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Horticulture/Syringa vulgaris

Syringa vulgaris (Lilac or Common Lilac) is a large shrub in the olive family Oleaceae, native to the Balkan Peninsula in southeastern Europe, where it grows on rocky hills.

Common Lilac is a very common ornamental plant in gardens and parks, because of the attractive, sweet smell of its flowers. Most garden plants are cultivars with flowers varying from white to dark lilac; some have double flowers with the stamens replaced by extra petals. The cultivar 'Aurea' has yellowish foliage. The majority of garden cultivars do not exceed 4-5 m tall. It is widely naturalised in western and northern Europe.

Description
It is a deciduous large shrub or small tree, growing to 6–7 m high, usually multi-stemmed, producing secondary shoots from the base or roots, with stem diameters of up to 20 cm. The bark is grey to grey-brown, smooth on young stems, longitudinally furrowed and flaking on older stems. The leaves are simple, 4–12 cm long and 3–8 cm broad, light green to glaucous, oval to cordate, with pinnate leaf venation, a mucronate apex and an entire margin. They are arranged opposite pairs or occasionally in whorls of three. The flowers have a tubular base to the corolla 6–10 mm long with an open four-lobed apex 5–8 mm across, usually lilac to mauve, occasionally white. They are arranged in a dense, terminal panicle 8-18 cm long. The fruit is a dry, smooth brown capsule, 1–2 cm long, splitting in two to release the two winged seeds.

Growing Conditions
Common lilac does best in full sun, tolerating most soils except wet soil. Siting for morning sun and good air circulation can help reduce the occurrence of powdery mildews, which are a major problem for this plant in humid climates.

Varieties
Numerous cultivars have been selected for size, flower color and form, and more recently for mildew resistance.

Uses
Usually grown as a specimen, but also for cut flowers.

Maintenance
Tolerates harsh pruning, but should only be pruned immediately after (or during) flowering to ensure the next year's bloom. The shrub produces copious suckers, which may either be pruned out or encouraged. To encourage a "tree-like form, remove all suckers as they emerge, or to keep size limited remove the oldest stems every year to keep the height under control.

Propagation
Propagate via cuttings or grafting to preserve follower color and form.

Harvest
Flowers hold up well in the vase if the leaves are removed.

Pests and Diseases
See ../Syringa/

title: Horticulture/Syringa vulgaris


text:
Horticulture/Toxicodendron radicans

Toxicodendron radicans (syn. Rhus toxicodendron, Rhus radicans; Poison ivy ) is a woody vine that is well known for its ability to produce urushiol, a skin irritant that causes an itching rash for most people, technically known as urushiol-induced contact dermatitis.

Poison ivy is subject to frequent taxonomic reclassification and confusion; it is currently divided into eastern and western species in the genus ../Toxicodendron/. At least six distinct subspecies of Toxicodendron radicans are recognized. Complicating identification and taxonomy are the fact that the species (even a particular subspecies) can be highly variable in growth habit and leaf appearance.

It is more common now than when Europeans first entered North America. Real estate development adjacent to wild, undeveloped land has created "edge effects", enabling it to form vast, lush colonies in such places. It is listed as a noxious weed in the U.S. states of Minnesota and Michigan.

Description
The plants can grow as a shrub up to about 1.2 meters (4 ft) tall, as a groundcover 10–25 centimeters (4–10 in) high, or as a climbing vine on various supports. Older vines on substantial supports send out lateral branches that may at first be mistaken for tree limbs.

The leaves are ternate with three almond-shaped leaflets. The berries (actually drupes) are a grayish-white color and are a favorite winter food of some birds. Hence the mnemonic,

"'Leaves of three, let it be; berries white, danger in sight.'"

Another version is:

"'Leaves of three let it be; if it's hairy, it's a berry.'"

The color ranges from light green (usually the younger leaves) to dark green (mature leaves), turning bright red in fall. The leaflets of mature leaves are somewhat shiny.The leaflets are 3-12 cm long, rarely up to 30 cm. Each leaflet has a few or no teeth along its edge, and the leaf surface is smooth.

Leaflet clusters are alternate on the vine, and the plant has no thorns. These three characteristics: (a) clusters of three leaflets, (b) alternate, and (c) lack of thorns, are sufficient to positively identify the plant. If it is growing up the trunk of a tree, the presence of root-hairs will identify it.

The color ranges from light green (usually the younger leaves) to dark green (mature leaves), turning bright red in fall. The leaflets of mature leaves are somewhat shiny.The leaflets are 3-12 cm long, rarely up to 30 cm. Each leaflet has a few or no teeth along its edge, and the leaf surface is smooth.

Leaflet clusters are alternate on the vine, and the plant has no thorns. These three characteristics: (a) clusters of three leaflets, (b) alternate, and (c) lack of thorns, are sufficient to positively identify the plant. If it is growing up the trunk of a tree, the presence of root-hairs will identify it.

The plants can grow as a shrub up to about 1.2 meters (4 ft) tall, as a groundcover 10–25 centimeters (4–10 in) high, or as a climbing vine on various supports. Older vines on substantial supports send out lateral branches that may at first be mistaken for tree limbs.

The leaves are ternate with three almond-shaped leaflets. The berries (actually drupes) are a grayish-white color and are a favorite winter food of some birds. Hence the mnemonic,

"'Leaves of three, let it be; berries white, danger in sight.'"

Another version is:

"'Leaves of three let it be; if it's hairy, it's a berry.'"

Growing Conditions
It grows throughout much of North America, including all Canadian provinces except Newfoundland (but not the territories) and all U.S. states except Alaska, and is normally found in wooded areas, especially along edge areas. It also grows in exposed rocky areas, in open fields and disturbed areas, and even in areas with wet soils. It rarely grows at altitudes above 1,500 meters (5,000 ft).

Varieties
Aside from the many subspecies, individual plants can vary greatly in the shape of their leaflets.

Confusion with other plants

 * Boxelder (../Acer negundo/) saplings can look almost indistinguishable from poison ivy. While Boxelder Maples often have five or seven leaflets, three leaflets are also common. The two can be differentiated by the fact that Poison-ivy has alternate leaves, while the maple has opposite leaves; in other words, by observing where the leaf stalk (the "branch" the three leaflets are attached to) meets the main branch. Another leaf stalk directly on the opposite side is characteristic of Boxelder Maple. If the three-leaflet leaves alternate along the main branch, it may be Poison-ivy.

 * Virginia creeper (../Parthenocissus quinquefolia/) vines can look like poison ivy. The younger leaves can consist of three leaflets (as opposed to the usual five) but have a few more serrations along the leaf edge, and the leaf surface is somewhat wrinkled. The rootlets of a climbing Virginia creeper are paler and much stouter than the hairy roots of poison ivy, which are dark red. Virginia creeper and poison ivy grown in the same habitat and frequently co-occur, often on the same trees.

 * Poison Sumac (Toxicodendron vernix) has compound leaves with 7–15 leaflets. Poison sumac never has only three leaflets.

 * Kudzu (../Pueraria lobata/) is a non-toxic edible vine that scrambles extensively over lower vegetation or grows high into trees. Kudzu is an invasive species in the southern United States. Like poison ivy it has three leaflets, but the leaflets are bigger than those of poison ivy and are pubescent underneath with hairy margins.

 * Blackberry and raspberry vines bear a passing resemblance to poison ivy, with which may share territory. The chief difference between blackberry vines and poison ivy is that blackberry vines have spines on them, whereas poison ivy is smooth. Also, the three-leaflet pattern of blackberry vine leaves changes as the plant grows: the two bottom leaves both split into two leaves, for a total of five in a cluster. They have many teeth along the leaf edge, and the top surface of their leaves is very wrinkled where the veins are, and the bottom of the leaves is light minty - greenish white, while poison ivy is all green. The stem and vine of poison ivy are brown and woody, while blackberry stems are green with thorns.

Toxic effects

 * See ../Urushiol-induced contact dermatitis/ for more details about the rash, including prevention and treatment.

The reaction caused by poison-ivy, urushiol-induced contact dermatitis, is an allergic reaction. Around 15% to 30% of people have no allergic response, but most if not all will become sensitized over time with repeated or more concentrated exposure to urushiol.

For those who are affected by urushiol, it causes a very irritating rash. In extreme cases, corticosteroids are needed to treat rashes and severe itching. The first symptom of contact is a severe itching of the skin that develops into reddish colored inflammation or non-colored bumps, and then blistering of the skin occurs. In severe cases, clear fluids ooze from open blistered sores. The urushiol poison is quickly bound to the skin after contact.

The oozing fluids released by itching blisters do not spread the poison. The appearance of a spreading rash indicates that some areas received more of the poison and reacted sooner than other areas. The blisters and oozing result from blood vessels that develop gaps and leak fluid through the skin; if the skin is cooled, the vessels constrict and leak less. If poison ivy is burned and the smoke then inhaled, this rash will appear on the lining of the lungs, causing extreme pain and possibly fatal respiratory difficulty. If poison ivy is eaten, the digestive tract, airway, kidneys or other organs can be damaged.

Understanding why new lesions may develop for two weeks (studied on forearm) after one exposure was made clear by a University of Miami scientist: Larger amounts have earliest onset and largest reaction, smaller amounts produce a delayed reaction. The overall severity "progresses" with the combined active lesions. Therefore, the last new lesion should occur at two weeks after last exposure, the total rash (untreated) may go on for 3-4 weeks.

Urushiol oil can remain active for several years, so handling dead leaves or vines can cause a reaction. In addition, oil transferred from the plant to other objects, such as pet fur or gardening tools, can cause the rash if it comes into contact with the skin.

People who are sensitive to poison-ivy can also experience a similar rash from mangoes; the skin of mangoes has a chemical compound similar to urushiol. Similar reactions have been reported occasionally from contact with the related aromatic sumac or Japanese lacquer tree.

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

title: Horticulture/Toxicodendron radicans


text:
Horticulture/Urushiol-induced contact dermatitis

Urushiol-induced contact dermatitis (also called Toxicodendron dermatitis and Rhus dermatitis) is the medical name given to allergic rashes produced by oil urushiol, which is contained in various plants, including the plants of the genus ../Toxicodendron/ (including poison ivy, poison oak, and poison Sumac), as well as other plants in the family Anacardiaceae (mango, Rengas tree, Burmese lacquer tree, India marking nut tree, and the shell of the cashew nut), and even unrelated plants such as ../Ginkgo biloba/.

Symptoms of the rash include itching, inflammation, oozing, and in severe cases a burning sensation. The American Academy of Dermatology estimates that there are up to 50 million cases of urushiol-induced dermatitis annually in the United States alone, accounting for 10% of all lost-time injuries in the United States Forest Service. Poison oak is a significant problem in the rural western and southern U.S., while poison-ivy is most rampant in the eastern U.S. Dermatitis from poison sumac is less common, but just as problematic.

Exposure
Urushiol-induced contact dermatitis is contracted by contact with a plant or any other object containing urushiol oil. Clothing or other materials that contact the plant and then, before being washed, contact the skin are common causes of exposure. Normally, it takes about 24 hours for the rash to first appear, though it may worsen during the next few days and may appear to spread, when in fact what is happening is that areas that received a lesser dose are reacting. The rash can take one to two weeks to run its course, and in some cases up to five weeks.

Urushiol is primarily found in the spaces between plant cells beneath the outer skin of the plant, so the effects of urushiol rash are less severe if the plant tissue remains undamaged on contact. Once the oil and resin are thoroughly washed from the skin, the rash is not contagious. Urushiol does not spread once it has bound with the skin, and it is not found in weeping blisters. Although the rash may worsen during the first few days and may appear to spread to new areas, this is usually simply latent reaction.

Although simple skin exposure is most common, ingestion can also lead to serious, more systemic reactions. Burning plant material is commonly said to create urushiol-laden smoke that causes systemic reaction as well as rash inside the throat and on the eyes. A high-temperature fully inflamed bonfire might incinerate the urushiol before it can cause harm, while a smoldering fire could vaporize the volatile oil and spread it as white smoke. However, some sources dispute the danger of burning urushiol-containing plant material.

Mechanism
The toxic effects of urushiol are largely indirect, mediated by an induced autoimmune response. Urushiol chemically reacts with, binds to and changes the shape of cell surface proteins on exposed skin cells. Affected proteins interfere with the immune systems ability to recognize these cells as normal parts of the body. These abnormally coated cells (perhaps confused by the immune system with invading parasites) are recognized as foreign, initiating a T-cell mediated immune response. This immune response is directed towards the complex of urushiol derivatives which are bound up in the skin proteins and attacks the cells as if they were a foreign agent. The result is an allergic eczematous contact dermatitis characterized by redness, swelling, papules, vesicles, blisters, and streaking. People vary greatly in their sensitivity to urushiol. In approximately 15% to 30% of people urishiol does not initiate an immune system response, while at least 25% of people have very strong immune responses resulting in severe symptoms. Since the skin reaction is an allergic one, people may develop an increasingly strong reactions after repeated exposures, or show no immune response on their first exposure, but show sensitivity on following exposures.

The rash takes one to two weeks to run its course, but normally does not leave scars. Severe cases will have small (1–2 mm) clear fluid-filled blisters on the skin. Pus-filled vesicles, containing a whitish fluid, may indicate a secondary infection. Most poison ivy rashes, without infections, will self-resolve within 14 days without treatment. Excessive scratching may result in secondary infection, commonly by staphylococcal and streptococcal species. These may require the use of antibiotics.

Treatments
Primary treatment involves washing exposed skin thoroughly with soap and water as soon as possible after exposure is discovered. Soap or detergent is necessary, as urushiol is a hydrophobic (oily) substance and is not washed off by plain water. Once an outbreak has occurred topical application of cold compresses, Burow's solution, calamine lotion, antihistamines, aloe vera and hydrocortisone ointment are common home-remedies used to abate the symptoms. Oral administration of aspirin and antihistamines may provide some relief from the itch and irritation.

No vaccine has been developed to counter urushiol symptoms, so the most effective "cures" are generally held to be those products that physically remove the urushiol. After about 15 minutes of exposure, the urushiol is chemically bonded to the skin and can only be removed with pharmaceutical products, which vary by person in effectiveness. Two of these products, which are both over the counter drugs in the United States, are:
 * Tecnu: Originally developed early in the Cold War as a treatment for radiation exposure, it was discovered later that Tecnu provided some relief for poison ivy exposure. It is a milky liquid and the main active ingredient is octylphenoxy-polyethoxyethanol. The four octyl groups of this chemical are too large to surround the non-polar molecules in the urushiol, which remains partially active and requires multiple applications. Also, the chemical makeup of the product requires that it be applied no later than eight hours after exposure to urushiol.
 * Zanfel: Developed in 1999, this paste uses an ethoxylate molecule with the large octyl groups removed. This allows the molecule to "wrap" around the non-polar molecules of the urushiol and inactivate it. The other ingredient, sodium lauryl sarcosinate, allows the ethoxylate to form a micelle around the urushiol molecule. This creates a large molecule that contains flexible non-polar groups and soluble polar groups, allowing it to be rinsed away with water. In rigorous company-funded studies, it appears to be effective, even in cases of advanced rash. Unlike Tecnu, Zanfel is effective even many days after exposure, removing the urushiol, stopping the itching, and beginning healing of the rash after only a small number of applications. It is a fairly expensive product, about $40US for a small bottle (2007 price), but cost-effective due to the degree of suffering it alleviates, in proportion to its cost. A small bottle provides many applications, so the cost per dose is relatively low.
 * Tecnu Extreme: Developed in 2005, this is also a paste with surfactants and micro-fine scrubbing particles to break the bond the urushiol has with the proteins in the skin, so the urushiol can be rinsed away with water. The product contains an active ingredient, grindelia robusta, for itch relief. It is most helpful if a rash has already started, but it can also be used to remove urushiol after exposure--before the rash has broken out.

In cases of extreme symptoms, steroids such as Prednisone are sometimes administered to attenuate the immune response. If bacterial secondary infection of affected areas occurs, antibiotics may also be necessary.

There are many myths that deal with treating toxicodendrons such as poison ivy. Most have been discredited, but persist despite their falsehood. Some clarifications (these statements are true):

 * Scrubbing with plain soap and water will remove the urushiol from skin if it is done within a few minutes of exposure, before it bonds.
 * Ordinary laundering with laundry detergent will remove urushiol from most clothing, but not leather or suede.
 * The fluid from the resulting blisters does not spread poison ivy to others.
 * Poison ivy is not harmless when the leaves have fallen off as the toxic resin is very persistent. Every part of the plant contains urushiol, and can cause a rash with exposure at any time of the year.
 * Burning any part of the poison ivy, poison oak or poison sumac plants can produce a fatal systemic reaction in any person who comes in contact with the smoke, even a mile or more away in certain conditions.
 * Ice, water, soap, lotions, dry cold air, do not help cure poison ivy rashes, they only soothe the itch.
 * Urinating on the affected areas has no effect.


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User:SKYNET X7000~enwikibooks

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Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called SKYNET X7000. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name SKYNET X7000~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:39, 17 March 2015 (UTC)

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Pages SKYNET X7000 is Monitoring

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text: User:SKYNET X7000~enwikibooks/Guestbook

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Cookbook:Salată de Boeuf (Romanian Beef Salad)

This is a traditional Romanian dish, generally served during all festive and special occasions. It consists of a combination of finely chopped beef and root vegetables, folded in mayonnaise and finished with pickled vegetable garnishes. The name suggests a French culinary influence as the word boeuf is old French for cow and several well know French dishes such as Beef Bourguignon still use the term. The dish is usually made up in large quantities for the whole party. It's eaten as a side dish/salad to fried meats or as an appetiser/entree. Slight differences exist in quantities and these vary according to taste. The recipe below is my mother's and grandmother's. It requires a home made mayonnaise, for which a recipe is included.

Salad

 * 1 kg (2 lb 3 oz) red potatoes
 * 350 g (12 oz) carrots, peeled and cut in half along width and length
 * 350 g roasting beef, cut in half
 * 1 can of peas or 300 grams (10.5 oz) fresh peas
 * 350 g pickled gherkins (not too sweet and very firm)

Mayonnaise

 * 2 hard boiled eggs, yolks removed
 * 1 fresh egg yolk
 * 250 ml (8.5 oz) canola or vegetable oil
 * 1 lemon, juiced
 * 1 tsp (5 ml) French mustard

Garnish

 * Boiled egg white, sliced into long thin strips
 * Gherkins, sliced into long thin strips
 * Pickled red peppers, sliced into long thin strips
 * Sliced olives

Salad

 * 1) Boil the potatoes gently in their skins until tender. Cool, then remove the skins.
 * 2) Boil the carrots until tender.
 * 3) Gently boil the beef for 1 hour.
 * 4) If using fresh peas, boil or steam them well.
 * 5) Cube the potatoes, carrots, and beef about 5 mm across—essentially, everything should be about the size of the peas.
 * 6) Cut the gherkins very finely by cutting 3 mm (⅛ inch) thick slices and then cutting them at 3 mm intervals again along the length and width.
 * 7) Fold everything together gently. Do not season.

Mayonnaise

 * 1) Beat the cooked egg yolks and the raw yolk until well mixed.
 * 2) Slowly add the oil while beating the eggs until they start to thicken and form a mayonnaise.
 * 3) Add the juice of the lemon and the mustard.

Assembly

 * 1) Reserve a small quantity of mayonnaise for garnish.
 * 2) Fold the rest of the mayonnaise into the cubed meat and vegetables, making a nice consistency where the ingredients are well covered in mayonnaise but not suspended in it.
 * 3) Season with salt and pepper.
 * 4) Place the salata de boeuf into one large or several smaller bowls.
 * 5) Spread reserved mayonnaise over the top and garnish with the garnishes, arranging them in attractive shapes.


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User:Dungodung

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text:
VHDL for FPGA Design/Multiplexer

Video Links

 * Video of Simulation
 * Video of how to get to the Multiplexer RTL Schematic

VHDL-kieli FPGA-suunnittelussa/Multiplekseri

title: VHDL for FPGA Design/Multiplexer


text:
Famous Theorems of Mathematics/Boy's surface

Property of R. Bryant's parametrization
If z is replaced by the negative reciprocal of its complex conjugate, $$ - {1 \over z^\star},$$ then the functions g1, g2, and g3 of z are left unchanged.

Proof
Let g1′ be obtained from g1 by substituting z with $$ - {1 \over z^\star}.$$ Then we obtain
 * $$ g_1' = -{3 \over 2} \mathrm{Im} \left( {- {1 \over z^\star} \left( 1 - {1 \over z^{\star 4} } \right) \over {1 \over z^{\star 6}} - \sqrt{5} {1 \over z^{\star 3}} - 1} \right). $$

Multiply both numerator and denominator by $$ z^{\star 6},$$
 * $$ g_1' = -{3 \over 2} \mathrm{Im} \left( {-z^\star (z^{\star 4} - 1) \over 1 - \sqrt{5} z^{\star 3} - z^{\star 6} } \right).$$

Multiply both numerator and denominator by -1,
 * $$ g_1' = -{3 \over 2} \mathrm{Im} \left( {z^\star (z^{\star 4} - 1) \over z^{\star 6} + \sqrt{5} z^{\star 3} - 1} \right).$$

It is generally true for any complex number z and any integral power n that
 * $$ (z^\star)^n = (z^n)^\star,$$

therefore
 * $$ g_1' = -{3 \over 2} \mathrm{Im} \left( { z^\star (z^4 - 1)^\star \over (z^6 + \sqrt{5} z^3 - 1)^\star } \right), $$
 * $$ g_1' = -{3 \over 2} \mathrm{Im} \left( - \left( {z (1 - z^4) \over z^6 + \sqrt{5} z^3 - 1} \right)^\star \right) $$

therefore $$ g_1' = g_1 $$ since, for any complex number z,
 * $$ \mathrm{Im} (-z^\star) = \mathrm{Im}(z). $$

Let g2′ be obtained from g2 by substituting z with $$ - {1 \over z^\star}.$$ Then we obtain
 * $$ g_2' = -{3 \over 2} \mathrm{Re} \left( { - {1 \over z^\star} \left( 1 + {1 \over z^{\star 4}} \right) \over {1 \over z^{\star 6}} - \sqrt{5} {1 \over z^{\star 3}} - 1 } \right),$$
 * $$ = -{3 \over 2} \mathrm{Re} \left( { z^\star (z^{\star 4} + 1) \over z^{\star 6} + \sqrt{5} z^{\star 3} - 1 } \right), $$
 * $$ = -{3 \over 2} \mathrm{Re} \left( { z^\star (z^{4 \star} + 1) \over z^{6 \star} + \sqrt{5} z^{3 \star} - 1 } \right), $$
 * $$ = -{3 \over 2} \mathrm{Re} \left( { z^\star (z^4 + 1)^\star \over (z^6 + \sqrt{5} z^3 - 1)^\star } \right), $$
 * $$ = -{3 \over 2} \mathrm{Re} \left( \left( { z (z^4 + 1) \over z^6 + \sqrt{5} z^3 - 1} \right)^\star \right), $$

therefore $$ g_2' = g_2 $$ since, for any complex number z,
 * $$ \mathrm{Re} (z^\star) = \mathrm{Re} (z). $$

Let g3′ be obtained from g3 by substituting z with $$ - {1 \over z^\star}.$$ Then we obtain
 * $$ g_3' = \mathrm{Im} \left( { 1 + {1 \over z^{\star 6}} \over {1 \over z^{\star 6}} - \sqrt{5} {1 \over z^{\star 3}} - 1} \right), $$
 * $$ = \mathrm{Im} \left( { z^{\star 6} + 1 \over 1 - \sqrt{5} z^{\star 3} - z^{\star 6}} \right), $$
 * $$ = \mathrm{Im} \left( { z^{6 \star} + 1 \over 1 - \sqrt{5} z^{3 \star} - z^{6 \star}} \right), $$
 * $$ = \mathrm{Im} \left( - { (z^6 + 1)^\star \over (z^6 + \sqrt{5} z^3 - 1)^\star} \right), $$
 * $$ = \mathrm{Im} \left( - \left( { z^6 + 1 \over z^6 + \sqrt{5} z^3 - 1} \right)^\star \right), $$

therefore $$ g_3' = g_3.$$ Q.E.D.

Symmetry of the Boy's surface
Boy's surface has 3-fold symmetry. This means that it has an axis of discrete rotational symmetry: any 120° turn about this axis will leave the surface looking exactly the same. The Boy's surface can be cut into three mutually congruent pieces.

Proof
Two complex-algebraic identities will be used in this proof: let U and V be complex numbers, then
 * $$ \mathrm{Re}(U V) = \mathrm{Re}(U) \mathrm{Re}(V) - \mathrm{Im}(U) \mathrm{Im}(V), \,\!$$
 * $$ \mathrm{Im}(U V) = \mathrm{Re}(U) \mathrm{Im}(V) + \mathrm{Im}(U) \mathrm{Re}(V). \,\!$$

Given a point P(z) on the Boy's surface with complex parameter z inside the unit disk in the complex plane, we will show that rotating the parameter z 120° about the origin of the complex plane is equivalent to rotating the Boy's surface 120° about the Z-axis (still using R. Bryant's parametric equations given above).

Let
 * $$ z' = z e^{i 2 \pi / 3} \,\!$$

be the rotation of parameter z. Then the "raw" (unscaled) coordinates g1, g2, and g3 will be converted, respectively, to g′1, g′2, and g′3.

Substitute z′ for z in g3(z), resulting in
 * $$ g_3'(z') = \mathrm{Im} \left( {1 + z'^6 \over z'^6 + \sqrt{5} z'^3 - 1} \right) - {1 \over 2}, $$
 * $$ g_3'(z) = \mathrm{Im} \left( {1 + z^6 e^{i 4 \pi} \over z^6 e^{i 4 \pi} + \sqrt{5} z^{i 2 \pi} - 1} \right) - {1 \over 2}. $$

Since $$ e^{i 4 \pi} = e^{i 2 \pi} = 1,$$ it follows that
 * $$ g_3' = \mathrm{Im}\left( {1 + z^6 \over z^6 + \sqrt{5} z^3 - 1} \right) - {1 \over 2} $$

therefore $$ g_3' = g_3.$$ This means that the axis of rotational symmetry will be parallel to the Z-axis.

Plug in z′ for z in g1(z), resulting in
 * $$ g_1'(z) = -{3 \over 2} \mathrm{Im} \left( { z e^{i 2 \pi / 3} (1 - z^4 e^{i 8 \pi / 3}) \over z^6 e^{i 4 \pi} + \sqrt{5} z^3 e^{i 2 \pi} - 1} \right). $$

Noticing that $$ e^{i 8 \pi / 3} = e^{i 2 \pi / 3},$$
 * $$ g_1' = -{3 \over 2} \mathrm{Im} \left( {z e^{i 2 \pi / 3} (1 - z^4 e^{i 2 \pi / 3}) \over z^6 + \sqrt{5} z^3 - 1} \right). $$

Then, letting $$ e^{i 4 \pi / 3} = e^{-i 2 \pi / 3} $$ in the denominator yields
 * $$ g_1' = -{3 \over 2} \mathrm{Im} \left( { z (e^{i 2 \pi / 3} - z^4 e^{-i 2 \pi / 3}) \over z^6 + \sqrt{5} z^3 - 1} \right). $$

Now, applying the complex-algebraic identity, and letting
 * $$ z'' = {z \over z^6 + \sqrt{5} z^3 - 1} $$

we get
 * $$ g_1' = -{3 \over 2} \left[ \mathrm{Im}(z) \mathrm{Re}(e^{i 2 \pi / 3} - z^4 e^{-i 2 \pi / 3}) + \mathrm{Re}(z) \mathrm{Im}(e^{i 2 \pi / 3} - z^4 e^{-i 2 \pi / 3}) \right]. $$

Both $$\mathrm{Re}$$ and $$\mathrm{Im}$$ are distributive with respect to addition, and
 * $$ \mathrm{Re}(e^{i \theta}) = \cos \theta, \,\!$$
 * $$ \mathrm{Im}(e^{i \theta}) = \sin \theta, \,\!$$

due to Euler's formula, so that
 * $$ g_1' = -{3 \over 2} \left[ \mathrm{Im}(z) \left( \cos {2 \pi \over 3} - \mathrm{Re}(z^4 e^{-i 2 \pi / 3}) \right) + \mathrm{Re}(z) \left( \sin {2 \pi \over 3} - \mathrm{Im}(z^4 e^{-i 2 \pi / 3}) \right) \right]. $$

Applying the complex-algebraic identities again, and simplifying $$ \cos {2 \pi \over 3} $$ to -1/2 and $$ \sin {2 \pi \over 3} $$ to $$ \sqrt{3} / 2,$$ produces
 * $$ g_1' = -{3 \over 2} \left[ \mathrm{Im}(z) \left( -{1 \over 2} - [ \mathrm{Re}(z^4) \mathrm{Re}(e^{-i 2 \pi / 3}) - \mathrm{Im}(z^4) \mathrm{Im}(e^{-i 2 \pi / 3}) ] \right) + \mathrm{Re}(z) \left( {\sqrt{3} \over 2} - [ \mathrm{Im}(z^4) \mathrm{Re}(e^{-i 2 \pi / 3}) + \mathrm{Re}(z^4) \mathrm{Im} (e^{-i 2 \pi / 3})] \right) \right]. $$

Simplify constants,
 * $$ g_1' = -{3 \over 2} \left[ \mathrm{Im}(z) \left( -{1 \over 2} - \left[ -{1 \over 2} \mathrm{Re}(z^4) + {\sqrt{3} \over 2} \mathrm{Im}(z^4) \right] \right) + \mathrm{Re}(z) \left( {\sqrt{3} \over 2} - \left[ -{1 \over 2} \mathrm{Im}(z^4) - {\sqrt{3} \over 2} \mathrm{Re}(z^4) \right] \right) \right],$$

therefore
 * $$ g_1' = -{3 \over 2} \left[ -{1 \over 2} \mathrm{Im}(z) + {1 \over 2} \mathrm{Im}(z) \mathrm{Re}(z^4) - {\sqrt{3} \over 2} \mathrm{Im}(z) \mathrm{Im}(z^4) + {\sqrt{3} \over 2} \mathrm{Re}(z) + {1 \over 2} \mathrm{Re}(z) \mathrm{Im}(z^4) + {\sqrt{3} \over 2} \mathrm{Re}(z) \mathrm{Re}(z^4) \right].$$

Applying the complex-algebraic identity to the original g1 yields
 * $$ g_1 = -{3 \over 2} [ \mathrm{Im}(z) \mathrm{Re}(1 - z^4) + \mathrm{Re}(z) \mathrm{Im}(1 - z^4) ], $$
 * $$ g_1 = -{3 \over 2} [ \mathrm{Im}(z) (1 - \mathrm{Re}(z^4)) + \mathrm{Re}(z) (-\mathrm{Im}(z^4))], $$
 * $$ g_1 = -{3 \over 2} [ \mathrm{Im}(z) - \mathrm{Im}(z) \mathrm{Re}(z^4) - \mathrm{Re}(z'') \mathrm{Im}(z^4) ]. $$

Plug in z′ for z in g2(z), resulting in
 * $$ g_2' = -{3 \over 2} \mathrm{Re} \left( {z e^{i 2 \pi / 3} (1 + z^4 e^{i 8 \pi / 3}) \over z^6 e^{i 4 \pi} + \sqrt{5} z^3 e^{i 2 \pi} - 1} \right) .$$

Simplify the exponents,
 * $$ g_2' = -{3 \over 2} \mathrm{Re} \left( {z e^{i 2 \pi / 3} (1 + z^4 e^{i 2 \pi / 3}) \over z^6 + \sqrt{5} z^3 - 1} \right), $$
 * $$ = -{3 \over 2} \mathrm{Re} ( z'' (e^{i 2 \pi / 3} + z^4 e^{-i 2 \pi / 3})). $$

Now apply the complex-algebraic identity to g′2, obtaining
 * $$ g_2' = -{3 \over 2} \left[ \mathrm{Re}(z) \mathrm{Re}(e^{i 2 \pi / 3} + z^4 e^{-i 2 \pi / 3}) - \mathrm{Im}(z) \mathrm{Im}(e^{i 2 \pi / 3} + z^4 e^{-i 2 \pi / 3}) \right]. $$

Distribute the $$\mathrm{Re}$$ with respect to addition, and simplify constants,
 * $$ g_2' = -{3 \over 2} \left[ \mathrm{Re}(z) \left(-{1 \over 2} + \mathrm{Re}(z^4 e^{-i 2 \pi / 3}) \right) - \mathrm{Im}(z) \left({\sqrt{3} \over 2} + \mathrm{Im}(z^4 e^{-i 2 \pi / 3}) \right) \right]. $$

Apply the complex-algebraic identities again,
 * $$ g_2' = -{3 \over 2} \left[ \mathrm{Re}(z) \left(-{1 \over 2} + \mathrm{Re}(z^4) \mathrm{Re}(e^{-i 2 \pi / 3}) - \mathrm{Im}(z^4) \mathrm{Im}(e^{-i 2 \pi \over 3}) \right) - \mathrm{Im}(z) \left({\sqrt{3} \over 2} + \mathrm{Im}(z^4) \mathrm{Re}(e^{-i 2 \pi / 3}) + \mathrm{Re}(z^4) \mathrm{Im}(e^{-i 2 \pi / 3}) \right) \right]. $$

Simplify constants,
 * $$ g_2' = -{3 \over 2} \left[ \mathrm{Re}(z) \left( -{1 \over 2} - {1 \over 2} \mathrm{Re}(z^4) + {\sqrt{3} \over 2} \mathrm{Im}(z^4) \right) - \mathrm{Im}(z) \left({\sqrt{3} \over 2} - {\sqrt{3} \over 2} \mathrm{Re}(z^4) - {1 \over 2} \mathrm{Im}(z^4) \right) \right], $$

then distribute with respect to addition,
 * $$ g_2' = -{3 \over 2} \left[ -{1 \over 2} \mathrm{Re}(z) - {1 \over 2}\mathrm{Re}(z) \mathrm{Re}(z^4) + {\sqrt{3}\over 2} \mathrm{Re}(z) \mathrm{Im}(z^4) - {\sqrt{3}\over 2} \mathrm{Im}(z) + {\sqrt{3}\over 2} \mathrm{Im}(z) \mathrm{Re}(z^4) + {1 \over 2} \mathrm{Im}(z) \mathrm{Im}(z^4) \right]. $$

Applying the complex-algebraic identity to the original g2 yields
 * $$ g_2 = -{3 \over 2} \left( \mathrm{Re}(z) \mathrm{Re}(1 + z^4) - \mathrm{Im}(z) \mathrm{Im}(1 + z^4) \right), $$
 * $$ g_2 = -{3 \over 2} \left[ \mathrm{Re}(z) (1 + \mathrm{Re}(z^4)) - \mathrm{Im}(z) \mathrm{Im}(z^4) \right], $$
 * $$ g_2 = -{3 \over 2} \left[ \mathrm{Re}(z) + \mathrm{Re}(z) \mathrm{Re}(z^4) - \mathrm{Im}(z'') \mathrm{Im}(z^4) \right]. $$

The raw coordinates of the pre-rotated point are
 * $$ g_1 = -{3 \over 2} [ \mathrm{Im}(z) - \mathrm{Im}(z) \mathrm{Re}(z^4) - \mathrm{Re}(z'') \mathrm{Im}(z^4) ], $$
 * $$ g_2 = -{3 \over 2} \left[ \mathrm{Re}(z) + \mathrm{Re}(z) \mathrm{Re}(z^4) - \mathrm{Im}(z'') \mathrm{Im}(z^4) \right], $$

and the raw coordinates of the post-rotated point are
 * $$ g_1' = -{3 \over 2} \left[ -{1 \over 2} \mathrm{Im}(z) + {1 \over 2} \mathrm{Im}(z) \mathrm{Re}(z^4) - {\sqrt{3} \over 2} \mathrm{Im}(z) \mathrm{Im}(z^4) + {\sqrt{3} \over 2} \mathrm{Re}(z) + {1 \over 2} \mathrm{Re}(z) \mathrm{Im}(z^4) + {\sqrt{3} \over 2} \mathrm{Re}(z) \mathrm{Re}(z^4) \right], $$
 * $$ g_2' = -{3 \over 2} \left[ -{1 \over 2} \mathrm{Re}(z) - {1 \over 2}\mathrm{Re}(z) \mathrm{Re}(z^4) + {\sqrt{3}\over 2} \mathrm{Re}(z) \mathrm{Im}(z^4) - {\sqrt{3}\over 2} \mathrm{Im}(z) + {\sqrt{3}\over 2} \mathrm{Im}(z) \mathrm{Re}(z^4) + {1 \over 2} \mathrm{Im}(z) \mathrm{Im}(z^4) \right]. $$

Comparing these four coordinates we can verify that
 * $$ g_1' = -{1 \over 2} g_1 + {\sqrt{3} \over 2} g_2, $$
 * $$ g_2' = -{\sqrt{3} \over 2} g_1 -{1 \over 2} g_2. $$

In matrix form, this can be expressed as
 * $$ \begin{bmatrix} g_1' \\ g_2' \\ g_3' \end{bmatrix} =

\begin{bmatrix} -{1 \over 2} & {\sqrt{3}\over 2} & 0 \\ -{\sqrt{3}\over 2} & -{1 \over 2} & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} g_1 \\ g_2 \\ g_3 \end{bmatrix} = \begin{bmatrix} \cos {-2 \pi \over 3} & -\sin {-2 \pi \over 3} & 0 \\ \sin {-2 \pi \over 3} & \cos {-2 \pi \over 3} & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} g_1 \\ g_2 \\ g_3 \end{bmatrix}.$$ Therefore rotating z by 120° to z′ on the complex plane is equivalent to rotating P(z) by -120° about the Z-axis to P(z′). This means that the Boy's surface has 3-fold symmetry, quod erat demonstrandum.


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title: User talk:Hwwong


text:
User:Neoptolemus

Hello, my name is Andrew Moffett, though to avoid confusion with other Andrews on Wikibooks, you can refer to me as Neoptolemus, or simply Neo. I am currently a freshman at Centre College in Danville, Kentucky, working towards a double major in History and Spanish. When not reverting vandalism or cleaning up redirects, my edits center around books on history and foreign languages.

I invite you to look at the new book list shown below. Let me know if you are interested in working with me on any of these ideas. Also, if by looking at my list you think I might be interested in working with you on some idea of yours, I would be grateful if you would like to share some of your ideas for future books with me as well.  /To do list/

 Contacting me I can be reached in a number of ways, including the following: AIM: neoptol3mus E-mail: E-mail this user IRC: #wikibooks WB: My discussion page

title: User:Neoptolemus


text:
User:Narendra Sisodiya~enwikibooks

You can find more about me at http://narendra.techfandu.org/aboutme

title: User:Narendra Sisodiya~enwikibooks


text:
User talk:Neoptolemus

{|class="userboxes" style="margin-left: em;; margin-bottom: 0.5em; width: 248px; border: solid 1px; background-color:#F8FCFF; color: ; float: ; "

Apologies...
...for my extended absence. I went to Mexico for three weeks to study Spanish, and could have sworn I left a note here saying I'd be gone. It appears I didn't press 'save' or something, because it's definitely not there! Sorry everyone! Νεοπτόλεμος ( talk | email | contribs ) 01:33, 24 June 2008 (UTC)

 * Studying a language. I have learned how hard that can be. By the way, thank you for your support in me request for adminship. Red4tribe (talk) 03:42, 2 July 2008 (UTC)

 * No, thank YOU for your excellent contributions to history-related books. They need some dedicated contributors! Νεοπτόλεμος ( talk | email | contribs ) 03:44, 2 July 2008 (UTC)

You're back!
YAY! — Mike.lifeguard | talk 01:48, 24 June 2008 (UTC)
 * Sorry for the unexplained absence for so long, I feel like an idiot! Νεοπτόλεμος ( talk | email | contribs ) 01:50, 24 June 2008 (UTC)
 * Oh, not a problem at all, just glad to see you back after a break. — Mike.lifeguard | talk 01:57, 24 June 2008 (UTC)

 * Ditto, glad to see you back. Nothing big has changed in the past few weeks, although Mike is a bcrat now. If you have any questions about the goings-on, let us know, otherwise happy editing! --Whiteknight (Page) (Talk) 02:00, 24 June 2008 (UTC)
 * Congrats to Mike! And glad to be back... can't wait to get started again! Νεοπτόλεμος ( talk | email | contribs ) 02:02, 24 June 2008 (UTC)

Good catch on the vandal last night. — Mike.lifeguard | talk 11:45, 26 July 2008 (UTC)

World History and Ancient History
After looking through the book, I believe that would be the best thing to do. As you said, it would solve the scope issues. My only question is, is how we can do it. Do you want to break it down into different sections of ancient history, and make their own chapters in the World History book?Red4tribe (talk) 00:44, 4 August 2008 (UTC)

 * It looks good for the most part. I won't be able to do it right now, but I will get around to it. Red4tribe (talk) 14:25, 4 August 2008 (UTC)

 * Alright then. Sounds good. Let me know if you need help. Red4tribe (talk) 20:22, 4 August 2008 (UTC)

American Founding Fathers
I made a suggestion on Wikijunior:New Title Suggestions for a new book called "American Founding Fathers" where there would be some basic information on each of the founding fathers. Would you be interested in a book like this? Let me know. Thanks. Red4tribe (talk) 19:14, 21 August 2008 (UTC)

US history
We would appreciate your assistance in rewriting a book about US history. There is considerable controversy about whether to start a new book or edit the current featured book text book "US History". I have never done a textbook before. what is the process- in what way could I make it a more collaborative effort. besides, your past efforts at writing textbooks would be very valuable for me.--JoliePA (talk) 17:48, 22 October 2008 (UTC)
 * They will probably want to bring AP United States History up to snuff rather than US History (though I'm unclear whether those texts have significantly different audiences/scopes/etc) — Mike.lifeguard | talk 19:01, 22 October 2008 (UTC)

Removal of admin tools due to inactivity
You have been nominated for having your administrative tools removed due to the policy on inactivity. If you wish to contest this, please visit Wikibooks:Requests for permissions. -- Adrignola talk contribs 15:40, 28 November 2009 (UTC)

title: User talk:Neoptolemus


text:
User talk:80.228.182.53

Welcome!
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We hope that you choose to become a Wikibookian and create an account. Feel free to ask me any questions you may have on my talk page. By the way, make sure to sign your posts and comments with four tildes (~~~~), which will let others know who left it. --Panic (talk) 20:36, 22 December 2007 (UTC)
 * I already am a Wikibookian ... at the german version, known as Techni-Tom I just need soom images at Commons

title: User talk:80.228.182.53


text: Category:Book:Editing Wikitext

title: Category:Book:Editing Wikitext


text:
Category:Pizza recipes

| Cuisine of Italy | Cuisine of the United States

title: Category:Pizza recipes


text:
User:VSimonian/Message

I bought some powdered water, but I didn't know what to add.

Past Messages of the Day (from newest to oldest)
寧三天不食 莫一日無茶 - Rather go three days without food than one day without tea. (Chinese proverb) Ladies do not start fights, but they may finish them. This page is 1337.

title: User:VSimonian/Message


text:
User talk:VSimonian/Message

[ Suggest a message of the day] or go back to my regular talk page.

title: User talk:VSimonian/Message


text:
User:VSimonian/Calm talk

 * To change the template's background color, just use  , or whatever color is preferred.

w:es:Plantilla:Discusión sosegada w:fr:Modèle: Appel au calme w:ja:Template:Calm talk w:zh:Template:Calm talk

title: User:VSimonian/Calm talk


text:
Template:Usercomment

 ''Welcome to my talk page. Please sign and date your entries by inserting   at the end. [ Start a new talk topic.]''

Usage
Add  to the top of your user talk page.

title: Template:Usercomment


text:
Template:CP Block

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title: Template:CP Block


text:
User:Aunk

TechnoCultural Activist, author and technologist. Founder of the Cultural Literacy Project and AnkhTowers.

My friends know me as Aunk (The Cultural Health Guy) WebSie:

title: User:Aunk


text:
Rebol Programming/Examples

You may try out the following examples, launching do followed by one of the link below: or copy and paste in the console the code of the following examples:

REBOL [	Title: "Calculator" Version: 1.2.2 Purpose: {Simple numeric calculator.} ] auto-clear: true calculate: does [ if error? try [text-box/text: form do text-box/text][ text-box/text: "Error" text-box/color: red ]	auto-clear: true show text-box ] clear-box: does [ clear text-box/text text-box/color: snow auto-clear: false show text-box ] calculator: layout [ style btn btn 40x24 style kc btn red [clear-box] style k= btn [calculate] style k btn [ if auto-clear [clear-box] append text-box/text face/text show text-box ]	origin 10 space 4 backeffect base-effect text-box: field "0" 172x24 bold snow right feel none pad 4 across kc "C" keycode [#"C" #"c" page-down] k "(" #"(" k ")" #")"  k " / " #"/" return k "7" #"7" k "8" #"8"  k "9" #"9"  k " * " #"*" return k "4" #"4" k "5" #"5"  k "6" #"6"  k " - " #"-" return k "1" #"1" k "2" #"2"  k "3" #"3"  k " + " #"+" return k "0" #"0" k "-"       k "." #"."	k= green "=" keycode [#"=" #"^m"] return key keycode [#"^(ESC)" #"^q"] [quit] ] view center-face calculator

REBOL [ title: "REBtris" author: "Frank Sievertsen" version: 1.0.2 date: 2-Apr-2001 ;30-Jul-2000 copyright: "Freeware" ]

rebtris: context [ field-size: 10x20 stone-size: 20x20 stones: { xxxx

xxx x

xxx x

xxx x

xx xx

xx		xx

xx xx }	walls: none lay: none pan: none stone: none akt-falling: none stoning: none pause: no	points: 0 points-pane: none level: 1 preview: none start-button: none new-start: func [/local ex col rnd] [ if not empty? preview/pane [hide preview/pane/1 insert pan/pane akt-falling: preview/pane/1 clear preview/pane ] insert preview/pane make pick walls random length? walls [] preview/pane/1/parent-face: preview ex: preview/pane/1/pane col: poke 200.200.200 random 3 0 col: poke col random 3 0 forall ex [ change ex make first ex compose/deep [effect: [gradient 1x1 (col) (col / 2)]] ]		preview/pane/1/rotate/norot preview/pane/1/offset: preview/size - preview/pane/1/size / 2 if not akt-falling [new-start exit] akt-falling/parent-face: pan akt-falling/offset: field-size * 1x0 / 2 - 1x0 * stone/size points: points + level show [points-pane preview pan akt-falling] ]	init: func [/local ex] [ walls: copy/deep akt-column: akt-row: 1 layout [ stone: image (stone-size) 200.200.0 effect [gradient 1x1 200.200.0 100.100.0] ]		if not parse/all stones [newline tabs some [end-up | no-stone | one-stone | new-row | new-wall]] [make error! [user message "parse error"]] forall walls [ layout [ ex: box 100x100 with [ old-pos: none rotate: func [/norot /local minx miny maxx maxy] [ foreach face pane [ if not norot [face/offset: reverse face/offset * -1x1] if none? minx [ minx: face/offset/x miny: face/offset/y ]							minx: min minx face/offset/x miny: min miny face/offset/y ]						maxx: maxy: 0 foreach face pane [ face/offset/x: face/offset/x - minx face/offset/y: face/offset/y - miny maxx: max maxx face/offset/x maxy: max maxy face/offset/y ]						size: stone/size + to-pair reduce [maxx maxy] ]					poses: func [/local out] [ out: make block! length? pane foreach face pane [ append out offset + face/offset + face/size ]						out ]					legal?: func [/local val out] [ out: make block! length? pane foreach val out: poses [ if any [ val/x > pan/size/x val/y > pan/size/y val/x < stone/size/x val/y < stone/size/y find stoning val ] [								restore-pos return false ]						]						save-pos out ]					del-line: func [num /local pos changed maxy] [ foreach pos poses [ either pos/y = num [ remove pane changed: yes ] [								if pos/y < num [changed: yes pane/1/offset/y: pane/1/offset/y + stone/size/y] pane: next pane ]						]						pane: head pane if changed [ maxy: 0 foreach p pane [ maxy: max maxy p/offset/y ]							size/y: maxy + stone/size/y show self ]					]					save-pos: func [] [ old-pos: make block! 2 + length? pane repend/only old-pos [offset size] foreach face pane [ repend/only old-pos [face/offset] ]					]					restore-pos: func [/local pos] [ if not old-pos [exit] set [offset size] first old-pos pos: next old-pos foreach face pane [ face/offset: pos/1/1 pos: next pos ]					]				]			]			ex/pane: copy [] foreach pos first walls [ append ex/pane make stone [offset: pos - 1x1 * stone/size] ]			change walls ex			stoning: copy [] ]		walls: head walls lay: layout [ backdrop effect [gradient 1x1 100.100.100 0.0.0] panel 0.0.0 effect [gradient 0x1 100.0.0 0.80.0] edge [color: gray size: 1x1] [ size (field-size * stone/size) sens: sensor 1x1 rate 2 feel [ engage: func [face action event /local tmp] [ switch action [ time [ if pause [exit] if akt-falling [ akt-falling/offset: akt-falling/offset + (stone/size * 0x1) if not akt-falling/legal? [										show akt-falling append stoning tmp: akt-falling/legal? check-lines new-start if not akt-falling/legal? [akt-falling: none start-button/text: "Start" show start-button] eat-queue exit ]									show akt-falling ]							]						]					]				]			]			return banner "REBtris" vh1 "Frank Sievertsen" with [font: [size: 12]] panel 0.0.0 [ size (stone/size * 5x4) ]			style button button with [effect: [gradient 1x1 180.180.100 100.100.100]] start-button: button "Start" [ either akt-falling [start-button/text: "Start" show start-button akt-falling: none] [sens/rate: 2 show sens start-button/text: "Stop" show start-button pause: no points: 0 if points-pane [show points-pane] clear pan/pane clear stoning show pan new-start] ]			button "Pause" [pause: not pause] vh1 "Level:" level-pane: banner "888" feel [ redraw: func [face] [face/text: to-string level] ] with [font: [align: 'left]] vh1 "Points:" points-pane: banner "88888888" feel [ redraw: func [face /local mem tmp] [ mem: [1] if mem/1 < (tmp: to-integer points / 1000) [level: level + 1 show level-pane sens/rate: level + 1 show sens] mem/1: tmp face/text: to-string points ]			] with [font: [align: 'left]] ]		lay/feel: make lay/feel [ detect: func [face event] [ if event/type = 'down [system/view/focal-face: none] event ]		]		pan: lay/pane/2 if not pan/pane [pan/pane: copy []] preview: lay/pane/5 if not preview/pane [preview/pane: copy []] remove find pan/pane sens insert lay/pane sens ]	check-lines: func [/local lines full tmp pos] [ lines: head insert/dup make block! field-size/y 0 field-size/y full: copy [] foreach e stoning [ e: e / stone/size poke lines e/y tmp: (pick lines e/y) + 1 if tmp = field-size/x [append full e/y] ]		sort full foreach e full [ foreach face pan/pane [ face/del-line e * stone/size/y ]			pos: pan/pane forall pos [ while [all [not tail? pos empty? pos/1/pane]] [hide pos/1 remove pos] ]			points: 100 + points show points-pane ]		clear stoning foreach face pan/pane [ append stoning face/poses ]	]	akt-column: akt-row: 1 tabs: [some "^(tab)"] end-up: [newline tab end] no-stone: [" " (akt-column: akt-column + 1) ]	one-stone: ["x" (append/only last walls to-pair reduce [akt-column akt-row]) (akt-column: akt-column + 1) ]	new-row: [newline tabs (akt-row: akt-row + 1) (akt-column: 1) ]	new-wall: [newline newline tabs (akt-row: akt-column: 1) (append/only walls copy []) ]	eat-queue: func [/local port] [ port: open [scheme: 'event] while [wait [port 0]] [error? try [first port]] close port ] ]

insert-event-func func [face event] bind [ if all [ event/type = 'key not system/view/focal-face find [up down left right #"p"] event/key akt-falling (not pause) or (event/key = #"p") ] [		switch event/key [ left	[akt-falling/offset: akt-falling/offset - (stone/size * 1x0)] right	[akt-falling/offset: akt-falling/offset + (stone/size * 1x0)] down	[akt-falling/offset: akt-falling/offset + (stone/size * 0x1)] up	[akt-falling/rotate] #"p"	[pause: not pause] ]		akt-falling/legal? show akt-falling return none ]	event ] in rebtris 'self

if any [not system/script/args empty? form system/script/args] [ random/seed now rebtris/init view rebtris/lay ]

title: Rebol Programming/Examples


text:
Algorithms/Unweighted Graph Algorithms

Please edit and omit unweighted in title

Adjacency Matrix
The rows/columns are the source/target vertex, the matrix is a square matrix with non-negative entries, 0 if there is no edge between the vertices, n if there are n edges from the source to the target vertex. This is efficient for dense multigraphs. For undirected graphs you either extend the matrix as being symmetric or you only use it as a triangular matrix.

Adjacency List
A vector with entries the list of adjacent vertices. If you need to represent a multigraph, then you need a vector of dictionaries where the key is the target vector and the value the multiplicity of the edge. This is efficient for sparse graphs. For undirected graphs you either fix an order of the vertices on an edge or you enter each edge twice (once at each vertex).

Comparison
the list might work better with level 1 cache with adjacency objects (which node, visited, inPath, pathWeight, fromWhere).

Pseudocode
dfs(vertex w)   if w has already been marked visited return mark w as visited for each adjacent vertex v     dfs(v)

Non recursive DFS is more difficult. It requires that each node keep memory of the last child visited, as it descends the current child. One implementation uses a indexed array of iterators, so on visiting a node, the node's number is an index into an array that stores the iterator for the nodes child. Then the first iterator value is pushed onto the job stack. Peek not pop is used to examine the current top of the stack, and pop is only invoked when the iterator for the peeked node is exhausted.

Cross Edge
IT is good techniques from :Yogesh Jakhar

Pseudocode
bfs ( x ): q insert x;     while (q not empty ) y = remove head q        visit y        mark y        for each z adjacent y           q add tail z

Usage
A breadth first search can be used to explore a database schema, in an attempt to turn it into an xml schema. This is done by naming the root table, and then doing a referential breadth first search. The search is both done on the referring and referred ends, so if another table refers to to the current node being searched, than that table has a one-to-many relationship in the xml schema, otherwise it is many-to-one.

Directed graph cycle detection
In a directed graph, check is *acyclic* by having a second marker on before dfs recursive call and off after, and checking for second marker before original mark check in dfs adjacency traversal. If second marker present, then cycle exists.

Topological Sort of Directed Graph

 * 1) check for cycle as in previous section.
 * 2) dfs the acyclic graph. Reverse postorder by storing on stack instead of queue after dfs calls on adjacent nodes.

The last node on stack must be there from first dfs call, and removing the last node exposes the second node which can only have been reached by last node. Use induction to show topological order.

Strongly Connected Components in Directed Graphs

 * 1) Strong connected components have cycles within and must by acyclic between components ( the kernel directed acyclic graph).
 * 2) Difference between dfs reverse postorder of original graph vs the same on reverse graph is that first node is least dependent in latter. Thus all non strong connected nodes will be removed first by dfs on the original graph in the latter's order, and then dfs will remove only strongly connected nodes by marking, one SC component at each iteration over reverse postorder of reverse graph , visiting unmarked nodes only. Each outgoing edge from a SC component being traversed will go to an already marked node due to reverse postorder on reverse graph.

title: Algorithms/Unweighted Graph Algorithms


text:
Telugu/Alphabet

Vowels (అచ్చులు atchulu)
Telugu has 18 vowels of which 3 are virtually phased out and hence do not have transliterations. Like other major Dravidian languages, the Telugu vowel set adds short /e/ and /o/ in addition to the long /eː/ and /oː/ of the Indo-Aryan languages.

The rhotics ఋ and ౠ (originally /r/ and /rː/), like the liquids ఌ and ౡ (originally /l/ and /lː/) have now turned into the syllables /ru/, /ruː/, /lu/, /luː/ respectively. They are fast going out of currency and are no longer included in the standard Telugu school textbooks issued by the government of Andhra Pradesh, which now prefers the actual consonants with a /u/ appended (e.g. /ruʃɪ/ (monk) used to be written ఋషి but nowadays, రుషి is preferred).

Consonants (హల్లులు hallulu)
The consonants in Telugu, followed by their last characters.

The consonants correspond almost one-to-one to the set in Sanskrit, with two exceptions. One is the historical form of /r/ఱ which is now again being phased out by the current form ర. (e.g. /gurːam/ (horse) was written గుఱ్ఱం but is now written గుర్రం). The other is the retroflex lateral ళ /ɭ/.

(k kh g gh ṅ) and చ ఛ జ ఝ ఞ (c ch j jh ñ) and all the letters in the fifth row, ప ఫ బ భ మ (p ph b bh m)are pronounced exactly as they are in English. In other words, a Telugu k sounds like an English "k" (without aspiration).
 * The last (nasal) consonants of the first two rows, ఙ (ṅ) and ఞ(ñ) are almost never found written alone; they are usually conjuncted (more on conjuncts later) with another consonant in their corresponding rows, as the other nasal consonants often are.
 * The third row, ట ఠ డ ఢ ణ (ṭ ṭh ḍ ḍh ṇ) are pronounced using the retroflex version. To achieve these sounds, curl the tongue back and touch the tip to the roof of the mouth.
 * The fourth row, త థ ద ధ న (t th d dh n) are dental consonants and are spelled exactly like the t or d in Spanish, with the tongue touching the back of the upper teeth.
 * Voiced, aspirated consonants (gh, bh, etc.) are by far the hardest sounds for the English speaker to learn how to make; however, with some practice they are not overly difficult.
 * య (y) is very similar to its corresponding English sound.
 * ర (r,) like most non-English "r" sounds, is flipped, but not rolled.
 * ల (l) is the same as the English "l".
 * వ (w (v)) has a somewhat flexible pronunciation, depending on context and regional dialects. Sometimes it is pronounced like the English "w" (as in the word swami), and other times it is closer to the English "v". It is often pronounced somewhere in between the two sounds.
 * శ(ś) does not exist in english.It is pronounced without touching the tip of tongue to lower teeth.
 * ష(ṣ) is also similar to "sh" in English.while it is pronounced the middle of the tongue touches somewhere in the middle of the upper part of mouth
 * స (s) is the same as "s" in English.while it is pronounced the tip of the tongue touches lower teeth
 * హ (h) is pronounced the same as "h" in English.
 * ళ ( ḷa ) is pronounced by touching the tongue to the roof of the mouth.
 * క్ష ( kṣa ) is pronounced as (ksha) ct in action or friction is pronounced in English.

Telugu is known as Italian of the East as all words in this language end with a vowel. It is fourth largest spoken language in INDIA. This language has typical grammar with connection mathematics.

title: Telugu/Alphabet


text:
Telugu/History

It is possible to broadly define four stages in the linguistic history of the Telugu language:

400 CE - 500 CE
The discovery of a Brahmi label inscription reading Thambhaya Dhaanam is engraved on the soap stone reliquary datable to 2nd century BCE on Paleographical ground proves the fact that Telugu language predates the known conception in Andhra Pradesh. Primary sources are Prakrit/Sanskrit inscriptions found in the region, in which Telugu places and personal names are found. Telugu words appear in the Maharashtri Prakrit anthology of poems (the Gathasaptashathi) collected by the first century BCE Satavahana King Hala. Telugu speakers were probably the oldest peoples inhabiting the land between the Krishna and Godavari rivers.

500 CE - 1100 CE
The first inscription that is entirely in Telugu corresponds to the second phase of Telugu history. This inscription dated 575 CE was found in the Kadapa and Kurnool district region and is attributed to the Renati Cholas. They broke with the prevailing fashion of using Sanskrit and introduced the tradition of writing royal proclamations in the local language. During the next fifty years, Telugu inscriptions appeared in the neighboring Anantapuram and all the surrounding regions. The first available Telugu inscription in the coastal Andhra Pradesh comes from about 633 CE. Around the same time, the Chalukya kings of Telangana also started using Telugu for inscriptions. Telugu was most exposed to the influence of Sanskrit, as opposed to Prakrit, during this period. This period mainly corresponded to the advent of literature in Telugu. This literature was initially found in inscriptions and poetry in the courts of the rulers, and later in written works such as Nannayya's Mahabharatam (1022 CE). During the time of Nannayya, the literary language diverged from the popular language. This was also a period of phonetic changes in the spoken language.

1100 CE - 1400 CE
The third phase is marked by further stylization and sophistication of the literary language. Ketana (thirteenth century) in fact prohibited the use of spoken words in poetic works. This period also saw the beginning of Muslim rule in the Telugu speaking regions.

During this period the separation of Telugu script from the common Telugu-Kannada script took place. Tikkana wrote his works in this script.

1400 CE - 1900 CE
During the fourth phase, Telugu underwent a great deal of change (as did other Indian languages), progressing from medieval to modern. The language of the Telangana region started to split into a distinct dialect due to Muslim influence: Sultanate rule under the Tughlaq dynasty had been established earlier in the northern Deccan during the fourteenth century. South of the Godavari river (Rayalaseema region), however, the Vijayanagara empire gained dominance from 1336 till the late 1600s, reaching its peak during the rule of Krishnadevaraya in the sixteenth century, when Telugu literature experienced what is considered to be its golden age. Padakavithapithamaha, Annamayya, contributed many atcha (pristine) Telugu Padaalu to this great language. In the latter half of the seventeenth century, Muslim rule extended further south, culminating in the establishment of the princely state of Hyderabad by the Asaf Jah dynasty in 1724. This heralded an era of Persian/Arabic influence on the Telugu language, especially among the people of Hyderabad. The effect is also felt in the prose of the early 19th century, as in the Kaifiyats.

1900 CE to date
The period of the late nineteenth and the early twentieth centuries saw the influence of the English language and modern communication/printing press as an effect of the British rule, especially in the areas that were part of the Madras Presidency. Literature from this time had a mix of classical and modern traditions and included works by scholars like Kandukuri Viresalingam and Panuganti Lakshminarasimha Rao.

Since the 1940s, what was considered an elite literary form of the Telugu language has now spread to the common people with the introduction of mass media like television, radio and newspapers. This form of the language is also taught in schools as a standard. In the current decade the Telugu language, like other Indian languages, has undergone globalization due to the increasing settlement of Telugu-speaking people abroad. Modern Telugu movies, although still retaining their dramatic quality, are linguistically separate from post-Independence films.

At present, a committee of scholars have approved a classical language tag for Telugu based on its antiquity. A final notification from the Government of India is awaited.

title: Telugu/History


text:
VHDL for FPGA Design/Priority Encoder

Generated Logic Circuit

VHDL-kieli FPGA-suunnittelussa/Prioriteettienkooderi

title: VHDL for FPGA Design/Priority Encoder


text:
Telugu/Literature

Telugu literature can be broadly discussed in to six ages as mentioned below:

 * 1) 	Pre-Nannaya period (up to 1000 A.D.)
 * 2) 	Age of Puranas (1000 A.D. - 1400 A.D.)
 * 3) 	Age of Poet Srinatha (1400 A.D. – 1500 A.D.)
 * 4) 	Age of Prabandhas (1500 A.D. -1600 A.D.)
 * 5) 	Southern Region period (1600 A.D. -1800 A.D.)
 * 6) 	Modern Age (1800 A.D. – Till date)

During the age of Pre-Nannaya period, there were only inscriptions since 575 A.D. Nannayya Bhattaraka (11th Century A.D.) translated the Sanskrit Mahabharata into Telugu and this can be quoted as the first best citation of Telugu literature. The diction was highly mastered by Nannaya that many historians’ school of thought says that there might have been earlier works in Telugu, which base his major work.

Tikkanamatyulu (13th century) and Yerrana also called Yerrapragada (14th century) resumed the translation of the remaining portions of Mahabharata started by Adi Kavi Nannaya Bhattaraka. In the age of Srinatha Kavi Sarvabhowma (popular poet in 14th century) few poets translated Sanskrit slokas and dramas and others came out with native narrative poems. The popular Telugu literary form, Prabandha was evolved during this period.

The first Ramayana in Telugu is reffred as the Ranganatha Ramayanam, works done by by Gona Buddha Reddi. Later, the memorable religious poets such as Potan (14th Century), Jakkana (14th century) and Gaurana (first half of the 15th century) have done greatest works in these roots.

Golden period of Telugu literature was in between 16th - 17th centuries when Sri Krishnadevaraya has shown interest in Telugu Literature. Manucharitra by Peddana is another outstanding Mahakavya other than Sri Krishna Devaraya’s Amukthamalyada. As the Telugu literature flourished in the south in the Samsthanas like Madurai, Tanjavur etc., which renamed this age as `Southern Period'.

Mughals conquered Deccan in 1687 A.D., with which the Telugu Literature lost its speciality growth. The period of transition emerged after a long gap of 200 years, when a memorable Europeans, C.P.Brown played an important role in the development of Telugu language and literature. Later the Telugu Literature was also influenced by the European literary forms such as novels, short stories, dramas etc.

Kandukuri Viresalingam Pantulu, the father of modern Telugu literature inspired by the Vicar of Wakefield wrote a novel called Rajasekhara Charitamu. He was the first and the greatest among modern times, who used literature to suppress social evils and superstitions. The age was followed by other famous Telugu writers such as Rayaprolu Subba Rao, Gurazada Appa Rao, Viswanatha Satyanarayana, Jashuva, Devulapalli Krishna Sastry, Sri Sri, Puttaparty Narayana Charyulu and many others.

title: Telugu/Literature


text:
Horticulture/Wisteria sinensis

Wisteria sinensis (Chinese Wisteria) is a woody, deciduous, perennial climbing vine, native to China in the provinces of Guangxi, Guizhou, Hebei, Henan, Hubei, Shaanxi, and Yunnan. While this plant is a climbing vine, it can be trained into a tree-like shape, usually with a wavy trunk and a flattened top. It was introduced from China to Europe and North America in 1816 and has secured a place as one of the most popular flowering vines for home gardens due to its flowering habit. It has however become an invasive species in some areas of the eastern United States where the climate closely matches that of China.

All parts of the plant contain a glycoside called wisterin which is toxic and if ingested and may cause nausea, vomiting, stomach pains, and diarrhea. Wisterias have caused poisoning in children of many countries, producing mild to severe gastroenteritis.

Description
It can grow 20-30 m long over supporting trees by counter-clockwise-twining stems. The leaves are shiny, green, pinnately compound, 10-30 cm in length, with 9-13 oblong leaflets that are each 2-6 cm long. The flowers are white, violet, or blue, produced on 15-20 cm racemes in spring, usually reaching their peak in mid-May. The flowers on each raceme open simultaneously before the foliage has expanded, and have a distinctive fragrance similar to that of grapes. Though it has shorter racemes than Wisteria floribunda (Japanese Wisteria), it often has a higher quantity of racemes. The fruit is a flattened, brown, velvety, bean-like pod 5-10 cm long with thick disk-like seeds around 1 cm in diameter spaced evenly inside; they mature in summer and crack and twist open to release the seeds; the empty pods often persist until winter. However seed production is often low, and most regenerative growth occurs through layering and suckering.

Growing Conditions
It is hardy in USDA plant hardiness zones 5-9, and prefers moist soils. It is considered shade tolerant, but will flower only when exposed to partial or full sun. It will also flower only after passing from juvenile to adult stage, a transition that may take many years. It can live for over 100 years.

Propagation
Generally Wisterias are propagated with cuttings (hardwood). But it can be possible to make use of their seeds(in their flowers) but takes more time to have a real tree! In some articles the softwood cutting is also recommended but I checked it doesen't work well. Because the herbaceous (soft)stem will rot (within a few days) before rooting!

title: Horticulture/Wisteria sinensis


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Horticulture/Using Templates

This book uses a number of templates both for providing a consistent layout for various sorts of pages, as well as providing categories for plant finding.

General uses

 *   - creates new pages for plants. When possible, new pages are based on transwikied Wikipedia articles in order to take advantage of free content that is already available.

More specific versions below should be used when applicable.

Weed (control)

 *   - creates new pages profiling a weed that is never cultivated.
 *   - creates new pages profiling a weed that is occasionally cultivated.
 *   -  creates new pages profiling a herbicide.

Pest (control)

 *   - creates new pages profiling a pest.
 *   - creates new pages profiling a pesticide.
 *   - creates new pages profiling a biological pest control.

Disease

 *   - creates new pages profiling a plant disease.

/Project

title: Horticulture/Using Templates


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User talk:85.189.155.140

Harry Potter
Please stop changing the text like that - it links correctly as it was, thanks -- Herby talk thyme 14:33, 23 December 2007 (UTC)

title: User talk:85.189.155.140


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Common Lisp/First steps

 * 1) /Features/ - what can Common Lisp show off with?
 * 2) /Installation/ - how to obtain, install and use a Common Lisp environment
 * 3) /Beginner tutorial/ - Common Lisp as a first programming language
 * 4) /Experienced tutorial/ - a quick and dirty introduction if you already know about programming

title: Common Lisp/First steps


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Common Lisp/Basic topics

 * 1) /Lists/
 * 2) /Functions/
 * 3) /Macros/

title: Common Lisp/Basic topics


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Common Lisp/Advanced topics

 * 1) /Numbers/ - Common Lisp mathematics
 * 2) Example 1: find a single root of some function in the given area by calculating complex path integrals.
 * 3) /Strings/ all you ever wanted to know about string manipulation
 * 4) /Hash tables/ which programmer can do without their comfort?
 * 5) /Dates and Times/ date and time data processing of all sorts
 * 6) /Files and Directories/ all kinds of file processing and related I/O tasks
 * 7) Lisp manipulation of C structures
 * 8) /Packages/ - Using packages
 * 9) /Advanced Lists/ - advanced list processing
 * 10) /Sequences/ - arrays
 * 11) /Loop macro/ - Iteration constructs in Common Lisp
 * 12) /CLOS/ - Common Lisp Object System
 * 13) Example 1: edit a file with subtitles to a movie, so that subtitles are delayed by a specified time. Using CLOS and CL-PPCRE.
 * 14) /Condition System/ - Exception handling
 * 15) /Input and Output/ - Interaction with the user
 * 16) /Simple Printing/ - PRINT, FORMAT and streams
 * 17) /The Printer/ - How Common Lisp prints output
 * 18) /The Reader/ - How Common Lisp reads your input
 * 19) /Advanced Functions and Macros/ - Revisiting an important topic
 * 20) /Functional/ - Functions as first class objects (functions that return functions, currying functions, closures, multiple values...)

title: Common Lisp/Advanced topics


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Common Lisp/Beyond ANSI Common Lisp

The implementation-dependent features which exist on most implementations but not a part of ANSI Common Lisp standard.

Since there are no agreed upon interfaces to these facilities, each implementation does these things differently. To make things simpler for the user, oftentimes compatibility packages are maintained to provide a standard interface.

 * 1) /Debugging/ - debugging Lisp systems
 * 2) /OS/ - communicating with the underlying OS (shell access, etc.)
 * 3) /Streams/ - user-defined streams (a.k.a. Gray Streams)
 * 4) /Sockets/ - using sockets (using IOLib)
 * 5) /MOP/ - Meta Object Protocol (using closer-mop)
 * 6) /FFI/ - Foreign Function interface (using CFFI compatibility layer)
 * 7) /Threads/ - writing multi-threaded programs (using bordeaux-threads)
 * 8) /User Control of GC/ - opening the black box of the Garbage Collector (using trivial-garbage)
 * 9) CLX — X Window Programming in Common Lisp

title: Common Lisp/Beyond ANSI Common Lisp


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Common Lisp/External libraries

Common Lisp libraries exist for many purposes. Here we will showcase a small sampling of mature, useful, and free packages available, showing some of the functionality they provide.

System Utilities

 * 1) /ASDF/ — Another System Definition Facility
 * 2) /clbuild/ — A script to update/install the latest versions of all the most important Common Lisp packages
 * 3) Roswell - An implementation installer and script launcher

Language Extension
These libraries add new control structures to the Common Lisp language.

 * 1) Serapeum - Another general-purpose utility library.
 * 2) rutils - radical yet reasonable syntactic utilities for Common Lisp.
 * 3) /Iterate/ — Easy and extensible iteration
 * 4) /Extended Binding/ — Pattern matching, anaphoric control structures, and more
 * 5) /Cells/ — A constraint based programming paradigm that operates in a way similar to spread sheets
 * 6) /Screamer/ — Efficient, nondeterminism for Common Lisp
 * 7) /FSet/ — Functional programming in Common Lisp
 * 8) generic-cl - Generic function interface to standard Common Lisp functions (equality, comparison, arithmetic, objects, iterator, sequences,…).
 * 9) cl21 An experimental project that brings more modern idioms into Common Lisp (unmaintained)

Data Structures

 * 1) /CL-CONTAINERS/ — A library for abstracting data structures details
 * 2) FSet - A functional, set-theoretic collections data structure library.
 * 3) cl-data-structures - a portable collection of data structures and algorithms (mainly dicts and sequences, with some statistical functions).
 * 4) cl-competitive - Common Lisp algorithms collection for competitive programming.

Database

 * 1) cl-dbi - A database independant interface
 * 2) postmodern - A library for interacting with PostgreSQL databases
 * 3) Mito - An ORM, with migrations, relationships and DB schema versioning
 * 4) Crane - An ORM, based on the CL Objects System, with migrations

Parsing and Text processing

 * 1) /CL-PPCRE/ — regular expressions library
 * 2) /CXML/ — An XML parsing library
 * 3) /CL-HTML-Parse/ — Parsing HTML
 * 4) /CL-YACC/ — A parser generator
 * 5) /CL-Walker/ — A Common Lisp parser for Common Lisp

Serialization and Persistent data

 * 1) /Serialization/ — serialization of Common Lisp data (via cl-serialization and cl-store)
 * 2) /ELEPHANT/ — A persistent object system
 * 3) /CL-Perec/ — A persistent object system

GUI

 * 1) /Ltk/ — Common Lisp interface to Tk (portable GUI library)
 * 2) /McCLIM/ — A Common Lisp GUI builder
 * 3) IUP- CFFI bindings to the IUP Portable User Interface library. IUP is cross-platform (Windows, macOS, GNU/Linux, with new Android, iOs, Cocoa and Web Assembly drivers), has many widgets, has a small api and is actively developed.

Graphics

 * 1) /Vecto/ — A library for drawing and rastering vector graphic images
 * 2) /CL-OpenGL/ — A set of GL, GLU, and GLUT bindings

Audio

 * 1) Open Music - a visual programming, computer-aided composition environment.
 * 2) CLM - Common Lisp Music is a music synthesis and signal processing package in the Music V family. It provides much the same functionality as Stk, Csound, SuperCollider, PD, CMix, cmusic, and Arctic — a collection of functions that create and manipulate sounds, aimed primarily at composers (in CLM's case anyway).
 * 3) Incudine -  Music/DSP programming environment for Common Lisp. Useful to design software synthesizers or sound plugins from scratch. It is also a compositional tool that allows to produce high quality sounds controllable at the sample level, defining and redefining the digital signal processors and the musical structures on-the-fly.

Web and Network

 * 1) Dexador — A full featured HTTP client (that aims at replacing /Drakma/)
 * 2) /Portable Allegro Serve/ — A fairly light weight, multithreaded, HTTP server
 * 3) /Hunchentoot/ — A Web application server written in Common Lisp
 * 4) Caveman - A fully featured web framework
 * 5) Plump - An html/xml parser, tolerant on malformed markup
 * 6) lquery - A jquery-like DOM/HTML manipulation library
 * 7) Djula - A port of Django templates
 * 8) Parenscript - A translator from Common Lisp to Javascript
 * 9) Wuwei - Examples on how to do Ajax in Lisp

title: Common Lisp/External libraries


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Differential Geometry/Osculating Plane

The term osculating plane, which was first used by Tinseau in 1780, of a curve C parametrized by a function f(t) at a point f(a) is the plane that is approached when it is spanned by two vectors f(x)-f(a) and f(y)-f(a) when x and y both approach a.

First, assume that the curve C is at least of class 2.

Then consider the points $$x$$, $$x+h_1$$, and $$x+h_2$$ and consider the points $$P=f(x)$$, $$P_1=f(x+h_1)$$, and $$P_2=f(x+h_2)$$. The segments $$PP_1$$ and $$PP_2$$ are the vectors $$s_i=f(x+h_i)-f(x)$$. If these vectors are linearly independent, then they span a plane.

We can divide each of those vectors by $$h_i$$, meaning that the plane is also spanned by the vectors $$a_i=\frac{s_i}{h_i}$$.

We can also replace the second vector by $$b=\frac{2(a_2-a_1)}{h_2-h_1}$$ and it is easy to see that $$a_1$$ and w span the same plane as the original vectors.

Using Taylor's formula, we get

$$f(x+h_i)-f(x)=h_if'(x)+\frac{h_i}{2!}f''(x)+o(h_i^2)$$.

This indicates that $$a_1=f'(x)+\frac{h_1}{2}f(x)+o(h_1)$$ and that $$b=f(x)+o(1)$$

Thus, as both $$h_1$$ and $$h_2$$ approach 0, $$a_1$$ approaches f'(x) and $$b$$ approaches f''(x). The osculating plane is consequently spanned by f'(x) and f''(x), and consequently contains the tangent line.

Consider the position vector $$x_1$$ of any point on the osculating plane.

Then it is obvious that the following scalar triple product is equal to 0:

$$|(x_1-f(x))f'(x)f''(x)|=0$$.

The intersection of the osculating plane and the normal plane is called the principal normal line.

If it happens to be the case that f'(x) and f''(x) are linearly dependent, then we can consider every plane containing the tangent line to be the osculating plane.

title: Differential Geometry/Osculating Plane


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User:Qubodup

 * sings* In the toown, where I was boorn...

title: User:Qubodup


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User talk:Qubodup

Welcome!
Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.-- – Mike.lifeguard  | talk 16:42, 23 December 2007 (UTC)

title: User talk:Qubodup


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Common Lisp/First steps/Features

 * Common Lisp is a high-level programming language with automatic storage management (aka garbage collection).
 * Common Lisp is a multi-paradigm language. It allows you to write programs in the procedural/imperative, functional/applicative and object-oriented styles. These styles may be freely mixed in a Common Lisp program. This allows you to choose the approach and paradigm according to your application domain.
 * Common Lisp is written in a fully-parenthesized, prefix notation. This means that applying the function func to arguments x and "hello" is written (func x "hello") rather than the more conventional func(x, "hello"). This might make the syntax harder to learn if you are accustomed to other languages, but after some practice it becomes quite natural. It also makes macros possible.
 * Macros allow you to extend the Lisp syntax. They can be used to define new keywords. Common Lisp macros are much more powerful than (for example) C macros: Lisp macros are code generating programs in their own right.
 * Common Lisp has an interactive top-level. Most implementations allow you to type in programs at a prompt as well as loading them from a file, allowing explorative programming. The prompt can also be used for interactive debugging.
 * Common Lisp allows incremental compilation. Most implementations have a compiler (either native-code or bytecode) as well as an interactive top-level. Compiled and interpreted code may be freely mixed.
 * Common Lisp can provide high performance (but this is highly dependent on the implementation). Some implementations can compete with C/C++ compilers.

title: Common Lisp/First steps/Features


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User talk:Bowers.debra

Welcome!
Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.--Whiteknight (Page) (Talk) 17:38, 23 December 2007 (UTC)

title: User talk:Bowers.debra