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F

F, or f, is the sixth letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ef (pronounced ), and the plural is efs.

History
The origin of 'F' is the Semitic letter waw that represented a sound like or. Graphically it originally probably depicted either a hook or a club. It may have been based on a comparable Egyptian hieroglyph such as that which represented the word mace (transliterated as ḥ(dj)):

The Phoenician form of the letter was adopted into Greek as a vowel, upsilon (which resembled its descendant 'Y' but was also the ancestor of the Roman letters 'U', 'V', and 'W'); and, with another form, as a consonant, digamma, which indicated the pronunciation, as in Phoenician. Latin 'F,' despite being pronounced differently, is ultimately descended from digamma and closely resembles it in form.

After sound changes eliminated from spoken Greek, digamma was used only as a numeral. However, the Greek alphabet also gave rise to other alphabets, and some of these retained letters descended from digamma. In the Etruscan alphabet, 'F' probably represented, as in Greek, and the Etruscans formed the digraph 'FH' to represent. (At the time these letters were borrowed, there was no Greek letter that represented /f/: the Greek letter phi 'Φ' then represented an aspirated voiceless bilabial plosive, although in Modern Greek it has come to represent .) When the Romans adopted the alphabet, they used 'V' (from Greek upsilon) not only for the vowel , but also for the corresponding semivowel , leaving 'F' available for. And so out of the various vav variants in the Mediterranean world, the letter F entered the Roman alphabet attached to a sound which the Greeks did not have. The Roman alphabet forms the basis of the alphabet used today for English and many other languages.

The lowercase 'f' is not related to the visually similar long s, 'ſ' (or medial s). The use of the long s largely died out by the beginning of the 19th century, mostly to prevent confusion with 'f' when using a short mid-bar.

English
In the English writing system $⟨f⟩$ is used to represent the sound, the voiceless labiodental fricative. It is often doubled at the end of words. Exceptionally, it represents the voiced labiodental fricative in the common word "of" and its derivatives.

F is the eleventh least frequently used letter in the English language (after G, Y, P, B, V, K, J, X, Q, and Z), with a frequency of about 2.23% in words.

Other languages
In the writing systems of other languages, $⟨f⟩$ commonly represents, or.
 * In French orthography, $⟨f⟩$ is used to represent . It may also be silent at the end of words.
 * In Spanish orthography, $⟨f⟩$ is used to represent.
 * In Esperanto orthography, $⟨f⟩$ is used to represent.
 * In the Hepburn romanization of Japanese, $⟨f⟩$ is used to represent . This sound is usually considered to be an allophone of, which is pronounced in different ways depending upon its context; Japanese is pronounced as  before.
 * In Welsh orthography, $⟨f⟩$ represents while $⟨f⟩$ represents.
 * In Slavic languages, $⟨ff⟩$ is used primarily in words of foreign (Hellenic, Romance, or Germanic) origin.
 * In spoken Icelandic, $⟨f⟩$ in the middle of a word is often voiced to (e.g., Að sofa – to sleep).

Other systems
The International Phonetic Alphabet uses ⟨f⟩ to represent the voiceless labiodental fricative.

Other uses

 * In the hexadecimal (base 16) numbering system, F is a number that corresponds to the number 15 in decimal (base 10) counting.
 * The italic letter $⟨f⟩$ is conventionally used to denote an arbitrary function. Closely on f with hook (ƒ).
 * A bold italic letter is used in musical notation as a dynamic indicator for "loud or strong". It stands for the Italian word forte.
 * In countries such as the United States, the letter "F" is defined as a failure in terms of academic evaluation. Other countries that use this system include Saudi Arabia, Venezuela, and the Netherlands.
 * The letter F has become an Internet meme, where it is used to pay respects. This use is derived from the 2014 video game Call of Duty: Advanced Warfare, where in a quick-time event, protagonist Jack Mitchell must pay his respects to his friend Will Irons who fell in combat in a previous mission, represented by the player pressing F when playing the PC version. People on the Internet use the letter F sometimes in a genuine way to express respect, sadness, or condolences towards other Internet personalities, Internet memes, or other players on certain events.

Ancestors, descendants and siblings

 * F with diacritics:
 * Ƒ|Ƒ ƒ
 * Ḟ ḟ
 * ᵮ
 * ᶂ
 * Ꞙ ꞙ : F with stroke is used in the Anthropos phonetic transcription system and older Ewe writing
 * ꬵ : Lenis F is used in the Teuthonista phonetic transcription system
 * f: Superscript "f", encoded as in the Phonetic Extensions Supplement block of Unicode, is used in some forms of the International Phonetic Alphabet.
 * ꜰ : Small capital F was used in the Icelandic First Grammatical Treatise to mark gemination
 * ꟳ : Modifier letter capital F – Used to mark tone for the Chatino orthography in Oaxaca, Mexico; Used as a generic transcription for a falling tone; used in para-IPA notation.
 * Ꝼ ꝼ : Insular F is used in Norse and Old English contexts
 * ꟻ : Reversed F was used in ancient Roman texts to stand for filia (daughter) or femina (woman)
 * Ⅎ ⅎ : Claudian letters
 * 𐤅: Semitic letter Waw, from which the following symbols originally derive:
 * Ϝ ϝ : Greek letter Digamma, from which F derives:
 * 𐌅 : Old Italic V/F (originally used for V, in languages such as Etruscan and Oscan), which derives from Greek Digamma, and is the ancestor of modern Latin F
 * Y y : Latin letter Y, sharing its roots with F
 * V v : Latin letter V, also sharing its roots with F
 * U u : Latin letter U, which is descended from V
 * W w : Latin letter W, also descended from V

Ligatures and abbreviations

 * ₣ : French franc, Latin capital letter F with stroke
 * ℉ : degree Fahrenheit
 * F : Fluorine, a chemical element uses the symbol F

Computing
These are the code points for the forms of the letter in various systems:

 * 1 Also for encodings based on ASCII, including the DOS, Windows, ISO-8859 and Macintosh families of encodings.

title: F


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Food preservation

Food preservation includes processes that make food more resistant to microorganism growth and slow the oxidation of fats. This slows down the decomposition and rancidification process. Food preservation may also include processes that inhibit visual deterioration, such as the enzymatic browning reaction in apples after they are cut during food preparation. By preserving food, food waste can be reduced, which is an important way to decrease production costs and increase the efficiency of food systems, improve food security and nutrition and contribute towards environmental sustainability. For instance, it can reduce the environmental impact of food production.

Many processes designed to preserve food involve more than one food preservation method. Preserving fruit by turning it into jam, for example, involves boiling (to reduce the fruit's moisture content and to kill bacteria, etc.), sugaring (to prevent their re-growth) and sealing within an airtight jar (to prevent recontamination).

Different food preservation methods have different impacts on the quality of the food and food systems. Some traditional methods of preserving food have been shown to have a lower energy input and carbon footprint compared to modern methods. Some methods of food preservation are also known to create carcinogens.

Traditional techniques
Some techniques of food preservation pre-date the dawn of agriculture. Others were discovered more recently.

Boiling
Boiling liquids can kill any existing microbes. Milk and water are often boiled to kill any harmful microbes that may be present in them.

Burial
Burial of food can preserve it due to a variety of factors: lack of light, lack of oxygen, cool temperatures, pH level, or desiccants in the soil. Burial may be combined with other methods such as salting or fermentation. Most foods can be preserved in soil that is very dry and salty (thus a desiccant) such as sand, or soil that is frozen.

Many root vegetables are very resistant to spoilage and require no other preservation than storage in cool dark conditions, for example by burial in the ground, such as in a storage clamp (not to be confused with a root cellar). Cabbage was traditionally buried during autumn in northern US farms for preservation. Some methods keep it crispy while other methods produce sauerkraut. A similar process is used in the traditional production of kimchi.

Sometimes meat is buried under conditions that cause preservation. If buried on hot coals or ashes, the heat can kill pathogens, the dry ash can desiccate, and the earth can block oxygen and further contamination. If buried where the earth is very cold, the earth acts like a refrigerator, or, in areas of permafrost, a freezer.

In Odisha, India, it is practical to store rice by burying it underground. This method helps to store for three to six months during the dry season.

Butter and similar substances have been preserved as bog butter in Irish peat bogs for centuries. Century eggs are traditionally created by placing eggs in alkaline mud (or other alkaline substance), resulting in their "inorganic" fermentation through raised pH instead of spoiling. The fermentation preserves them and breaks down some of the complex, less flavorful proteins and fats into simpler, more flavorful ones.

Canning

Canning involves cooking food, sealing it in sterilized cans or jars, and boiling the containers to kill or weaken any remaining bacteria as a form of sterilization. It was invented by the French confectioner Nicolas Appert. By 1806, this process was used by the French Navy to preserve meat, fruit, vegetables, and even milk. Although Appert had discovered a new way of preservation, it was not understood until 1864 when Louis Pasteur found the relationship between microorganisms, food spoilage, and illness.

Foods have varying degrees of natural protection against spoilage and may require that the final step occurs in a pressure cooker. High-acid fruits like strawberries require no preservatives to can and only a short boiling cycle, whereas marginal vegetables such as carrots require longer boiling and the addition of other acidic elements. Low-acid foods, such as vegetables and meats, require pressure canning. Food preserved by canning or bottling is at immediate risk of spoilage once the can or bottle has been opened.

Lack of quality control in the canning process may allow ingress of water or micro-organisms. Most such failures are rapidly detected as decomposition within the can cause gas production and the can will swell or burst. However, there have been examples of poor manufacture (underprocessing) and poor hygiene allowing contamination of canned food by the obligate anaerobe Clostridium botulinum, which produces an acute toxin within the food, leading to severe illness or death. This organism produces no gas or obvious taste and remains undetected by taste or smell. Its toxin is denatured by cooking, however. Cooked mushrooms, when handled poorly and then canned, can support the growth of Staphylococcus aureus, which produces a toxin that is not destroyed by canning or subsequent reheating.

Confit
Meat can be preserved by salting it, cooking it at or near 100 C in some kind of fat (such as lard or tallow), and then storing it immersed in the fat. These preparations were popular in Europe before refrigerators became ubiquitous. They are still popular in France, where the term originates. The preparation will keep longer if stored in a cold cellar or buried in cold ground.

Cooling
Cooling preserves food by slowing down the growth and reproduction of microorganisms and the action of enzymes that causes the food to rot. The introduction of commercial and domestic refrigerators drastically improved the diets of many in the Western world by allowing food such as fresh fruit, salads and dairy products to be stored safely for longer periods, particularly during warm weather.

Before the era of mechanical refrigeration, cooling for food storage occurred in the forms of root cellars and iceboxes. Rural people often did their own ice cutting, whereas town and city dwellers often relied on the ice trade. Today, root cellaring remains popular among people who value various goals, including local food, heirloom crops, traditional home cooking techniques, family farming, frugality, self-sufficiency, organic farming, and others.

Curing

The earliest form of curing was dehydration or drying, used as early as 12,000BC. Smoking and salting techniques improve on the drying process and add antimicrobial agents that aid in preservation. Smoke deposits a number of pyrolysis products onto the food, including the phenols syringol, guaiacol and catechol. Salt accelerates the drying process using osmosis and also inhibits the growth of several common strains of bacteria. More recently nitrites have been used to cure meat, contributing a characteristic pink colour.

In 2015, the International Agency for Research on Cancer of the World Health Organization classified processed meat—i.e., meat that has undergone salting, curing, and smoking—as "carcinogenic to humans".

Fermentation
Some foods, such as many cheeses, wines, and beers, use specific micro-organisms that combat spoilage from other less-benign organisms. These micro-organisms keep pathogens in check by creating an environment toxic for themselves and other micro-organisms by producing acid or alcohol. Methods of fermentation include, but are not limited to, starter micro-organisms, salt, hops, controlled (usually cool) temperatures and controlled (usually low) levels of oxygen. These methods are used to create the specific controlled conditions that will support the desirable organisms that produce food fit for human consumption.

Fermentation is the microbial conversion of starch and sugars into alcohol. Not only can fermentation produce alcohol, but it can also be a valuable preservation technique. Fermentation can also make foods more nutritious and palatable. For example, drinking water in the Middle Ages was dangerous because it often contained pathogens that could spread disease. When the water is made into beer, the boiling during the brewing process kills any bacteria in the water that could make people sick. Additionally, the water now has the nutrients from the barley and other ingredients, and the microorganisms can also produce vitamins as they ferment.

Freezing
Freezing is also one of the most commonly used processes, both commercially and domestically, for preserving a very wide range of foods, including prepared foods that would not have required freezing in their unprepared state. For example, potato waffles are stored in the freezer, but potatoes themselves require only a cool dark place to ensure many months' storage. Cold stores provide large-volume, long-term storage for strategic food stocks held in case of national emergency in many countries.

Heating
Heating to temperatures which are sufficient to kill microorganisms inside the food is a method used with perpetual stews.

Jellying
Food may be preserved by cooking in a material that solidifies to form a gel. Such materials include gelatin, agar, maize flour, and arrowroot flour.

Some animal flesh forms a protein gel when cooked. Eels and elvers, and sipunculid worms, are a delicacy in Xiamen, China, as are jellied eels in the East End of London, where they are eaten with mashed potatoes. British cuisine has a rich tradition of potted meats. Meat off-cuts were, until the 1950s, preserved in aspic, a gel made from gelatin and clarified meat broth. Another form of preservation is setting the cooked food in a container and covering it with a layer of fat. Potted chicken liver can be prepared in this way, and so can potted shrimps, to be served on toast. Calf's foot jelly used to be prepared for invalids.

Jellying is one of the steps in producing traditional pâtés. Many jugged meats (see below) are also jellied.

Another type of jellying is fruit preserves, which are preparations of cooked fruits, vegetables and sugar, often stored in glass jam jars and Mason jars. Many varieties of fruit preserves are made globally, including sweet fruit preserves, such as those made from strawberry or apricot, and savory preserves, such as those made from tomatoes or squash. The ingredients used and how they are prepared determine the type of preserves; jams, jellies, and marmalades are all examples of different styles of fruit preserves that vary based upon the fruit used. In English, the word preserves, in plural form, is used to describe all types of jams and jellies.

Kangina
In rural Afghanistan, grapes are preserved in disc-shaped vessels made of mud and straw, called kangina. The vessels, which can preserve fresh grapes for up to 6 months, passively control their internal environments to restrict gas exchange and water loss, prolonging the lives of late-harvested grapes stored within them.

Jugging
Meat can be preserved by jugging. Jugging is the process of stewing the meat (commonly game or fish) in a covered earthenware jug or casserole. The animal to be jugged is usually cut into pieces, placed into a tightly sealed jug with brine or gravy, and stewed. Red wine and/or the animal's own blood is sometimes added to the cooking liquid. Jugging was a popular method of preserving meat up until the middle of the 20th century.

Lye
Sodium hydroxide (lye) makes food too alkaline for bacterial growth. Lye will saponify fats in the food, which will change its flavor and texture. Lutefisk uses lye in its preparation, as do some olive recipes. Modern recipes for century eggs also call for lye.

Pickling
Pickling is a method of preserving food in an edible, antimicrobial liquid. Pickling can be broadly classified into two categories: chemical pickling and fermentation pickling.

In chemical pickling, the food is placed in an edible liquid that inhibits or kills bacteria and other microorganisms. Typical pickling agents include brine (high in salt), vinegar, alcohol, and vegetable oil. Many chemical pickling processes also involve heating or boiling so that the food being preserved becomes saturated with the pickling agent. Common chemically pickled foods include cucumbers, peppers, corned beef, herring, and eggs, as well as mixed vegetables such as piccalilli.

In fermentation pickling, bacteria in the liquid produce organic acids as preservation agents, typically by a process that produces lactic acid through the presence of lactobacillales. Fermented pickles include sauerkraut, nukazuke, kimchi, and surströmming.

Sugaring
The earliest cultures have used sugar as a preservative, and it was commonplace to store fruit in honey. Similar to pickled foods, sugar cane was brought to Europe through the trade routes. In northern climates without sufficient sun to dry foods, preserves are made by heating the fruit with sugar. "Sugar tends to draw water from the microbes (plasmolysis). This process leaves the microbial cells dehydrated, thus killing them. In this way, the food will remain safe from microbial spoilage." Sugar is used to preserve fruits, either in an antimicrobial syrup with fruit such as apples, pears, peaches, apricots, and plums, or in crystallized form where the preserved material is cooked in sugar to the point of crystallization and the resultant product is then stored dry. This method is used for the skins of citrus fruit (candied peel), angelica, and ginger. Sugaring can be used in the production of jam and jelly.

Modern industrial techniques
Techniques of food preservation were developed in research laboratories for commercial applications.

Aseptic processing
Aseptic processing works by placing sterilized food (typically by heat, see ultra-high temperature processing) into sterlized packaging material under sterile conditions. The result is a sealed, sterile food product similar to canned food, but depending on the technique used, damage to food quality is typically reduced compared to canned food. A greater variety of packaging materials can be used as well.

Besides UHT, aseptic processing may be used in conjunction with any of the microbe-reduction technologies listed below. With pasteurization and "high pressure pasteurization", the food may not be completely sterilized (instead achieving a specified log reduction), but the use of sterile packaging and environments is retained.

Pasteurization
Pasteurization is a process for preservation of liquid food. It was originally applied to combat the souring of young local wines. Today, the process is mainly applied to dairy products. In this method, milk is heated at about 70 C for 15–30 seconds to kill the bacteria present in it and cooling it quickly to 10 C to prevent the remaining bacteria from growing. The milk is then stored in sterilized bottles or pouches in cold places. This method was invented by Louis Pasteur, a French chemist, in 1862.

Vacuum packing
Vacuum-packing stores food in a vacuum environment, usually in an air-tight bag or bottle. The vacuum environment strips bacteria of oxygen needed for survival. Vacuum-packing is commonly used for storing nuts to reduce loss of flavor from oxidization. A major drawback to vacuum packaging, at the consumer level, is that vacuum sealing can deform contents and rob certain foods, such as cheese, of its flavor.

Preservatives
Preservative food additives can be antimicrobial – which inhibit the growth of bacteria or fungi, including mold – or antioxidant, such as oxygen absorbers, which inhibit the oxidation of food constituents. Common antimicrobial preservatives include nisin, sorbates, calcium propionate, sodium nitrate/nitrite, sulfites (sulfur dioxide, sodium bisulfite, potassium hydrogen sulfite, etc.), EDTA, hinokitiol, and ε-polylysine. Antioxidants include tocopherols (Vitamin E), butylated hydroxyanisole (BHA) and butylated hydroxytoluene (BHT). Other preservatives include ethanol.

There is also another approach of impregnating packaging materials (plastic films or other) with antioxidants and antimicrobials.

Irradiation
Irradiation of food is the exposure of food to ionizing radiation. Multiple types of ionizing radiation can be used, including beta particles (high-energy electrons) and gamma rays (emitted from radioactive sources such as cobalt-60 or cesium-137). Irradiation can kill bacteria, molds, and insect pests, reduce the ripening and spoiling of fruits, and at higher doses induce sterility. The technology may be compared to pasteurization; it is sometimes called "cold pasteurization", as the product is not heated. Irradiation may allow lower-quality or contaminated foods to be rendered marketable.

National and international expert bodies have declared food irradiation as "wholesome"; organizations of the United Nations, such as the World Health Organization and Food and Agriculture Organization, endorse food irradiation. Consumers may have a negative view of irradiated food based on the misconception that such food is radioactive; in fact, irradiated food does not and cannot become radioactive. Activists have also opposed food irradiation for other reasons, for example, arguing that irradiation can be used to sterilize contaminated food without resolving the underlying cause of the contamination. International legislation on whether food may be irradiated or not varies worldwide from no regulation to a full ban.

Approximately 500,000 tons of food items are irradiated per year worldwide in over 40 countries. These are mainly spices and condiments, with an increasing segment of fresh fruit irradiated for fruit fly quarantine.

Pulsed electric field electroporation
Pulsed electric field (PEF) electroporation is a method for processing cells by means of brief pulses of a strong electric field. PEF holds potential as a type of low-temperature alternative pasteurization process for sterilizing food products. In PEF processing, a substance is placed between two electrodes, then the pulsed electric field is applied. The electric field enlarges the pores of the cell membranes, which kills the cells and releases their contents. PEF for food processing is a developing technology still being researched. There have been limited industrial applications of PEF processing for the pasteurization of fruit juices. To date, several PEF treated juices are available on the market in Europe. Furthermore, for several years a juice pasteurization application in the US has used PEF. For cell disintegration purposes especially potato processors show great interest in PEF technology as an efficient alternative for their preheaters. Potato applications are already operational in the US and Canada. There are also commercial PEF potato applications in various countries in Europe, as well as in Australia, India, and China.

Modified atmosphere
Modifying atmosphere is a way to preserve food by operating on the atmosphere around it. It is often used to package:
 * Fresh fruits and vegetables, especially salds crops, which contain living cells that respire even while refrigerated. Reducing oxygen (O2) concentration and increasing the carbon dioxide concentration slows down their respiration, conserves stored energy, and therefore increases shelf life. High humidity is also used to reduce water loss.
 * Red meat, which needs high O2 to reduce oxidation of myoglobin and maintain an attractive bright red color of the meat.
 * Other meat and fish, which uses higher CO2 to reduce oxidation and slow down some microbes.

Nonthermal plasma
This process subjects the surface of food to a "flame" of ionized gas molecules, such as helium or nitrogen. This causes micro-organisms to die off on the surface.

High-pressure food preservation
High pressure can be used to disable harmful microorganisms and spoilage enzymes while retaining the food's fresh appearance, flavor, texture and nutrients. By 2005, the process was being used for products ranging from orange juice to guacamole to deli meats and widely sold. Depending on temperature and pressure settings, HP processing can achieve either pasteurization-equivalent log reduction or go all the way to achieve sterilization of all microbes.

Biopreservation

Biopreservation is the use of natural or controlled microbiota or antimicrobials as a way of preserving food and extending its shelf life. Beneficial bacteria or the fermentation products produced by these bacteria are used in biopreservation to control spoilage and render pathogens inactive in food. It is a benign ecological approach which is gaining increasing attention.

Lactic acid bacteria (LAB) have antagonistic properties that make them particularly useful as biopreservatives. When LABs compete for nutrients, their metabolites often include active antimicrobials such as lactic acid, acetic acid, hydrogen peroxide, and peptide bacteriocins. Some LABs produce the antimicrobial nisin, which is a particularly effective preservative.

LAB bacteriocins are used in the present day as an integral part of hurdle technology. Using them in combination with other preservative techniques can effectively control spoilage bacteria and other pathogens, and can inhibit the activities of a wide spectrum of organisms, including inherently resistant Gram-negative bacteria.

Hurdle technology
Hurdle technology is a method of ensuring that pathogens in food products can be eliminated or controlled by combining more than one approach. These approaches can be thought of as "hurdles" the pathogen has to overcome if it is to remain active in the food. The right combination of hurdles can ensure all pathogens are eliminated or rendered harmless in the final product.

Hurdle technology has been defined by Leistner (2000) as an intelligent combination of hurdles that secures the microbial safety and stability as well as the organoleptic and nutritional quality and the economic viability of food products. The organoleptic quality of the food refers to its sensory properties, that is its look, taste, smell, and texture.

Examples of hurdles in a food system are high temperature during processing, low temperature during storage, increasing the acidity, lowering the water activity or redox potential, and the presence of preservatives or biopreservatives. According to the type of pathogens and how risky they are, the intensity of the hurdles can be adjusted individually to meet consumer preferences in an economical way, without sacrificing the safety of the product.

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

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Frequency modulation

Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing.

In analog frequency modulation, such as radio broadcasting, of an audio signal representing voice or music, the instantaneous frequency deviation, i.e. the difference between the frequency of the carrier and its center frequency, has a functional relation to the modulating signal amplitude.

Digital data can be encoded and transmitted with a type of frequency modulation known as frequency-shift keying (FSK), in which the instantaneous frequency of the carrier is shifted among a set of frequencies. The frequencies may represent digits, such as '0' and '1'. FSK is widely used in computer modems, such as fax modems, telephone caller ID systems, garage door openers, and other low-frequency transmissions. Radioteletype also uses FSK.

Frequency modulation is widely used for FM radio broadcasting. It is also used in telemetry, radar, seismic prospecting, and monitoring newborns for seizures via EEG, two-way radio systems, sound synthesis, magnetic tape-recording systems and some video-transmission systems. In radio transmission, an advantage of frequency modulation is that it has a larger signal-to-noise ratio and therefore rejects radio frequency interference better than an equal power amplitude modulation (AM) signal. For this reason, most music is broadcast over FM radio.

However, under severe enough multipath conditions it performs much more poorly than AM, with distinct high frequency noise artifacts that are audible with lower volumes and less complex tones. With high enough volume and carrier deviation audio distortion starts to occur that otherwise wouldn't be present without multipath or with an AM signal.

Frequency modulation and phase modulation are the two complementary principal methods of angle modulation; phase modulation is often used as an intermediate step to achieve frequency modulation. These methods contrast with amplitude modulation, in which the amplitude of the carrier wave varies, while the frequency and phase remain constant.

Theory
If the information to be transmitted (i.e., the baseband signal) is $$x_m(t)$$ and the sinusoidal carrier is $$x_c(t) = A_c \cos (2 \pi f_c t)\,$$, where fc is the carrier's base frequency, and Ac is the carrier's amplitude, the modulator combines the carrier with the baseband data signal to get the transmitted signal:

 * $$\begin{align}

y(t) &= A_c \cos\left(2\pi \int_0^t f(\tau) d\tau\right) \\ &= A_c \cos\left(2\pi \int_0^t \left[f_c + f_\Delta x_m(\tau)\right] d\tau\right) \\ &= A_c \cos\left(2\pi f_c t + 2\pi f_\Delta \int_0^t x_m(\tau) d\tau\right) \\ \end{align}$$

where $$f_\Delta = K_f A_m$$, $$K_f$$ being the sensitivity of the frequency modulator and $$A_m$$ being the amplitude of the modulating signal or baseband signal.

In this equation, $$f(\tau)\,$$ is the instantaneous frequency of the oscillator and $$f_\Delta\,$$ is the frequency deviation, which represents the maximum shift away from fc in one direction, assuming xm(t) is limited to the range ±1.

It is important to realize that this process of integrating the instantaneous frequency to create an instantaneous phase is quite different from what the term "frequency modulation" naively implies, namely directly adding the modulating signal to the carrier frequency
 * $$\begin{align}

y(t) &= A_c \cos\left(2\pi \left[f_c + f_\Delta x_m(t)\right] t \right) \end{align}$$ which would result in a modulated signal that has spurious local minima and maxima that do not correspond to those of the carrier.

While most of the energy of the signal is contained within fc ± fΔ, it can be shown by Fourier analysis that a wider range of frequencies is required to precisely represent an FM signal. The frequency spectrum of an actual FM signal has components extending infinitely, although their amplitude decreases and higher-order components are often neglected in practical design problems.

Sinusoidal baseband signal
Mathematically, a baseband modulating signal may be approximated by a sinusoidal continuous wave signal with a frequency fm. This method is also named as single-tone modulation. The integral of such a signal is:

 * $$\int_0^t x_m(\tau)d\tau = \frac{\sin\left(2\pi f_m t\right)}{2\pi f_m}\,$$

In this case, the expression for y(t) above simplifies to:

 * $$y(t) = A_c \cos\left(2\pi f_c t + \frac{f_\Delta}{f_m} \sin\left(2\pi f_m t\right)\right)\,$$

where the amplitude $$A_m\,$$ of the modulating sinusoid is represented in the peak deviation $$f_\Delta = K_f A_m$$ (see frequency deviation).

The harmonic distribution of a sine wave carrier modulated by such a sinusoidal signal can be represented with Bessel functions; this provides the basis for a mathematical understanding of frequency modulation in the frequency domain.

Modulation index
As in other modulation systems, the modulation index indicates by how much the modulated variable varies around its unmodulated level. It relates to variations in the carrier frequency:

 * $$h = \frac{\Delta{}f}{f_m} = \frac{f_\Delta \left|x_m(t)\right|}{f_m}$$

where $$f_m\,$$ is the highest frequency component present in the modulating signal xm(t), and $$\Delta{}f\,$$ is the peak frequency-deviation – i.e. the maximum deviation of the instantaneous frequency from the carrier frequency. For a sine wave modulation, the modulation index is seen to be the ratio of the peak frequency deviation of the carrier wave to the frequency of the modulating sine wave.

If $$h \ll 1$$, the modulation is called narrowband FM (NFM), and its bandwidth is approximately $$2f_m\,$$. Sometimes modulation index $$h < 0.3$$ is considered NFM and other modulation indices are considered wideband FM (WFM or FM).

For digital modulation systems, for example, binary frequency shift keying (BFSK), where a binary signal modulates the carrier, the modulation index is given by:

 * $$h = \frac{\Delta{}f}{f_m} = \frac{\Delta{}f}{\frac{1}{2T_s}} = 2\Delta{}fT_s \ $$

where $$T_s\,$$ is the symbol period, and $$f_m = \frac{1}{2T_s}\,$$ is used as the highest frequency of the modulating binary waveform by convention, even though it would be more accurate to say it is the highest fundamental of the modulating binary waveform. In the case of digital modulation, the carrier $$f_c\,$$ is never transmitted. Rather, one of two frequencies is transmitted, either $$f_c + \Delta f$$ or $$f_c - \Delta f$$, depending on the binary state 0 or 1 of the modulation signal.

If $$h \gg 1$$, the modulation is called wideband FM and its bandwidth is approximately $$2f_\Delta\,$$. While wideband FM uses more bandwidth, it can improve the signal-to-noise ratio significantly; for example, doubling the value of $$\Delta{}f\,$$, while keeping $$f_m$$ constant, results in an eight-fold improvement in the signal-to-noise ratio. (Compare this with chirp spread spectrum, which uses extremely wide frequency deviations to achieve processing gains comparable to traditional, better-known spread-spectrum modes).

With a tone-modulated FM wave, if the modulation frequency is held constant and the modulation index is increased, the (non-negligible) bandwidth of the FM signal increases but the spacing between spectra remains the same; some spectral components decrease in strength as others increase. If the frequency deviation is held constant and the modulation frequency increased, the spacing between spectra increases.

Frequency modulation can be classified as narrowband if the change in the carrier frequency is about the same as the signal frequency, or as wideband if the change in the carrier frequency is much higher (modulation index > 1) than the signal frequency. For example, narrowband FM (NFM) is used for two-way radio systems such as Family Radio Service, in which the carrier is allowed to deviate only 2.5 kHz above and below the center frequency with speech signals of no more than 3.5 kHz bandwidth. Wideband FM is used for FM broadcasting, in which music and speech are transmitted with up to 75 kHz deviation from the center frequency and carry audio with up to a 20 kHz bandwidth and subcarriers up to 92 kHz.

Bessel functions

For the case of a carrier modulated by a single sine wave, the resulting frequency spectrum can be calculated using Bessel functions of the first kind, as a function of the sideband number and the modulation index. The carrier and sideband amplitudes are illustrated for different modulation indices of FM signals. For particular values of the modulation index, the carrier amplitude becomes zero and all the signal power is in the sidebands.

Since the sidebands are on both sides of the carrier, their count is doubled, and then multiplied by the modulating frequency to find the bandwidth. For example, 3 kHz deviation modulated by a 2.2 kHz audio tone produces a modulation index of 1.36. Suppose that we limit ourselves to only those sidebands that have a relative amplitude of at least 0.01. Then, examining the chart shows this modulation index will produce three sidebands. These three sidebands, when doubled, gives us (6 × 2.2 kHz) or a 13.2 kHz required bandwidth.

Carson's rule
A rule of thumb, Carson's rule states that nearly all (≈98 percent) of the power of a frequency-modulated signal lies within a bandwidth $$ B_T\, $$ of:

 * $$B_T = 2\left(\Delta f + f_m\right) = 2f_m(\beta + 1)$$

where $$\Delta f\,$$, as defined above, is the peak deviation of the instantaneous frequency $$f(t)\,$$ from the center carrier frequency $$f_c$$, $$\beta$$ is the Modulation index which is the ratio of frequency deviation to highest frequency in the modulating signal and $$f_m\,$$is the highest frequency in the modulating signal. Condition for application of Carson's rule is only sinusoidal signals. For non-sinusoidal signals:

 * $$B_T = 2(\Delta f + W) = 2W(D + 1)$$

where W is the highest frequency in the modulating signal but non-sinusoidal in nature and D is the Deviation ratio which the ratio of frequency deviation to highest frequency of modulating non-sinusoidal signal.

Noise reduction
FM provides improved signal-to-noise ratio (SNR), as compared for example with AM. Compared with an optimum AM scheme, FM typically has poorer SNR below a certain signal level called the noise threshold, but above a higher level – the full improvement or full quieting threshold – the SNR is much improved over AM. The improvement depends on modulation level and deviation. For typical voice communications channels, improvements are typically 5–15 dB. FM broadcasting using wider deviation can achieve even greater improvements. Additional techniques, such as pre-emphasis of higher audio frequencies with corresponding de-emphasis in the receiver, are generally used to improve overall SNR in FM circuits. Since FM signals have constant amplitude, FM receivers normally have limiters that remove AM noise, further improving SNR.

Modulation
FM signals can be generated using either direct or indirect frequency modulation:
 * Direct FM modulation can be achieved by directly feeding the message into the input of a voltage-controlled oscillator.
 * For indirect FM modulation, the message signal is integrated to generate a phase-modulated signal. This is used to modulate a crystal-controlled oscillator, and the result is passed through a frequency multiplier to produce an FM signal. In this modulation, narrowband FM is generated leading to wideband FM later and hence the modulation is known as indirect FM modulation.

Demodulation
Many FM detector circuits exist. A common method for recovering the information signal is through a Foster–Seeley discriminator or ratio detector. A phase-locked loop can be used as an FM demodulator. Slope detection demodulates an FM signal by using a tuned circuit which has its resonant frequency slightly offset from the carrier. As the frequency rises and falls the tuned circuit provides a changing amplitude of response, converting FM to AM. AM receivers may detect some FM transmissions by this means, although it does not provide an efficient means of detection for FM broadcasts. In Software-Defined Radio implementations the demodulation may be carried out by using the Hilbert transform (implemented as a filter) to recover the instantaneous phase, and thereafter differentiating this phase (using another filter) to recover the instantaneous frequency. Alternatively, a complex mixer followed by a bandpass filter may be used to translate the signal to baseband, and then proceeding as before.

Doppler effect
When an echolocating bat approaches a target, its outgoing sounds return as echoes, which are Doppler-shifted upward in frequency. In certain species of bats, which produce constant frequency (CF) echolocation calls, the bats compensate for the Doppler shift by lowering their call frequency as they approach a target. This keeps the returning echo in the same frequency range of the normal echolocation call. This dynamic frequency modulation is called the Doppler Shift Compensation (DSC), and was discovered by Hans Schnitzler in 1968.

Magnetic tape storage
FM is also used at intermediate frequencies by analog VCR systems (including VHS) to record the luminance (black and white) portions of the video signal. Commonly, the chrominance component is recorded as a conventional AM signal, using the higher-frequency FM signal as bias. FM is the only feasible method of recording the luminance ("black-and-white") component of video to (and retrieving video from) magnetic tape without distortion; video signals have a large range of frequency components – from a few hertz to several megahertz, too wide for equalizers to work with due to electronic noise below −60 dB. FM also keeps the tape at saturation level, acting as a form of noise reduction; a limiter can mask variations in playback output, and the FM capture effect removes print-through and pre-echo. A continuous pilot-tone, if added to the signal – as was done on V2000 and many Hi-band formats – can keep mechanical jitter under control and assist timebase correction.

These FM systems are unusual, in that they have a ratio of carrier to maximum modulation frequency of less than two; contrast this with FM audio broadcasting, where the ratio is around 10,000. Consider, for example, a 6-MHz carrier modulated at a 3.5-MHz rate; by Bessel analysis, the first sidebands are on 9.5 and 2.5 MHz and the second sidebands are on 13 MHz and −1 MHz. The result is a reversed-phase sideband on +1 MHz; on demodulation, this results in unwanted output at 6 – 1 = 5 MHz. The system must be designed so that this unwanted output is reduced to an acceptable level.

Sound
FM is also used at audio frequencies to synthesize sound. This technique, known as FM synthesis, was popularized by early digital synthesizers and became a standard feature in several generations of personal computer sound cards.

Radio
Edwin Howard Armstrong (1890–1954) was an American electrical engineer who invented wideband frequency modulation (FM) radio. He patented the regenerative circuit in 1914, the superheterodyne receiver in 1918 and the super-regenerative circuit in 1922. Armstrong presented his paper, "A Method of Reducing Disturbances in Radio Signaling by a System of Frequency Modulation", (which first described FM radio) before the New York section of the Institute of Radio Engineers on November 6, 1935. The paper was published in 1936.

As the name implies, wideband FM (WFM) requires a wider signal bandwidth than amplitude modulation by an equivalent modulating signal; this also makes the signal more robust against noise and interference. Frequency modulation is also more robust against signal-amplitude-fading phenomena. As a result, FM was chosen as the modulation standard for high frequency, high fidelity radio transmission, hence the term "FM radio" (although for many years the BBC called it "VHF radio" because commercial FM broadcasting uses part of the VHF band – the FM broadcast band). FM receivers employ a special detector for FM signals and exhibit a phenomenon known as the capture effect, in which the tuner "captures" the stronger of two stations on the same frequency while rejecting the other (compare this with a similar situation on an AM receiver, where both stations can be heard simultaneously). Frequency drift or a lack of selectivity may cause one station to be overtaken by another on an adjacent channel. Frequency drift was a problem in early (or inexpensive) receivers; inadequate selectivity may affect any tuner.

A wideband FM signal can also be used to carry a stereo signal; this is done with multiplexing and demultiplexing before and after the FM process. The FM modulation and demodulation process is identical in stereo and monaural processes.

FM is commonly used at VHF radio frequencies for high-fidelity broadcasts of music and speech. In broadcast services, where audio fidelity is important, wideband FM is generally used. Analog TV sound is also broadcast using FM. Narrowband FM is used for voice communications in commercial and amateur radio settings. In two-way radio, narrowband FM (NBFM) is used to conserve bandwidth for land mobile, marine mobile and other radio services.

A high-efficiency radio-frequency switching amplifier can be used to transmit FM signals (and other constant-amplitude signals). For a given signal strength (measured at the receiver antenna), switching amplifiers use less battery power and typically cost less than a linear amplifier. This gives FM another advantage over other modulation methods requiring linear amplifiers, such as AM and QAM.

There are reports that on October 5, 1924, Professor Mikhail A. Bonch-Bruevich, during a scientific and technical conversation in the Nizhny Novgorod Radio Laboratory, reported about his new method of telephony, based on a change in the period of oscillations. Demonstration of frequency modulation was carried out on the laboratory model.

Hearing assistive technology
Frequency modulated systems are a widespread and commercially available assistive technology that make speech more understandable by improving the signal-to-noise ratio in the user's ear. They are also called auditory trainers, a term which refers to any sound amplification system not classified as a hearing aid. They intensify signal levels from the source by 15 to 20 decibels. FM systems are used by hearing-impaired people as well as children whose listening is affected by disorders such as auditory processing disorder or ADHD. For people with sensorineural hearing loss, FM systems result in better speech perception than hearing aids. They can be coupled with behind-the-ear hearing aids to allow the user to alternate the setting. FM systems are more convenient and cost-effective than alternatives such as cochlear implants, but many users use FM systems infrequently due to their conspicuousness and need for recharging.

title: Frequency modulation


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Faith and rationality

Faith and rationality exist in varying degrees of conflict or compatibility. Rationality is based on reason or facts. Faith is belief in inspiration, revelation, or authority. The word faith sometimes refers to a belief that is held in spite of or against reason or empirical evidence, or it can refer to belief based upon a degree of evidential warrant.

Relationship between faith and reason
Rationalists point out that many people hold irrational beliefs, for many reasons. There may be evolutionary causes for irrational beliefs—irrational beliefs may increase our ability to survive and reproduce.

One more reason for irrational beliefs can perhaps be explained by operant conditioning. For example, in one study by B. F. Skinner in 1948, pigeons were awarded grain at regular time intervals regardless of their behaviour. The result was that each of the pigeons developed their own idiosyncratic response which had become associated with the consequence of receiving grain.

Believers in the value of faith—for example those who believe salvation is possible through faith alone—frequently suggest that everyone holds beliefs arrived at by faith, not reason.

One form of belief held "by faith" may be seen existing in a faith as based on warrant. In this view some degree of evidence provides warrant for faith; it consists in other words in "explain[ing] great things by small."

Catholic views
Thomas Aquinas was the first to write a full treatment of the relationship, differences, and similarities between faith, which he calls "an intellectual assent", and reason.

Dei Filius was a dogmatic constitution of the First Vatican Council on the Roman Catholic faith. It was adopted unanimously on 24 April 1870. It states that "not only can faith and reason never be opposed to one another, but they are of mutual aid one to the other".

Recent popes have spoken about faith and rationality: Fides et ratio, an encyclical letter promulgated by Pope John Paul II on 14 September 1998, deals with the relationship between faith and reason. Pope Benedict XVI's Regensburg lecture, delivered on 12 September 2006, was on the subject of "faith, reason and the university".

Reformed views
Alvin Plantinga upholds that faith may be the result of evidence testifying to the reliability of the source of truth claims, but although it may involve this, he sees faith as being the result of hearing the truth of the gospel with the internal persuasion by the Holy Spirit moving and enabling him to believe. "Christian belief is produced in the believer by the internal instigation of the Holy Spirit, endorsing the teachings of Scripture, which is itself divinely inspired by the Holy Spirit. The result of the work of the Holy Spirit is faith."

Evangelical views
American biblical scholar Archibald Thomas Robertson stated that the Greek word pistis used for faith in the New Testament (over two hundred forty times), and rendered "assurance" in Acts 17:31 (KJV), is "an old verb to furnish, used regularly by Demosthenes for bringing forward evidence." Likewise Tom Price (Oxford Centre for Christian Apologetics) affirms that when the New Testament talks about faith positively it only uses words derived from the Greek root [pistis] which means "to be persuaded."

In contrast to faith meaning blind trust, in the absence of evidence, even in the teeth of evidence, Alister McGrath quotes Oxford Anglican theologian W. H. Griffith-Thomas (1861–1924), who states faith is "not blind, but intelligent" and "commences with the conviction of the mind based on adequate evidence", which McGrath sees as "a good and reliable definition, synthesizing the core elements of the characteristic Christian understanding of faith."

Jewish views
The 14th-century Jewish philosopher Levi ben Gerson tried to reconcile faith and reason. He wrote: "the Law cannot prevent us from considering to be true that which our reason urges us to believe."

title: Faith and rationality


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List of film institutes

Some notable institutions celebrating film, including both national film institutes and independent and non-profit organizations. For the purposes of this list, institutions that do not have their own article on Wikipedia are not considered notable.

 * American Film Institute
 * Asia Pacific Film Institute
 * Asian Academy of Film & Television
 * Australian Film Institute
 * British Film Institute
 * Canadian Film Institute
 * Danish Film Institute
 * Doha Film Institute
 * Film and Television Institute of India
 * Finnish Film Foundation
 * German Film Institute
 * Irish Film Institute
 * K. R. Narayanan National Institute of Visual Science and Arts
 * Mowelfund Film Institute
 * Norwegian Film Institute
 * Satyajit Ray Film and Television Institute
 * Sundance Institute
 * Swedish Film Institute
 * University of the Philippines Film Institute

title: List of film institutes


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Forth

Forth or FORTH may refer to:

Arts and entertainment

 * forth magazine, an Internet magazine
 * Forth (album), by The Verve, 2008
 * Forth, a 2011 album by Proto-Kaw
 * Radio Forth, a group of independent local radio stations in Scotland

People

 * Eric Forth (1944–2006), British politician
 * Frederick Forth (1808–1876), British colonial administrator
 * Hugh Forth (1610–1676), English politician
 * Jane Forth (born 1953), American actress and model
 * John Forth (c. 1769 – 1848), British jockey and racehorse trainer
 * Lisette Denison Forth (c. 1786 – 1866), American slave who became a landowner and philanthropist
 * Tasman Forth, pen name of Alexander Rud Mills (1885–1964), Australian Odinist

Places

 * Forth, Tasmania, Australia
 * Forth, Eckental, Germany
 * Forth, South Lanarkshire, Scotland
 * River Forth, in Scotland
 * River Forth (Tasmania), Australia
 * Forth (County Carlow barony), Ireland
 * Forth (County Wexford barony), Ireland
 * Forth (Edinburgh ward), Scotland

Ships

 * HMS Forth, the name of several ships of the Royal Navy
 * Forth, a sailing ship built at Calcutta, British India
 * Forth, a sailing ship built at Leith, Scotland

Other uses

 * Forth (programming language)
 * Foundation for Research & Technology – Hellas, a research centre in Greece

title: Forth


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F wave

In neuroscience, an F wave is one of several motor responses which may follow the direct motor response (M) evoked by electrical stimulation of peripheral motor or mixed (sensory and motor) nerves. F-waves are the second of two late voltage changes observed after stimulation is applied to the skin surface above the distal region of a nerve, in addition to the H-reflex (Hoffman's Reflex) which is a muscle reaction in response to electrical stimulation of innervating sensory fibers. Traversal of F-waves along the entire length of peripheral nerves between the spinal cord and muscle, allows for assessment of motor nerve conduction between distal stimulation sites in the arm and leg, and related motoneurons (MN's) in the cervical and lumbosacral cord. F-waves are able to assess both afferent and efferent loops of the alpha motor neuron in its entirety. As such, various properties of F-wave motor nerve conduction are analyzed in nerve conduction studies (NCS), and often used to assess polyneuropathies, resulting from states of neuronal demyelination and loss of peripheral axonal integrity.

With respect to its nomenclature, the F-wave is so named as it was initially studied in the smaller muscles of the foot. The observation of F-waves in the same motor units (MU) as those present in the direct motor response (M), along with the presence of F-waves in deafferented animal and human models, indicates that F-waves require direct activation of motor axons to be elicited, and do not involve conduction along afferent sensory nerves. Thus, the F-wave is considered a wave, as opposed to a reflex.

Physiology
F-waves are evoked by strong electrical stimuli (supramaximal) applied to the skin surface above the distal portion of a nerve. This impulse travels both in orthodromic fashion (towards the muscle fibers) and antidromic fashion (towards the cell body in the spinal cord) along the alpha motor neuron. As the orthodromic impulse reaches innervated muscle fibers, a strong direct motor response (M) is evoked in these muscle fibers, resulting in a primary compound muscle action potential (CMAP). As the antidromic impulse reaches the cell bodies within the anterior horn of the motor neuron pool by retrograde transmission, a select portion of these alpha motor neurons, (roughly 5-10% of available motor neurons), 'backfire' or rebound. This antidromic 'backfiring' elicits an orthodromic impulse that follows back down the alpha motor neuron, towards innervated muscle fibers. Conventionally, axonal segments of motor neurons previously depolarized by preceding antidromic impulses enter a hyperpolarized state, disallowing the travel of impulses along them. However, these same axonal segments remains excitable or relatively depolarized for a sufficient period of time, allowing for rapid antidromic backfiring, and thus the continuation of the orthodromic impulse towards innervated muscle fibers. This successive orthodromic stimulus then evokes a smaller population of muscle fibers, resulting in a smaller CMAP known as an F-wave.

Several physiological factors may possibly influence the presence of F-waves after peripheral nerve stimulation. The shape and size of F-waves, along with the probability of their presence is small, as a high degree of variability exists in motor unit (MU) activation for any given stimulation. Thus, the generation of CMAP's which elicit F-waves is subject to the variability in activation of motor units in a given pool over successive stimuli. Moreover, stimulation of peripheral nerve fibers account for both orthodromic impulses (along sensory fibers, towards the dorsal horn), as well as antidromic activity (along alpha motor neurons towards the ventral horn). Antidromic activity along collateral branches of alpha motor neurons may result in the activation of inhibitory Renshaw cells or direct inhibitory collaterals between motorneurons. Inhibition by these means may lower excitability of adjacent motor neurons and decrease the potential for antidromic backfiring and resultant F-waves; although it has been argued Renshaw cells preferentially inhibit smaller alpha motor neurons limited influence on modulation of antidromic backfiring.

Because a different population of anterior horn cells is stimulated with each stimulation, F waves are characterized as ubiquitous, low amplitude, late motor responses, which can vary in amplitude, latency and configuration across a series of stimuli.

Properties
F waves can be analyzed by several properties including:
 * amplitude (μV) - height or voltage of F wave
 * duration (ms) - length of F wave
 * latency (ms) - period between initial stimulation and F wave elicitation

Measurements
Several measurements can be done on the F responses, including:
 * minimal and maximal F wave latencies (ms) - frequently used in the assessment of demyelinating neuropathic conditions including Guillain-Barré syndrome.
 * chronodispersion - difference in maximal and minimal latencies across a series of F waves
 * F wave persistence - measure of alpha motor neuron excitability calculated as the number of F responses elicited divided by the number of stimuli presented.

The minimal F wave latency is typically 25-32 ms in the upper extremities and 45-56 ms in the lower extremities.

F wave persistence is the number of F waves obtained per the number of stimulations, which is normally 80-100% (or above 50%).

title: F wave


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Fruit

In botany, a fruit is the seed-bearing structure in flowering plants that is formed from the ovary after flowering (see Fruit anatomy).

Fruits are the means by which flowering plants (also known as angiosperms) disseminate their seeds. Edible fruits in particular have long propagated using the movements of humans and other animals in a symbiotic relationship that is the means for seed dispersal for the one group and nutrition for the other; humans and many other animals have become dependent on fruits as a source of food. Consequently, fruits account for a substantial fraction of the world's agricultural output, and some (such as the apple and the pomegranate) have acquired extensive cultural and symbolic meanings.

In common language usage, fruit normally means the seed-associated fleshy structures (or produce) of plants that typically are sweet or sour and edible in the raw state, such as apples, bananas, grapes, lemons, oranges, and strawberries. In botanical usage, the term fruit also includes many structures that are not commonly called 'fruits' in everyday language, such as nuts, bean pods, corn kernels, tomatoes, and wheat grains.

Botanical vs. culinary

Many common language terms used for fruit and seeds differ from botanical classifications. For example, in botany, a fruit is a ripened ovary or carpel that contains seeds, e.g., an orange, pomegranate, tomato or a pumpkin. A nut is a type of fruit (and not a seed), and a seed is a ripened ovule.

In culinary language, a fruit is the sweet- or not sweet- (even sour-) tasting produce of a specific plant (e.g., a peach, pear or lemon); nuts are hard, oily, non-sweet plant produce in shells (hazelnut, acorn). Vegetables, so-called, typically are savory or non-sweet produce (zucchini, lettuce, broccoli, and tomato). but some may be sweet-tasting (sweet potato).

Examples of botanically classified fruit that are typically called vegetables include cucumber, pumpkin, and squash (all are cucurbits); beans, peanuts, and peas (all legumes); and corn, eggplant, bell pepper (or sweet pepper), and tomato. Many spices are fruits, botanically speaking, including black pepper, chili pepper, cumin and allspice. In contrast, rhubarb is often called a fruit when used in making pies, but the edible produce of rhubarb is actually the leaf stalk or petiole of the plant. Edible gymnosperm seeds are often given fruit names, e.g., ginkgo nuts and pine nuts.

Botanically, a cereal grain, such as corn, rice, or wheat is a kind of fruit (termed a caryopsis). However, the fruit wall is thin and fused to the seed coat, so almost all the edible grain-fruit is actually a seed.

Structure
The outer layer, often edible, of most fruits is called the pericarp. Typically formed from the ovary, it surrounds the seeds; in some species, however, other structural tissues contribute to or form the edible portion. The pericarp may be described in three layers from outer to inner, i.e., the epicarp, mesocarp and endocarp.

Fruit that bears a prominent pointed terminal projection is said to be beaked.

Development
A fruit results from the fertilizing and maturing of one or more flowers. The gynoecium, which contains the stigma-style-ovary system, is centered in the flower-head, and it forms all or part of the fruit. Inside the ovary(ies) are one or more ovules. Here begins a complex sequence called double fertilization: a female gametophyte produces an egg cell for the purpose of fertilization. (A female gametophyte is called a megagametophyte, and also called the embryo sac.) After double fertilization, the ovules will become seeds.

Ovules are fertilized in a process that starts with pollination, which is the movement of pollen from the stamens to the stigma-style-ovary system within the flower-head. After pollination, a pollen tube grows from the (deposited) pollen through the stigma down the style into the ovary to the ovule. Two sperm are transferred from the pollen to a megagametophyte. Within the megagametophyte, one sperm unites with the egg, forming a zygote, while the second sperm enters the central cell forming the endosperm mother cell, which completes the double fertilization process. Later, the zygote will give rise to the embryo of the seed, and the endosperm mother cell will give rise to endosperm, a nutritive tissue used by the embryo.

As the ovules develop into seeds, the ovary begins to ripen and the ovary wall, the pericarp, may become fleshy (as in berries or drupes), or it may form a hard outer covering (as in nuts). In some multi-seeded fruits, the extent to which a fleshy structure develops is proportional to the number of fertilized ovules. The pericarp typically is differentiated into two or three distinct layers; these are called the exocarp (outer layer, also called epicarp), mesocarp (middle layer), and endocarp (inner layer).

In some fruits, the sepals, petals, stamens or the style of the flower fall away as the fleshy fruit ripens. However, for simple fruits derived from an inferior ovary – i.e., one that lies the attachment of other floral parts – there are parts (including petals, sepals, and stamens) that fuse with the ovary and ripen with it. For such a case, when floral parts other than the ovary form a significant part of the fruit that develops, it is called an accessory fruit. Examples of accessory fruits include apple, rose hip, strawberry, and pineapple.

Because several parts of the flower besides the ovary may contribute to the structure of a fruit, it is important to understand how a particular fruit forms. There are three general modes of fruit development:

 * Apocarpous fruits develop from a single flower (while having one or more separate, unfused, carpels); they are the simple fruits.
 * Syncarpous fruits develop from a single gynoecium (having two or more carpels fused together).
 * Multiple fruits form from many flowers – i.e., an inflorescence of flowers.

Classification of fruits

Consistent with the three modes of fruit development, plant scientists have classified fruits into three main groups: simple fruits, aggregate fruits, and multiple (or composite) fruits. The groupings reflect how the ovary and other flower organs are arranged and how the fruits develop, but they are not evolutionarily relevant as diverse plant taxa may be in the same group.

While the section of a fungus that produces spores is called a fruiting body, fungi are members of the fungi kingdom and not of the plant kingdom.

Simple fruits
Simple fruits are the result of the ripening-to-fruit of a simple or compound ovary in a single flower with a single pistil. In contrast, a single flower with numerous pistils typically produces an aggregate fruit; and the merging of several flowers, or a 'multiple' of flowers, results in a 'multiple' fruit. A simple fruit is further classified as either dry or fleshy.

To distribute their seeds, dry fruits may split open and discharge their seeds to the winds, which is called dehiscence. Or the distribution process may rely upon the decay and degradation of the fruit to expose the seeds; or it may rely upon the eating of fruit and excreting of seeds by frugivores – both are called indehiscence. Fleshy fruits do not split open, but they also are indehiscent and they may also rely on frugivores for distribution of their seeds. Typically, the entire outer layer of the ovary wall ripens into a potentially edible pericarp.

Types of dry simple fruits, (with examples) include:
 * Achene – most commonly seen in aggregate fruits (e.g., strawberry, see below).
 * Capsule – (Brazil nut: botanically, it is not a nut).
 * Caryopsis – (cereal grains, including wheat, rice, oats, barley).
 * Cypsela – an achene-like fruit derived from the individual florets in a capitulum: (dandelion).
 * Fibrous drupe – (coconut, walnut: botanically, neither is a true nut.).
 * Follicle – follicles are formed from a single carpel, and opens by one suture: (milkweed); also commonly seen in aggregate fruits: (magnolia, peony).
 * Legume – (bean, pea, peanut: botanically, the peanut is the seed of a legume, not a nut).
 * Loment – a type of indehiscent legume: (sweet vetch or wild potato).
 * Nut – (beechnut, hazelnut, acorn (of the oak): botanically, these are true nuts).
 * Samara – (ash, elm, maple key).
 * Schizocarp, see below – (carrot seed).
 * Silique – (radish seed).
 * Silicle – (shepherd's purse).
 * Utricle – (beet, Rumex).

Fruits in which part or all of the pericarp (fruit wall) is fleshy at maturity are termed fleshy simple fruits.

Types of fleshy simple fruits, (with examples) include:
 * Berry – the berry is the most common type of fleshy fruit. The entire outer layer of the ovary wall ripens into a potentially edible "pericarp", (see below).
 * Stone fruit or drupe – the definitive characteristic of a drupe is the hard, "lignified" stone (sometimes called the "pit"). It is derived from the ovary wall of the flower: apricot, cherry, olive, peach, plum, mango.
 * Pome – the pome fruits: apples, pears, rosehips, saskatoon berry, etc., are a syncarpous (fused) fleshy fruit, a simple fruit, developing from a half-inferior ovary. Pomes are of the family Rosaceae.

Berries

Berries are a type of simple fleshy fruit that issue from a single ovary. (The ovary itself may be compound, with several carpels.) The botanical term true berry includes grapes, currants, cucumbers, eggplants (aubergines), tomatoes, chili peppers, and bananas, but excludes certain fruits that are called "-berry" by culinary custom or by common usage of the term – such as strawberries and raspberries. Berries may be formed from one or more carpels (i.e., from the simple or compound ovary) from the same, single flower. Seeds typically are embedded in the fleshy interior of the ovary.

Examples include:
 * Tomato – in culinary terms, the tomato is regarded as a vegetable, but it is botanically classified as a fruit and a berry.
 * Banana – the fruit has been described as a "leathery berry". In cultivated varieties, the seeds are diminished nearly to non-existence.
 * Pepo – berries with skin that is hardened: cucurbits, including gourds, squash, melons.
 * Hesperidium – berries with a rind and a juicy interior: most citrus fruit.
 * Cranberry, gooseberry, redcurrant, grape.

The strawberry, regardless of its appearance, is classified as a dry, not a fleshy fruit. Botanically, it is not a berry; it is an aggregate-accessory fruit, the latter term meaning the fleshy part is derived not from the plant's ovaries but from the receptacle that holds the ovaries. Numerous dry achenes are attached to the outside of the fruit-flesh; they appear to be seeds but each is actually an ovary of a flower, with a seed inside.

Schizocarps are dry fruits, though some appear to be fleshy. They originate from syncarpous ovaries but do not actually dehisce; rather, they split into segments with one or more seeds. They include a number of different forms from a wide range of families, including carrot, parsnip, parsley, cumin.

Aggregate fruits
An aggregate fruit is also called an aggregation, or etaerio; it develops from a single flower that presents numerous simple pistils. Each pistil contains one carpel; together, they form a fruitlet. The ultimate (fruiting) development of the aggregation of pistils is called an aggregate fruit, etaerio fruit, or simply an etaerio.

Different types of aggregate fruits can produce different etaerios, such as achenes, drupelets, follicles, and berries.

 * For example, the Ranunculaceae species, including Clematis and Ranunculus, produces an etaerio of achenes;
 * Rubus species, including raspberry: an etaerio of drupelets;
 * Calotropis species: an etaerio of follicles fruit;
 * Annona species: an etaerio of berries.

Some other broadly recognized species and their etaerios (or aggregations) are:
 * Teasel; fruit is an aggregation of cypselas.
 * Tuliptree; fruit is an aggregation of samaras.
 * Magnolia and peony; fruit is an aggregation of follicles.
 * American sweet gum; fruit is an aggregation of capsules.
 * Sycamore; fruit is an aggregation of achenes.

The pistils of the raspberry are called drupelets because each pistil is like a small drupe attached to the receptacle. In some bramble fruits, such as blackberry, the receptacle, an accessory part, elongates and then develops as part of the fruit, making the blackberry an aggregate-accessory fruit. The strawberry is also an aggregate-accessory fruit, of which the seeds are contained in the achenes. Notably in all these examples, the fruit develops from a single flower, with numerous pistils.

Multiple fruits
A multiple fruit is formed from a cluster of flowers, (a 'multiple' of flowers) – also called an inflorescence. Each ('smallish') flower produces a single fruitlet, which, as all develop, all merge into one mass of fruit. Examples include pineapple, fig, mulberry, Osage orange, and breadfruit. An inflorescence (a cluster) of white flowers, called a head, is produced first. After fertilization, each flower in the cluster develops into a drupe; as the drupes expand, they develop as a connate organ, merging into a multiple fleshy fruit called a syncarp.

Progressive stages of multiple flowering and fruit development can be observed on a single branch of the Indian mulberry, or noni. During the sequence of development, a progression of second, third, and more inflorescences are initiated in turn at the head of the branch or stem.

Accessory fruit forms
Fruits may incorporate tissues derived from other floral parts besides the ovary, including the receptacle, hypanthium, petals, or sepals. Accessory fruits occur in all three classes of fruit development – simple, aggregate, and multiple. Accessory fruits are frequently designated by the hyphenated term showing both characters. For example, a pineapple is a multiple-accessory fruit, a blackberry is an aggregate-accessory fruit, and an apple is a simple-accessory fruit.

Seedless fruits
Seedlessness is an important feature of some fruits of commerce. Commercial cultivars of bananas and pineapples are examples of seedless fruits. Some cultivars of citrus fruits (especially grapefruit, mandarin oranges, navel oranges), satsumas, table grapes, and of watermelons are valued for their seedlessness. In some species, seedlessness is the result of parthenocarpy, where fruits set without fertilization. Parthenocarpic fruit-set may (or may not) require pollination, but most seedless citrus fruits require a stimulus from pollination to produce fruit. Seedless bananas and grapes are triploids, and seedlessness results from the abortion of the embryonic plant that is produced by fertilization, a phenomenon known as stenospermocarpy, which requires normal pollination and fertilization.

Seed dissemination
Variations in fruit structures largely depend on the modes of dispersal applied to their seeds. Dispersal is achieved by wind or water, by explosive dehiscence, and by interactions with animals.

Some fruits present their outer skins or shells coated with spikes or hooked burrs; these evolved either to deter would-be foragers from feeding on them or to serve to attach themselves to the hair, feathers, legs, or clothing of animals, thereby using them as dispersal agents. These plants are termed zoochorous; common examples include cocklebur, unicorn plant, and beggarticks (or Spanish needle).

By developments of mutual evolution, the fleshy produce of fruits typically appeals to hungry animals, such that the seeds contained within are taken in, carried away, and later deposited (i.e., defecated) at a distance from the parent plant. Likewise, the nutritious, oily kernels of nuts typically motivate birds and squirrels to hoard them, burying them in soil to retrieve later during the winter of scarcity; thereby, uneaten seeds are sown effectively under natural conditions to germinate and grow a new plant some distance away from the parent.

Other fruits have evolved flattened and elongated wings or helicopter-like blades, e.g., elm, maple, and tuliptree. This mechanism increases dispersal distance away from the parent via wind. Other wind-dispersed fruit have tiny "parachutes", e.g., dandelion, milkweed, salsify.

Coconut fruits can float thousands of miles in the ocean, thereby spreading their seeds. Other fruits that can disperse via water are nipa palm and screw pine.

Some fruits have evolved propulsive mechanisms that fling seeds substantial distances – perhaps up to 100 m in the case of the sandbox tree – via explosive dehiscence or other such mechanisms (see impatiens and squirting cucumber).

Food uses
A cornucopia of fruits – fleshy (simple) fruits from apples to berries to watermelon; dry (simple) fruits including beans and rice and coconuts; aggregate fruits including strawberries, raspberries, blackberries, pawpaw; and multiple fruits such as pineapple, fig, mulberries – are commercially valuable as human food. They are eaten both fresh and as jams, marmalade and other fruit preserves. They are used extensively in manufactured and processed foods (cakes, cookies, baked goods, flavorings, ice cream, yogurt, canned vegetables, frozen vegetables and meals) and beverages such as fruit juices and alcoholic beverages (brandy, fruit beer, wine). Spices like vanilla, black pepper, paprika, and allspice are derived from berries. Olive fruit is pressed for olive oil and similar processing is applied to other oil-bearing fruits and vegetables. Some fruits are available all year round, while others (such as blackberries and apricots in the UK) are subject to seasonal availability.

Fruits are also used for socializing and gift-giving in the form of fruit baskets and fruit bouquets.

Typically, many botanical fruits – "vegetables" in culinary parlance – (including tomato, green beans, leaf greens, bell pepper, cucumber, eggplant, okra, pumpkin, squash, zucchini) are bought and sold daily in fresh produce markets and greengroceries and carried back to kitchens, at home or restaurant, for preparation of meals.

Storage
All fruits benefit from proper post-harvest care, and in many fruits, the plant hormone ethylene causes ripening. Therefore, maintaining most fruits in an efficient cold chain is optimal for post-harvest storage, with the aim of extending and ensuring shelf life.

Nutritional value

Various culinary fruits provide significant amounts of fiber and water, and many are generally high in vitamin C. An overview of numerous studies showed that fruits (e.g., whole apples or whole oranges) are satisfying (filling) by simply eating and chewing them.

The dietary fiber consumed in eating fruit promotes satiety, and may help to control body weight and aid reduction of blood cholesterol, a risk factor for cardiovascular diseases. Fruit consumption is under preliminary research for the potential to improve nutrition and affect chronic diseases. Regular consumption of fruit is generally associated with reduced risks of several diseases and functional declines associated with aging.

Food safety
For food safety, the CDC recommends proper fruit handling and preparation to reduce the risk of food contamination and foodborne illness. Fresh fruits and vegetables should be carefully selected; at the store, they should not be damaged or bruised; and precut pieces should be refrigerated or surrounded by ice.

All fruits and vegetables should be rinsed before eating. This recommendation also applies to produce with rinds or skins that are not eaten. It should be done just before preparing or eating to avoid premature spoilage.

Fruits and vegetables should be kept separate from raw foods like meat, poultry, and seafood, as well as from utensils that have come in contact with raw foods. Fruits and vegetables that are not going to be cooked should be thrown away if they have touched raw meat, poultry, seafood, or eggs.

All cut, peeled, or cooked fruits and vegetables should be refrigerated within two hours. After a certain time, harmful bacteria may grow on them and increase the risk of foodborne illness.

Allergies
Fruit allergies make up about 10 percent of all food-related allergies.

Nonfood uses
Because fruits have been such a major part of the human diet, various cultures have developed many different uses for fruits they do not depend on for food. For example:

 * Bayberry fruits provide a wax often used to make candles;
 * Many dry fruits are used as decorations or in dried flower arrangements (e.g., annual honesty, cotoneaster, lotus, milkweed, unicorn plant, and wheat). Ornamental trees and shrubs are often cultivated for their colorful fruits, including beautyberry, cotoneaster, holly, pyracantha, skimmia, and viburnum.
 * Fruits of opium poppy are the source of opium, which contains the drugs codeine and morphine, as well as the biologically inactive chemical theabaine from which the drug oxycodone is synthesized.
 * Osage orange fruits are used to repel cockroaches.
 * Many fruits provide natural dyes (e.g., cherry, mulberry, sumac, and walnut).
 * Dried gourds are used as bird houses, cups, decorations, dishes, musical instruments, and water jugs.
 * Pumpkins are carved into Jack-o'-lanterns for Halloween.
 * The fibrous core of the mature and dry Luffa fruit is used as a sponge.
 * The spiny fruit of burdock or cocklebur inspired the invention of Velcro.
 * Coir fiber from coconut shells is used for brushes, doormats, floor tiles, insulation, mattresses, sacking, and as a growing medium for container plants. The shell of the coconut fruit is used to make bird houses, bowls, cups, musical instruments, and souvenir heads.
 * The hard and colorful grain fruits of Job's tears are used as decorative beads for jewelry, garments, and ritual objects.
 * Fruit is often a subject of still life paintings.

title: Fruit


text:
French materialism

French materialism is the name given to a handful of French 18th-century philosophers during the Age of Enlightenment, many of them clustered around the salon of Baron d'Holbach. Although there are important differences between them, all of them were materialists who believed that the world was made up of a single substance, matter, the motions and properties of which could be used to explain all phenomena.

Prominent French materialists of the 18th century include:

 * Julien Offray de La Mettrie
 * Denis Diderot
 * Baron d'Holbach
 * Claude Adrien Helvétius
 * Pierre Jean Georges Cabanis
 * Jacques-André Naigeon

title: French materialism


text:
February

February is the second month of the year in the Julian and Gregorian calendars. The month has 28 days in common years or 29 in leap years, with the 29th day being called the leap day. It is the first of five months not to have 31 days (the other four being April, June, September, and November) and the only one to have fewer than 30 days. February is the third and last month of meteorological winter in the Northern Hemisphere. In the Southern Hemisphere, February is the third and last month of meteorological summer (being the seasonal equivalent of what is August in the Northern Hemisphere).

Pronunciation
"February" is pronounced in several different ways. The beginning of the word is commonly pronounced either as  or  ; many people drop the first "r", replacing it with, as if it were spelled "Febuary". This comes about by analogy with "January", as well as by a dissimilation effect whereby having two "r"s close to each other causes one to change. The ending of the word is pronounced  in the US and   in the UK.

A colloquial pronunciation (by haplology and metathesis) seen across dialects is (as if written Febry, an attested vulgar form in e.g. unlearned writing, poetry, abbreviation).

History
The Roman month Februarius was named after the Latin term februum, which means "purification", via the purification ritual Februa held on February 15 (full moon) in the old lunar Roman calendar. January and February were the last two months to be added to the Roman calendar, since the Romans originally considered winter a monthless period. They were added by Numa Pompilius about 713 BC. February remained the last month of the calendar year until the time of the decemvirs (c. 450 BC), when it became the second month. At certain times February was truncated to 23 or 24 days, and a 27-day intercalary month, Intercalaris, was occasionally inserted immediately after February to realign the year with the seasons.

February observances in Ancient Rome included Amburbium (precise date unknown), Sementivae (February 2), Februa (February 13–15), Lupercalia (February 13–15), Parentalia (February 13–22), Quirinalia (February 17), Feralia (February 21), Caristia (February 22), Terminalia (February 23), Regifugium (February 24), and Agonium Martiale (February 27). These days do not correspond to the modern Gregorian calendar.

Under the reforms that instituted the Julian calendar, Intercalaris was abolished, leap years occurred regularly every fourth year, and in leap years February gained a 29th day. Thereafter, it remained the second month of the calendar year, meaning the order that months are displayed (January, February, March, ..., December) within a year-at-a-glance calendar. Even during the Middle Ages, when the numbered Anno Domini year began on March 25 or December 25, the second month was February whenever all twelve months were displayed in order. The Gregorian calendar reforms made slight changes to the system for determining which years were leap years, but also contained a 29-day February.

Historical names for February include the Old English terms Solmonath (mud month) and Kale-monath (named for cabbage) as well as Charlemagne's designation Hornung. In Finnish, the month is called helmikuu, meaning "month of the pearl"; when snow melts on tree branches, it forms droplets, and as these freeze again, they are like pearls of ice. In Polish and Ukrainian, respectively, the month is called luty or лютий, meaning the month of ice or hard frost. In Macedonian the month is (сечко), meaning month of cutting (wood). In Czech, it is called únor, meaning month of submerging (of river ice).

In Slovene, February is traditionally called svečan, related to icicles or Candlemas. This name originates from sičan, written as svičan in the New Carniolan Almanac from 1775 and changed to its final form by Franc Metelko in his New Almanac from 1824. The name was also spelled sečan, meaning "the month of cutting down of trees". In 1848, a proposal was put forward in Kmetijske in rokodelske novice by the Slovene Society of Ljubljana to call this month talnik (related to ice melting), but it did not stick. The idea was proposed by a priest, Blaž Potočnik. Another name of February in Slovene was vesnar, after the mythological character Vesna.

Patterns
Having only 28 days in common years, February is the only month of the year that can pass without a single full moon. Using Coordinated Universal Time as the basis for determining the date and time of a full moon, this last happened in 2018 and will next happen in 2037. The same is true regarding a new moon: again using Coordinated Universal Time as the basis, this last happened in 2014 and will next happen in 2033.

February is also the only month of the calendar that, at intervals alternating between one of six years and two of eleven years, has exactly four full 7-day weeks. In countries that start their week on a Monday, it occurs as part of a common year starting on Friday, in which February 1st is a Monday and the 28th is a Sunday; the most recent occurrence was 2021, and the next one will be 2027. In countries that start their week on a Sunday, it occurs in a common year starting on Thursday; the most recent occurrence was 2015 and the next occurrence will be 2026. The pattern is broken by a skipped leap year, but no leap year has been skipped since 1900 and no others will be skipped until 2100.

Astronomy
February meteor showers include the Alpha Centaurids (appearing in early February), the March Virginids (lasting from February 14 to April 25, peaking around March 20), the Delta Cancrids (appearing December 14 to February 14, peaking on January 17), the Omicron Centaurids (late January through February, peaking in mid-February), Theta Centaurids (January 23 – March 12, only visible in the southern hemisphere), Eta Virginids (February 24 and March 27, peaking around March 18), and Pi Virginids (February 13 and April 8, peaking between March 3 and March 9).

Symbols
The zodiac signs of February are Aquarius (until February 18) and Pisces (February 19 onward).

Its birth flowers are the violet (Viola), the common primrose (Primula vulgaris), and the Iris. Its birthstone is the amethyst, which symbolizes piety, humility, spiritual wisdom, and sincerity.

Observances
This list does not necessarily imply either official status nor general observance.

Month-long

 * In Catholic tradition, February is the Month of the Purification of the Blessed Virgin Mary.
 * American Heart Month (United States)
 * Black History Month (United States, Canada)
 * National Bird-Feeding Month (United States)
 * National Children's Dental Health Month (United States)
 * Season for Nonviolence: January 30 – April 4 (International observance)
 * Turner Syndrome Awareness Month (United States)
 * LGBT History Month (United Kingdom, Ireland)

Non-Gregorian
(All Baha'i, Islamic, and Jewish observances begin at the sundown prior to the date listed, and end at sundown of the date in question unless otherwise noted.)
 * List of observances set by the Bahá'í calendar
 * List of observances set by the Chinese calendar
 * List of observances set by the Hebrew calendar
 * List of observances set by the Islamic calendar
 * List of observances set by the Solar Hijri calendar

Movable
First Saturday First Sunday  First Week of February (first Monday, ending on Sunday) First Monday First Friday  Second Saturday  Second Sunday Second Monday Second Tuesday  Week of February 22  Third Monday Third Thursday Third Friday  Last Friday Last Saturday Last day of February
 * Food Freedom Day (Canada): Date changes each year
 * Safer Internet Day: First day of second week
 * National Day of the Sun (Argentina): Date varies based on province
 * Ice Cream for Breakfast Day
 * Mother's Day (Kosovo)
 * Doppelganger Week
 * World Interfaith Harmony Week
 * Constitution Day (Mexico)
 * National Frozen Yogurt Day (United States)
 * National Wear Red Day (United States)
 * International Purple Hijab Day
 * Autism Sunday (United Kingdom)
 * Children's Day (Cook Islands, Nauru, Niue, Tokelau, Cayman Islands)
 * Mother's Day (Norway)
 * Super Bowl Sunday (United States)
 * World Marriage Day
 * Meal Monday (Scotland)
 * National Sports Day (Qatar)
 * National Engineers Week (U.S.)
 * Family Day (Canada) (provinces of British Columbia, Alberta, Saskatchewan, Manitoba, Ontario, New Brunswick and Prince Edward Island.)
 * President's Day/Washington's Birthday (United States)
 * Global Information Governance Day
 * Yukon Heritage Day (Canada)
 * International Stand Up to Bullying Day
 * Open That Bottle Night
 * Rare Disease Day

Fixed

 * February 1
 * Abolition of Slavery Day (Mauritius)
 * Air Force Day (Nicaragua)
 * Federal Territory Day (Kuala Lumpur, Labuan and Putrajaya, Malaysia)
 * Heroes' Day (Rwanda)
 * Imbolc (Ireland, Scotland, Isle of Man, and some Neopagan groups in the Northern hemisphere)
 * Lammas (some Neopagan groups in the Southern hemisphere)
 * Memorial Day of the Republic (Hungary)
 * National Freedom Day (United States)
 * February 2
 * Anniversary of Treaty of Tartu (Estonia)
 * Constitution Day (Philippines)
 * Day of Youth (Azerbaijan)
 * Feast of the Presentation of Jesus at the Temple (or Candlemas) (Western Christianity), and its related observances:
 * A quarter day in the Christian liturgical calendar (due to Candlemas) (Scotland)
 * Celebration of Yemanja (Candomblé)
 * Groundhog Day (United States and Canada)
 * Marmot Day (Alaska, United States)
 * Inventor's Day (Thailand)
 * National Tater Tot Day (United States)
 * World Wetlands Day
 * February 3
 * Anniversary of The Day the Music Died (United States)
 * Communist Party of Vietnam Foundation Anniversary (Vietnam)
 * Day of the Virgin of Suyapa (Honduras)
 * Heroes' Day (Mozambique)
 * Martyrs' Day (São Tomé and Príncipe)
 * Setsubun (Japan)
 * Veterans' Day (Thailand)
 * February 4
 * Day of the Armed Struggle (Angola)
 * Independence Day (Sri Lanka)
 * Rosa Parks Day (California and Missouri, United States)
 * World Cancer Day
 * February 5
 * Crown Princess Mary's birthday (Denmark)
 * Kashmir Solidarity Day (Pakistan)
 * Liberation Day (San Marino)
 * National Weatherperson's Day (United States)
 * Runeberg's Birthday (Finland)
 * Unity Day (Burundi)
 * February 6
 * International Day of Zero Tolerance to Female Genital Mutilation
 * Ronald Reagan Day (California, United States)
 * Sami National Day (Russia, Finland, Norway and Sweden)
 * Waitangi Day (New Zealand)
 * February 7
 * Independence Day (Grenada)
 * February 8
 * Parinirvana Day (some Mahayana Buddhist traditions, most celebrate on February 15)
 * Prešeren Day (Slovenia)
 * Propose Day
 * February 9
 * National Pizza Day (United States)
 * St. Maroun's Day (Maronite Church, Eastern Orthodox Church, public holiday in Lebanon)
 * February 10
 * Feast of St. Paul's Shipwreck (Public holiday in Malta)
 * Fenkil Day (Eritrea)
 * National Memorial Day of the Exiles and Foibe (Italy)
 * February 11
 * 112 day (European Union)
 * Armed Forces Day (Liberia)
 * Day of Revenue Service (Azerbaijan)
 * Evelio Javier Day (Panay Island, the Philippines)
 * Feast day of Our Lady of Lourdes (Catholic Church), and its related observance:
 * World Day of the Sick (Roman Catholic Church)
 * Inventors' Day (United States)
 * National Foundation Day (Japan)
 * Youth Day (Cameroon)
 * February 12
 * Darwin Day (International)
 * Georgia Day (Georgia (U.S. state))
 * International Day of Women's Health
 * Lincoln's Birthday (United States)
 * National Freedom to Marry Day (United States)
 * Red Hand Day (United Nations)
 * Sexual and Reproductive Health Awareness Day (Canada)
 * Union Day (Myanmar)
 * Youth Day (Venezuela)
 * February 13
 * Children's Day (Myanmar)
 * World Radio Day
 * February 14
 * Statehood Day (Arizona, United States)
 * Statehood Day (Oregon, United States)
 * Presentation of Jesus at the Temple (Armenian Apostolic Church)
 * V-Day (movement) (International)
 * Valentine's Day (International)
 * Singles Awareness Day
 * February 15
 * Candlemas (Eastern Orthodox Church)
 * International Duties Memorial Day (Russia, regional)
 * John Frum Day (Vanuatu)
 * Liberation Day (Afghanistan)
 * National Flag of Canada Day (Canada)
 * National I Want Butterscotch Day (United States)
 * Parinirvana Day (most Mahayana Buddhist traditions, some celebrate on February 8)
 * Serbia's National Day
 * Statehood Day (Serbia)
 * Susan B. Anthony Day (United States)
 * The ENIAC Day (Philadelphia, United States)
 * Total Defence Day (Singapore)
 * February 16
 * Day of the Shining Star (North Korea)
 * Restoration of Lithuania's Statehood Day (Lithuania)
 * February 17
 * Independence Day (Kosovo)
 * Random Acts of Kindness Day (United States)
 * Revolution Day (Libya)
 * February 18
 * National Democracy Day (Nepal)
 * Dialect Day (Amami Islands, Japan)
 * Independence Day (Gambia)
 * Kurdish Students Union Day (Iraqi Kurdistan)
 * Wife's Day (Iceland)
 * February 19
 * Armed Forces Day (Mexico)
 * Brâncuși Day (Romania)
 * Commemoration of Vasil Levski (Bulgaria)
 * Flag Day (Turkmenistan)
 * Shivaji Jayanti (Maharashtra, India)
 * February 20
 * Day of Heavenly Hundred Heroes (Ukraine)
 * World Day of Social Justice
 * February 21
 * International Mother Language Day
 * Language Movement Day (Bangladesh)
 * February 22
 * Feast of the Chair of Saint Peter (Roman Catholic Church)
 * Independence Day (Saint Lucia)
 * Founder's Day (Saudi Arabia)
 * Founder's Day or "B.-P. day" (World Organization of the Scout Movement)
 * National Margarita Day (United States)
 * World Thinking Day (World Association of Girl Guides and Girl Scouts)
 * February 23
 * Mashramani-Republic Day (Guyana)
 * Meteņi (Latvia)
 * National Banana Bread Day (United States)
 * National Day (Brunei)
 * Red Army Day or Day of Soviet Army and Navy in the former Soviet Union, also held in various former Soviet republics:
 * Defender of the Fatherland Day (Russia)
 * Defender of the Fatherland and Armed Forces day (Belarus)
 * Emperor's Birthday (Japan)
 * February 24
 * Dragobete (Romania)
 * Engineer's Day (Iran)
 * Flag Day in Mexico
 * Independence Day (Estonia)
 * National Artist Day (Thailand)
 * Sepandārmazgān or "Women's Day" (Zoroastrian, Iran)
 * February 25
 * Armed Forces Day (Dominican Republic)
 * Kitano Baika-sai or "Plum Blossom Festival" (Kitano Tenman-gū Shrine, Kyoto, Japan)
 * Meher Baba's birthday (followers of Meher Baba)
 * Memorial Day for the Victims of the Communist Dictatorships (Hungary)
 * National Day (Kuwait)
 * People Power Day (Philippines)
 * Revolution Day (Suriname)
 * Soviet Occupation Day (Georgia)
 * February 26
 * Liberation Day (Kuwait)
 * Day of Remembrance for Victims of Khojaly massacre (Azerbaijan)
 * National Wear Red Day (United Kingdom)
 * Saviours' Day (Nation of Islam)
 * February 27
 * Anosmia Awareness Day (International observance)
 * Doctors' Day (Vietnam)
 * International Polar Bear Day
 * Majuba Day (some Afrikaners in South Africa)
 * Marathi Language Day (Maharashtra, India)
 * Independence Day (Dominican Republic)
 * Anti-Bullying Day (Canada)
 * February 28
 * Day of Remembrance for Victims of Massacres in Armenia (Armenia)
 * Andalusia Day (Andalusia, Spain)
 * Kalevala Day (Finland)
 * National Science Day (India)
 * Peace Memorial Day (Taiwan)
 * Teachers' Day (Arab states)
 * February 29
 * Bachelor's Day (Ireland, United Kingdom)
 * National Frog Legs Day (United States)

title: February