History.

The CPT theorem appeared for the first time, implicitly, in the work of Julian Schwinger in 1951 to prove the connection between spin and statistics. In 1954, Gerhart Lüders and Wolfgang Pauli derived more explicit proofs, so this theorem is sometimes known as the Lüders–Pauli theorem. At about the same time, and independently, this theorem was also proved by John Stewart Bell. These proofs are based on the principle of Lorentz invariance and the principle of locality in the interaction of quantum fields. Subsequently, Res Jost gave a more general proof in the framework of axiomatic quantum field theory.  Efforts during the late 1950s revealed the violation of P-symmetry by phenomena that involve the weak force, and there were well-known violations of C-symmetry as well. For a short time, the CP-symmetry was believed to be preserved by all physical phenomena, but that was later found to be false too, which implied, by CPT invariance, violations of T-symmetry as well.

Derivation of the CPT theorem.

Consider a Lorentz boost in a fixed direction "z". This can be interpreted as a rotation of the time axis into the "z" axis, with an imaginary rotation parameter. If this rotation parameter were real, it would be possible for a 180° rotation to reverse the direction of time and of "z". Reversing the direction of one axis is a reflection of space in any number of dimensions. If space has 3 dimensions, it is equivalent to reflecting all the coordinates, because an additional rotation of 180° in the "x-y" plane could be included.  This defines a CPT transformation if we adopt the Feynman–Stueckelberg interpretation of antiparticles as the corresponding particles traveling backwards in time. This interpretation requires a slight analytic continuation, which is well-defined only under the following assumptions:  When the above hold, quantum theory can be extended to a Euclidean theory, defined by translating all the operators to imaginary time using the Hamiltonian. The commutation relations of the Hamiltonian, and the Lorentz generators, guarantee that Lorentz invariance implies rotational invariance, so that any state can be rotated by 180 degrees.  Since a sequence of two CPT reflections is equivalent to a 360-degree rotation, fermions change by a sign under two CPT reflections, while bosons do not. This fact can be used to prove the spin-statistics theorem.

Consequences and implications.

The implication of CPT symmetry is that a "mirror-image" of our universe — with all objects having their positions reflected through an arbitrary point (corresponding to a parity inversion), all momenta reversed (corresponding to a time inversion) and with all matter replaced by antimatter (corresponding to a charge inversion) — would evolve under exactly our physical laws. The CPT transformation turns our universe into its "mirror image" and vice versa. CPT symmetry is recognized to be a fundamental property of physical laws.  In order to preserve this symmetry, every violation of the combined symmetry of two of its components (such as CP) must have a corresponding violation in the third component (such as T); in fact, mathematically, these are the same thing. Thus violations in T symmetry are often referred to as CP violations.  The CPT theorem can be generalized to take into account pin groups.  In 2002 Oscar Greenberg published an apparent proof that CPT violation implies the breaking of Lorentz symmetry. If correct, this would imply that any study of CPT violation also includes Lorentz violation. However, Chaichian "et al" later disputed the validity of Greenberg's result. Greenberg replied that the model used in their paper meant that their "proposed objection was not relevant to my result".  The overwhelming majority of experimental searches for Lorentz violation have yielded negative results. A detailed tabulation of these results was given in 2011 by Kostelecky and Russell.

Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T). CPT is the only combination of C, P, and T that is observed to be an exact symmetry of nature at the fundamental level. The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry.


Synopsis.

The plot depends on a tangled set of village relationships. Before the opera begins, the mill-owner Grandmother Buryja's two sons have both married twice, fathered children, and died. Their wives have also died, except for the Kostelnička (widow of the churchwarden), the younger son's second wife and Jenůfa's stepmother. Custom dictates that only Števa, the elder son's child by his first marriage, will inherit the mill, leaving his half-brother Laca and cousin Jenůfa to earn their livings.

Act 1.

Jenůfa, Laca, and Grandmother Buryja wait for Števa to return home. Jenůfa, in love with Števa and secretly pregnant with his child, worries that he may have been drafted into the army. Laca, in love with Jenůfa, expresses bitterness against his half-brother's favored position at home. As he complains he plays with a knife and, finding it blunt, gives it to the mill foreman to be sharpened.  The foreman informs the family that Števa has not been drafted, to Jenůfa's relief and Laca's increased frustration. The others leave, and Jenůfa waits to greet Števa. He appears with a group of soldiers, drunk and boasting of his prowess with the girls. He calls for music and drags the miserable Jenůfa into dancing with him.  Then Kostelnička steps into this rowdy scene, silences the musicians and, shocked by Števa's behavior, forbids him to marry Jenůfa until he can stay sober for one full year. The soldiers and the family leave Števa and Jenůfa alone, and she begs him to love her, but he, unaware of her pregnancy, gives her casual answers and leaves.  Laca returns, as bitter as ever. He attempts to goad Jenůfa into criticizing Števa, but she takes her lover's side despite everything. Laca rages that Števa would never even look at her if it weren't for her rosy cheeks, then slashes her across the cheek with his knife.

Act 2.

Months later, it is winter. The baby has been born, but Števa has not yet come to visit his child. Jenůfa's face is still disfigured, but she is happy in her love for the baby. While Jenůfa sleeps, the Kostelnička summons Števa and demands that he take responsibility. He answers that while he will provide money in secret, no one must know the baby is his. His love for Jenůfa died when Laca spoiled her beauty, and he is now engaged to marry Karolka, the mayor's pretty daughter.  Števa leaves, and Laca enters. He still doesn't know the truth about the baby, and when the Kostelnička tells him, his first reaction is disgust at the thought of taking Števa's child under his wing. Fearful that Jenůfa will be left with no one to marry, Kostelnička hastily lies that the baby is dead. Laca leaves, and the Kostelnička is faced with the necessity of making the lie true. She wraps the baby in a shawl and leaves the house.  Jenůfa wakes up and says a prayer for her child's future, but the Kostelnička, returning, tells her that the baby died while she slept. Laca appears and comforts Jenůfa gently, asking that they spend the rest of their lives together. Seeing the tenderness of the couple, the Kostelnička tries to convince herself that she has acted for the best.

Act 3.

It is now spring, and Laca and Jenůfa's wedding day. All seems right again, except that the Kostelnička is a nervous wreck. Števa and Karolka visit, and a chorus of village girls sings a wedding song. Just then, screams are heard. The body of the baby has been discovered in the mill-stream under the melting ice. Jenůfa immediately says that the baby is hers, and in her grief appears guilty of the murder. The village is ready to exact immediate justice against Jenůfa, but the Kostelnička calms them and says that the crime is hers. Hearing the whole story, Jenůfa forgives her stepmother. The crowd takes the Kostelnička off to jail. Jenůfa and Laca are left alone. Jenůfa asks Laca to leave her, as she cannot expect him to marry her now. He replies that he will not leave her, and that he wishes to spend the rest of his life with her.

References.

Notes Sources

Její pastorkyňa ("Her Stepdaughter"; commonly known as Jenůfa ) is an opera in three acts by Leoš Janáček to a Czech libretto by the composer, based on the play "Její pastorkyňa" by Gabriela Preissová. It was first performed at the National Theatre, Brno on 21 January 1904. Composed between 1896 and 1902, it is among the first operas written in prose.


Geography.

The town is situated on the Olza river, a tributary of the Oder River, which forms the border with the Czech Republic. It is located within the western Silesian Foothills north of the Silesian Beskids and Mt. Czantoria Wielka, a popular ski resort. Cieszyn is the heart of the historical region of Cieszyn Silesia, the southeasternmost part of Upper Silesia. Until the end of World War I in 1918 it was a seat of the Dukes of Teschen.  In 1920 Cieszyn Silesia was divided between the two newly created states of Poland and Czechoslovakia, with the smaller western suburbs of Teschen becoming part of Czechoslovakia as a new town called Český Těšín. The larger part of the town joined Poland as Cieszyn. Three bridges connect the twin towns. After Poland and the Czech Republic joined the European Union and its passport-free Schengen zone, border controls were abolished and residents of both the Polish and Czech part could move freely across the border. The combined population of Polish and Czech parts of the city is 61,201 inhabitants. Cieszyn is the southern terminus of the Polish National road 1 leading to Gdańsk on the Baltic coast.  The town combines both Polish and Old–Austrian peculiarities in the style of its buildings. Because of several major fires and subsequent reconstructions (the last one in the late 18th century), the picturesque old town is sometimes called "Little Vienna". The only relic of the ancient castle is a square tower, dating from the 14th century and 11th century romanesque chapel.

History.

The area has been populated by Slavic peoples since at least the 7th century. According to legend, in 810 three sons of a prince – Bolko, Leszko and Cieszko, met here after a long pilgrimage, found a spring, and decided to found a new settlement. They called it Cieszyn, from the words "cieszym się" ("I'm happy"). This well can be found at "ulica Trzech Braci" ("Three Brothers Street"), just west of the town square.  The town was the capital of the Duchy of Teschen since 1290, which was ruled by Piast dynasty until 1653 and by the Habsburg Dynasty of Austria until 1918. It was in Teschen that Maria Theresa and Frederick II on in May 1779 signed the Teschen Peace Treaty, which put an end to the War of the Bavarian Succession. In the 19th century Teschen was known for its ethnic, religious and cultural diversity, containing mostly German, Polish, Jewish and Czech communities. There was also a small Hungarian community in the town consisting mostly of officers and clerks.  The town was divided in July 1920, by the Spa Conference, a body formed by the Versailles Treaty, leaving a Polish minority on the Czechoslovak side. Its smaller western suburbs became what is now the town of Český Těšín in the Czech Republic. During the interwar period two villages were merged into Cieszyn: Błogocice in 1923 and Bobrek in 1932. After 1920 many ethnic Germans left the town, while many Poles from the Czechoslovakian part of the region moved in. According to the Polish census of 1921, Cieszyn had 15,268 inhabitants, of whom 9,241 (60.5%) were Poles, 4,777 (31.2%) were Germans, 1014 (6.6%) were Jews, and 195 (1.3%) were Czechs. The census from 1931 indicated 14,707 inhabitants, of whom 12,145 (82.7%) were Poles, while the rest consisted mostly of Germans and Jews (in 1937 estimated to be 12 and 8% respectively).  Cieszyn and Český Těšín were merged again in October 1938 when Poland annexed the Zaolzie area together with Český Těšín. In 1939 Cieszyn Silesia was occupied by German forces and during World War II it was part of Nazi Germany. Almost the entire Jewish community was murdered by the Nazis.  After World War II, the border between Poland and Czechoslovakia was restored to that of 1920. Most Germans fled or were expelled and were replaced with Poles expelled from the Polish areas annexed by the Soviet Union. Signs of the former German presence in the town were removed by a special committee.  On 19 July 1970, five firefighters from Cieszyn died when a bridge they were on fell into the Olza River, due to heavy flooding. In 1977, Boguszowice, Gułdowy, Kalembice, Krasna, Mnisztwo, Pastwiska were amalgamated with Cieszyn and Marklowice.

Culture.

Since the 18th century Cieszyn Silesia has been an important centre of Polish Protestantism when the Jesus Church was built as the only one in Upper Silesia. Currently Cieszyn is also the site of the Cieszyn Summer Film Festival, one of the most influential film festivals in Poland. There is also an earlier established Czech-Polish-Slovak film festival.

Industry.

Cieszyn is an important centre of the electromechanical industry. It is also the site of the "Olza Cieszyn" sweets factory (where the famous Prince Polo wafers are made) and the Brackie Browar, where Żywiec Porter is brewed. The main source of income for many citizens is trade with the nearby Czech Republic and retail trade associated with transit across the two bridges over the Olza to Český Těšín. In the past, the city was home to many furniture factories.

Twin towns – sister cities.

Cieszyn is twinned with:

Cieszyn (; ; ; ) is a border town in southern Poland on the east bank of the Olza River, and the administrative seat of Cieszyn County, Silesian Voivodeship. The town has 34,513 inhabitants (as of 2019), and lies opposite Český Těšín in the Czech Republic's Karviná District, Moravian-Silesian Region. Both towns belonged to the historical region of Austrian Silesia and formerly as one town composed the capital of the region of Cieszyn Silesia.


Description.

The common madder can grow up to 1.5 m in height. The evergreen leaves are approximately 5–10 cm long and 2–3 cm broad, produced in whorls of 4–7 starlike around the central stem. It climbs with tiny hooks at the leaves and stems. The flowers are small (3–5 mm across), with five pale yellow petals, in dense racemes, and appear from June to August, followed by small (4–6 mm diameter) red to black berries. The roots can be over a metre long, up to 12 mm thick and the source of red dyes known as rose madder and Turkey red. It prefers loamy soils (sand and clay soil) with a constant level of moisture. Madder is used as a food plant by the larvae of some Lepidoptera species including the hummingbird hawk moth.

Uses.

It has been used since ancient times as a vegetable red dye for leather, wool, cotton and silk. For dye production, the roots are harvested after two years. The outer red layer gives the common variety of the dye, the inner yellow layer the refined variety. The dye is fixed to the cloth with help of a mordant, most commonly alum. Madder can be fermented for dyeing as well ("Fleurs de garance"). In France, the remains were used to produce a spirit.  The roots contain the acid ruberthyrin. By drying, fermenting, or a treatment with acids, this is changed to sugar, alizarin and purpurin, which were first isolated by the French chemist Pierre Jean Robiquet in 1826. Purpurin is normally not coloured, but is red when dissolved in alkaline solutions. Mixed with clay and treated with alum and ammonia, it gives a brilliant red colourant (madder lake).  The pulverised roots can be dissolved in sulfuric acid, which leaves a dye called "garance" (the French name for madder) after drying. Another method of increasing the yield consisted of dissolving the roots in sulfuric acid after they had been used for dyeing. This produces a dye called "garanceux". By treating the pulverized roots with alcohol, colorin was produced. It contained 40–50 times the amount of alizarin of the roots.  The chemical name for the pigment is alizarin, of the anthraquinone-group, and was used to make the alizarine ink in 1855 by Professor Leonhardi of Dresden, Germany. In 1869, the German chemists Graebe and Liebermann synthesised artificial alizarin, which was produced industrially from 1871 onwards, effectively ending the cultivation of madder. In the 20th century, madder was only grown in some areas of France.  The plant's roots contain several polyphenolic compounds, such as 1,3-Dihydroxyanthraquinone (purpuroxanthin), 1,4-Dihydroxyanthraquinone (quinizarin), 1,2,4-Trihydroxyanthraquinone (purpurin) and 1,2-dihydroxyanthraquinone (alizarin). This last compound gives it its red colour to a textile dye known as Rose madder. It was also used as a colourant, especially for paint, that is referred to as madder lake. The substance was also derived from another species, "Rubia cordifolia".

History.

Early evidence of dyeing comes from India where a piece of cotton dyed with madder has been recovered from the archaeological site at Mohenjo-daro (3rd millennium BCE). In Sanskrit, this plant is known by the name Manjishtha. It was used by hermits to dye their clothes saffron. Dioscorides and Pliny the Elder (De Re Natura) mention the plant (which the Romans called rubia passiva). In Viking Age levels of York, remains of both woad and madder have been excavated. The oldest European textiles dyed with madder come from the grave of the Merovingian queen Arnegundis in Saint-Denis near Paris (between 565 and 570 AD). In the "Capitulare de villis" of Charlemagne, madder is mentioned as "warentiam". The herbal of Hildegard of Bingen mentions the plant as well. The red coats of the British Redcoats were dyed with madder, after earlier being dyed with cochineal.. Madder is mentioned in the talmud (e.g., tractate Sabbath 61b) where the madder plant is termed "puah" in Arameic and translated into old French by Rashi (loc cit).  Turkey red was a strong, very fast red dye for cotton obtained from madder root via a complicated multistep process involving "sumac and oak galls, calf's blood, sheep's dung, oil, soda, alum, and a solution of tin." Turkey red was developed in India and spread to Turkey. Greek workers familiar with the methods of its production were brought to France in 1747, and Dutch and English spies soon discovered the secret. A sanitized version of Turkey red was being produced in Manchester by 1784, and roller-printed dress cottons with a Turkey red ground were fashionable in England by the 1820s.

Folk medicine.

According to Culpeper's herbal, the plant is ""an herb of Mars"" and ""hath an opening quality, and afterwards to bind and strengthen"". The root was recommended in the treatment of yellow jaundice, obstruction of the spleen, the melancholy humour, palsy, sciatica, and of bruises. The leaves were advised for women “"that have not their courses"” and for the treatment of freckles and other discolorations of the skin.

Risks.

Madder root may cause birth defects and miscarriages in humans when taken internally.

Rubia tinctorum, the rose madder or common madder or dyer's madder, is a herbaceous perennial plant species belonging to the bedstraw and coffee family Rubiaceae.


Branches of group representation theory.

The representation theory of groups divides into subtheories depending on the kind of group being represented. The various theories are quite different in detail, though some basic definitions and concepts are similar. The most important divisions are:  Representation theory also depends heavily on the type of vector space on which the group acts. One distinguishes between finite-dimensional representations and infinite-dimensional ones. In the infinite-dimensional case, additional structures are important (e.g. whether or not the space is a Hilbert space, Banach space, etc.).  One must also consider the type of field over which the vector space is defined. The most important case is the field of complex numbers. The other important cases are the field of real numbers, finite fields, and fields of p-adic numbers. In general, algebraically closed fields are easier to handle than non-algebraically closed ones. The characteristic of the field is also significant; many theorems for finite groups depend on the characteristic of the field not dividing the order of the group.

Definitions.

A representation of a group "G" on a vector space "V" over a field "K" is a group homomorphism from "G" to GL("V"), the general linear group on "V". That is, a representation is a map such that  Here "V" is called the representation space and the dimension of "V" is called the dimension of the representation. It is common practice to refer to "V" itself as the representation when the homomorphism is clear from the context.  In the case where "V" is of finite dimension "n" it is common to choose a basis for "V" and identify GL("V") with, the group of "n"-by-"n" invertible matrices on the field "K".

Examples.

Consider the complex number "u" = e which has the property "u" = 1. The cyclic group "C" = {1, "u", "u"} has a representation ρ on C given by:  This representation is faithful because ρ is a one-to-one map.  Another representation for "C" on C, isomorphic to the previous one, is σ given by:  The group "C" may also be faithfully represented on R by τ given by:  where

Reducibility.

A subspace "W" of "V" that is invariant under the group action is called a "subrepresentation". If "V" has exactly two subrepresentations, namely the zero-dimensional subspace and "V" itself, then the representation is said to be irreducible; if it has a proper subrepresentation of nonzero dimension, the representation is said to be reducible. The representation of dimension zero is considered to be neither reducible nor irreducible, just like the number 1 is considered to be neither composite nor prime.  Under the assumption that the characteristic of the field "K" does not divide the size of the group, representations of finite groups can be decomposed into a direct sum of irreducible subrepresentations (see Maschke's theorem). This holds in particular for any representation of a finite group over the complex numbers, since the characteristic of the complex numbers is zero, which never divides the size of a group.  In the example above, the first two representations given (ρ and σ) are both decomposable into two 1-dimensional subrepresentations (given by span{(1,0)} and span{(0,1)}), while the third representation (τ) is irreducible.

Generalizations.

Set-theoretical representations.

A "set-theoretic representation" (also known as a group action or "permutation representation") of a group "G" on a set "X" is given by a function ρ : "G" → "X", the set of functions from "X" to "X", such that for all "g", "g" in "G" and all "x" in "X":  where formula_11 is the identity element of "G". This condition and the axioms for a group imply that ρ("g") is a bijection (or permutation) for all "g" in "G". Thus we may equivalently define a permutation representation to be a group homomorphism from G to the symmetric group S of "X".  For more information on this topic see the article on group action.

Representations in other categories.

Every group "G" can be viewed as a category with a single object; morphisms in this category are just the elements of "G". Given an arbitrary category "C", a "representation" of "G" in "C" is a functor from "G" to "C". Such a functor selects an object "X" in "C" and a group homomorphism from "G" to Aut("X"), the automorphism group of "X".  In the case where "C" is Vect, the category of vector spaces over a field "K", this definition is equivalent to a linear representation. Likewise, a set-theoretic representation is just a representation of "G" in the category of sets.  When "C" is Ab, the category of abelian groups, the objects obtained are called "G"-modules.  For another example consider the category of topological spaces, Top. Representations in Top are homomorphisms from "G" to the homeomorphism group of a topological space "X".  Two types of representations closely related to linear representations are:

In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations (i.e. automorphisms) of vector spaces; in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. Representations of groups are important because they allow many group-theoretic problems to be reduced to problems in linear algebra, which is well understood. They are also important in physics because, for example, they describe how the symmetry group of a physical system affects the solutions of equations describing that system.


Early life and education.

Bill was born in Winterthur. After an apprenticeship as a silversmith during 1924–1927, Bill took up studies at the Bauhaus in Dessau under many teachers including Wassily Kandinsky, Paul Klee and Oskar Schlemmer from 1927 to 1929, after which he moved to Zurich.

Work.

Art and design.

After working on graphic designs for the few modern buildings being constructed, he built his first work, his own house and studio (1932–3) in Zurich-Höngg. From 1937 onwards he was a prime mover behind the Allianz group of Swiss artists.  Bill is widely considered the single most decisive influence on Swiss graphic design beginning in the 1950s with his theoretical writing and progressive work. His connection to the days of the Modern Movement gave him special authority. As an industrial designer, his work is characterized by a clarity of design and precise proportions. Examples are the elegant clocks and watches designed for Junghans, a long-term client. Among Bill's most notable product designs is the ""Ulmer Hocker"" of 1954, a stool that can also be used as a shelf element, a speaker's desk, a tablet or a side table. Although the stool was a creation of Bill and Ulm school designer Hans Gugelot, it is often called ""Bill Hocker"" because the first sketch on a cocktail napkin was Bill's work.  As a designer and artist, Bill sought to create forms which visually represent the New Physics of the early 20th century. He sought to create objects so that the new science of form could be understood by the senses: that is as a concrete art. Thus Bill is not a rationalist – as is typically thought – but rather a phenomenologist. One who understands embodiment as the ultimate expression of a concrete art. In this way he is not so much extending as re-interpreting Bauhaus theory. Yet curiously Bill's critical interpreters have not really grasped this fundamental issue. He made spare geometric paintings and spherical sculptures, some based on the Möbius strip, in stone, wood, metal and plaster. His architectural work included an office building in Germany, a radio studio in Zurich, and a bridge in eastern Switzerland.  He continued to produce architectural designs, such as those for a museum of contemporary art (1981) in Florence and for the Bauhaus Archive (1987) in Berlin. In 1982 he also entered a competition for an addition to the Neue Nationalgalerie in Berlin, built to a design by Mies van der Rohe. "Pavillon-Skulptur (1979–83)", a large granite sculpture, was installed adjacent to the Bahnhofstrasse, Zürich in 1983. As is often the case with modern art in public places, the installation generated some controversy. "Endlose Treppe" (1991), a sculpture made of North American granite, was designed for the philosopher Ernst Bloch.  In 1982 he was awarded the Sir Misha Black award and was added to the College of Medallists.

Teaching.

In 1944, Bill became a professor at the Kunstgewerbeschule Zürich. In 1953, alongside Inge Aicher-Scholl and Otl Aicher, he founded the Ulm School of Design (German: "Hochschule für Gestaltung - HfG Ulm") in Ulm, Germany, a design school initially created in the tradition of the Bauhaus and which later developed a new design education approach integrating art and science. The school was notable for its inclusion of semiotics as a field of study. The school closed in 1968. Faculty and students included Tomás Maldonado, Otl Aicher, Josef Albers, Johannes Itten, John Lottes, Walter Zeischegg, and Peter Seitz.  Bill was a professor at the Hochschule für bildende Künste Hamburg and chair of Environmental Design from 1967 to 1974. In 1973 he became an associate member of the Royal Flemish Academy of Science, Literature and Fine Art in Brussels. In 1976 he became a member of the Berlin Academy of Arts. In addition to his teaching, Bill wrote and lectured extensively on art, architecture and design, appearing at symposiums and design conferences around the world. In particular, he wrote books about Le Corbusier, Kandinsky, Ludwig Mies van der Rohe, and artistic theory.

Exhibitions.

Bill executed many public sculptures in Europe and exhibited extensively in galleries and museums, including a retrospective at the Kunsthaus Zürich in 1968–69. He had his first exhibition in the United States at the Staempfli Gallery in New York City in 1963 and was the subject of retrospectives at the Albright-Knox Art Gallery in Buffalo and the Los Angeles County Museum of Art in 1974, and the Solomon R. Guggenheim Museum in New York City in 1988. He participated in documentas I (1955), II (1959), and III (1964). In 1993, he received the Praemium Imperiale for sculpture, awarded by the Emperor of Japan.  Bill is credited with having been "the spark that lighted the fuse of Brazil's artistic revolution" and the country's "movement toward concrete art" with his 1951 retrospective at the São Paulo Museum of Modern Art. He strongly influenced Brazilian artists like Franz Weissmann.

Private life.

After a liaison with Nusch Éluard, Bill married the cellist and photographer Binia Mathilde Spoerri in January 1931. She died in 1988. From 1974 he was living together with art historian Angela Thomas; they married in 1991.  Bill was also involved in politics. He was elected to the Zurich municipal council in 1961. From 1967 to 1971, he served as a member of the Swiss National Council.  Bill died en route to a hospital after collapsing from a heart attack at Berlin Tegel Airport. He was 85 and lived in Zumikon, a Zürich suburb.  In 1996, Jakob Bill, the son of Max, founded the Swiss Max Bill Foundation ("max, binia + jakob bill stiftung") and implemented the idea of his father. The purpose of the foundation is to collect and take care of the works in possession of the Bill family, as well as the promotion of scientific research.

Max Bill (22 December 1908 – 9 December 1994) was a Swiss architect, artist, painter, typeface designer, industrial designer and graphic designer.


Meaning.

In object-oriented programming languages, and other related fields, encapsulation refers to one of two related but distinct notions, and sometimes to the combination thereof:  Some programming language researchers and academics use the first meaning alone or in combination with the second as a distinguishing feature of object-oriented programming, while some programming languages that provide lexical closures view encapsulation as a feature of the language orthogonal to object orientation.  The second definition is motivated by the fact that in many object-oriented languages, and other related fields, the components are not hidden automatically and this can be overridden; thus, information hiding is defined as a separate notion by those who prefer the second definition.  The features of encapsulation are supported using classes in most object-oriented languages, although other alternatives also exist.

Encapsulation and inheritance.

The authors of "Design Patterns" discuss the tension between inheritance and encapsulation at length and state that in their experience, designers overuse inheritance. They claim that inheritance often breaks encapsulation, given that inheritance exposes a subclass to the details of its parent's implementation. As described by the Yo-yo problem, overuse of inheritance and therefore encapsulation, can become too complicated and hard to debug.

Information hiding.

Under the definition that encapsulation "can be used to hide data members and member functions", the internal representation of an object is generally hidden from view outside of the object's definition. Typically, only the object's own methods can directly inspect or manipulate its fields. Hiding the internals of the object protects its integrity by preventing users from setting the internal data of the component into an invalid or inconsistent state. A supposed benefit of encapsulation is that it can reduce system complexity, and thus increase robustness, by allowing the developer to limit the interdependencies between software components.  Some languages like Smalltalk and Ruby only allow access via object methods, but most others (e.g., C++, Delphi or Java) offer the programmer a degree of control over what is hidden, typically via keywords like codice_1 and codice_2. ISO C++ standard refers to codice_3, codice_2 and codice_1 as "access specifiers" and that they do not "hide any information". Information hiding is accomplished by furnishing a compiled version of the source code that is interfaced via a header file.  Almost always, there is a way to override such protection – usually via reflection API (Ruby, Java, C#, etc.), sometimes by mechanism like name mangling (Python), or special keyword usage like codice_6 in C++.

Examples.

Restricting data fields.

Languages like C++, C#, Java, PHP, Swift, and Delphi offer ways to restrict access to data fields.  Below is an example in C# that shows how access to a data field can be restricted through the use of a codice_2 keyword:  class Program {  Below is an example in Java: public class Employee {  Encapsulation is also possible in non-object-oriented languages. In C, for example, a structure can be declared in the public API via the header file for a set of functions that operate on an item of data containing data members that are not accessible to clients of the API with the codice_8 keyword.  // Header file "api.h"  struct Entity; // Opaque structure with hidden members  // API functions that operate on 'Entity' objects extern struct Entity * open_entity(int id); extern int process_entity(struct Entity *info); extern void close_entity(struct Entity *info); // extern keywords here are redundant, but don't hurt. // extern defines functions that can be called outside the current file, the default behavior even without the keyword Clients call the API functions to allocate, operate on, and deallocate objects of an opaque data type. The contents of this type are known and accessible only to the implementation of the API functions; clients cannot directly access its contents. The source code for these functions defines the actual contents of the structure:  // Implementation file "api.c"  struct Entity {  // API function implementations struct Entity * open_entity(int id)  int process_entity(struct Entity *info)  void close_entity(struct Entity *info)

Name mangling.

Below is an example of Python, which does not support variable access restrictions. However, the convention is that a variable whose name is prefixed by an underscore should be considered private. class Car(object): redcar = Car() redcar.drive() # This will print 'Maximum speed is 200.'  redcar._maxspeed = 10 redcar.drive() # This will print 'Maximum speed is 10.'

In object-oriented programming (OOP), encapsulation refers to the bundling of data with the methods that operate on that data, or the restricting of direct access to some of an object's components. Encapsulation is used to hide the values or state of a structured data object inside a class, preventing unauthorized parties' direct access to them. Publicly accessible methods are generally provided in the class (so-called "getters" and "setters") to access the values, and other client classes call these methods to retrieve and modify the values within the object.


Pre-Revolution.

Prince Lvov was born in Dresden, Germany, and descended from the sovereign Rurik dynasty princes of Yaroslavl. His family moved home to Popovka in the Aleksin district of Tula Governorate from Germany soon after his birth. He graduated from the University of Moscow with a degree in law, then worked in the civil service until 1893. During the Russo-Japanese War he organized relief work in the East and in 1905 joined the liberal Constitutional Democratic Party. A year later he won election to the First Duma, and was nominated for a ministerial position. He became chairman of the All-Russian Union of Zemstvos in 1914, and in 1915 he became a leader of the Union of Zemstvos as well as a member of Zemgor, a joint committee of the Union of Zemstvos and the Union of Towns that hecember 1916, after Prince Lvov's tirades at the Congress of Zemstvos, the Voluntary Organisations would allow no one to work for the government unless thelped supply the military and tend to the wounded from World War I. In Deir collaboration were purchased by political concessions.  He married Countess Julia Alexeievna Bobrinskaya (1867–1903), great-great-granddaughter of Grigory Orlov and Catherine the Great, without issue.

Later years.

During the first Russian Revolution and the abdication of Nicholas II, emperor of Russia, Lvov was made head of the provisional government founded by the Duma on 2 March. Unable to rally sufficient support, he resigned in July 1917 in favour of his Minister of War, Alexander Kerensky.  After the October Revolution he settled in Tyumen. In the winter of 1917 he was arrested and transferred to Yekaterinburg. Three months later, Lvov and two other prisoners (Lopukhin and Prince Golitsyn) were released before the court under a written undertaking not to leave the place. The local war commissar, Filipp Goloshchekin, intended to execute Lvov and the other prisoners, but was ordered not to by Isaac Steinberg, the People's Commissar for Justice, a Left-Socialist Revolutionary while they were still in coalition with the Bolsheviks. Lvov immediately left Yekaterinburg, made his way to Omsk, occupied by the anti-Bolshevik Czechoslovak Legion. The Provisional Siberian Government, headed by Pyotr Vologodsky, was formed in Omsk and instructed Lvov to leave for the United States (since it was believed that this country was capable of providing the fastest and most effective assistance to anti-Bolshevik forces) to meet with President Woodrow Wilson and other statesmen to inform them on the aims of the anti-Soviet forces and receiving assistance from former allies of Russia in the First World War. In October 1918 he came to the United States but was late as in November of the same year the First World War ended and preparations began for the peace conference in Paris, where the centre of world politics moved.  Having failed to achieve any practical results in the USA, Lvov returned to France, where in 1918–1920 he was at the head of the Russian political meeting in Paris. He was at the source of the labor exchanges system to help Russian emigrants, transferred to their disposal the funds of Zemgor, stored in the National Bank of the United States. Later he left politics, living in Paris in poverty, working at handicraft and writing his memoirs.

Memorials.

There is a memorial to Prince Lvov in Aleksin as well as a small exhibition on him in the town museum. In Popovka there is another memorial opposite his local church and a plaque on the wall of the local school he founded. He died in Boulogne-sur-Seine and is buried in Sainte-Geneviève-des-Bois Russian Cemetery in France.  A relative of his by the name of Prince Andre Nikita Lwoff (1901–1933), variously described as either Georgy Lvov's son or nephew, is buried in the old cemetery in Menton.

Further reading.

Lvov wrote an autobiography, 'Воспоминания' ("Memories"), while in exile and a biography was also written in 1932 by Tikhon Polner entitled 'Жизненный путь князя Георгія Евгеніевича Львова. Личность. Взгляды. Условія дѣятельности' ("The Life Course of Prince Georgy Yevgenievich Lvov. Personality. Views. Conditions of Activity"). Neither has been translated but both have been reprinted and are still available in Russian.

Notes.

Note on transliteration: An older French form, Lvoff, is used on his tombstone. Georgy can be written as Georgi and is sometimes seen in its translated form, George or Jorge.

Prince Georgy Yevgenyevich Lvov (; 7/8 March 1925) was a Russian statesman and the first post-imperial prime minister of Russia, from 15 March to 21 July 1917.


Location.

The region is only accessible for a few months of the year. Being situated in the rain shadow to the northeast of the Vatnajökull glacier, the area receives only about 450 mm of rainfall annually. The area was used during training for the Apollo program to prepare astronauts for the lunar missions. Their main objective in Askja was to study geology.

Eruptions.

Askja was virtually unknown until the tremendous eruption which started on March 29, 1875. Especially in the eastern fjords of Iceland, the ashfall was heavy enough to poison the land and kill livestock. Ash, or tephra from this eruption was wind-blown to Norway, Sweden, Germany and Poland. The eruption triggered a substantial wave of emigration from Iceland. Another less well-known eruption, called Askja-S, occurred in the early Holocene, ca 11,000 years ago. Tephra from this eruption has been found in south-east Sweden, Northern Ireland and north Norway and recently as far south as Romania, which makes it one of the most far-travelled Icelandic tephras. The last eruption of Askja was in 1961.  The outer caldera of Askja, representing a prehistoric eruption, is about 50 km2, and there is evidence of other later caldera-forming events within it. The main crater floor lies at about 1,100 m.  In June 2010, Volcano expert Hazel Rymer said seismic activity was increasing at Askja and that an eruption could be around the corner The increased earthquake activity is located to the northeast of the central volcano, in the direction of Herðubreið. It was ruled out that any activity from Eyjafjallajökull was responsible for the increase in activity at Askja. The news came as scientists continue to watch Katla.  In early April 2012 it was noted that the lake in the caldera was totally clear of ice, which usually does not happen until in June or July in a normal year. It is believed that increased geothermal activity in the volcano is heating the lake. Travel in the area was restricted until further research could be carried out.

Öskjuvatn lake.

Öskjuvatn is a large lake that fills much of the smaller caldera resulting from the 1875 eruption. Its surface lies about 50 m below the level of the main caldera floor and covers about 12 km2. When the lake originally formed it was warm, but today it is frozen over for most of the year. Öskjuvatn is the second deepest lake in Iceland at 220 m deep.

Missing scientists.

In 1907, the German scientists Walter von Knebel and Max Rudloff visited Askja to study the caldera. While exploring Öskjuvatn in a small boat, they disappeared without a trace. Von Knebel's fiancée Ina von Grumbkow led an expedition to search for them, but no indication of what happened to them was ever found. Recent observations on the effects of a landslide, on 21 July 2014, has led to renewed speculation that the scientists were killed by a similar sudden event, a massive wave similar to the one estimated to be 30 meters high seen in 2014.

Sights and tourism in the area.

In the Dyngjufjöll mountains which surround the Askja caldera can be found the impressive "Drekagil", the canyon of dragons. Not far from Askja, there are two other interesting volcanic systems: Herðubreið and Kverkfjöll.  Askja is a popular tourist destination. There are two mountain huts and a campsite at Dreki, by Drekagil, which is about 100 km by a 4x4 F-road, from the Icelandic ring-road. The road continues 8 km up from Dreki into the Askja caldera. It is a walk of about 2.5 km from the car park to Öskjuvatn and Víti. The roads are usually only open for about three to four months, from late June until early October.

Askja () is an active volcano situated in a remote part of the central highlands of Iceland. The name Askja refers to a complex of nested calderas within the surrounding Dyngjufjöll mountains, which rise to, "askja" meaning "box" or "caldera" in Icelandic


Early life.

Signoret was born Simone Henriette Charlotte Kaminker in Wiesbaden, Germany, to André and Georgette (Signoret) Kaminker, as the eldest of three children, with two younger brothers. Her father, a pioneering interpreter who worked in the League of Nations, was a French-born army officer from a Polish Jewish family, who brought the family to Neuilly-sur-Seine on the outskirts of Paris. Her mother, Georgette, from whom she acquired her stage name, was a French Catholic.  Signoret grew up in Paris in an intellectual atmosphere and studied English, German and Latin. After completing secondary school during the Nazi occupation, Simone was responsible for supporting her family and forced to take work as a typist for a French collaborationist newspaper, "Les nouveaux temps", run by Jean Luchaire.

Career.

During the German occupation of France, Signoret mixed with an artistic group of writers and actors who met at the Café de Flore in the Saint-Germain-des-Prés quarter. By this time, she had developed an interest in acting and was encouraged by her friends, including her lover, Daniel Gélin, to follow her ambition. In 1942, she began appearing in bit parts and was able to earn enough money to support her mother and two brothers as her father, who was a French patriot, had fled the country in 1940 to join General De Gaulle in England. She took her mother's maiden name for the screen to help hide her Jewish roots.  Signoret's sensual features and earthy nature led to type-casting and she was often seen in roles as a prostitute. She won considerable attention in "La Ronde" (1950), a film which was banned briefly in New York as immoral. She won further acclaim, including an acting award from the British Film Academy, for her portrayal of another prostitute in Jacques Becker's "Casque d'or" (1951). She appeared in many notable films in France during the 1950s, including "Thérèse Raquin" (1953), directed by Marcel Carné, "Les Diaboliques" (1954), and "The Crucible" ("Les Sorcières de Salem"; 1956), based on Arthur Miller's "The Crucible". In 1958, Signoret acted in the English independent film, "Room at the Top" (1959), which won her numerous awards including the Best Female Performance Prize at Cannes and the Academy Award for Best Actress. She was the only French cinema actress to receive an Oscar until Juliette Binoche in 1997 (Supporting Actress) and Marion Cotillard in 2008 (Best Actress), and the first woman to win the award appearing in a foreign film. She was offered films in Hollywood, but turned them down, continuing to work in France and England—notably opposite Laurence Olivier in "Term of Trial" (1962)—until 1965. Earning another Oscar nomination for her work on what would be Vivien Leigh's final film—Columbia Pictures' "Ship of Fools", also starring Lee Marvin—Signoret appeared in a few other Hollywood films before returning to France in 1969.  In 1962, Signoret translated Lillian Hellman's play "The Little Foxes" into French for a production in Paris that ran for six months at the Theatre Sarah-Bernhardt. She played the Regina role as well. Hellman was displeased with the production, although the translation was approved by scholars selected by Hellman.  Signoret's one attempt at Shakespeare, performing Lady Macbeth opposite Alec Guinness at the Royal Court Theatre in London in 1966 proved to be ill-advised, with some harsh critics; one referred to her English as "impossibly Gallic".  Signoret was never concerned with glamour, ignored sexist and ageist insults and continued giving finely etched performances. She won more acclaim for her portrayal of a weary madam in "Madame Rosa" (1977) and as an unmarried sister who unknowingly falls in love with her paralyzed brother via anonymous correspondence in "" (1980). She was in many movies up to her death in 1985.

Personal life.

Signoret's memoirs, "Nostalgia Isn't What It Used To Be", were published in 1978. She also wrote a novel, "Adieu Volodya", published in 1985, the year of her death.  Signoret first married filmmaker Yves Allégret (1944–49), with whom she had a daughter Catherine Allégret, herself an actress. Her second marriage was to the Italian-born French actor Yves Montand in 1951, a union which lasted until her death. They had no children.  Signoret died of pancreatic cancer in Autheuil-Authouillet, France, aged 64. She was buried in Père Lachaise Cemetery in Paris and Yves Montand was later buried next to her.

Television award.

Emmy Awards

Simone Signoret (; 25 March 192130 September 1985) was a French cinema actress often hailed as one of France's greatest film stars. She became the second French person to win an Academy Award, for her role in "Room at the Top" (1959).


Life & career.

He was Chairman from 1953-1959 of the "Deutsche Gesellschaft für Soziologie".  In 1959 he became foreign member of the Royal Netherlands Academy of Arts and Sciences.

Philosophy.

Plessner's material(ist) "a priori".

Plessner developed a philosophical biology and anthropology which amounted to a hermeneutics of nature. According to Plessner, life expresses itself, and part of this expression is in terms of sentient lifeforms. In expressing itself through the human senses, it provides the (material) "a priori" constituents of perception (to replace Kant's cognitive idealism of "a priori" categories and intuitions produced by transcendental subjectivity as the filter through which we spontaneously order experience of the world). In other words, the formal qualities that make up our consciousness "a priori" — given as the conditions through which we experience things — conditions such as time, space, causality and number, and, indeed, the laws of physics, however we may then conceptualize them, are given to us both in our own physical nature, and in the physical nature of the environments we inhabit, through our growth from and interactions within these environments.

The three categories of nature's "a priori" and the "eccentricity" of human intentionality.

From Husserl and Scheler, Plessner adapted the idea of the intentionality of consciousness away from the need for a transcendental ego or apperception and instead grounds it in the behaviour (in the broadest sense of the term) of environmentally interactive organisms as a realizing of borders that represents the point where the impulses or growth of organisms meet with their environments, are realized in the act of self-positioning. These are the scopes of action and understanding that define consciousness and which at the same time ground it in the material world of nature. In terms of plants, their self-expression is utterly open—their borders are defined by only very simple forms of feedback, and the plant has no ability to express intentional preferences regarding its environment; animals, on the other hand, are aware of their own borders and are constantly pressed back within them, thus exhibiting a closed kind of intentionality trapped by its own borders, this is the limit of their expression; finally, humans alternate between open and closed intentionality — we "are" these borders, but also, we "have" them, and the limits of these borders of human action, influence and being Plessner described as the "eccentricity" of human intentionality in its environmental relations and determination. For Plessner, our own subjectivity can be understood in terms of the expressive "a priori" in nature, and our experience of and relationship to it.

Wiesbadener Helmuth Plessner Preis.

The city of Wiesbaden has created an award in honor of Helmuth Plessner in 2014. It serves to promote and appreciate excellent scientists and intellectuals who have worked and work in reference to Plessner. It is awarded every three years and is donated with 20,000 euros. The first prizewinner is Michael Tomasello.

Helmuth Plessner (4 September 1892, Wiesbaden – 12 June 1985, Göttingen) was a German philosopher and sociologist, and a primary advocate of "philosophical anthropology".


Geography.

Issyk-Kul Lake is long, up to wide, and its area is. It is the second-largest mountain lake in the world behind Lake Titicaca in South America. It is at an altitude of, and reaches in depth.  About 118 rivers and streams flow into the lake; the largest are the Djyrgalan and Tyup. It is fed by springs, including many hot springs, and snow melt. The lake has no current outlet, but some hydrologists hypothesize that the lake's water filters deep underground into the Chu River. The bottom of the lake contains the mineral monohydrocalcite: one of the few known lacustrine deposits.  The lake's southern shore is dominated by the ruggedly beautiful Teskey Ala-Too Range of the Tian Shan mountains. The Kungey Alatau of the Tian Shan runs parallel to the north shore.  The lake water's salinity is approx. 0.6% – compared to 3.5% salinity of typical seawater – and, although the lake level is still currently some 8 metres (26 ft) higher than in medieval times, its level now drops by approximately per year due to water diversion.  Administratively, the lake and the adjacent land are within Issyk-Kul Region of Kyrgyzstan.

Tourism.

During the Soviet era, the lake became a popular vacation resort, with numerous sanatoria, boarding houses and vacation homes along its northern shore, many concentrated in and around the town of Cholpon-Ata. These fell on hard times after the break-up of the USSR, but now hotel complexes are being refurbished and simple private bed-and-breakfast rentals are being established for a new generation of health and leisure visitors.  The city of Karakol (formerly Przhevalsk, after the Russian explorer Przhevalsky, who died there) is the administrative seat of Issyk-Kul Region of Kyrgyzstan. It is near the east tip of the lake and is a good base for excursions into the surrounding area. Its small old core contains an impressive wooden mosque, built without metal nails by the Dungan people, and a wooden Orthodox church that was used as a stable during Soviet times (see state atheism).

History.

Issyk-Kul Lake was a stopover on the Silk Road, a land route for travelers from the Far East to Europe. The great Chinese Buddhist scholar-monk Xuanzang passed by this lake and noted the details in the classic travelogue "Great Tang Records on the Western Regions" in the 7th century. The Lake was once owned by the Qing Dynasty of China and was ceded to Russia – along with the surrounding territory – after the Treaty of Tarbagatai. Many historians believe that the lake was the point of origin for the Black Death that plagued Europe and Asia during the early and mid-14th century. The lake's status as a byway for travelers allowed the plague to spread across these continents via medieval merchants who unknowingly carried infested vermin along with them. The lake level is some higher than in medieval times. Divers have found the remains of submerged settlements in shallow areas around the lake. In December 2007, a report was released by a team of Kyrgyz historians, led by Vladimir Ploskikh, vice president of the Kyrgyz Academy of Sciences, that archaeologists have discovered the remains of a 2500-year-old advanced civilization at the bottom of the Lake. The data and artifacts obtained suggest that the ancient city was a metropolis in its time. The discovery consisted of formidable walls, some stretching for and traces of a large city with an area of several square kilometers. Other findings included Scythian burial mounds eroded over the centuries by waves, and numerous well-preserved artifacts, including bronze battleaxes, arrowheads, self-sharpening daggers, objects discarded by smiths, casting molds, and money.  Articles identified as the world's oldest extant coins were found underwater, with gold wire rings used as small change and a large hexahedral goldpiece. Also found was a bronze cauldron with a level of craftsmanship that is today achieved by using an inert gas environment.  In 1916 the monastery at Issyk-Kul was attacked by Kyrgyz rebels, and seven monks were killed.

Environment.

Specially protected areas.

The first nature reserve in Kyrgyzstan, Issyk-Kul State Reserve was established in 1948 to protect unique nature landscapes and waterfowl at Issyk-Kul. In 1975, it was acknowledged as a Ramsar site. Biosphere Reserve Issyk-Kul covered by UNESCO World Network of Biosphere Reserves was established in year 2000 within the administrative borders of Issyk-Kul Region.

Fish.

The lake contains highly endemic fish biodiversity, and some of the species, including four endemics, are seriously endangered. In recent years catches of all species of fish have declined markedly, due to a combination of over-fishing, heavy predation by two of the introduced species (the Pike perch and the Rainbow trout), and the cessation of lake restocking with juvenile fish from hatcheries. At least four commercially targeted endemic fish species are sufficiently threatened to be included in the Red Book of the Kyrgyz Republic: Schmidt's dace ("Leuciscus schmidti"), Issyk-Kul dace ("Leuciscus bergi"), marinka ("Schizothorax issyk-kuli"), and sheer or naked osman ("Diptychus dybovskii"). Seven other endemic species are almost certainly threatened as by-catch or are indirectly impacted by fishing activity and changes to the structure and balance of the lake's fish population.  Sevan trout, a fish endemic to Lake Sevan in Armenia, was introduced into Issyk-Kul in the 1970s. While this fish is an endangered species in its "home" lake, it has a much better chance to survive in Lake Issyk-Kul where it has ravaged the indigenous species.

Creation legend.

In pre-Islamic legend, the king of the Ossounes had donkey's ears. He would hide them, and had his barbers killed to hide his secret. One barber yelled the secret into a well, but he did not cover the well afterwards. As a result, the well water rose and flooded the kingdom. The kingdom is today under the waters of Issyk-Kul. According to the legend, this is how the lake was formed. Other legends say that four drowned cities lie at the bottom of the lake. Substantial archaeological finds indicating the presence of an advanced civilization in ancient times have been made in shallow waters of the lake.

Russian Navy test site.

During the Soviet period, the Soviet Navy operated an extensive facility at the lake's east end, where submarine and torpedo technology was evaluated. In March 2008, Kyrgyz newspapers reported that around the Karabulan Peninsula on the lake would be leased for an indefinite period to the Russian Navy, which is planning to establish new naval testing facilities as part of the 2007 bilateral Agreement on Friendship, Cooperation, Mutual Help, and Protection of Secret Materials. The Russian military will pay $4.5 million annually to lease the area. India also plans to invest in the facility to test all types of torpedoes such as heavy weight torpedoes and those that have thermal navigation system. Another advantage that works for the testing center is that the torpedoes fired can also be recovered allowing scientists to make physical verification of a torpedo structure for further study. India is also planning to use the torpedo test facility to test the autonomous underwater vehicle being developed by NSTL. For this, India has proposed to engage local companies with know-how in torpedo technology to further co-develop the facility.

Lakeside towns.

Towns and some villages around the lake, listed clockwise from the lake's western tip:

Issyk-Kul (also Ysyk Köl, Issyk-Kol:,,, ;, ) is an endorheic lake in the northern Tian Shan mountains in eastern Kyrgyzstan. It is the seventh deepest lake in the world, the tenth largest lake in the world by volume (though not in surface area), and the second largest saline lake after the Caspian Sea. Issyk-Kul means "warm lake" in the Kyrgyz language; although it is surrounded by snow-capped peaks, it never freezes.


Life and career.

Bülow was born in Dresden, to members of the prominent Bülow family. From the age of nine, he was a student of Friedrich Wieck (the father of Clara Schumann). However, his parents insisted that he study law instead of music, and they sent him to Leipzig. There he met Franz Liszt, and on hearing some music of Richard Wagner—specifically, the premiere of "Lohengrin" in 1850—he decided to ignore the dictates of his parents and make himself a career in music instead. He studied the piano in Leipzig with the famous pedagogue Louis Plaidy. He obtained his first conducting job in Zurich, on Wagner's recommendation, in 1850.  Bülow had a strongly acerbic personality and a loose tongue; this alienated many musicians whom he worked with. He was dismissed from his Zurich job for this reason, but at the same time he was beginning to win renown for his ability to conduct new and complex works without a score. In 1851, he became a student of Liszt, marrying his daughter Cosima in 1857. They had two daughters: Daniela, born in 1860 and Blandina, born in 1863. During the 1850s and early 1860s he was active as a pianist, conductor, and writer, and became well known throughout Germany as well as Russia. In 1857, he premiered Liszt's Piano Sonata in B minor in Berlin.  In 1864 he became the Hofkapellmeister in Munich, and it was at this post he achieved his principal renown. He conducted the premieres of two Wagner operas, "Tristan und Isolde" and "Die Meistersinger von Nürnberg", in 1865 and 1868 respectively; both were immensely successful. Meanwhile, however, Cosima had been carrying on an affair with Richard Wagner and gave birth to their daughter Isolde in 1865. Two years later, they had another daughter, Eva. Although Cosima and Wagner's affair was now open knowledge, Bülow still refused to grant his wife a divorce. Finally, she gave birth to one final child––a son, Siegfried––and it was only then that the conductor at last relented. Their divorce was finalized in 1870, after which Cosima and Wagner married. Bülow never spoke to Wagner again and he did not see his former wife for 11 years afterwards, although he apparently continued to respect the composer on a professional level, as he still conducted his works and mourned Wagner's death in 1883. In July 1882 he married the actress Marie Schanzer.  In 1867 Bülow became director of the newly reopened Königliche Musikschule in Munich. He taught piano there in the manner of Liszt. He remained as director of the Conservatory until 1869. Bülow's students in Berlin included Asger Hamerik and Joseph Pache.  In addition to championing the music of Wagner, Bülow was a supporter of the music of both Brahms and Tchaikovsky. He was the soloist in the world premiere of the Tchaikovsky Piano Concerto No. 1 in B-flat minor in Boston in 1875. He was also a devotee of Frédéric Chopin's music; he came up with epithets for all of Chopin's Opus 28 Preludes, but these have generally fallen into disuse. On the other hand, the D-flat major Prelude No. 15 is widely known by his title, the "Raindrop."  He was the first to perform (from memory) the complete cycle of Beethoven's piano sonatas, and with Sigmund Lebert, he co-produced an edition of the sonatas.  For the winter season of 1877–1878 he was appointed as conductor of the orchestral subscription concerts presented at the newly opened St Andrew's Hall in Glasgow by Glasgow Choral Union, touring with their orchestra to repeat these programmes in other Scottish cities. Among the works he conducted there was the recently revised version of Brahms Symphony No 1.  From 1878 to 1880 he was Hofkapellmeister in Hanover but was forced to leave after fighting with a tenor singing the "Knight of the Swan ["Schwan"]" role in "Lohengrin"; Bülow had called him the "Knight of the Swine ["Schwein"]". In 1880 he moved to Meiningen where he took the equivalent post, and where he built the Meiningen Court Orchestra into one of the finest in Germany; among his other demands, he insisted that the musicians learn to play all their parts from memory.  It was during his five years in Meiningen that he met Richard Strauss (though the meeting actually took place in Berlin). His first opinion of the young composer was not favorable, but he changed his mind when he was confronted with a sample of Strauss's "Serenade". Later on, he used his influence to give Strauss his first regular employment as a conductor. Like Strauss, Bülow was attracted to the ideas of Max Stirner, whom he reputedly had known personally. In April 1892 Bülow closed his final performance with the Berlin Philharmonic (where he had been serving as Principal Conductor since 1887) with a speech "exalting" the ideas of Stirner. Together with John Henry Mackay, Stirner's biographer, he placed a memorial plaque at Stirner's last residence in Berlin.  Some of his orchestral innovations included the addition of the five-string bass and the pedal timpani; the pedal timpani have since become standard instruments in the symphony orchestra. His accurate, sensitive, and profoundly musical interpretations established him as the prototype of the virtuoso conductors who flourished at a later date. He was also an astute and witty musical journalist.  In the late 1880s he settled in Hamburg, but continued to tour, both conducting and performing on the piano.  Bülow suffered from chronic neuralgiforme headaches, which were caused by a tumor of the cervical radicular nerves. After about 1890 his mental and physical health began to fail, and he sought a warmer, drier climate for recovery; he died in a hotel in Cairo, Egypt at the age of 64, only ten months after his final concert performance.

Hans Guido Freiherr von Bülow (January 8, 1830February 12, 1894) was a German conductor, virtuoso pianist, and composer of the Romantic era. As one of the most distinguished conductors of the 19th century, his activity was critical for establishing the successes of several major composers of the time, especially Richard Wagner and Johannes Brahms. Alongside Carl Tausig, Bülow was perhaps the most prominent of the early students of Hungarian virtuoso pianist, conductor and composer Franz Liszt—therein performed the first public performance of Liszt's Sonata in B minor in 1857. He became acquainted with, fell in love and eventually married Liszt's daughter Cosima, who later left him for Wagner. Noted for his interpretation of the works of Ludwig van Beethoven, he was one of the earliest European musicians to tour the United States.


Location.

Located approximately 40 km north of the Red Sea, Yotvata is the first, biggest, and most prosperous Kibbutz in Hevel Eilot Regional Council. Being relatively far from major urban centers (41 kilometers north of Eilat and 130 kilometers south of Dimona), it is the center of the region, where most regional facilities are based: regional school, regional council offices, community center, sports center, movies and concerts hall and local airfield.

History.

Establishment.

Yotvata started in 1951 as a Nahal settlement named Ein Radian. In 1957 it was established as the first kibbutz in the southern Arabah region by Ihud HaKvutzot VeHaKibbutzim. The kibbutz is named after an Israelite encampment mentioned in Numbers 33:34 and Deuteronomy 10:7: "...from there they went to Gudgodah, and then to Jotbatha, a land of streaming water." Althme debates over the exact location of the biblical Yotvata (some say that it is closer to the Red Sea near Taba), the idea of a desert oasis for Israelis was in the founders' mind; the local oasis was the Ein Radian wellspring.  The founders, a small group of men and women 20 years of age and just out of the military service, decided to pursue a life of pioneering and built their home in the desert. They had massive challenges presented by the desert: the burning sun, the heat, shortage of water, salty land and water, limited transportation and no secure source of income. They started making all kinds of agricultural trials growing grapes, pomegranates and vegetables; they raised cattle and chickens - all with little success. The dates plantation proved more suitable to the arid conditions.  And then came the initiative to found a dairy that would provide milk to Eilat, which was expected to grow rapidly. Breeding milking cows in the desert was considered an impossible mission. In 1962 the dairy was founded, with four cows, the member who led the vision and the operation was "Ori Horazo (1939-1966)". The members tried to get funds from the Jewish Agency, but failed. Eventually, they received funding from the Israeli Trade and Industry Minister, Pinhas Sapir. In the first year, the dairy produced 500,000 liters of milk. By 2008, it was producing 62 million liters a year and controlled 63% of the Israeli dairy beverages market (making NIS400 million a year), and 49% of the fortified milk market (making NIS 250 million a year). It employed 130 workers and had 700 cows. The dairies of Kibbutz Yahel, Lotan, and Ketura provide milk for Yotvata.  In 1960 the first children of the community were born, and six years later the school opened with three first graders; today there are 200 kids in the kibbutz, and 600 students from all of the region communities attend Maale Shaharut School (from 1st to 12th grades) in Yotvata.

Archaeology.

Judging by the numerous historic forts surrounding the Kibbutz, Yotvata's location was a strategic one:

Economy and community.

Yotvata is a cooperative community, where most adult residents work on the kibbutz in production, services or education. The revenues are equally distributed among the members regardless of their position, along the idea of "each one gives as much as he can and gets as much as he needs". Most of daily affairs are conducted communally - education, holidays, dining (three meals a day conducted in the commune dining-room are giving the community more relaxed time to get together) and more.  Yotvata Dairy is a milk products factory which provides the kibbutz with its main source of income and occupies the highest number of members.  Agriculture ranks second in terms of income but perhaps first in importance to the community character and pride. Agriculture branches are irrigated land (onions, potatoes, corn, animal feed, garlic and pumpkins), plantations (dates and mangos) and a big and modern dairy farm.  There is also a big road stop shop on the Arabah Road providing refreshments for travelers.  Other small branches are a picturesque horse stable that lies in the date plantation east to the kibbutz and few artistic studios.  All members take turns contributing to the kibbutz service branches - kitchen, dining-room, laundry, security, etc.  The kibbutz gets all its drinking and irrigation water from aquifer wells in the Arabah valley.

Attractions.

Yotvata Hai-Bar Nature Reserve is dedicated to reintroducing extinct species mentioned in the Bible, as well as other endangered desert animals, to the wild. It has three parts: a park for herbivorous animals; the Predators Center that displays reptiles, small desert animals and large predators; and the Desert Night Life Exhibition Hall to observe nocturnal animals during their active hours.  15 km south of Yotvata lies Timna valley, where the sandstone and calcareous rock formations present some breathtaking desert features such as the Solomon's Pillars, Mushrooms, Arches and more. Timna is also known for its ancient copper mines.  The area provides many great desert walks including canyons, roman routes, sand dunes, fossil hunting, rock-climbing and more.

Yotvata (, ) is a kibbutz in southern Israel. Located on the Arabah road in the southern Negev, it falls under the jurisdiction of Hevel Eilot Regional Council. In it had a population of.


Biography.

Early life.

Torquemada was born on October 14, 1420, either in Valladolid, in the Kingdom of Castile, or in the nearby village of Torquemada. He came from a family of conversos (converts from Judaism); his uncle, Juan de Torquemada, was a celebrated theologian and cardinal, whose grandmother was a "conversa." The 15th Century chronicler Hernando del Pulgar, a contemporary to de Torquemada and himself a "converso", recorded that Tomás de Torquemada's uncle, Juan de Torquemada, had an ancestor, Álvar Fernández de Torquemada, who was married to a first-generation "conversa".  Torquemada entered the local San Pablo Dominican monastery at a very young age. As a zealous advocate of church orthodoxy, he earned a solid reputation for learning, piety, and austerity. As a result, he was promoted to prior of the monastery of Santa Cruz at Segovia. Around this time, he met the young Princess Isabella I, and the two immediately established religious and ideological rapport. For a number of years, Torquemada served as her regular confessor and personal advisor. He was present at Isabella's coronation in 1474, remained her closest ally and supporter and even advised her to marry King Ferdinand of Aragon in 1469 to consolidate their kingdoms and form a power base he could draw on for his own purposes.

Establishment of the Holy Office of the Inquisition.

Torquemada deeply feared the Marranos and Moriscos as a menace to Spain's welfare by both their increasing religious influence and their economic domination of Spain. The Crown of Aragon had Dominican inquisitors almost continuously throughout much of the 14th and the 15th centuries. King Ferdinand and Queen Isabella petitioned Pope Sixtus IV to grant their request for a Holy Office to administer an inquisition in Spain. The Pope granted their request and established the Holy Office for the Propagation of the Faith in late 1478.  The papal bull gave the sovereigns full powers to name inquisitors. Rome retained the right to formally appoint the royal nominees. Henry Charles Lea observed that the Spanish Inquisition in both Castile and Aragon remained firmly under Ferdinand's direction throughout the joint reign.

Grand Inquisitor.

The Pope went on to appoint a number of inquisitors for the Spanish Kingdoms in early 1482, including Torquemada. A year later he was named Grand Inquisitor of Spain, which he remained until his death in 1498. In the fifteen years under his direction, the Spanish Inquisition grew from the single tribunal at Seville to a network of two dozen Holy Offices. As Grand Inquisitor, Torquemada reorganized the Spanish Inquisition (originally based in Castile in 1478), establishing tribunals in Sevilla, Jaén, Córdoba, Ciudad Real and (later) Saragossa. His quest was to rid Spain of all heresy. The Spanish chronicler Sebastián de Olmedo called him "the hammer of heretics, the light of Spain, the savior of his country, the honor of his order."  Torquemada saw that the condemned were made to wear a sanbenito, a penitential garment worn over clothing, bearing a design that specified the type of penitence, if any. One type, worn by those sentenced to death, had designs of hell's flames or sometimes demons, dragons and/or snakes on it. Another type had a cross and was worn instead of imprisonment and then hung in the parish church.  The Treaty of Granada (1491), as negotiated at the final surrender of the Muslim state of Al-Andalus, clearly mandated protection of religious rights, but this was reversed just over 3 months later by the Alhambra Decree of March 31, 1492. Under the new Decree, approximately 40,000 Jews were expelled from Spain with only their personal possessions. Approximately 50,000 other Jews received a Christian baptism to remain in Spain. Many of them, derogatorily dubbed "Marranos" by the Old Christian majority, secretly kept some of their Jewish traditions. They were one of the chief targets of the Inquisition, but it also pursued anyone who would criticize it.  There are various estimates of the number of victims of the Spanish Inquisition during Torquemada's reign as Grand Inquisitor. Hernando del Pulgar, Queen Isabella's secretary, wrote that 2,000 executions took place throughout the entirety of her reign, which extended well beyond Torquemada's death.

Death.

During his final years, Torquemada's failing health, coupled with widespread complaints, caused Pope Alexander VI to appoint four assistant inquisitors in June 1494 to restrain the Spanish Inquisition. After fifteen years as Spain's Grand Inquisitor, Torquemada died in the monastery of St. Thomas Aquinas in Ávila on September 16, 1498, and was interred there. His tomb was ransacked in 1832, only two years before the Inquisition was finally disbanded. His bones were allegedly stolen and ritually incinerated in the same manner as an "auto-da-fé".

Tomás de Torquemada (October 14, 1420 – September 16, 1498), also anglicized as Thomas of Torquemada, was a Castilian Dominican friar and first Grand Inquisitor in Spain's movement to homogenize religious practices with those of the Catholic Church in the late 15th century, otherwise known as the Spanish Inquisition, which resulted in the expulsion from Spain of thousands of people of Jewish and Muslim faith and heritage.


Life.

Hermite was born in Dieuze, Moselle, on 24 December 1822, with a deformity in his right foot that would impair his gait throughout his life. He was the sixth of seven children of Ferdinand Hermite and his wife, Madeleine née Lallemand. Ferdinand worked in the drapery business of Madeleine's family while also pursuing a career as an artist. The drapery business relocated to Nancy in 1828, and so did the family. Hermite obtained his secondary education at Collège de Nancy and then, in Paris, at Collège Henri IV and at the Lycée Louis-le-Grand. He read some of Joseph-Louis Lagrange's writings on the solution of numerical equations and Carl Friedrich Gauss's publications on number theory.  Hermite wanted to take his higher education at École Polytechnique, a military academy renowned for excellence in mathematics, science, and engineering. Tutored by mathematician Eugène Charles Catalan, Hermite devoted a year to preparing for the notoriously difficult entrance examination. In 1842 he was admitted to the school. However, after one year the school would not allow Hermite to continue his studies there because of his deformed foot. He struggled to regain his admission to the school, but the administration imposed strict conditions. Hermite did not accept this, and he quit the École Polytechnique without graduating.  In 1842, "Nouvelles Annales de Mathématiques" published Hermite's first original contribution to mathematics, a simple proof of Niels Abel's proposition of concerning the impossibility of an algebraic solution to equations of the fifth degree.  A correspondence with Carl Jacobi, begun in 1843 and continued the next year, resulted in the insertion, in the complete edition of Jacobi's works, of two articles by Hermite, one concerning the extension to Abelian functions of one of the theorems of Abel on elliptic functions, and the other concerning the transformation of elliptic functions.  After spending five years working privately towards his degree, in which he befriended eminent mathematicians Joseph Bertrand, Carl Gustav Jacob Jacobi, and Joseph Liouville, he took and passed the examinations for the baccalauréat, which he was awarded in 1847. He married Joseph Bertrand's sister, Louise Bertrand, in 1848.  In 1848, Hermite returned to the École Polytechnique as "répétiteur and examinateur d'admission". In 1856 he contracted smallpox. Through the influence of Augustin-Louis Cauchy and of a nun who nursed him, he resumed the practice of his Catholic faith. In July 1848, he was elected to the French Academy of Sciences. In 1869, he succeeded Jean-Marie Duhamel as professor of mathematics, both at the École Polytechnique, where he remained until 1876, and at the University of Paris, where he remained until his death. From 1862 to 1873 he was lecturer at the École Normale Supérieure. Upon his 70th birthday, he was promoted to grand officer in the French Legion of Honour.  Hermite died in Paris on 14 January 1901, aged 78.

Contribution to mathematics.

An inspiring teacher, Hermite strove to cultivate admiration for simple beauty and discourage rigorous minutiae. His correspondence with Thomas Stieltjes testifies to the great aid he gave those beginning scientific life. His published courses of lectures have exercised a great influence. His important original contributions to pure mathematics, published in the major mathematical journals of the world, dealt chiefly with Abelian and elliptic functions and the theory of numbers. During 1858 he solved the equation of the fifth degree by elliptic functions; and during 1873 he proved "e", the base of the natural system of logarithms, to be transcendental. This last was used by Ferdinand von Lindemann to prove during 1882 the same for π.

Publications.

The following is a list of his works:  "This article incorporates text from the public-domain Catholic Encyclopedia of 1913."

Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.


Life.

Born in Detmold, the son of a prison officer, he began to write plays in the age of sixteen, while attending the "Gymnasium". A scholarship awarded by Princess Pauline enabled him to study law at the universities of Leipzig and Berlin, where he became acquainted with Heinrich Heine. After graduating in 1823, he unsuccessfully applied as a theatre director.  Grabbe returned to Detmold, he passed the final "Staatsexamen" and tried to find an employment as a legal officer, though also to no avail. Finally in 1826 he was appointed to act as a military legal advisor, initially without remuneration. From 1831 he increasingly suffered from alcoholism. After his fiancée turned away from him, he married his beloved Louise Christina Clostermeier in 1833, but the marriage quickly turned out to be unhappy. The next year Grabbe quit and left Detmold for Frankfurt, where he also fell out with his publisher.  He proceeded to Düsseldorf, where he temporarily worked at the Altes Theater with Karl Leberecht Immermann. Grabbe returned to Detmold in 1836 as a broken man, his wife filed for divorce. He died from general paresis in the same year.

Legacy.

With Georg Büchner, Grabbe was one of the principal German dramatists of his time. His debut "Herzog Theodor von Gothland" overtaxed contemporary critics by its all-pervasive nihilism. Influenced by Shakespeare and the "Sturm und Drang" movement, his plays were very ambitious, with crowd scenes and rapid scene changes that challenged the technical capacity of the theaters of the time. He resolved the strict forms of the classical drama in a loose series of scenes that were a precursor of the realist drama. His plays "Napoleon oder Die hundert Tage" or "Hannibal" reveal a realistic, heterogeneous concept of history.  After his death, he was at first forgotten, but his work was rediscovered by the Naturalist and Expressionist dramatists. He was honored by the Nazis as a great national poet, based on occasional antisemitic statements (particularly in "Aschenbrödel"), and on his nationalistic portrayal of German history, like "Die Hermannsschlacht" on the Battle of the Teutoburg Forest. In the 1930s, numerous streets were named after him.  The city of Detmold awards the Christian-Dietrich-Grabbe Prize for new dramatic literature since 1994 in association with the "Grabbe-Gesellschaft" literary society and the "Landesverband Lippe" municipal association.

Christian Dietrich Grabbe (11 December 1801 – 12 September 1836) was a German dramatist of the "Vormärz" era. He wrote many historical plays conceiving a disillusioned and pessimistic world view, with some shrill scenes. Heinrich Heine saw him as one of Germany's foremost dramatists, calling him "a drunken Shakespeare" and Sigmund Freud described Grabbe as "an original and rather peculiar poet."


Etymology.

It is named after the Oymyakon River, whose name reportedly comes from the Even word "kheium", meaning "unfrozen patch of water; place where fish spend the winter". However, another source states that the Even word "heyum" (hэjум) ("kheium" may be a misspelling) means "frozen lake".

Geography.

Oymyakon has two main valleys beside it. These valleys trap wind inside the town and create the colder climate. The temperatures here are extremely cold throughout the year, and it snows frequently. Schools are closed if it is colder than.

History.

During World War II, an airfield was built in the district of Aeroport, for the Alaska-Siberian (ALSIB) air route, used to ferry American Lend-Lease aircraft to the Eastern Front.  Over the last few decades, the population of Oymyakon has shrunk significantly. The village had a peak population of roughly 2,500 inhabitants, but that number has decreased to fewer than 900 in 2018.

Climate.

With an extreme subarctic climate (Köppen climate classification "Dfd/Dwd"), Oymyakon is known as one of the places considered the Northern Pole of Cold, the other being the town of Verkhoyansk, located away by air. The ground is permanently frozen (continuous permafrost).  There is a monument built around the town square commemorating a reading in January 1924 of. This was shown on the Australian program "60 Minutes" in a 2012 documentary. On February 6, 1933, a temperature of was recorded at Oymyakon's weather station. This was the coldest officially recorded temperature in the Northern Hemisphere. Only Antarctica has recorded lower official temperatures (the lowest being, recorded at Vostok Station on 21 July 1983).  The weather station is in a valley between Oymyakon and Tomtor. The station is at above sea level and the surrounding mountains at, causing cold air to pool in the valley: in fact, recent studies show that winter temperatures in the area "increase" with altitude by as much as.  Some years the temperature drops below in late September and may remain below freezing until mid-April. In Oymyakon sometimes the average minimum temperature for December, January, and February remains below. Sometimes summer months can also be quite cold, but June and July are the only months where the temperature has never dropped below. Oymyakon and Verkhoyansk are the only two permanently inhabited places in the world that have recorded temperatures below for every day in January.  Oymyakon has never recorded an above-freezing temperature between October 25 and March 17.  Although winters in Oymyakon are long and extremely cold, summers are mild to warm, sometimes hot. The warmest month on record is July 2010 with an average temperature of. In June, July and August temperatures over are not rare during the day. On July 28, 2010, Oymyakon recorded a record high temperature of, yielding a temperature range of. Verkhoyansk, Yakutsk, and Fort Vermilion, Canada are the only other known places in the world that have a temperature amplitude higher than.  The climate is quite dry, but as average monthly temperatures are below freezing for seven months of the year, substantial evaporation occurs only in summer months. Summers are much wetter than winters.

Oymyakon (, ;, "Öymököön", ) is a rural locality (a "selo") in Oymyakonsky District of the Sakha Republic, Russia, located along the Indigirka River, northwest of Tomtor on the Kolyma Highway. It is one of the coldest permanently inhabited settlements on Earth.


Morphology.

These table-top mountains are the remains of a large sandstone plateau that once covered the granite basement complex between the north border of the Amazon Basin and the Orinoco, between the Atlantic coast and the Rio Negro. This area is part of the remnants of the supercontinent Gondwana. Throughout the course of the history of Earth, the plateau was eroded, and the tepuis were formed from the remaining monadnocks.  There are 115 such mesas in the Gran Sabana in the south-east of Venezuela on the border with Guyana and Brazil, where the highest concentration of tepuis is found. The precipitous mountains tower over the surrounding area by up to.  Tepuis range in elevation from. The total surface area of all 115 tepuis is approximately 5000 km2, or the size of Trinidad. Because of their great age, some tepuis exhibit surface features and caves typical of karst topography, formed in more water-soluble rocks such as limestone. Caves here include the Abismo Guy Collet, the deepest quartzite cave in the world. Some of the mesas are pocked with giant sinkholes up to in diameter and with sheer walls up to deep. These sinkholes are formed when the roofs of tunnels carved by underground rivers collapse.

Flora and fauna.

The plateaus of the tepuis are completely isolated from the ground forest, making them ecological islands. The altitude causes them to have a different climate from the ground forest. The top presents cool temperatures with frequent rainfall, while the bases of the mountains have a tropical, warm and humid climate. The isolation has led to the presence of endemic flora and fauna through evolution over millennia of a different world of animals and plants, cut off from the rest of the world by the imposing rock walls. Some tepui sinkholes contain species that have evolved in these "islands within islands" that are unique to that sinkhole. The tepuis are often referred to as the Galápagos Islands of the mainland, having a large number of unique plants and animals not found anywhere else in the world. The floors of the mesas are poor in nutrients, which has led to a rich variety of carnivorous plants, such as drosera and most species of heliamphora, as well as a wide variety of orchids and bromeliads. The weathered, craggy nature of the rocky ground means no layers of humus are formed.  It has been hypothesized that endemics on tepuis represent relict fauna and flora that underwent vicariant speciation when the plateau got fragmented over geological time. However, recent studies suggest that tepuis are not as isolated as originally believed. For example, an endemic group of treefrogs, "Tepuihyla", have diverged after the tepuis were formed, that is, speciation followed colonization from the lowlands.  The tepuis, also known as 'islands above the rainforest', are a challenge for researchers, as they are home to a high number of new species that have yet to be described. A few of these mountains are cloaked by thick clouds almost the whole year round. Their surfaces could previously only be photographed by helicopter radar equipment.  Many tepuis are in the Canaima National Park in Venezuela, which has been classified as a World Heritage Site by UNESCO.

Selected tepuis.

A few of the most notable of the 60 tepuis:

Popular culture.

The hypothesis that endemic fauna and flora of tepuis represent remnants of ancient species was an inspiration to Arthur Conan Doyle's novel "The Lost World" (1912), which was set on a tepui.  In the 1990 film "Arachnophobia", a new species of spider with a highly potent, deadly venom that lives in social colonies and is the implied apex predator of its environment is discovered in a sinkhole enclosed by a tepui in the Venezuelan rainforest, also alluding to the unique ecological conditions of tepuis.  Much of the story of 2009 Pixar–Disney film "Up" takes place among the tepuis. The film also includes depictions of the numerous rock formations and an Angel Falls-like waterfall called "Paradise Falls".  Steve Backshall was part of the first expedition to successfully climb Mount Upuigma. The expedition was part of the program "Lost Land of the Jaguar" on BBC One in 2008. On the summit they discovered an endemic species of frog and mouse, and also footprints of an unidentified mammal.  In the novel "The 6th Extinction" (2014) by James Rollins, a tepui in the north of Brazil was featured as a secret lair for the villain Dr. Cutter Elwes.

A tepui, or tepuy (), is a table-top mountain or mesa found in the Guiana Highlands of South America, especially in Venezuela and western Guyana. The word tepui means "house of the gods" in the native tongue of the Pemon, the indigenous people who inhabit the Gran Sabana.