larger than necessary just for ice cubes) were introduced in 1940. Frozen foods, previously a luxury item, became commonplace.

Freezer units are used in households as well as in industry and commerce. Commercial refrigerator and freezer units were in use for almost 40 years prior to the common home models. The freezer-over-refrigerator style had been the basic style since the 1940s, until modern, side-by-side refrigerators broke the trend. A vapor compression cycle is used in most household refrigerators, refrigerator–freezers and freezers. Newer refrigerators may include automatic defrosting, chilled water, and ice from a dispenser in the door.

Domestic refrigerators and freezers for food storage are made in a range of sizes. Among the smallest are Peltier-type refrigerators designed to chill beverages. A large domestic refrigerator stands as tall as a person and may be about 1 m wide with a capacity of 0.6 m3. Refrigerators and freezers may be free standing, or built into a kitchen. The refrigerator allows the modern household to keep food fresh for longer than before. Freezers allow people to buy perishable food in bulk and eat it at leisure, and make bulk purchases.

Technology development
Ancient origins

Ancient Iranians were among the first to invent a form of cooler utilizing the principles of evaporative cooling and radiative cooling called yakhchāls. These complexes used subterranean storage spaces, a large thickly insulated above-ground domed structure, and outfitted with badgirs (wind-catchers) and series of qanats (aqueducts).

Pre-electric refrigeration

In modern times, before the invention of the modern electric refrigerator, icehouses and iceboxes were used to provide cool storage for most of the year. Placed near freshwater lakes or packed with snow and ice during the winter, they were once very common. Natural means are still used to cool foods today. On mountainsides, runoff from melting snow is a convenient way to cool drinks, and during the winter one can keep milk fresh much longer just by keeping it outdoors. The word "refrigeratory" was used at least as early as the 17th century.

Artificial refrigeration The history of artificial refrigeration began when Scottish professor William Cullen designed a small refrigerating machine in 1755. Cullen used a pump to create a partial vacuum over a container of diethyl ether, which then boiled, absorbing heat from the surrounding air. The experiment even created a small amount of ice, but had no practical application at that time.

In 1805, American inventor Oliver Evans described a closed vapor-compression refrigeration cycle for the production of ice by ether under vacuum. In 1820, the British scientist Michael Faraday liquefied ammonia and other gases by using high pressures and low temperatures, and in 1834, an American expatriate in Great Britain, Jacob Perkins, built the first working vapor-compression refrigeration system. It was a closed-cycle device that could operate continuously. A similar attempt was made in 1842, by American physician, John Gorrie, who built a working prototype, but it was a commercial failure. American engineer Alexander Twining took out a British patent in 1850 for a vapor compression system that used ether.

The first practical vapor compression refrigeration system was built by James Harrison, a Scottish Australian. His 1856 patent was for a vapor compression system using ether, alcohol or ammonia. He built a mechanical ice-making machine in 1851 on the banks of the Barwon River at Rocky Point in Geelong, Victoria, and his first commercial ice-making machine followed in 1854. Harrison also introduced commercial vapor-compression refrigeration to breweries and meat packing houses, and by 1861, a dozen of his systems were in operation.

The first gas absorption refrigeration system (compressor-less and powered by a heat-source) was developed by Edward Toussaint of France in 1859 and patented in 1860. It used gaseous ammonia dissolved in water ("aqua ammonia").

Carl von Linde, an engineering professor at the Technological University Munich in Germany, patented an improved method of liquefying gases in 1876, creating the first reliable and efficient compressed-ammonia refrigerator. His new process made possible the use of gases such as ammonia (NH3), sulfur dioxide (SO2) and methyl chloride (CH3Cl) as refrigerants, which were widely used for that purpose until the late 1920s despite safety concerns. In 1895 he discovered the refrigeration cycle.

Electric refrigerators
In 1894, Hungarian inventor and industrialist István Röck started to manufacture a large industrial ammonia refrigerator which was powered by electric compressors (together with the Esslingen Machine Works). Its electric compressors were manufactured by the Ganz Works. At the 1896 Millennium Exhibition, Röck and the Esslingen Machine Works presented a 6-tonne capacity artificial ice producing plant. In 1906, the first large Hungarian cold store (with a capacity of 3,000 tonnes, the largest in Europe) opened in Tóth Kálmán Street, Budapest, the machine was manufactured by the Ganz Works. Until nationalisation after the Second World War, large-scale industrial refrigerator production in Hungary was in the hands of Röck and Ganz Works.

Commercial refrigerator and freezer units, which go by many other names, were in use for almost 40 years prior to the common home models. They used gas systems such as ammonia (R-717) or sulfur dioxide (R-764), which occasionally leaked, making them unsafe for home use. Practical household refrigerators were introduced in 1915 and gained wider acceptance in the United States in the 1930s as prices fell and non-toxic, non-flammable synthetic refrigerants such as Freon-12 (R-12) were introduced. However, R-12 proved to be damaging to the ozone layer, causing governments to issue a ban on its use in new refrigerators and air-conditioning systems in 1994. The less harmful replacement for R-12, R-134a (tetrafluoroethane), has been in common use since 1990, but R-12 is still found in many old systems.

The glass-fronted beverage cooler is mostly used as a commercial refrigerator. These types of appliances are usually designed for specific load requirements, resulting in a larger cooling mechanism. This ensures that they are able to cope with a large throughput of drinks and frequent door opening. As a result, it is common for these types of commercial refrigerators to compose up to 50% of the energy usage of a supermarket.

Residential refrigerators
In 1913, the first electric refrigerators for home and domestic use were invented and produced by Fred W. Wolf of Fort Wayne, Indiana, with models consisting of a unit that was mounted on top of an ice box. His first device, produced over the next few years in several hundred units, was called DOMELRE. In 1914, engineer Nathaniel B. Wales of Detroit, Michigan, introduced an idea for a practical electric refrigeration unit, which later became the basis for the Kelvinator. A self-contained refrigerator, with a compressor on the bottom of the cabinet was invented by Alfred Mellowes in 1916. Mellowes produced this refrigerator commercially but was bought out by William C. Durant in 1918, who started the Frigidaire company to mass-produce refrigerators. In 1918, Kelvinator company introduced the first refrigerator with any type of automatic control. The absorption refrigerator was invented by Baltzar von Platen and Carl Munters from Sweden in 1922, while they were still students at the Royal Institute of Technology in Stockholm. It became a worldwide success and was commercialized by Electrolux. Other pioneers included Charles Tellier, David Boyle, and Raoul Pictet. Carl von Linde was the first to patent and make a practical and compact refrigerator.

These home units usually required the installation of the mechanical parts, motor and compressor, in the basement or an adjacent room while the cold box was located in the kitchen. There was a 1922 model that consisted of a wooden cold box, water-cooled compressor, an ice cube tray and a 9 cuft compartment, and cost $714. (A 1922 Model-T Ford cost about $476.) By 1923, Kelvinator held 80 percent of the market for electric refrigerators. Also in 1923 Frigidaire introduced the first self-contained unit. About this same time porcelain-covered metal cabinets began to appear. Ice cube trays were introduced more and more during the 1920s; up to this time freezing was not an auxiliary function of the modern refrigerator.

The first refrigerator to see widespread use was the General Electric "Monitor-Top" refrigerator introduced in 1927, so-called, by the public, because of its resemblance to the gun turret on the ironclad warship USS Monitor of the 1860s. The compressor assembly, which emitted a great deal of heat, was placed above the cabinet, and enclosed by a decorative ring. Over a million units were produced. As the refrigerating medium, these refrigerators used either sulfur dioxide, which is corrosive to the eyes and may cause loss of vision, painful skin burns and lesions, or methyl formate, which is highly flammable, harmful to the eyes, and toxic if inhaled or ingested.

The introduction of Freon in the 1920s expanded the refrigerator market during the 1930s and provided a safer, low-toxicity alternative to previously used refrigerants. Separate freezers became common during the 1940s; the term for the unit, popular at the time, was deep freeze. These devices, or appliances, did not go into mass production for use in the home until after World War II. The 1950s and 1960s saw technical advances like automatic defrosting and automatic ice making. More efficient refrigerators were developed in the 1970s and 1980s, even though environmental issues led to the banning of very effective (Freon) refrigerants. Early refrigerator models (from 1916) had a cold compartment for ice cube trays. From the late 1920s fresh vegetables were successfully processed through freezing by the Postum Company (the forerunner of General Foods), which had acquired the technology when it bought the rights to Clarence Birdseye's successful fresh freezing methods.

Styles of refrigerators
In the early 1950s most refrigerators were white, but from the mid-1950s to the present day, designers and manufacturers have put color onto refrigerators. In the late-1950s/early-1960s, pastel colors, like turquoise and pink, became popular, and brushed chrome-plating (similar to a stainless steel finish) was available on some models. In the late 1960s and throughout the 1970s, earth tone colors were popular, including Harvest Gold, Avocado Green and almond. In the 1980s, black became fashionable. In the late 1990s stainless steel came into vogue. Since 1961 the Color Marketing Group has attempted to coordinate the colors of appliances and other consumer goods.

Freezer
Freezer units are used in households and in industry and commerce. Food stored at or below -18 °C is safe indefinitely. Most household freezers maintain temperatures from -23 to -18 C, although some freezer-only units can achieve −34 °C and lower. Refrigerator freezers generally do not achieve lower than -23 °C, since the same coolant loop serves both compartments: Lowering the freezer compartment temperature excessively causes difficulties in maintaining above-freezing temperature in the refrigerator compartment. Domestic freezers can be included as a separate compartment in a refrigerator, or can be a separate appliance. Domestic freezers may be either upright, resembling a refrigerator, or chest freezers, wider than tall with the lid or door on top, sacrificing convenience for efficiency and partial immunity to power outages. Many modern upright freezers come with an ice dispenser built into their door. Some upscale models include thermostat displays and controls.

Home freezers as separate compartments (larger than necessary just for ice cubes), or as separate units, were introduced in the United States in 1940. Frozen foods, previously a luxury item, became commonplace.

In 1955 the domestic deep freezer, which was cold enough to allow the owners to freeze fresh food themselves rather than buying food already frozen with Clarence Birdseye's process, went on sale.

Walk-in freezer
There are walk in freezers, as the name implies, they allow for one to walk into the freezer. Safety regulations requires an emergency releases and employers should check to ensure no one will trapped inside when the unit gets locked as hypothermia is possible if one is in freezer for longer periods of time.

Compressor refrigerators
A vapor compression cycle is used in most household refrigerators, refrigerator–freezers and freezers. In this cycle, a circulating refrigerant such as R134a enters a compressor as low-pressure vapor at or slightly below the temperature of the refrigerator interior. The vapor is compressed and exits the compressor as high-pressure superheated vapor. The superheated vapor travels under pressure through coils or tubes that make up the condenser; the coils or tubes are passively cooled by exposure to air in the room. The condenser cools the vapor, which liquefies. As the refrigerant leaves the condenser, it is still under pressure but is now only slightly above room temperature. This liquid refrigerant is forced through a metering or throttling device, also known as an expansion valve (essentially a pin-hole sized constriction in the tubing) to an area of much lower pressure. The sudden decrease in pressure results in explosive-like flash evaporation of a portion (typically about half) of the liquid. The latent heat absorbed by this flash evaporation is drawn mostly from adjacent still-liquid refrigerant, a phenomenon known as auto-refrigeration. This cold and partially vaporized refrigerant continues through the coils or tubes of the evaporator unit. A fan blows air from the compartment ("box air") across these coils or tubes and the refrigerant completely vaporizes, drawing further latent heat from the box air. This cooled air is returned to the refrigerator or freezer compartment, and so keeps the box air cold. Note that the cool air in the refrigerator or freezer is still warmer than the refrigerant in the evaporator. Refrigerant leaves the evaporator, now fully vaporized and slightly heated, and returns to the compressor inlet to continue the cycle.

Modern domestic refrigerators are extremely reliable because motor and compressor are integrated within a welded container, "sealed unit", with greatly reduced likelihood of leakage or contamination. By comparison, externally-coupled refrigeration compressors, such as those in automobile air conditioning, inevitably leak fluid and lubricant past the shaft seals. This leads to a requirement for periodic recharging and, if ignored, possible compressor failure.

Dual compartment designs
Refrigerators with two compartments need special design to control the cooling of refrigerator or freezer compartments. Typically, the compressors and condenser coils are mounted at the top of the cabinet, with a single fan to cool them both. This arrangement has a few downsides: each compartment cannot be controlled independently and the more humid refrigerator air is mixed with the dry freezer air.

Multiple manufacturers offer dual compressor models. These models have separate freezer and refrigerator compartments that operate independently of each other, sometimes mounted within a single cabinet. Each has its own separate compressor, condenser and evaporator coils, insulation, thermostat, and door.

A hybrid between the two designs is using a separate fan for each compartment, the Dual Fan approach. Doing so allows for separate control and airflow on a single compressor system.

Absorption refrigerators
An absorption refrigerator works differently from a compressor refrigerator, using a source of heat, such as combustion of liquefied petroleum gas, solar thermal energy or an electric heating element. These heat sources are much quieter than the compressor motor in a typical refrigerator. A fan or pump might be the only mechanical moving parts; reliance on convection is considered impractical.

Other uses of an absorption refrigerator (or "chiller") include large systems used in office buildings or complexes such as hospitals and universities. These large systems are used to chill a brine solution that is circulated through the building.

Peltier effect refrigerators
The Peltier effect uses electricity to pump heat directly; refrigerators employing this system are sometimes used for camping, or in situations where noise is not acceptable. They can be totally silent (if a fan for air circulation is not fitted) but are less energy-efficient than other methods.

Ultra-low temperature refrigerators
"Ultra-cold" or "ultra-low temperature (ULT)" (typically -80 or −86 °C) freezers, as used for storing biological samples, also generally employ two stages of cooling, but in cascade. The lower temperature stage uses methane, or a similar gas, as a refrigerant, with its condenser kept at around −40°C by a second stage which uses a more conventional refrigerant.

For much lower temperatures, laboratories usually purchase liquid nitrogen (-196 °C), kept in a Dewar flask, into which the samples are suspended. Cryogenic chest freezers can achieve temperatures of down to -150 °C, and may include a liquid nitrogen backup.

Other refrigerators
Alternatives to the vapor-compression cycle not in current mass production include:

 * Acoustic cooling
 * Air cycle
 * Magnetic cooling
 * Malone engine
 * Pulse tube
 * Stirling cycle
 * Thermoelectric cooling
 * Thermionic cooling
 * Vortex tube
 * Water cycle systems.

Architecture
Many modern refrigerator/freezers have the freezer on top and the refrigerator on the bottom. Most refrigerator-freezers—except for manual defrost models or cheaper units—use what appears to be two thermostats. Only the refrigerator compartment is properly temperature controlled. When the refrigerator gets too warm, the thermostat starts the cooling process and a fan circulates the air around the freezer. During this time, the refrigerator also gets colder. The freezer control knob only controls the amount of air that flows into the refrigerator via a damper system. Changing the refrigerator temperature will inadvertently change the freezer temperature in the opposite direction. Changing the freezer temperature will have no effect on the refrigerator temperature. The freezer control may also be adjusted to compensate for any refrigerator adjustment.

This means the refrigerator may become too warm. However, because only enough air is diverted to the refrigerator compartment, the freezer usually re-acquires the set temperature quickly, unless the door is opened. When a door is opened, either in the refrigerator or the freezer, the fan in some units stops immediately to prevent excessive frost build up on the freezer's evaporator coil, because this coil is cooling two areas. When the freezer reaches temperature, the unit cycles off, no matter what the refrigerator temperature is. Modern computerized refrigerators do not use the damper system. The computer manages fan speed for both compartments, although air is still blown from the freezer.

Features

Newer refrigerators may include: These older freezer compartments were the main cooling body of the refrigerator, and only maintained a temperature of around -6 °C, which is suitable for keeping food for a week.
 * Automatic defrosting
 * A power failure warning that alerts the user by flashing a temperature display. It may display the maximum temperature reached during the power failure, and whether frozen food has defrosted or may contain harmful bacteria.
 * Chilled water and ice from a dispenser in the door. Water and ice dispensing became available in the 1970s. In some refrigerators, the process of making ice is built-in so the user doesn't have to manually use ice trays. Some refrigerators have water chillers and water filtration systems.
 * Cabinet rollers that lets the refrigerator roll out for easier cleaning
 * Adjustable shelves and trays
 * A status indicator that notifies when it is time to change the water filter
 * An in-door ice caddy, which relocates the ice-maker storage to the freezer door and saves approximately 60 L of usable freezer space. It is also removable, and helps to prevent ice-maker clogging.
 * A cooling zone in the refrigerator door shelves. Air from the freezer section is diverted to the refrigerator door, to cool milk or juice stored in the door shelf.
 * A drop down door built into the refrigerator main door, giving easy access to frequently used items such as milk, thus saving energy by not having to open the main door.
 * A Fast Freeze function to rapidly cool foods by running the compressor for a predetermined amount of time and thus temporarily lowering the freezer temperature below normal operating levels. It is recommended to use this feature several hours before adding more than 1 kg of unfrozen food to the freezer. For freezers without this feature, lowering the temperature setting to the coldest will have the same effect.
 * Freezer Defrost: Early freezer units accumulated ice crystals around the freezing units. This was a result of humidity introduced into the units when the doors to the freezer were opened condensing on the cold parts, then freezing. This frost buildup required periodic thawing ("defrosting") of the units to maintain their efficiency. Manual Defrost (referred to as Cyclic) units are still available. Advances in automatic defrosting eliminating the thawing task were introduced in the 1950s, but are not universal, due to energy performance and cost. These units used a counter that only defrosted the freezer compartment (Freezer Chest) when a specific number of door openings had been made. The units were just a small timer combined with an electrical heater wire that heated the freezer's walls for a short amount of time to remove all traces of frost/frosting. Also, early units featured freezer compartments located within the larger refrigerator, and accessed by opening the refrigerator door, and then the smaller internal freezer door; units featuring an entirely separate freezer compartment were introduced in the early 1960s, becoming the industry standard by the middle of that decade.

 * Butter heater: In the early 1950s, the butter conditioner's patent was filed and published by the inventor Nave Alfred E. This feature was supposed to "provide a new and improved food storage receptacle for storing butter or the like which may quickly and easily be removed from the refrigerator cabinet for the purpose of cleaning." Because of the high interest to the invention, companies in UK, New Zealand, and Australia started to include the feature into the mass refrigerator production and soon it became a symbol of the local culture. However, not long after that it was removed from production as according to the companies this was the only way for them to meet new ecology regulations and they found it inefficient to have a heat generating device inside a refrigerator.

Later advances included automatic ice units and self compartmentalized freezing units.

Types of domestic refrigerators
Domestic refrigerators and freezers for food storage are made in a range of sizes. Among the smallest is a 4 L Peltier refrigerator advertised as being able to hold 6 cans of beer. A large domestic refrigerator stands as tall as a person and may be about 1 m wide with a capacity of 600 L. Some models for small households fit under kitchen work surfaces, usually about 86 cm high. Refrigerators may be combined with freezers, either stacked with refrigerator or freezer above, below, or side by side. A refrigerator without a frozen food storage compartment may have a small section just to make ice cubes. Freezers may have drawers to store food in, or they may have no divisions (chest freezers).

Refrigerators and freezers may be free-standing, or built into a kitchen's cabinet.

Three distinct classes of refrigerator are common:

Compressor refrigerators

 * Compressor refrigerators are by far the most common type; they make a noticeable noise, but are most efficient and give greatest cooling effect. Portable compressor refrigerators for recreational vehicle (RV) and camping use are expensive but effective and reliable. Refrigeration units for commercial and industrial applications can be made in various sizes, shapes and styles to fit customer needs. Commercial and industrial refrigerators may have their compressors located away from the cabinet (similar to split system air conditioners) to reduce noise nuisance and reduce the load on air conditioning in hot weather.

Absorption refrigerator

 * Absorption refrigerators may be used in caravans and trailers, and dwellings lacking electricity, such as farms or rural cabins, where they have a long history. They may be powered by any heat source: gas (natural or propane) or kerosene being common. Models made for camping and RV use often have the option of running (inefficiently) on 12 volt battery power.

Peltier refrigerators

 * Peltier refrigerators are powered by electricity, usually 12 volt DC, but mains-powered wine coolers are available. Peltier refrigerators are inexpensive but inefficient and become progressively more inefficient with increased cooling effect; much of this inefficiency may be related to the temperature differential across the short distance between the "hot" and "cold" sides of the Peltier cell. Peltier refrigerators generally use heat sinks and fans to lower this differential; the only noise produced comes from the fan. Reversing the polarity of the voltage applied to the Peltier cells results in a heating rather than cooling effect.

Other specialized cooling mechanisms may be used for cooling, but have not been applied to domestic or commercial refrigerators.

Magnetic refrigerator

 * Magnetic refrigerators are refrigerators that work on the magnetocaloric effect. The cooling effect is triggered by placing a metal alloy in a magnetic field.
 * Acoustic refrigerators are refrigerators that use resonant linear reciprocating motors/alternators to generate a sound that is converted to heat and cold using compressed helium gas. The heat is discarded and the cold is routed to the refrigerator.

Energy efficiency

In a house without air-conditioning (space heating and/or cooling) refrigerators consumed more energy than any other home device. In the early 1990s a competition was held among the major manufacturers to encourage energy efficiency. Current US models that are Energy Star qualified use 50% less energy than the average models made in 1974. The most energy-efficient unit made in the US consumes about half a kilowatt-hour per day (equivalent to 20 W continuously). But even ordinary units are quite efficient; some smaller units use less than 0.2 kWh per day (equivalent to 8 W continuously). Larger units, especially those with large freezers and icemakers, may use as much as 4 kW·h per day (equivalent to 170 W continuously). The European Union uses a letter-based mandatory energy efficiency rating label instead of the Energy Star; thus EU refrigerators at the point of sale are labelled according to how energy-efficient they are.

For US refrigerators, the Consortium on Energy Efficiency (CEE) further differentiates between Energy Star qualified refrigerators. Tier 1 refrigerators are those that are 20% to 24.9% more efficient than the Federal minimum standards set by the National Appliance Energy Conservation Act (NAECA). Tier 2 are those that are 25% to 29.9% more efficient. Tier 3 is the highest qualification, for those refrigerators that are at least 30% more efficient than Federal standards. About 82% of the Energy Star qualified refrigerators are Tier 1, with 13% qualifying as Tier 2, and just 5% at Tier 3.

Besides the standard style of compressor refrigeration used in ordinary household refrigerators and freezers, there are technologies such as absorption refrigeration and magnetic refrigeration. Although these designs generally use a much larger amount of energy compared to compressor refrigeration, other qualities such as silent operation or the ability to use gas can favor these refrigeration units in small enclosures, a mobile environment or in environments where unit failure would lead to devastating consequences.

Many refrigerators made in the 1930s and 1940s were far more efficient than most that were made later. This is partly attributable to the addition of new features, such as auto-defrost, that reduced efficiency. Additionally, after World War 2, refrigerator style became more important than efficiency. This was especially true in the US in the 1970s, when side-by-side models (known as American fridgefreezers outside of the US) with ice dispensers and water chillers became popular. However, the reduction in efficiency also arose partly from reduction in the amount of insulation to cut costs.

Today

Because of the introduction of new energy efficiency standards, refrigerators made today are much more efficient than those made in the 1930s; they consume the same amount of energy while being three times as large.

The efficiency of older refrigerators can be improved by defrosting (if the unit is manual defrost) and cleaning them regularly, replacing old and worn door seals with new ones, adjusting the thermostat to accommodate the actual contents (a refrigerator needn't be colder than 4 °C to store drinks and non-perishable items) and also replacing insulation, where applicable. Some sites recommend cleaning condenser coils every month or so on units with coils on the rear, to add life to the coils and not suffer an unnoticeable deterioration in efficiency over an extended period, the unit should be able to ventilate or "breathe" with adequate spaces around the front, back, sides and above the unit. If the refrigerator uses a fan to keep the condenser cool, then this must be cleaned or serviced, at per individual manufactures recommendations.

Auto defrosting
Frost-free refrigerators or freezers use electric fans to cool the appropriate compartment. This could be called a "fan forced" refrigerator, whereas manual defrost units rely on colder air lying at the bottom, versus the warm air at the top to achieve adequate cooling. The air is drawn in through an inlet duct and passed through the evaporator where it is cooled, the air is then circulated throughout the cabinet via a series of ducts and vents. Because the air passing the evaporator is supposedly warm and moist, frost begins to form on the evaporator (especially on a freezer's evaporator). In cheaper and/or older models, a defrost cycle is controlled via a mechanical timer. This timer is set to shut off the compressor and fan and energize a heating element located near or around the evaporator for about 15 to 30 minutes at every 6 to 12 hours. This melts any frost or ice build-up and allows the refrigerator to work normally once more. It is believed that frost free units have a lower tolerance for frost, due to their air-conditioner-like evaporator coils. Therefore, if a door is left open accidentally (especially the freezer), the defrost system may not remove all frost, in this case, the freezer (or refrigerator) must be defrosted.

If the defrosting system melts all the ice before the timed defrosting period ends, then a small device (called a defrost limiter) acts like a thermostat and shuts off the heating element to prevent too large a temperature fluctuation, it also prevents hot blasts of air when the system starts again, should it finish defrosting early. On some early frost-free models, the defrost limiter also sends a signal to the defrost timer to start the compressor and fan as soon as it shuts off the heating element before the timed defrost cycle ends. When the defrost cycle is completed, the compressor and fan are allowed to cycle back on.

Frost-free refrigerators, including some early frost-free refrigerators/freezers that used a cold plate in their refrigerator section instead of airflow from the freezer section, generally don't shut off their refrigerator fans during defrosting. This allows consumers to leave food in the main refrigerator compartment uncovered, and also helps keep vegetables moist. This method also helps reduce energy consumption, because the refrigerator is above freeze point and can pass the warmer-than-freezing air through the evaporator or cold plate to aid the defrosting cycle.

Inverter
With the advent of digital inverter compressors, the energy consumption is even further reduced than a single-speed induction motor compressor, and thus contributes far less in the way of greenhouse gases.

The energy consumption of a refrigerator is also dependent on the type of refrigeration being done. For instance, Inverter Refrigerators consume comparatively less energy than a typical non-inverter refrigerator. In an inverter refrigerator, the compressor is used conditionally on requirement basis. For instance, an inverter refrigerator might use less energy during the winters than it does during the summers. This is because the compressor works for a shorter time than it does during the summers.

Further, newer models of inverter compressor refrigerators take into account various external and internal conditions to adjust the compressor speed and thus optimize cooling and energy consumption. Most of them use at least 4 sensors which help detect variance in external temperature, internal temperature owing to opening of the refrigerator door or keeping new food inside; humidity and usage patterns. Depending on the sensor inputs, the compressor adjusts its speed. For example, if door is opened or new food is kept, the sensor detects an increase in temperature inside the cabin and signals the compressor to increase its speed till a pre-determined temperature is attained. After which, the compressor runs at a minimum speed to just maintain the internal temperature. The compressor typically runs between 1200 and 4500 rpm. Inverter compressors not only optimizes cooling but is also superior in terms of durability and energy efficiency. A device consumes maximum energy and undergoes maximum wear and tear when it switches itself on. As an inverter compressor never switches itself off and instead runs on varying speed, it minimizes wear and tear and energy usage. LG played a significant role in improving inverter compressors as we know it by reducing the friction points in the compressor and thus introducing Linear Inverter Compressors. Conventionally, all domestic refrigerators use a reciprocating drive which is connected to the piston. But in a linear inverter compressor, the piston which is a permanent magnet is suspended between two electromagnets. The AC changes the magnetic poles of the electromagnet, which results in the push and pull that compresses the refrigerant. LG claims that this helps reduce energy consumption by 32% and noise by 25% compared to their conventional compressors.

Form factor
The physical design of refrigerators also plays a large part in its energy efficiency. The most efficient is the chest-style freezer, as its top-opening design minimizes convection when opening the doors, reducing the amount of warm moist air entering the freezer. On the other hand, in-door ice dispensers cause more heat leakage, contributing to an increase in energy consumption.

Global adoption
The gradual global adoption of refrigerators marks a transformative era in food preservation and domestic convenience. Since the refrigerators introduction in the 20th century, refrigerators have transitioned from being luxurious items to everyday commodities which have altered the understandings of food storage practices. Refrigerators have significantly impacted various aspects of many individual's daily lives by providing food safety to people around the world spanning across a wide variety of cultural and socioeconomic backgrounds.

The global adoption of refrigerators has also changed how societies handle their food supply. The introduction of the refrigerator in different societies has resulted in the monetization and industrialized mass food production systems which are commonly linked to increased food waste, animal wastes, and dangerous chemical wastes being traced back into different ecosystems. In addition, refrigerators have also provided an easier way to access food for many individuals around the world, with man options that commercialization has promoted leaning towards low-nutrient dense foods.

After consumer refrigerators became financially viable for production and sale on a large scale, their prevalence around the globe expanded greatly. In the United States an estimated 99.5% of households have a refrigerator. Refrigerator ownership are more common in developed western countries, but has stayed relatively low in eastern and developing countries despite its growing popularity. Throughout Eastern Europe and the Middle East, only 80% of its population own refrigerators. In addition to this, 65% of the population in China are stated to have refrigerators. The distribution of consumer refrigerators are also skewed as urban areas exhibit larger refrigeration ownership percentages compared to rural areas.

Supplantation of the Ice Trade
The Ice Trade was a industry in the 19th and 20th century of the harvesting, transportation, and sale of natural and artificial ice for the purposes of refrigeration and consumption. The majority of the ice used for trade was harvested from North America and transported globally with some smaller operations working out of Norway. With the introduction of more affordable large and home scale refrigeration around the 1920's, the need for large scale ice harvest and transportation was no longer needed, and the Ice Trade subsequently slowed and shrank to smaller scale local services or disappeared altogether.

Effect on diet and lifestyle
The refrigerator allows households to keep food fresh for longer than before. The most notable improvement is for meat and other highly perishable wares, which previously needed to be preserved or otherwise processed for long term storage and transport. This change in the supply chains of food products led to a marked increase in the quality of food in areas where refrigeration was being used. Additionally, the increased freshness and shelf life of food caused by the advent of refrigeration in addition to growing global communication methods has resulted in an increase in cultural exchange through food products from different regions of the world. There have also been claims that this increase in the quality of food is responsible for an increased in the height of United States citizens around the early 1900's.

Refrigeration has also contributed to a decrease in the quality of food in some regions. By allowing, in part, for the phenomena of Globalization in the food sector, refrigeration has made the creation and transportation of ultra-processed foods and convenience foods inexpensive leading to their prevalence, especially in lower-income regions. These regions of lessened access to higher quality foods are referred to as Food Deserts.

Freezers allow people to buy food in bulk and eat it at leisure, and bulk purchases may save money. Ice cream, a popular commodity of the 20th century, could previously only be obtained by traveling to where the product was made and eating it on the spot. Now it is a common food item. Ice on demand not only adds to the enjoyment of cold drinks, but is useful for first-aid, and for cold packs that can be kept frozen for picnics or in case of emergency.

Residential units
The capacity of a refrigerator is measured in either liters or cubic feet. Typically the volume of a combined refrigerator-freezer is split with 1/3rds to 1/4th of the volume allocated to the freezer although these values are highly variable.

Temperature settings for refrigerator and freezer compartments are often given arbitrary numbers by manufacturers (for example, 1 through 9, warmest to coldest), but generally 3 to 5 C is ideal for the refrigerator compartment and -18 °C for the freezer. Some refrigerators must be within certain external temperature parameters to run properly. This can be an issue when placing units in an unfinished area, such as a garage.

Some refrigerators are now divided into four zones to store different types of food:
 * -18 °C (freezer)
 * 0 °C (meat zone)
 * 5 °C (cooling zone)
 * 10 °C (crisper)

European freezers, and refrigerators with a freezer compartment, have a four star rating system to grade freezers.

Although both the three and four star ratings specify the same storage times and same minimum temperature of -18 °C, only a four star freezer is intended for freezing fresh food, and may include a "fast freeze" function (runs the compressor continually, down to as low as -26 °C) to facilitate this. Three (or fewer) stars are used for frozen food compartments that are only suitable for storing frozen food; introducing fresh food into such a compartment is likely to result in unacceptable temperature rises. This difference in categorization is shown in the design of the 4-star logo, where the "standard" three stars are displayed in a box using "positive" colours, denoting the same normal operation as a 3-star freezer, and the fourth star showing the additional fresh food/fast freeze function is prefixed to the box in "negative" colours or with other distinct formatting.

Most European refrigerators include a moist cold refrigerator section (which does require (automatic) defrosting at irregular intervals) and a (rarely frost free) freezer section.

Commercial refrigeration temperatures
(from warmest to coolest)
 * Refrigerators : 35 to 38 F, and not greater than maximum refrigerator temperature at 41 F
 * Freezer, Reach-in : -10 to +5 F
 * Freezer, Walk-in : -10 to 0 F
 * Freezer, Ice Cream : -20 to -10 F

Cryogenics

 * Cryocooler: below -153°C (-243.4°F)
 * Dilution refrigerator: down to -273.148°C (-459.6664°F)

Disposal

An increasingly important environmental concern is the disposal of old refrigerators—initially because freon coolant damages the ozone layer—but as older generation refrigerators wear out, the destruction of CFC-bearing insulation also causes concern. Modern refrigerators usually use a refrigerant called HFC-134a (1,1,1,2-Tetrafluoroethane), which does not deplete the ozone layer, unlike Freon. R-134a is becoming much rarer in Europe, where newer refrigerants are being used instead. The main refrigerant now used is R-600a (also known as isobutane), which has a smaller effect on the atmosphere if released. There have been reports of refrigerators exploding if the refrigerant leaks isobutane in the presence of a spark. If the coolant leaks into the refrigerator, at times when the door is not being opened (such as overnight) the concentration of coolant in the air within the refrigerator can build up to form an explosive mixture that can be ignited either by a spark from the thermostat or when the light comes on as the door is opened, resulting in documented cases of serious property damage and injury or even death from the resulting explosion.

Disposal of discarded refrigerators is regulated, often mandating the removal of doors for safety reasons. Children playing hide-and-seek have been asphyxiated while hiding inside discarded refrigerators, particularly older models with latching doors, in a phenomenon called refrigerator death. Since 2 August 1956, under U.S. federal law, refrigerator doors are no longer permitted to latch and they can be opened from the inside. Modern units use a magnetic door gasket that holds the door sealed but allows it to be pushed open from the inside. This gasket was invented, developed and manufactured by Max Baermann (1903–1984) of Bergisch Gladbach/Germany.

Regarding total life-cycle costs, many governments offer incentives to encourage recycling of old refrigerators. One example is the Phoenix refrigerator program launched in Australia. This government incentive picked up old refrigerators, paying their owners for "donating" the refrigerator. The refrigerator was then refurbished, with new door seals, a thorough cleaning and the removal of items, such as the cover that is strapped to the back of many older units. The resulting refrigerators, now over 10% more efficient, were then distributed to low-income families.

Similar to the Australian program, the United States also has a program for collecting and replacing older less efficient refrigerators and other White Goods. These programs seek to collect large appliances that may be old and inefficient or breaking, and replace them with newer and more efficient appliances. This is in an effort to reduce the cost of the additional cost these appliances impose on lower-income families through their inefficient energy and gas usage, as well as reduce pollution caused by the continued use of these appliances.

title: Refrigerator


text:
Joe Murray (animator)

Joseph David Murray (born May 3, 1961) is an American animator, cartoonist, illustrator, writer, producer, and director. He is best known as the creator of Nickelodeon's Rocko's Modern Life, Cartoon Network's Camp Lazlo, and PBS Kids' Let's Go Luna!. Murray is the winner of two Primetime Emmy Awards for Camp Lazlo and the TV film Camp Lazlo: Where's Lazlo?.

Early life
Born and raised in San Jose, California, Joe Murray said that he developed an interest in working as an artist as a career when he was three years old, but his father didn't approve. According to Murray, his kindergarten teacher told his mother that he was the only student who drew zippers on pants and breasts on women. Murray credits his Leland High School art teacher Mark Briggs for teaching him "so much about my art." At age 16, he became a full-time artist, drawing caricatures of people and animals at an amusement park in his spare time.

Taking the position of political cartoonist for a newspaper in San Jose, Murray's cartoons often targeted then-President Jimmy Carter. In a 2007 entry on his website, he said that he admired Carter's post-presidential work.

Murray has cited Pablo Picasso, Henri Matisse, Walt Kelly, Mark O'Hare, Max Fleischer, Jay Ward, Tex Avery, Bob Clampett, and Chuck Jones as his main influences.

Career
As a young adult, Murray was hired as a designer at an agency. He invested his earnings from the company into independent animated films. At age 20, Murray founded his independent illustration company, Joe Murray Studios (or Joe Murray Productions), in 1981 while still in university. His early attempts at animation date back to 1986 when he joined De Anza College. Murray created several short animated films, his most successful was made in 1987, which was a two-minute animated short titled "The Chore," which focused on a harried husband who uses his cat as a novel solution while not wanting to do a chore for his wife. He drew the scenes on typing paper and shot the scenes with 16 mm film. For creating "The Chore" Murray earned the Merit Student Academy Award two years later in 1989. In the early 1990s, he did the storyboards and layouts on A Pup Named Scooby-Doo, Adventures of Sonic the Hedgehog, Bobby's World, and The Twisted Tales of Felix the Cat, while working as a freelancer at Drew Takahashi's now-defunct Colossal Pictures studio.

In 1988, he did two network IDs for MTV, and left in 1991 in hopes of starting his own projects. One of the MTV ID's Murray created involved the future Rocko's Modern Life character Heffer Wolfe; the ID featured Heffer being pushed out of a building with the MTV logo branded onto his buttocks.

My Dog Zero, released in 1992, was Murray's third independent film and first color film. Murray said that My Dog Zero was his "most gratifying" artistic project to date because of his own "stubbornness" in resolving the obstacles and issues involved in the production, such as lack of funding and lack of resources. With a grant he employed twelve people, mostly university students, to cel-paint the film. According to Murray, when he finished the film, several distributors refused to air it. He appeared at the Palace of Fine Arts in San Francisco with a copy of the film and persuaded the staff to air the film with the scheduled films. According to Murray, My Dog Zero received "good response".

To fund the film, Murray initially tried to pre-sell the television show rights to My Dog Zero but instead created a separate television series called Rocko's Modern Life.

Rocko's Modern Life
Murray created, and was the executive producer, for the animated series Rocko's Modern Life, which aired on Nickelodeon from 1993 to 1996. He voiced the character Ralph Bighead in the episodes "I Have No Son" and "Wacky Delly", and a caricature version of himself in "Short Story".

Originally, the character Rocko appeared in an unpublished comic book titled Travis. Murray tried selling the comic book in the late 1980s, but was never successful of getting it in production. Murray wanted funding for My Dog Zero, so he wanted Nickelodeon to pre-buy television rights for the series. Murray presented a pencil test to Nickelodeon Studios, which afterwards became interested in buying and airing the show. After deciding that My Dog Zero would not work as a television series, Murray combed through his sketchbooks, developed the Rocko's Modern Life concept and submitted it to Nickelodeon, believing that the concept would likely be rejected. According to Murray, around three or four months later he had "forgotten about" the concept and was working on My Dog Zero when Linda Simensky informed Murray that Nickelodeon wanted a pilot episode. Murray said that he was glad that he would get funding for My Dog Zero.

In 1992, two months prior to the production of season 1 of Rocko's Modern Life, Murray's first wife, Diane, committed suicide. Murray had blamed the show being taken as the reason for his wife's suicide. Murray felt that he had emotional and physical "unresolved issues" when he moved to Los Angeles. He describes the experience as like participating in "marathon with my pants around my ankles". Murray initially believed that he would create one season, move back to the San Francisco Bay Area and "clean up the loose ends I had left hanging". To his surprise Nickelodeon approved new seasons.

After season 3, he decided to hand the project to Stephen Hillenburg, who did most work for season 4 and created SpongeBob SquarePants shortly after that; Murray continued to manage the cartoon. Murray said that he would completely leave the production after season 4. Murray said that he encouraged the network to continue production. Nickelodeon decided to cancel the series. Murray described all 52 episodes as "top notch" and that, in his view, the quality of a television show may decline as production continues "when you are dealing with volume".

Post-Rocko's Modern Life
After completing 52 episodes of Rocko's Modern Life, Murray took a break from the animation business and produced two children's books and illustrated two others: Who Asked the Moon to Dinner? (1999), The Enormous Mister Schmupsle: An ABC Adventure (2003), Hugville (written by Court Crandall) (2005), and Funny Cryptograms (written by Shawn Kennedy).

Murray was working on a web-based cartoon named The Family Pop, which was produced in Flash and was in the middle of negotiations for this cartoon just prior to the onset of Camp Lazlo. On September 30, 2008, Murray added a new feature to his website, The Tin Box, where Murray posts some of his independent work. The first work posted was "Where's Poppa", a short episode of The Family Pop.

Camp Lazlo
Murray decided to return to television cartooning, this time selling his work to Cartoon Network Studios. In 2005, he produced a pilot for the cartoon Camp Lazlo, which was picked up for a 13-episode first season and ran for five seasons, with production ending in November 2007.

On September 8, 2007, the TV movie Where's Lazlo? won an Emmy for Outstanding Animated Program (For an Hour or More). During the production of Camp Lazlo, Murray underwent a divorce.

Recent work
Once production finished for Camp Lazlo, and the final episodes were delivered, Murray developed a new television series. While he is working out details about production and distribution, he has started work on his next independent film project, Fish Head, and publishing Creating Animated Cartoons with Character, a book on creating and producing an animated TV series, and working on producing a new short series, entitled Frog in a Suit for his web network; KaboingTV.

On April 20, 2010, Murray launched a donation drive on Kickstarter to fund the project, KaboingTV, a web network entirely dedicated to cartoons. By June 5, the project surpassed its goal of $16,800 and Murray developed episodes of his Frog in a Suit series for the platform. KaboingTV premiered on March 11, 2011.

Murray worked on the PBS animated series Let's Go Luna!, which aired from November 2018 to November 2022.

Murray also worked on the hour-long Rocko TV special Rocko's Modern Life: Static Cling, which premiered on Netflix on August 9, 2019. This included reprising his voice role as Rachel Bighead. In October 2019, Murray and his wife relocated from California to Belgium, and at the time Murray expressed interest in developing new series for Nickelodeon Europe.

In 2023, Murray completed work on his independent film, now entitled Fiego and the Magic Fish. A reimagining of the fairy tale "The Fisherman and His Wife", the short received a Cannes Film Festival award for Best Direction for an Animated Film in 2024.

Character creation process
On his personal website, Murray describes his character creation process as "sometimes like playing Frankenstein".
 * He starts with the personality. He shapes the conditions that make the character "tick", the character's imperfections, and the appeal. He asks himself, "Why would I want to tell stories about them?".
 * If he is working with an anthropomorphic series or book with varying animals, he chooses an animal that, in his eyes, match the created personality. According to Murray, this resulted in a social caricature in Rocko's Modern Life.
 * If he is working with an anthropomorphic series or book using one animal, he alters the specific character design to match the personality.
 * Murray likes to vary eyeballs by size and color. He also varies nostrils. Murray believes that inconsistencies "make it more interesting".
 * Murray then selects colors that, in his view, "feels right". He believes that yellow and bright colors "match a mood". If a character is "negative", he will pick a color that, in his opinion, matches the character.
 * If he has to teach a crew of artists how to draw the character, he creates a model sheet for the character.

Murray explains that one of the interesting aspects of character creation is the evolution of the personalities over time. In a one-time movie, the characters will have a static personality, but for a television series, the characters will change from season to season, developing new relationships, and even changing from mere background characters into a main character.

Written and illustrated

 * Who Asked the Moon to Dinner? (December 31, 1999) (Published in English and Korean )
 * The Enormous Mr. Schmupsle! (August 2003)
 * Crafting a Cartoon (September 12, 2008)
 * Creating Animated Cartoons with Character (August 24, 2010)

Illustrated

 * Funny Cryptograms (May 28, 2003)
 * Hugville (December 27, 2005)

Independent films

 * "The Chore" (1987)
 * '"My Dog Zero" (1992) (Murray's third independent film)
 * "The Affair" (2002)
 * "Fishing"
 * "Fish Head" (in production)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Joe Murray (animator)


text:
Wikipedia:Articles for deletion/Al Kharid

Al Kharid
Suitable for a game guide, not wikipedia Deus Ex 11:06, 3 Oct 2004 (UTC)

 * Delete-' P.S. this article is for runescape players only. Non-runescape players would not understand some terms used in this  ' -hardly encyclopedic... Jelly441 12:32, 3 Oct 2004 (UTC)
 * Delete. Non-encyclopedic fancruft. jni 07:40, 4 Oct 2004 (UTC)
 * Delete. Wikipedia is not GameFAQs.   — Gwalla | Talk 17:48, 4 Oct 2004 (UTC)
 * Delete. Concur with Gwalla. --Improv 21:35, 4 Oct 2004 (UTC)
 * Delete: More game junk. Games are great, but I'd rather play them than talk about them. Geogre 13:54, 8 Oct 2004 (UTC)


text:
John Freeman (poet)

John Frederick Freeman (29 January 1880 – 23 September 1929) was an English poet and essayist, who gave up a successful career in insurance to write full-time.

He was born in London, and started as an office boy aged 13. He was a close friend of Walter de la Mare from 1907, who lobbied hard with Edward Marsh to get Freeman into the Georgian Poetry series; with eventual success. De la Mare's biographer Theresa Whistler describes him as "tall, gangling, ugly, solemn, punctilious".

He won the Hawthornden Prize in 1920 with Poems 1909-1920. His Last Hours was set to music by Ivor Gurney.

Works

 * Fifty Poems (1911)
 * Happy is England (1914)
 * Presage of Victory (1916)
 * Stone Trees (1916)
 * The Moderns: Essays in Literary Criticism (1917); essays on George Bernard Shaw, H. G. Wells, Thomas Hardy, Maurice Maeterlinck, Henry James, Joseph Conrad, Coventry Patmore, Francis Thompson, and Robert Bridges.
 * Memories of Childhood and other Poems (1919)
 * Poems 1909-1920 (1920)
 * Music (1921)
 * The Red Path, A Narrative, And The Wounded Bird (1921)
 * A Portrait of George Moore in a Study of his Work (1922)
 * The Grove and Other Poems (1925)
 * Prince Absalom (1925)
 * Solomon and Balkis (1926)
 * Collected Poems (1928)
 * Last Poems (1930)
 * John Freeman's Letters (1936) posthumous; edited by Gertrude Freeman & Sir John Squire

title: John Freeman (poet)


text:
Finnveden

Finnveden or Finnheden is one of the ancient small lands of Småland. It corresponded to the hundreds of Sunnerbo, Östbo and Västbo. Finnveden had its own judicial system and laws, as did the other small lands. Finnveden is situated around lake Bolmen and the river Lagan. Most runestones in Finnveden describe men who died in England. Finnveden is today divided and is a part of the counties of Halland, Kronoberg and Jönköping. It was first mentioned by Jordanes when he referred to its population as the Finnaithae (derived from an old form of Finnheden, Finn(h)aith-) when describing the nations of Scandza in Getica.

Etymology
The Scandinavian placenames Finnveden, Finnmark and the province of Finland (which gave name to Finland) are all thought to be derived from finn, an ancient Germanic word for nomadic hunter-gatherers (cf. to find ).

title: Finnveden


text:
Talk:Amr Khaled

More background
This entry would be enhanced by some background on Amr Khaled's ideologies. —The preceding unsigned comment was added by 140.175.214.33 (talk • contribs).

New picture
I think someone should put a better picture, this one dosent look right. The one in the arabic wikipedia looks better. Bazel 17:12, 6 October 2006 (UTC)

 * I think this one is more recent than the one on the arwiki, it should do fine for now.. and please do not forget to sign your comments on wikipedia again.. -- PASSIVE (Talk|E-Mail) 10:06, 6 October 2006 (UTC)

 * I agree with Bazel 222.152.199.229 03:24, 14 October 2006 (UTC)

 * I've updated the profile image with a more recent one from his website, a snapshot of a promotional flash movie currently running to advertise for an online interview schedule. IMHO this image is indeed much more appealing than the previous one, however, feel free to change--NomadOfArabia 03:51, 26 March 2007 (UTC)

 * this picture looks a lot better, good job Nomadofarabia Bazel 03:57, 26 March 2007 (UTC)

 * I think both of the images are good ones. Before I saw the posts here, I restored the infobox image and positioned the new image in the Ministry and audience section of the article. I hope this hasn't offended anyone. — Athænara   ✉  05:45, 26 March 2007 (UTC)

 * I appreciate your comment Athaenara and no offense taken at all. The main reason for objecting to the original image and hence replacing it, IMO, was that the original one seemed to be rather awkward as a infobox image for the article. Although the image is taken from an interview, which may make it of more significance than promo images, however, there surely are better interview images of him. I guess the original intention of selecting this image in particular was to hint somehow Amr Khaled's appreciation for the intellectual approach of dealing with Islam (with the pointing of his finger to his head and all). Yet somehow the image IMHO ends up as some sort of a funny snapshot, taken of him while he gazes to what seems to be nowhere. On the other hand, I think that requiring other images to illustrate a section such as Ministry and audience currently comes as a second priority to selecting an appropriate main image for the article. Thus, preferring to preserve the new image for the article's infobox, I moved it back for now. However, I'm more than willing to discuss this further in the evidence of an opposing concession. --NomadOfArabia 11:05, 26 March 2007 (UTC)

wrong informations....!!!!
he's #13 in time 100

actually he IS 63 of 100 according to the TIMES site it self http://www.time.com/time/specials/2007/time100/article/0,28804,1595326_1615754_1616173,00.html GamerXp 21:12, 23 September 2007 (UTC)

NO according to the TIMES and his personal site he's 13..dunno where ppl got the rummor of this 62 number? —Preceding unsigned comment added by TAKEN00 (talk • contribs) 03:17, 10 December 2007 (UTC)

Check this out: http://www.time.com/time/specials/2007/time100walkup/article/0,28804,1611030_1612457,00.html the link you provided is just a list the actuall ranks are in this link. —Preceding unsigned comment added by TAKEN00 (talk • contribs) 03:33, 10 December 2007 (UTC)

title: Talk:Amr Khaled


text:
.22 BB

.22 BB Cap (Bulleted Breech Cap), also known as the 6mm Flobert, is a variety of .22 caliber rimfire ammunition. Invented by Louis-Nicolas Flobert in 1845, it was the first rimfire metallic cartridge. The .22 BB Cap and .22 CB Cap are interchangeable and are relatively quiet, low velocity cartridges, designed for indoor target shooting.

History
Frenchman Louis-Nicolas Flobert invented the first rimfire metallic cartridge in 1845. His cartridge consisted of a percussion cap with a bullet attached to the top. Flobert then made what he called "parlor guns" for this cartridge, as these rifles and pistols were designed to be shot in indoor shooting parlors in large homes. Usually derived in the 6 mm and 9 mm calibres, it is since then called the Flobert cartridge, but it does not contain any powder; the only propellant substance contained in the cartridge is within the percussion cap. In Europe, the .22 BB Cap and .22 CB Cap are both called 6mm Flobert and are considered the same cartridge.

Description
These rimfires closely resemble a .22 caliber air rifle in power and are often used for indoor shooting and close range pest control. Developed for indoor shooting galleries with special "gallery guns", the .22 BB Cap was the first rimfire cartridge, dating back to 1845. It has no separate propellant charge, relying on the impulse created by the primer alone to fire a round lead ball. This results in a low muzzle velocity of around 700 ft/s (210 m/s) or less. More common is the .22 CB cap, which fires a slightly heavier conical bullet and is available in a variety of cartridge lengths.

Specifications

 * Length:
 * Case: .284 in (7.2 mm)
 * Overall: .343 in (8.7 mm)
 * Bullet weight: 18 gr (1.17 g)

title: .22 BB


text:
Thumper

Thumper or The Thumper may refer to:

Film and television

 * Thumper (Bambi), a rabbit in the Disney animated film Bambi
 * Thumper (Dune), a mechanical device in the science fiction novel Dune
 * Thumper (film), a 2017 crime thriller by Jordan Ross
 * Thumper (Thomas the Tank Engine), a quarry driller in Thomas the Tank Engine and Friends
 * Thumper, Hopper's pet grasshopper in A Bug's Life
 * Thumper, a character in the James Bond film Diamonds Are Forever
 * Thumper, a character in the television show Veronica Mars

Gaming

 * Thumper (video game), a 2016 rhythm game by Drool
 * Thumper, a character from the Twisted Metal video game series
 * Coal thumper, a building from the Frostpunk computer game.

Literature

 * Thumper (Dune), a mechanical device in the science fiction novel Dune

Music

 * Thumper (EP), a 1990 EP by Man in the Wood
 * "Thumper" (song), a 2010 song by band Enter Shikari
 * "Thumper", a song by Raging Speedhorn on the album Raging Speedhorn
 * The Thumper, a 1960 album by Jimmy Heath
 * THUMPER, an Irish rock band

Places

 * Thumpertown Beach, Massachusetts, United States

Technology

 * Thumper (motorcycle), a four-stroke single cylinder motorcycle
 * Project Thumper, the earliest official anti-ballistic missile study
 * M79 grenade launcher (nickname Thumper)
 * Sun Fire X4500, storage server (code name Thumper)
 * Thumper, a collecting pot placed along the vapor-carrying line before the worm of a pot still
 * Thumper, one of the two Avro Lancaster bombers in flying condition, in the BBMF Museum at Coningsby RAF station
 * Thumper, a small arms ammunition concept popularized by gun writer Jeff Cooper

Other uses

 * Bible thumper, Christian fundamentalists (normally considered derogatory)
 * Thumper (magic trick), a device used in a variety of magic tricks
 * British Rail Class 205, Nicknamed “thumpers” due to their engine sound.

title: Thumper


text:
Order of the October Revolution

The Order of the October Revolution (Орден Октябрьской Революции, Orden Oktyabr'skoy Revolyutsii) was instituted on 31 October 1967, in time for the 50th anniversary of the October Revolution. It was conferred upon individuals or groups for services furthering communism or the state, or in enhancing the defenses of the Soviet Union, military and civil. It is the second-highest Soviet order, after the Order of Lenin.

The insignia of the Order consisted of a badge, which was a red star with golden rays between the arms; at the centre was a pentagon bearing the image of the cruiser Aurora participating in the October Revolution. Above this was a red flag bearing the words "October Revolution" in Russian. A Hammer and Sickle emblem was placed at the bottom. The badge was worn on the left chest with a red ribbon bearing five blue stripes at the centre.

The Aurora was itself awarded the Order, the only ship ever to have received the award. Military units and institutions receiving the award applied the order name to their title upon its reception.

title: Order of the October Revolution


text:
User talk:Bluebec

G'day Bec, welcome to Wikipedia. I'm grabbing first post on your talk page. ;) If you haven't already found it, there's a tutorial on how to edit on wikipedia, and you can also introduce yourself at the new users page should you feel like it. If you have any questions, you can ask at the help desk, or just quiz me.

There's also a special WikiProject Melbourne for dealing with content about Melbourne and its surrounds. You may find it interesting reading, and you'd be most welcome to join and contribute if you wish.

pjf 11:28, 3 Oct 2004 (UTC)

Well done!
G'day Bec, I just wanted to say that you're doing a great job. :) Jarich 12:54, 3 Oct 2004 (UTC)

title: User talk:Bluebec


text:
User talk:Jarich

G'day J, welcome to Wikipedia. I'm grabbing first post on your talk page. ;) If you haven't already found it, there's a tutorial on how to edit on wikipedia, and you can also introduce yourself at the new users page should you feel like it. If you have any questions, you can ask at the help desk, or just quiz me.

There's also a special WikiProject Melbourne for dealing with content about Melbourne and its surrounds. You may find it interesting reading, and you'd be most welcome to join and contribute if you wish.

pjf 11:30, 3 Oct 2004 (UTC)

Cleanup pages
G'day J,

As per your request, here are links to:

 * WikiProject_Wiki_Syntax
 * Cleanup

Best regards,

--pjf 05:14, 8 Nov 2004 (UTC)

The Humungous Image Tagging Project
Hi. You've helped with the WikiProject Wiki Syntax, so I thought it worth alerting you to the latest and greatest of Wikipedia fixing project, User:Yann/Untagged Images, which is seeking to put copyright tags on all of the untagged images. There are probably, oh, thirty thousand or so to do (he said, reaching into the air for a large figure). But hey: they're images ... you'll get to see lots of random pretty pictures. That must be better than looking for at at and the the, non? You know you'll love it. best wishes --Tagishsimon (talk)

thanks
for adding the links to rescue breathing! JamieJones 13:53, 29 December 2005 (UTC)

Barnstar

 * Very impressed by your work there - the ABC Religion report ran a story on them this week - more or less repeating what you have in the article anyways SatuSuro 23:23, 14 March 2007 (UTC)

Images
Hi there, I noticed you uploaded Image:Christmas Island red crab.jpg to Wikipedia. Would it be possible for you to move your images (luckily there are only 3!) to Wikimedia Commons? All you need to do is create an account there (if you don't have one already) and upload away. They will then be available for all WM projects to use. I've uploaded all my old images there myself, and hope you will do the same. Let me know if you need any help (e.g. categorizing them); I have an account there with the same name. Thanks. Richard001 (talk) 23:08, 20 February 2008 (UTC)

Speedy deletion of Image:Robber crab.jpg
A tag has been placed on Image:Robber crab.jpg requesting that it be speedily deleted from Wikipedia. This has been done under section I8 of the criteria for speedy deletion, because it is available as a bit-for-bit identical copy on the Wikimedia Commons under the same name, or all references to the image on Wikipedia have been updated to point to the title used at Commons.

If you think that this notice was placed here in error, you may contest the deletion by adding  to the top of the page that has been nominated for deletion (just below the existing speedy deletion or "db" tag), coupled with adding a note on  explaining your position, but be aware that once tagged for speedy deletion, if the article meets the criterion it may be deleted without delay. Please do not remove the speedy deletion tag yourself, but don't hesitate to add information to the article that would would render it more in conformance with Wikipedia's policies and guidelines. Lastly, please note that if the article does get deleted, you can contact one of these admins to request that a copy be emailed to you. ЭLСОВВОLД talk 14:27, 5 September 2008 (UTC)

ArbCom elections are now open!
MediaWiki message delivery (talk) 12:52, 23 November 2015 (UTC)

title: User talk:Jarich


text:
Talk:Tokyo Metro Yūrakuchō Line

Initial content
from Japanese Wikipedia Fg2 11:33, Oct 3, 2004 (UTC)

Overhead wiring?
Presumably 1500VDC overhead wiring, not third rail?

Tabletop 09:14, 27 Mar 2005 (UTC)

 * Yes. Overhead wiring. Per Japanese WP Fg2 12:22, Mar 27, 2005 (UTC)

Please Check
07系は未だ3本居ます.

西武6000系は全部で25本ありますが有楽町線に取り入れない車両が7本あるので有楽町線の車両としては18本です. 新たに乗り入れ改造を受けている車両が改造予定を含めると5本ありますがそれらはまだ有楽町線には乗り入れていません. ウィキペディアは未来予測をする場所ではありません. ですから無闇に推測などで書く人が現れないように現在進行のテンプレートを貼ってあります.

自分は実際に有楽町線を利用していて事実を見ています. 英語版では誤った情報が流れているのかもしれませんが誤った情報に注意してください. ウィキペディアは百科事典であるということを十分認識して下さい.

御願い致します. --219.125.56.214 12:01, 31 January 2007 (UTC)

 * ご親切ありがとうございます. できれば明日調べたいと思います. Fg2 12:07, 31 January 2007 (UTC)

 * ja:あまりに過剰に書いてしまいすみませんでした. 編集合戦等の防止の為自分の修正した数値差し戻された方及びこのノートにそれぞれ英語・日本語で記入させて頂いたのですが行き違いで既にご連絡を頂いておりました. Mr.Richard Harvey様とこのノートをご覧の方々には必要以上にお気を使わせてしまう事になり大変申し訳ございませんでした.
 * en:Sorry surplus action. Missing each other. I'm sorry Mr.Richard Harvey and watching people.--219.125.56.214 12:33, 31 January 2007 (UTC)

 * いいえ、謝る必要はないですよ. まず、Richard Harveyさんは、どうも内容を理解せず、当初イタズラと勘違いして戻したみたいです. 今のところは、編成の数がこれからも変わるようですから、正確な本数を入れないで「全編成が有楽町線乗り入れ可能ではない」ようなコメントを入れました. DAJF 12:44, 31 January 2007 (UTC)

Please visit WikiProject Trains in Japan. You can meet other editors who write about railways, including Japanese people as well as English speakers. Fg2 00:14, 1 February 2007 (UTC)

Operation Copyedit
I touched up the English a little in the Operation section where I felt it was unclear. There were two mentions of "down north" which I couldn't make any sense of so I removed the word "down" in both places. If someone else can rewrite the section to make sense of these mentions please replace my contributions. --Jarsyl (talk) 02:33, 13 June 2008 (UTC)

Linkage to the Hanzomon Line?
http://www.nikkei.com/article/DGXNZO31373680Q1A630C1L71000/ is too complicated for my poor Japanese, but the plans seem fairly definite and should probably be incorporated into the History section. Shanen (talk) 08:13, 6 June 2013 (UTC)
 * Indeed, these plans seem approaching finalisation, though it's still speculation from my understanding. This recent article is in English.
 * It seems that a line would branch from Toyosu Station (rather than continuing to Shin-Kiba Station), heading northbound to Tōyōchō Station (intersecting with the Tōzai Line) and eventually terminating at Sumiyoshi Station (intersecting with the Hanzōmon Line). Feel free to add this information to the article. — JKVeganAbroad (talk) 12:08, 17 October 2021 (UTC)

title: Talk:Tokyo Metro Yūrakuchō Line


text:
Chatswood railway station

Chatswood railway station is a railway station located in the Sydney suburb of Chatswood. It is served by Sydney Trains services; the T1 North Shore & Western Line and the T9 Northern Line, and Metro North West Line services.

History
Chatswood station opened on 1 January 1890 when the North Shore line opened from Hornsby to St Leonards. It and the suburb was named after Richard Garnett’s second wife’s pet who was called Chatty. An island platform was built on 23 May 1900 and a third dock platform brought into use on 12 July 1919. There was a small goods yard, similar to the one at St Leonards, on the western side of the station, beyond the northern end of the platforms. The dock platform on the eastern side of the station was used for electric parcel-van traffic and also for terminating some services from the city, until these were rescheduled to terminate further along the North Shore line from January 1992. It was removed in October 1994. Until 1958 there was a tram terminus in Victoria Avenue beside the station. The station entrance was later integrated with a shopping centre called The Interchange in the mid-1980s. With the construction of the Chatswood to Epping line, it was decided to redevelop the station to accommodate Chatswood's new role as a junction station. The original station, as well as the attached bus interchange and shopping centre were demolished in 2005 and a temporary station was opened where the former platform 3 was located. A new western island platform opened in place of the original island platform on 16 October 2006. The eastern island platform opened in 2008. The signal cabin that was located at the northern end of the station building, was saved and has been preserved as part of the bus interchange.

The new station precinct is known as the Chatswood Transport Interchange (CTI) and consists of the railway station, a bus interchange and pedestrian pathways connecting the precinct to the surrounding streets. The CTI was constructed as a Public Private Partnership and was to include a new shopping plaza called Metro Chatswood and three towers. The private developers, CRI Chatswood, went into receivership whilst construction was underway. As a result, the shopping centre remained closed until 2014 and major construction of the towers was delayed for several years.

From 26 May 2019, Chatswood station became the major terminus of the Metro North West Line which replaced the Epping to Chatswood railway line which closed on 29 September 2018. This will, at a later date be extended to Bankstown via the Sydney Harbour Rail Tunnel. This will leave Platforms 1 and 4 the only platforms served by Sydney Trains, while the two terminating roads are used by Metro North West Line.

Station layout
The station consists of two island platforms – a city-bound platform and an outbound platform. The two centre platforms now serve as the terminus of the Sydney Metro Northwest line. The outer platforms serve the Northern and North Shore lines. A turnback / stabling road is located to the south of the station and is used to terminate some trains from the Sydney Metro.

Access to Chatswood station is provided by a series of pedestrian walkways at three different intersections: Victoria Avenue and Railway Street, Chatswood Mall and Orchard Road, and Post Office Lane and Victor Street. Additional pedestrian entrances are available from Chatswood Central Plaza, adjacent to the north side of the station concourse.

Because the station and tracks are level with the ground, the concourse is actually below street level despite being open-air in nature. The installation of new "jump-proof" opal card ticket barriers in 2018 reduces fare evasion and ensures faster entry into the concourse which features stairs, lifts, and escalators to access the platforms. The station fulfills Sydney Trains' Easy Access criteria.

Services
Chatswood station is served by bus routes operated by Busways, CDC NSW, Keolis Downer Northern Beaches, Transit Systems, and two NightRide routes.

title: Chatswood railway station


text:
Whitwell

Whitwell may refer to:

Places

 * UK
 * Whitwell, Derbyshire
 * Whitwell Common, Derbyshire
 * Whitwell, Hertfordshire
 * Whitwell, Isle of Wight
 * Whitwell & Reepham railway station, Norfolk
 * Whitwell, North Yorkshire, near Catterick
 * Whitwell, Rutland
 * Whitwell-on-the-Hill, in between York and Malton
 * Whitwell House, County Durham

 * USA
 * Whitwell, Tennessee

People

 * Allan Whitwell (born 1954), English Olympic rower
 * John Whitwell (1812–1880), English Liberal politician
 * Field Marshal John Griffin Whitwell, 4th Baron Howard de Walden (1719–1797), British nobleman and soldier
 * Joseph Whitwell (1869–1932), English amateur first-class cricketer
 * Mike Whitwell, American football player
 * Philip Whitwell Wilson (1875–1956), British Liberal politician, writer and journalist
 * R. J. Whitwell (1859–1928), British medievalist
 * Sally Whitwell (born 1974), Australian pianist
 * Thomas Stedman Whitwell (1784–1840), English architect
 * William Whitwell (1867–1942), English amateur first-class cricketer

title: Whitwell


text:
Variation of parameters

In mathematics, variation of parameters, also known as variation of constants, is a general method to solve inhomogeneous linear ordinary differential equations.

For first-order inhomogeneous linear differential equations it is usually possible to find solutions via integrating factors or undetermined coefficients with considerably less effort, although those methods leverage heuristics that involve guessing and do not work for all inhomogeneous linear differential equations.

Variation of parameters extends to linear partial differential equations as well, specifically to inhomogeneous problems for linear evolution equations like the heat equation, wave equation, and vibrating plate equation. In this setting, the method is more often known as Duhamel's principle, named after Jean-Marie Duhamel (1797–1872) who first applied the method to solve the inhomogeneous heat equation. Sometimes variation of parameters itself is called Duhamel's principle and vice versa.

History
The method of variation of parameters was first sketched by the Swiss mathematician Leonhard Euler (1707–1783), and later completed by the Italian-French mathematician Joseph-Louis Lagrange (1736–1813).

A forerunner of the method of variation of a celestial body's orbital elements appeared in Euler's work in 1748, while he was studying the mutual perturbations of Jupiter and Saturn. In his 1749 study of the motions of the earth, Euler obtained differential equations for the orbital elements. In 1753, he applied the method to his study of the motions of the moon.

Lagrange first used the method in 1766. Between 1778 and 1783, he further developed the method in two series of memoirs: one on variations in the motions of the planets and another on determining the orbit of a comet from three observations. During 1808–1810, Lagrange gave the method of variation of parameters its final form in a third series of papers.

Description of method
Given an ordinary non-homogeneous linear differential equation of order n

Let $$y_1(x), \ldots, y_n(x)$$ be a basis of the vector space of solutions of the corresponding homogeneous equation

Then a particular solution to the non-homogeneous equation is given by

where the $$c_i(x)$$ are differentiable functions which are assumed to satisfy the conditions

Starting with ($$), repeated differentiation combined with repeated use of ($$) gives

One last differentiation gives

By substituting ($$) into ($$) and applying ($$) and ($$) it follows that

The linear system ($$ and $$) of n equations can then be solved using Cramer's rule yielding

 * $$c_i'(x) = \frac{W_i(x)}{W(x)}, \, \quad i=1,\ldots,n$$

where $$W(x)$$ is the Wronskian determinant of the basis $$y_1(x), \ldots, y_n(x)$$ and $$W_i(x)$$ is the Wronskian determinant of the basis with the i-th column replaced by $$(0, 0, \ldots, b(x)).$$

The particular solution to the non-homogeneous equation can then be written as

 * $$\sum_{i=1}^n y_i(x) \, \int \frac{W_i(x)}{W(x)}\, \mathrm dx.$$

Intuitive explanation
Consider the equation of the forced dispersionless spring, in suitable units:
 * $$x''(t) + x(t) = F(t).$$

Here $x$ is the displacement of the spring from the equilibrium $x = 0$, and $F(t)$ is an external applied force that depends on time. When the external force is zero, this is the homogeneous equation (whose solutions are linear combinations of sines and cosines, corresponding to the spring oscillating with constant total energy).

We can construct the solution physically, as follows. Between times $$t=s$$ and $$t=s+ds$$, the momentum corresponding to the solution has a net change $$F(s)\,ds$$ (see: Impulse (physics)). A solution to the inhomogeneous equation, at the present time $t > 0$, is obtained by linearly superposing the solutions obtained in this manner, for $s$ going between 0 and $t$.

The homogeneous initial-value problem, representing a small impulse $$F(s)\,ds$$ being added to the solution at time $$t=s$$, is
 * $$x''(t)+x(t)=0,\quad x(s)=0,\ x'(s)=F(s)\,ds.$$

The unique solution to this problem is easily seen to be $$x(t) = F(s)\sin(t-s)\,ds$$. The linear superposition of all of these solutions is given by the integral:
 * $$x(t) = \int_0^t F(s)\sin(t-s)\,ds.$$

To verify that this satisfies the required equation:
 * $$x'(t)=\int_0^t F(s)\cos(t-s)\,ds$$
 * $$x''(t) = F(t) - \int_0^tF(s)\sin(t-s)\,ds = F(t)-x(t),$$

as required (see: Leibniz integral rule).

The general method of variation of parameters allows for solving an inhomogeneous linear equation
 * $$Lx(t)=F(t)$$

by means of considering the second-order linear differential operator L to be the net force, thus the total impulse imparted to a solution between time s and s+ds is F(s)ds. Denote by $$x_s $$ the solution of the homogeneous initial value problem
 * $$Lx(t)=0, \quad x(s)=0,\ x'(s)=F (s)\,ds. $$

Then a particular solution of the inhomogeneous equation is
 * $$x (t)=\int_0^t x_s (t)\,ds,$$

the result of linearly superposing the infinitesimal homogeneous solutions. There are generalizations to higher order linear differential operators.

In practice, variation of parameters usually involves the fundamental solution of the homogeneous problem, the infinitesimal solutions $$x_s $$ then being given in terms of explicit linear combinations of linearly independent fundamental solutions. In the case of the forced dispersionless spring, the kernel $$\sin(t-s)=\sin t\cos s - \sin s\cos t $$ is the associated decomposition into fundamental solutions.

First-order equation

 * $$ y' + p(x)y = q(x) $$

The complementary solution to our original (inhomogeneous) equation is the general solution of the corresponding homogeneous equation (written below):
 * $$ y' + p(x)y = 0 $$

This homogeneous differential equation can be solved by different methods, for example separation of variables:
 * $$\frac{d}{dx} y + p(x)y = 0 $$

 * $$\frac{dy}{dx}=-p(x)y $$

 * $${dy \over y} = -{p(x)\,dx},$$

 * $$\int \frac{1}{ y} \, dy = -\int p(x) \, dx $$

 * $$\ln |y| = -\int p(x) \, dx + C $$

 * $$y = \pm e^{-\int p(x) \, dx +C } = C_0 e^{-\int p(x) \, dx}$$

The complementary solution to our original equation is therefore:
 * $$y_c = C_0 e^{-\int p(x) \, dx}$$

Now we return to solving the non-homogeneous equation:
 * $$ y' + p(x)y = q(x)$$

Using the method variation of parameters, the particular solution is formed by multiplying the complementary solution by an unknown function C(x):
 * $$y_p = C(x) e^{-\int p(x) \, dx}$$

By substituting the particular solution into the non-homogeneous equation, we can find C(x):
 * $$ C' (x) e^{-\int p(x) \, dx} - C(x) p(x) e^{-\int p(x) \, dx} + p(x) C(x) e^{-\int p(x) \, dx} = q(x)$$

 * $$ C' (x) e^{-\int p(x) \, dx} = q(x)$$

 * $$ C' (x) = q(x) e^{\int p(x) \, dx} $$

 * $$ C(x) =\int q(x) e^{\int p(x) \, dx} \, dx + C_1 $$

We only need a single particular solution, so we arbitrarily select $$C_1=0$$ for simplicity. Therefore the particular solution is:
 * $$y_p =e^{-\int p(x) \, dx} \int q(x) e^{\int p(x) \, dx} \, dx$$

The final solution of the differential equation is:
 * $$\begin{align}

y &= y_c + y_p\\ &=C_0 e^{-\int p(x) \, dx} + e^{-\int p(x) \, dx} \int q(x) e^{\int p(x) \, dx} \, dx \end{align}$$

This recreates the method of integrating factors.

Specific second-order equation
Let us solve
 * $$ y''+4y'+4y = \cosh x$$

We want to find the general solution to the differential equation, that is, we want to find solutions to the homogeneous differential equation
 * $$y''+4y'+4y=0. $$

The characteristic equation is:
 * $$\lambda^2+4\lambda+4=(\lambda+2)^2=0 $$

Since $$\lambda=-2$$ is a repeated root, we have to introduce a factor of x for one solution to ensure linear independence: $$ u_1 = e^{-2x} $$ and $$ u_2 =x e^{-2x}$$. The Wronskian of these two functions is

 * $$W=\begin{vmatrix}

e^{-2x} & xe^{-2x} \\ -2e^{-2x} & -e^{-2x}(2x-1)\\ \end{vmatrix} = -e^{-2x}e^{-2x}(2x-1)+2xe^{-2x}e^{-2x} = e^{-4x}. $$

Because the Wronskian is non-zero, the two functions are linearly independent, so this is in fact the general solution for the homogeneous differential equation (and not a mere subset of it).

We seek functions A(x) and B(x) so A(x)u1 + B(x)u2 is a particular solution of the non-homogeneous equation. We need only calculate the integrals

 * $$A(x) = - \int {1\over W} u_2(x) b(x)\,\mathrm dx,\; B(x) = \int {1 \over W} u_1(x)b(x)\,\mathrm dx$$

Recall that for this example

 * $$b(x) = \cosh x$$

That is,

 * $$A(x) = - \int {1\over e^{-4x}} xe^{-2x} \cosh x \,\mathrm dx = - \int xe^{2x}\cosh x \,\mathrm dx = -{1\over 18}e^x\left(9(x-1)+e^{2x}(3x-1)\right)+C_1$$
 * $$B(x) = \int {1 \over e^{-4x}} e^{-2x} \cosh x \,\mathrm dx = \int e^{2x}\cosh x\,\mathrm dx ={1\over 6}e^x\left(3+e^{2x}\right)+C_2 $$

where $$C_1$$ and $$C_2$$ are constants of integration.

General second-order equation
We have a differential equation of the form

 * $$u''+p(x)u'+q(x)u=f(x)$$

and we define the linear operator

 * $$L=D^2+p(x)D+q(x)$$

where D represents the differential operator. We therefore have to solve the equation $$L u(x)=f(x)$$ for $$u(x)$$, where $$L$$ and $$f(x)$$ are known.

We must solve first the corresponding homogeneous equation:

 * $$u''+p(x)u'+q(x)u=0$$

by the technique of our choice. Once we've obtained two linearly independent solutions to this homogeneous differential equation (because this ODE is second-order) — call them u1 and u2 — we can proceed with variation of parameters.

Now, we seek the general solution to the differential equation $$ u_G(x)$$ which we assume to be of the form

 * $$u_G(x)=A(x)u_1(x)+B(x)u_2(x).$$

Here, $$A(x)$$ and $$B(x)$$ are unknown and $$u_1(x)$$ and $$u_2(x)$$ are the solutions to the homogeneous equation. (Observe that if $$A(x)$$ and $$B(x)$$ are constants, then $$Lu_G(x)=0$$.) Since the above is only one equation and we have two unknown functions, it is reasonable to impose a second condition. We choose the following:

 * $$A'(x)u_1(x)+B'(x)u_2(x)=0.$$

Now,

 * $$\begin{align}

u_G'(x) &= \left (A(x)u_1(x)+B(x)u_2(x) \right )' \\ &= \left (A(x)u_1(x) \right )'+ \left (B(x)u_2(x) \right )'\\ &=A'(x)u_1(x)+A(x)u_1'(x)+B'(x)u_2(x)+B(x)u_2'(x)\\ &=A'(x)u_1(x)+B'(x)u_2(x)+A(x)u_1'(x)+B(x)u_2'(x) \\ &= A(x)u_1'(x)+B(x)u_2'(x) \end{align}$$

Differentiating again (omitting intermediary steps)

 * $$u_G(x)=A(x)u_1(x)+B(x)u_2''(x)+A'(x)u_1'(x)+B'(x)u_2'(x).$$

Now we can write the action of L upon uG as

 * $$Lu_G=A(x)Lu_1(x)+B(x)Lu_2(x)+A'(x)u_1'(x)+B'(x)u_2'(x).$$

Since u1 and u2 are solutions, then

 * $$Lu_G=A'(x)u_1'(x)+B'(x)u_2'(x).$$

We have the system of equations

 * $$\begin{bmatrix}

u_1(x) & u_2(x) \\ u_1'(x) & u_2'(x) \end{bmatrix} \begin{bmatrix} A'(x) \\ B'(x)\end{bmatrix} = \begin{bmatrix} 0 \\ f \end{bmatrix}.$$

Expanding,

 * $$\begin{bmatrix}

A'(x)u_1(x)+B'(x)u_2(x)\\ A'(x)u_1'(x)+B'(x)u_2'(x) \end{bmatrix} = \begin{bmatrix} 0\\f\end{bmatrix}.$$

So the above system determines precisely the conditions

 * $$A'(x)u_1(x)+B'(x)u_2(x)=0.$$
 * $$A'(x)u_1'(x)+B'(x)u_2'(x)=Lu_G=f.$$

We seek A(x) and B(x) from these conditions, so, given

 * $$\begin{bmatrix}

u_1(x) & u_2(x) \\ u_1'(x) & u_2'(x) \end{bmatrix} \begin{bmatrix} A'(x) \\ B'(x)\end{bmatrix} = \begin{bmatrix} 0\\ f\end{bmatrix}$$

we can solve for (A′(x), B′(x))T, so

 * $$\begin{bmatrix} A'(x) \\ B'(x) \end{bmatrix} =

\begin{bmatrix} u_1(x) & u_2(x) \\ u_1'(x) & u_2'(x) \end{bmatrix}^{-1} \begin{bmatrix} 0\\ f \end{bmatrix} =\frac{1}{W} \begin{bmatrix} u_2'(x) & -u_2(x) \\ -u_1'(x) & u_1(x) \end{bmatrix} \begin{bmatrix} 0\\ f \end{bmatrix},$$

where W denotes the Wronskian of u1 and u2. (We know that W is nonzero, from the assumption that u1 and u2 are linearly independent.) So,

 * $$ \begin{align}

A'(x) &= - {1\over W} u_2(x) f(x), & B'(x) &= {1 \over W} u_1(x)f(x) \\ A(x) &= - \int {1\over W} u_2(x) f(x)\,\mathrm dx, & B(x) &= \int {1 \over W} u_1(x)f(x)\,\mathrm dx \end{align}$$

While homogeneous equations are relatively easy to solve, this method allows the calculation of the coefficients of the general solution of the inhomogeneous equation, and thus the complete general solution of the inhomogeneous equation can be determined.

Note that $$A(x)$$ and $$ B(x)$$ are each determined only up to an arbitrary additive constant (the constant of integration). Adding a constant to $$A(x)$$ or $$B(x)$$ does not change the value of $$Lu_G(x)$$ because the extra term is just a linear combination of u1 and u2, which is a solution of $$L$$ by definition.

title: Variation of parameters


text:
Balgowlah Heights

Balgowlah Heights is a suburb of northern Sydney, in the state of New South Wales, Australia 11 kilometres north-east of the Sydney central business district in the local government area of Northern Beaches Council, in the Northern Beaches region. Balgowlah Heights shares the postcode 2093 with the adjacent Balgowlah and North Balgowlah.

Situated on a ridge up to 80 metres above North Harbour and Middle Harbour, some houses have panoramic views of the harbour, Eastern Suburbs and Spit Bridge. The suburb features remnant Sydney Harbour bushland, contained in the National Park around Dobroyd Head and Grotto Point. Tania Park at the eastern fringe offers relaxed recreation and one can watch the Manly ferry cut its way to Circular Quay.

History
Balgowlah was named in 1832 after an Aboriginal word meaning north harbour in reference to its position on Port Jackson. The area was not developed until the 1960s.

Demographics
According to the 2016 census, there were 3,342 residents in Balgowlah Heights. 67.3% of people were born in Australia. The next most common country of birth was England at 10.7%. 87.0% of people only spoke English at home. The most common responses for religious affiliation were No Religion 32.8%, Catholic 24.2% and Anglican 24.2%.

Schools
Balgowlah Heights Public School

Politics
Balgowlah Heights is in the federal electorate of Warringah (a seat no longer held by former PM Tony Abbott of the Liberal Party of Australia), the state electorate of Manly (a seat no longer held by Liberal Party MP and Premier Michael Baird) and is within the local council area of Manly. It used to be regarded as a safe Liberal seat, however in the 2019 election the seat was won by Independent, Zali Steggall.

title: Balgowlah Heights


text: Template:Software distribution

title: Template:Software distribution


text:
John & Mary

John & Mary is a United States-based folk rock duo featuring John Lombardo and Mary Ramsey both members of alternative rock band 10,000 Maniacs.

1989–1993
John & Mary was formed by John Lombardo and Mary Ramsey soon after they first met in Buffalo, NY in December 1989. Lombardo, one of the founding members of 10,000 Maniacs and responsible for much of their early sound, had left the band in 1986 due to "creative and political" differences. The pair signed with Rykodisc in 1990 and recorded their first album Victory Gardens which was released in 1991, and were the opening act for the Maniacs on the Time Capsule Tour in late 1990. They followed up with their second release, The Weedkiller's Daughter, also on Rykodisc, in 1993.

1994–2000
Both joined (or re-joined) the Maniacs as full-time members in 1994 after Natalie Merchant's departure. The duo released two albums with the Maniacs, 1997's Love Among the Ruins, which contained a cover of the Roxy Music song "More Than This" that reached number 25 on the U.S. Hot 100 chart, and 1999's The Earth Pressed Flat. Lombardo and Ramsey continued to perform occasionally as John & Mary between tours. After the death of the Maniacs' lead guitar player Rob Buck in December 2000, the Maniacs went on hiatus, following which, Ramsey was replaced with singer Oskar Saville from the Chicago-based band Rubygrass. Lombardo quit the group at the same time.

2001–2006
After leaving 10,000 Maniacs, John & Mary began work on a new album in 2001. The Pinwheel Galaxy was released in December 2002 and the duo began a ten date national tour to promote it. The two performed locally around Buffalo regularly from 2002 to 2006. Ramsey was rehired by 10,000 Maniacs as a viola player and backing vocalist for the 2006 shows with Oskar Saville and returned to the lead vocalist spot after the departure of Saville in 2007.

2007–present
In late 2006, John & Mary began working with a new backing band, the Valkyries, made up of some of the best local Buffalo musicians, and their latest album, Peace Bridge was released the following year. Lombardo and Ramsey both have continued to appear regularly with 10,000 Maniacs during 2008–2017 as well as doing regular shows as John & Mary with the Valkyries.

Band members

 * John Lombardo - Lombardo, an original member of 10,000 Maniacs, co-wrote most of the early Maniacs songs, but left the band in 1986. He returned in 1994 with Mary Ramsey, and picked up where he left off by writing and shaping the band's music for two albums, Love Among the Ruins (1997) and The Earth Pressed Flat (1999). He left the band again in 2002 and returned as a touring member in 2015.
 * Mary Ramsey - Ramsey opened up 10,000 Maniacs shows with John Lombardo as John & Mary in 1990, and played viola and sang backing vocals with the Maniacs on a few songs in 1990–1991. She was a touring musician with the band in 1992–1993, playing viola and singing backing vocals. When Natalie Merchant left 10,000 Maniacs in 1993, Ramsey replaced her on lead vocals and added the viola as a main instrument of the band, starting with live shows in 1994 and continuing on until 2001. Oskar Saville replaced her as lead singer in 2002, but Ramsey again became a touring musician with the band in 2006, singing backing vocals and playing viola on select songs. She was lead singer for the band again for their final show of 2007 after Oskar Saville left the band and continues in that role.
 * The Valkyries - the initial line up in 2006 and on their 2007 release Peace Bridge included Patrick Kane on lead guitar, Rob Lynch on drums, Joe Rozler on keyboards, Nelson Starr on keyboards, and Kent Weber on bass guitar.

John & Mary

 * Victory Gardens (1991)
 * The Weedkiller's Daughter (1993)
 * The Pinwheel Galaxy (2002)

John & Mary & the Valkyries

 * Peace Bridge (2007)

title: John & Mary