Examples.

The collection of all algebraic structures of a given type will usually be a proper class. Examples include the class of all groups, the class of all vector spaces, and many others. In category theory, a category whose collection of objects forms a proper class (or whose collection of morphisms forms a proper class) is called a large category.  The surreal numbers are a proper class of objects that have the properties of a field.  Within set theory, many collections of sets turn out to be proper classes. Examples include the class of all sets, the class of all ordinal numbers, and the class of all cardinal numbers.  One way to prove that a class is proper is to place it in bijection with the class of all ordinal numbers. This method is used, for example, in the proof that there is no free complete lattice on three or more generators.

Paradoxes.

The paradoxes of naive set theory can be explained in terms of the inconsistent tacit assumption that "all classes are sets". With a rigorous foundation, these paradoxes instead suggest proofs that certain classes are proper (i.e., that they are not sets). For example, Russell's paradox suggests a proof that the class of all sets which do not contain themselves is proper, and the Burali-Forti paradox suggests that the class of all ordinal numbers is proper. The paradoxes do not arise with classes because there is no notion of classes containing classes. Otherwise, one could, for example, define a class of all classes that do not contain themselves, which would lead to a Russell paradox for classes. A conglomerate, on the other hand, can have proper classes as members, although the "theory" of conglomerates is not yet well-established.

Classes in formal set theories.

ZF set theory does not formalize the notion of classes, so each formula with classes must be reduced syntactically to a formula without classes. For example, one can reduce the formula formula_1 to formula_2. Semantically, in a metalanguage, the classes can be described as equivalence classes of logical formulas: If formula_3 is a structure interpreting ZF, then the object language "class-builder expression" formula_4 is interpreted in formula_3 by the collection of all the elements from the domain of formula_3 on which formula_7 holds; thus, the class can be described as the set of all predicates equivalent to formula_8 (which includes formula_8 itself). In particular, one can identify the "class of all sets" with the set of all predicates equivalent to formula_10  Because classes do not have any formal status in the theory of ZF, the axioms of ZF do not immediately apply to classes. However, if an inaccessible cardinal formula_11 is assumed, then the sets of smaller rank form a model of ZF (a Grothendieck universe), and its subsets can be thought of as "classes".  In ZF, the concept of a function can also be generalised to classes. A class function is not a function in the usual sense, since it is not a set; it is rather a formula formula_12 with the property that for any set formula_13 there is no more than one set formula_14 such that the pair formula_15 satisfies formula_16 For example, the class function mapping each set to its successor may be expressed as the formula formula_17 The fact that the ordered pair formula_15 satisfies formula_19 may be expressed with the shorthand notation formula_20  Another approach is taken by the von Neumann–Bernays–Gödel axioms (NBG); classes are the basic objects in this theory, and a set is then defined to be a class that is an element of some other class. However, the class existence axioms of NBG are restricted so that they only quantify over sets, rather than over all classes. This causes NBG to be a conservative extension of ZF.  Morse–Kelley set theory admits proper classes as basic objects, like NBG, but also allows quantification over all proper classes in its class existence axioms. This causes MK to be strictly stronger than both NBG and ZF.  In other set theories, such as New Foundations or the theory of semisets, the concept of "proper class" still makes sense (not all classes are sets) but the criterion of sethood is not closed under subsets. For example, any set theory with a universal set has proper classes which are subclasses of sets.

In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. The precise definition of "class" depends on foundational context. In work on Zermelo–Fraenkel set theory, the notion of class is informal, whereas other set theories, such as von Neumann–Bernays–Gödel set theory, axiomatize the notion of "proper class", e.g., as entities that are not members of another entity.


Biography.

Early life.

Frederick Henry was born on 29 January 1584 in Delft, Holland, Dutch Republic. He was the youngest child of William the Silent and Louise de Coligny. His father William was stadtholder of Holland, Zeeland, Utrecht, and Friesland. His mother Louise was daughter of the Huguenot leader Gaspard de Coligny, and was the fourth wife of his father. He was thus the half brother of his predecessor Maurice of Orange, deceased in 1625.  Frederick Henry was born six months before his father's assassination on 10 July 1584. The boy was trained to arms by his elder brother Maurice, one of the finest generals of his age. After Maurice threatened to legitimize his illegitimate children if he did not marry, Frederick Henry married Amalia of Solms-Braunfels in 1625. His illegitimate son by Margaretha Catharina Bruyns (1595–1625), Frederick Nassau de Zuylestein was born in 1624 before his marriage. This son later became the governor of the young William III of England for seven years.

Stadtholder.

On the death of Maurice in 1625 without legitimate issue, Frederick Henry succeeded him in his paternal dignities and estates, and also in the stadtholderates of the five provinces of Holland, Zeeland, Utrecht, Overijssel and Guelders, and in the important posts of captain and admiral-general of the Union (commander-in-chief of the Dutch States Army and of the Dutch navy).  Frederick Henry proved himself almost as good a general as his brother, and a far more capable statesman and politician. For twenty-two years he remained at the head of government in the United Provinces, and in his time the power of the stadtholderate reached its highest point. The "Period of Frederick Henry," as it is usually styled by Dutch writers, is generally accounted the golden age of the republic. It was marked by great military and naval triumphs, by worldwide maritime and commercial expansion, and by a wonderful outburst of activity in the domains of art and literature.  The chief military exploits of Frederick Henry were the sieges and captures of Grol in 1627,'s-Hertogenbosch in 1629, of Maastricht in 1632, of Breda in 1637, of Sas van Gent in 1644, and of Hulst in 1645. During the greater part of his administration the alliance with France against Spain had been the pivot of Frederick Henry's foreign policy, but in his last years he sacrificed the French alliance for the sake of concluding a separate peace with Spain, by which the United Provinces obtained from that power all the advantages they had been seeking for eighty years.  Frederick Henry built the country houses Huis Honselaarsdijk, Huis ter Nieuwburg, and for his wife Huis ten Bosch, and he renovated the Noordeinde Palace in The Hague. Huis Honselaarsdijk and Huis ter Nieuwburg are now demolished.

Death.

Frederick Henry died on 14 March 1647 in The Hague, Holland, Dutch Republic. He left his wife Amalia of Solms-Braunfels, his son William II, Prince of Orange, four of his daughters, and his illegitimate son Frederick Nassau de Zuylestein.  On Frederick Henry's death, he was buried with great pomp beside his father and brother at Delft. The treaty of Munster, ending the long struggle between the Dutch and the Spaniards, was not actually signed until 30 January 1648, the illness and death of the stadtholder having caused a delay in the negotiations. Frederick Henry left an account of his campaigns in his "Mémoires de Frédéric Henri" (Amsterdam, 1743). See "Cambridge Mod. Hist." vol. iv. chap. 24.  His widow commissioned an elaborate mausoleum in the "Oranjezaal", a panoramic painted ballroom with scenes from his life and allegories of good government based on his achievements.

Children.

Frederick Henry and his wife Amalia of Solms-Braunfels had nine children, being seven daughters and two sons. Four of their children, including one son, died in childhood, leaving Frederick Henry with only a single son as heir. Ultimately, after the death of Frederick Henry's only male-line grandson, the stadtholdership was to pass to a distant agnatic cousin, who was married to Frederick Henry's daughter Albertine Agnes. Frederick Henry's children were:  Frederick Henry recognized one illegitimate child by Margaretha Catharina Bruyns:

Coat of arms and titles.

Frederick Henry, besides being Stadholder of several provinces and Captain-General, both non-hereditary and appointive titles:  Stadtholder of Holland, Zeeland, Utrecht, Guelders, and Overijssel;  he was the hereditary sovereign of the principality of Orange in what is today Provence in France. He also was the lord of many other estates, which formed his wealth:

List of military battles.

Frederick Henry participated in these battles as principal Dutch commander:

Frederick Henry (; 29 January 1584 – 14 March 1647) was the sovereign prince of Orange and stadtholder of Holland, Zeeland, Utrecht, Guelders, Overijssel in the Dutch Republic from 1625 until his death in 1647. The last seven years of his life he also was the stadtholder of Groningen (1640-1647).


Composition.

Imperial Estates could be either ecclesiastic or secular. The ecclesiastical Estates were led by: The secular Estates, most notably: Until 1582 the votes of the Free and Imperial Cities were only advisory. None of the rulers below the Holy Roman Emperor ranked as kings, with the exception of the Kings of Bohemia.  The status of Estate was normally attached to a particular territory within the Empire, but there were some ", or "persons with imperial statehood". Originally, the Emperor alone could grant that status, but in 1653, several restrictions on the Emperor's power were introduced. The creation of a new Estate required the assent of the College of Electors and of the College of Princes (see below). The ruler was required to agree to accept imperial taxation and military obligations. Furthermore, the Estate was required to obtain admittance into one of the Imperial Circles. Theoretically, personalist Estates were forbidden after 1653, but exceptions were often made. Once a territory attained the status of an Estate, it could lose that status under very few circumstances. A territory ceded to a foreign power ceased to be an Estate.  From 1648 onwards, inheritance of the Estate was limited to one family; a territory inherited by a different family ceased to be an Estate unless the Emperor explicitly allowed otherwise. Finally, a territory could cease to be an imperial Estate by being subjected to the Imperial ban (the most notable example involved the Elector Palatine Frederick V, who was banned in 1621 for his participation in the Bohemian Revolt).  In the German mediatization between 1803 and 1806, the vast majority of the Estates of the Holy Roman Empire were mediatised. They lost their imperial immediacy and became part of other Estates. The number of Estates was reduced from about three hundred to about thirty. Mediatisation went along with secularisation: the abolition of most of the ecclesiastical Estates. This dissolution of the constitution of the structure of the empire was soon followed by the dissolution of the empire itself, in 1806.

Rights and privileges.

Rulers of Imperial States enjoyed precedence over other subjects in the Empire. Electors were originally styled'(Serene Highness), princes'(high-born) and counts'(high and well-born). In the eighteenth century, the electors were upgraded to'(Most Serene Highness), princes to'(Serene Highness) and counts to'(Illustrious Highness).  Imperial States enjoyed several rights and privileges. Rulers had autonomy inasmuch as their families were concerned; in particular, they were permitted to make rules regarding the inheritance of their states without imperial interference. They were permitted to make treaties and enter into alliances with other Imperial States as well as with foreign nations. The electors, but not the other rulers, were permitted to exercise certain regalian powers, including the power to mint money, the power to collect tolls and a monopoly over gold and silver mines.

Imperial Diet.

From 1489 onwards, the Imperial Diet was divided into three ": the Council of Electors, the Council of Princes and the Council of Cities. Electoral states belonged to the first of the aforementioned councils; other states, whether ecclesiastical or secular, belonged to the Council of Princes.  Votes were held in right of the states, rather than personally. Consequently, an individual ruling several states held multiple votes; similarly, multiple individuals ruling parts of the same state shared a single vote. These rules were not formalized until 1582; prior to this time, when multiple individuals inherited parts of the same state, they sometimes received a vote each. Votes were either individual or collective. Princes and senior clerics generally held individual votes (but such votes, as noted above, were sometimes shared). Prelates (abbots and priors) without individual votes were classified into two benches—the Bench of the Rhine and the Bench of Swabia — each of which enjoyed a collective vote. Similarly, Counts were grouped into four comital benches with a collective vote each — the Upper Rhenish Bench of Wetterau, the Swabian Bench, the Franconian Bench and the Westphalian Bench.  No elector ever held multiple electorates; nor were electorates ever divided between multiple heirs. Hence, in the Council of Electors, each individual held exactly one vote. Electors who ruled states in addition to their electorates also voted in the Council of Princes; similarly, princes who also ruled comital territories voted both individually and in the comital benches. In the Reichstag in 1792, for instance, the Elector of Brandenburg held eight individual votes in the Council of Princes and one vote in the Bench of Westphalia. Similarly, among ecclesiastics, the Grand Master of the Teutonic Order held one individual vote in the Council of Princes and two in the Bench of the Rhine.

Quaternions.

The so-called imperial quaternions (German: "Quaternionen der Reichsverfassung" "quaternions of the imperial constitution"; from Latin "quaterniō" "group of four soldiers") were a conventional representation of the Imperial States of the Holy Roman Empire which first became current in the 15th century and was extremely popular during the 16th century.  Apart from the highest tiers of the emperor, kings, prince-bishops and the prince electors, the estates are represented in groups of four. The number of quaternions was usually ten, in descending order of precedence Dukes ("Duces"), Margraves ("Marchiones"), Landgraves ("Comites Provinciales"), Burggraves ("Comites Castrenses"), Counts ("Comites"), Knights ("Milites"), Noblemen ("Liberi"), Cities ("Metropoles"), Villages ("Villae") and Peasants ("Rustici"). The list could be shortened or expanded, by the mid-16th century to as many as 45. It is likely that this system was first introduced under Emperor Sigismund, who is assumed to have commissioned the frescoes in Frankfurt city hall in 1414.  As has been noted from an early time, this representation of the "imperial constitution" does not in fact represent the actual constitution of the Holy Roman Empire, as some imperial cities appear as "villages" or even "peasants". E.g. the four "peasants" are Cologne, Constance, Regensburg and Salzburg. The Burggrave of Stromburg (or Straburg, Strandeck, and variants) was an unknown entity even at the time. The representation of imperial subjects is also far from complete. The "imperial quaternions" are, rather, a more or less random selection intended to represent "pars pro toto" the structure of the imperial constitution.

An Imperial State or Imperial Estate (;, plural: ') was a part of the Holy Roman Empire with representation and the right to vote in the Imperial Diet ('). Rulers of these Estates were able to exercise significant rights and privileges and were "immediate", meaning that the only authority above them was the Holy Roman Emperor. They were thus able to rule their territories with a considerable degree of autonomy.


Style.

Their songs are mostly comical and weird in nature, but the lyrics contain hints of social criticism as well. For example, "Cinderella" (1994) is one of their "fun" songs, in which they tell the tale of Cinderella in a funny way: "Sie schlief im Kohlenkeller, trotzdem war sie bettelarm, weil sie von der vielen Kohle, die da lag, zu wenig nahm" ("She slept in the coal cellar, but she was dirt-poor, because she didn't take much of the plentiful coal that lay there"). The word "Kohle" ("coal") is a colloquial word for money in German.  More critical lyrics can be seen in the song "Burli" (1987), which tells the story of a boy born shortly after the Chernobyl accident in an exaggerated and humorous way: "Herr Anton hat ein Häuschen mit einem Gartenzwerg und davor, da steht ein Kernkraftwerk. Da gab es eines Tages eine kleine Havarie, die Tomaten war'n so groß wie nie..." ("Mr. Anton has a small house with a garden gnome, and nearby there's a nuclear power plant. One day there was a small accident - the tomatoes were bigger than ever before..."). Both "Burli" and the song "Afrika" led radio stations to boycott the band.  The band is known for open statements against political extremism especially on the right ("bacillus nationalis") and was sued by prominent politicians of the political right like Kurt Waldheim for drawing attention to his past in the 3rd Reich and Jörg Haider, then-head of the right-leaning FPÖ. Songs on this topic include e.g. "Eierkopf-Rudi" or "Wir marschieren".

Members.

Deaths of members.

In February 1981, group member Walter Hammerl (b. 1952) committed suicide by hanging. He had attempted suicide before. He was a close friend of Klaus Eberhartinger, who took over his duties. Bandmate Thomas Spitzer commented that it was worrying how the band got on and felt so close to Walter Hammerl, but without actually knowing him. Hammerl had mainly done managing and stage directing work for the band, however he did sing on a few tracks.  In May 2012, former group member Andy Töfferl died of a heart attack at the age of 56 years.  In July 2017, former singer Wilfried Scheutz died after a short battle with cancer at the age of 69 years.

The "EAV" (Erste Allgemeine Verunsicherung, German for "First General Confusion/Uncertainty/'Uninsurance'") was an Austrian band which was formed in 1977 and disbanded in 2019.


Etymology.

The term originated as an abstraction of the sequence: single, couple/double, triple, quadruple, quintuple, sextuple, septuple, octuple,..., ‐tuple,..., where the prefixes are taken from the Latin names of the numerals. The unique 0‐tuple is called the null tuple or empty tuple. A 1‐tuple is called a single (or singleton), a 2‐tuple is called an ordered pair or couple, and a 3‐tuple is called a triple (or triplet). The number can be any nonnegative integer. For example, a complex number can be represented as a 2‐tuple of reals, a quaternion can be represented as a 4‐tuple, an octonion can be represented as an 8‐tuple, and a sedenion can be represented as a 16‐tuple.  Although these uses treat "‐uple" as the suffix, the original suffix was "‐ple" as in "triple" (three-fold) or "decuple" (ten‐fold). This originates from medieval Latin "plus" (meaning "more") related to Greek ‐πλοῦς, which replaced the classical and late antique "‐plex" (meaning "folded"), as in "duplex".

Properties.

The general rule for the identity of two -tuples is  Thus a tuple has properties that distinguish it from a set.

Definitions.

There are several definitions of tuples that give them the properties described in the previous section.

Tuples as functions.

If we are dealing with sets, an -tuple can be regarded as a function,, whose domain is the tuple's implicit set of element indices,, and whose codomain,, is the tuple's set of elements. Formally: where: In slightly less formal notation this says:  Using this definition of formula_12-tuples, it follows that there is only one formula_13-tuple, the empty function.

Tuples as nested ordered pairs.

Another way of modeling tuples in Set Theory is as nested ordered pairs. This approach assumes that the notion of ordered pair has already been defined; thus a 2-tuple This definition can be applied recursively to the -tuple:  Thus, for example:  A variant of this definition starts "peeling off" elements from the other end: This definition can be applied recursively:  Thus, for example:

Tuples as nested sets.

Using Kuratowski's representation for an ordered pair, the second definition above can be reformulated in terms of pure set theory:  In this formulation:

-tuples of -sets.

In discrete mathematics, especially combinatorics and finite probability theory, -tuples arise in the context of various counting problems and are treated more informally as ordered lists of length. -tuples whose entries come from a set of elements are also called "arrangements with repetition", "permutations of a multiset" and, in some non-English literature, "variations with repetition". The number of -tuples of an -set is. This follows from the combinatorial rule of product. If is a finite set of cardinality, this number is the cardinality of the -fold Cartesian power. Tuples are elements of this product set.

Type theory.

In type theory, commonly used in programming languages, a tuple has a product type; this fixes not only the length, but also the underlying types of each component. Formally: and the projections are term constructors:  The tuple with labeled elements used in the relational model has a record type. Both of these types can be defined as simple extensions of the simply typed lambda calculus.  The notion of a tuple in type theory and that in set theory are related in the following way: If we consider the natural model of a type theory, and use the Scott brackets to indicate the semantic interpretation, then the model consists of some sets formula_31 (note: the use of italics here that distinguishes sets from types) such that: and the interpretation of the basic terms is:  The -tuple of type theory has the natural interpretation as an -tuple of set theory: The unit type has as semantic interpretation the 0-tuple.

In mathematics, a tuple is a finite ordered list (sequence) of elements. An -tuple is a sequence (or ordered list) of elements, where is a non-negative integer. There is only one 0-tuple, an empty sequence, or empty tuple, as it is referred to. An -tuple is defined inductively using the construction of an ordered pair. Tuples: 1- single 2- couple 3- triple 4- quadruple 5- quintuple 6- sextuple 7- septuple 8- octuple 9- nonuple (n-tuple) 10- decuple 20- viguple


Formation.

Numerous classification schemes have been proposed for bauxite but,, there was no consensus.  Vadász (1951) distinguished lateritic bauxites (silicate bauxites) from karst bauxite ores (carbonate bauxites):  In the case of Jamaica, recent analysis of the soils showed elevated levels of cadmium, suggesting that the bauxite originates from recent Miocene ash deposits from episodes of significant volcanism in Central America.

Production trends.

Australia is the largest producer of bauxite, followed by China. In 2017, China was the top producer of aluminium with almost half of the world's production, followed by Russia, Canada, and India. Although aluminium demand is rapidly increasing, known reserves of its bauxite ore are sufficient to meet the worldwide demands for aluminium for many centuries. Increased aluminium recycling, which has the advantage of lowering the cost in electric power in producing aluminium, will considerably extend the world's bauxite reserves.  In November 2010, Nguyen Tan Dung, the prime minister of Vietnam, announced that Vietnam's bauxite reserves might total 11,000 Mt (11 trillion kg); this would be the largest in the world.

Processing.

Bauxite is usually strip mined because it is almost always found near the surface of the terrain, with little or no overburden., approximately 70% to 80% of the world's dry bauxite production is processed first into alumina and then into aluminium by electrolysis. Bauxite rocks are typically classified according to their intended commercial application: metallurgical, abrasive, cement, chemical, and refractory.  Usually, bauxite ore is heated in a pressure vessel along with a sodium hydroxide solution at a temperature of. At these temperatures, the aluminium is dissolved as sodium aluminate (the Bayer process). The aluminium compounds in the bauxite may be present as gibbsite(Al(OH)), boehmite(AlOOH) or diaspore(AlOOH); the different forms of the aluminium component will dictate the extraction conditions. The undissolved waste, bauxite tailings, after the aluminium compounds are extracted contains iron oxides, silica, calcia, titania and some un-reacted alumina. After separation of the residue by filtering, pure gibbsite is precipitated when the liquid is cooled, and then seeded with fine-grained aluminium hydroxide. The gibbsite is usually converted into aluminium oxide, AlO, by heating in rotary kilns or fluid flash calciners to a temperature in excess of. This aluminium oxide is dissolved at a temperature of about in molten cryolite. Next, this molten substance can yield metallic aluminium by passing an electric current through it in the process of electrolysis, which is called the Hall–Héroult process, named after its American and French discoverers.  Prior to the invention of this process, and prior to the Deville process, aluminium ore was refined by heating ore along with elemental sodium or potassium in a vacuum. The method was complicated and consumed materials that were themselves expensive at that time. This made early elemental aluminium more expensive than gold.

Source of gallium.

Bauxite is the main source of the rare metal gallium.  During the processing of bauxite to alumina in the Bayer process, gallium accumulates in the sodium hydroxide liquor. From this it can be extracted by a variety of methods. The most recent is the use of ion-exchange resin. Achievable extraction efficiencies critically depend on the original concentration in the feed bauxite. At a typical feed concentration of 50 ppm, about 15 percent of the contained gallium is extractable. The remainder reports to the red mud and aluminium hydroxide streams.

Bauxite is a sedimentary rock with a relatively high aluminium content. It is the world's main source of aluminium and gallium. Bauxite consists mostly of the aluminium minerals gibbsite (Al(OH)), boehmite (γ-AlO(OH)) and diaspore (α-AlO(OH)), mixed with the two iron oxides goethite (FeO(OH)) and haematite (FeO), the aluminium clay mineral kaolinite (AlSiO(OH)) and small amounts of anatase (TiO) and ilmenite (FeTiO or FeO.TiO).


Early life and education.

Carstens was born in the City of Bremen, the son of a commercial school teacher, who had been killed at the Western Front of World War I shortly before his birth. He studied law and political science at the universities of Frankfurt, Dijon, Munich, Königsberg, and Hamburg from 1933 to 1936, gaining a doctorate in 1938 and taking the Second "Staatsexamen" degree in 1939. In 1949 he also received a Master of Laws (LL.M.) degree from Yale Law School.

World War II.

From 1939 to 1945, during the Second World War, Carstens was a member of an anti-aircraft artillery ("Flak") unit in the Luftwaffe, reaching the rank of "Leutnant" (Second Lieutenant) by the war's end. In 1940 he joined the Nazi Party; reportedly, he had applied for admission in 1937 to avoid detrimental treatment when he worked as a law clerk. He had, however, joined the Nazi "SA" paramilitary organisation already in 1934.

Post-war years.

In 1944 Carstens married the medical student Veronica Prior in Berlin. After the war he became a lawyer in his hometown Bremen, and from 1949 acted as a councillor of the city's Senate. From 1950 he also worked as lecturer at the University of Cologne, where he habilitated two years later. In 1954 he joined the diplomatic service of the German Foreign Office, serving as West German representative at the Council of Europe in Strasbourg. In 1955 he joined the Christian Democratic Union (CDU) under Chancellor Konrad Adenauer.  In July 1960 Carstens reached the position of secretary of state at the Foreign Office and in the same year was also appointed as professor for public and international law at Cologne University. During the grand coalition government of 1966-1969 under Chancellor Kurt Georg Kiesinger, he first served as secretary of state in the Ministry of Defence, and after 1968 as head of the German Chancellery.  In 1972 Carstens was first elected into the Bundestag, of which he was a member until 1979. From May 1973 until October 1976 he was chairman of the CDU/CSU parliamentary group, succeeding Rainer Barzel. During that time he was an outspoken critic of left-wing tendencies in the German student movement and particular accused the governing Social Democratic Party of Germany (SPD) of being too soft on left-wing extremists. He also famously denounced the author and Nobel laureate Heinrich Böll as a supporter of left-wing terrorism (specifically, the Baader-Meinhof Gang) for his 1974 novel "The Lost Honour of Katharina Blum".  After the 1976 federal elections, which made the CDU/CSU the largest group in parliament, Carstens was elected president of the Bundestag on 14 December 1976. The CDU/CSU had also reached a majority in the Federal Convention electing the President of Germany, and in 1979 the party nominated Carstens, though in contestation due to his Nazi past, as candidate, whereafter incumbent President Walter Scheel (FDP) chose to renounce a second term.

President of West Germany.

On 23 May 1979, Carstens was elected as the fifth President of the Federal Republic of Germany, prevailing against the SPD candidate Annemarie Renger in the first ballot. During his term of office, Carstens was well known for hiking Germany in order to decrease the gulf between politics and the people.  In December 1982, the new Chancellor Helmut Kohl (CDU), recently elected in a successful motion of no confidence against Helmut Schmidt (SPD) deliberately lost a vote of confidence in the Bundestag, in order to obtain a clearer majority in new general elections. Though already former Chancellor Willy Brandt had similarly proceeded in 1972, this action gave rise to a discussion whether such a step constitutes a "manipulation of the Constitution". On 7 January 1983, President Carstens nonetheless dissolved the Bundestag and called for new elections. In February 1983 his decision was approved by the Federal Constitutional Court so that 1983 general elections could take place on 6 March.  In 1984 Carstens decided not to seek a second term on account of his age and left office on 30 June 1984. He was succeeded by Richard von Weizsäcker.  Carstens was a member of the Evangelical Church in Germany.

Karl Carstens (14 December 1914 – 30 May 1992) was a German politician. He served as President of the Federal Republic of Germany (West Germany) from 1979 to 1984.


Research history.

Thor Heyerdahl's hypothesis.

In 1990, adventurer and publisher, Thor Heyerdahl, became aware of the "Canarian Pyramids" by reading an article written by Francisco Padrón in the Tenerife newspaper "Diario de Avisos" detailing "real pyramids on the Canaries". As Heyerdahl had hypothesized a transatlantic link between Egypt and Central America, he became intrigued by the Güímar pyramids and relocated to Tenerife. There Heyerdahl researched possible parallels between the Canarian terrace structures and pyramid structures in Egypt and Central America in pre-Columbian Mesoamerica as ceremonial areas.  Heyerdahl hypothesised that the Canarian pyramids formed a temporal and geographic stopping point on voyages between ancient Egypt and the Maya civilization, initiating a controversy in which historians, esoterics, archaeologists, astronomers, and those with a general interest in history took part.

Astronomical research and Freemasonry.

In 1991, research by Juan Antonio Belmonte Avilés, Antonio Aparicio Juan and César Esteban López, researchers of the Canary Institute of Astrophysics, shown that the long sides of some of the terrace structures at Güímar marked the direction of both solstices. The main limiting wall points to the sunset in the Summer solstice and the pyramids have stairs on their western side which face the direction of the rising sun on the Winter solstice. Also, standing on the platform of the largest pyramid on the day of the Summer solstice it is possible to experience a double sunset, as first the sun sets behind a mountain top, then it emerges again from behind the mountain and sets a second time behind a neighbouring peak. However, considering the room for interpretation, it is impossible based solely on these observations to conclude what was the intention of the builders or the building date.  In 2005, a book was published in Spanish by Aparicio and Esteban titled "The Pyramids of Güímar: Myth and Reality". Aparicio and Esteban suggest that the solstitial orientations of the pyramids were potentially motivated by the Masonic symbolism. These authors argue that solstices are very important in the symbolism of Freemasonry, and that the owner of the land in the epoch in which the pyramids were built was himself a Freemason. This motivation would be only an aesthetic one and would not modify in any rate the fundamental motivation (agriculture) and date of construction.

Archaeological excavations.

Between 1991 and 1998, with the agreement of Thor Heyerdahl, multiple excavations of the site by archaeologists of the University of La Laguna (Departamento de Prehistoria, Antropología e Historia Antigua) took place. In 1996 the results of the 1991 excavation were presented at a colloquium (published in 1998), providing evidence for the dating of the pyramids. According to the preceding geophysical Georadar-Survey eight locations adjacent to the pyramids, each with an area of 25 m2, were investigated in layers down to the solid lava-floor. In doing so it was possible to establish three specific sediment layers. Starting from the top these were:  Furthermore, under the border edge of one of the pyramids, a natural lava cave was discovered. It had been walled up and yielded artefacts from the time of the Guanches. Since the pyramids lie stratigraphically above the cave, the Guanche finds from between 600 and 1000 AD can only support conclusions on the date of human use of the cave. The above survey indicates that the pyramids themselves cannot be older than the 19th century.

Conclusions.

The archaeologists involved maintain that the creation of the terrace structures followed from the practices of the 19th century rural population, who created these structures while clearing cultivatable land of stones, as they piled the stones into these terrace shapes. The excavations and subsequent research support a date for the construction of the structures no earlier than the 19th century.  Heyerdahl suggested that the structures were not haphazardly piled-up stones. Heyerdahl maintained a belief in the hypothesis that the pyramids were connected with Guanches until his death. The association of the Guanches and the pyramids continues to be elaborated upon both in "Pyramid park" and on its official website.  Aparicio and Esteban's theory connects the facts that the pyramids were built in the 19th century with the acknowledgement that they are not simply piles of stones.

Ethnographic park.

Following the completion of the excavations in 1998, the 65,000 m2 area surrounding the pyramids was made accessible to the public. Heyerdahl received financial support from his friend the Canarian businessman Fred Olsen, who owns the largest transport company in the Canaries and whose family came to the islands from Norway in the 20th century. An information centre provides visitors with information about Heyerdahl’s research trips and his previous ideas regarding the pyramids. Two pavilions contain exhibits relating to Heyerdahl along with models of his boats; a replica of the Ra II in its original size, amongst others. In spite of the conclusions regarding the age of the pyramids outlined above, Heyerdahl continued to maintain a belief "in a possible relationship between the existence of the pyramids and the pre Hispanic civilisation on Tenerife". The objects found in the Guanche cave are shown in the "museum" in heavily enlarged photos, whilst the imported ceramics from the 19th century are mentioned only briefly on an information board – without illustration.

The Pyramids of Güímar are six rectangular pyramid-shaped, terraced structures built from lava stone without the use of mortar. They are located in the district of Chacona, part of the town of Güímar on the island of Tenerife in the Canary Islands, Spain. The structures have been dated to the 19th century AD and they may originally have been a byproduct of contemporary agricultural techniques.


Formation.

The Sierra Nevada was formed during the Alpine Orogeny, a mountain-building event that also formed the European Alps to the east and the Atlas Mountains of northern Africa across the Mediterranean Sea to the south. The Sierra as observed today formed during the Paleogene and Neogene Periods (66 to 1.8 million years ago) from the collision of the African and Eurasian continental plates.

Geography.

Central to the mountain range is a ridge running broadly west-south-west - east-north-east. For a substantial distance, the watershed stays consistently above.  On the southern side of the range, several long, (but) narrow river valleys lead off towards the south-west, separated by a number of subsidiary ridges.  On the steeper and craggier northern side, the valleys have less regular orientations. This side is dominated by the Rio Genil which starts near Mulhacén and into which many of the other rivers flow.

Climate.

According to the Köppen climate classification, Sierra Nevada has a Mediterranean subalpine climate (Dsc), due to the location's high elevation and low summer precipitation. With June and September being around the threshold of in mean temperature to avoid the subarctic classification, the climate at a slightly lower elevation is continental highland climate. At an elevation slightly lower than that classification area; where February means average above ; it falls into the normal cool-summer mediterranean classification transitioning with the hot-summer variety in surrounding lowland areas. This renders Sierra Nevada's climate a highland cooled-down variety of a typical mediterranean climate. Summer and winter daytime temperatures are some 12° C cooler than found in Granada, differences that are even greater in spring as Sierra Nevada takes longer to approach the short summers. In May daytime highs in Sierra Nevada are around with Granada having an average of. The yearly temperature of is in stark contrast to Granada's and coastal Málaga's.

Sierra Nevada (; meaning "mountain range covered in snow") is a mountain range in the region of Andalucia, in the province of Granada and, a little further, Málaga and Almería in Spain. It contains the highest point of continental Spain: Mulhacén, at above sea level.


Biology of the species.

Morphology.

Adults are usually long, cylindrical and robust, black or brownish-black. Elytral declivity is slightly shiny, with 4 teeth on each margin side. The third tooth is the biggest and club like on its top. The egg is yellowish-white. The larva is white and legless. The pupa is also white.

Life cycle and interactions.

Bark beetles are so named because they reproduce in the inner bark, living and dead phloem tissues, of trees. Adult beetles hibernate in forest litter and host trees when environmental conditions are not favorable for reproduction. When conditions are right, they travel up to half a mile in search of a vulnerable host. Once the host is located, the adult burrows through the weakened bark in order to build tunnels where they can mate and lay eggs. They release pheromones to attract more individuals to the host tree. Two to five weeks after contamination, they may migrate to another host and repeat the process. Once the larvae hatch, they feed and pupate under the bark. Up to three generations are produced per year.  Bark beetles communicate with one another using semiochemicals, compounds or mixtures that carry messages. Some electrophysiological and behavioral statistics show that bark beetles can not only sense olfactory signals directly from other bark beetles, but also some compounds from trees.  It is also possible that beetles are attracted to the pheromone ipslure. They are also thought to be attracted to ethanol, one of the byproducts of microbial growth in dead woody tissues.  Bark beetles can form a symbiotic relationship with certain Ophiostomatales fungi. These phloem-feeding bark beetles use phloem-infesting fungi as an addition to their diet.

Dispersal ability.

European bark beetles have the ability to spread quickly over large areas. Some scientists hypothesize that long-distance movements originating from the Iberian Peninsula may have contributed to their invasion of northern Norway spruce forests. Movements like this can happen when various environmental factors such as severe storms, drought, or mass fungal infections damage or kill host trees. Trees in the genera "Picea" (spruce), "Abies" (fir), "Pinus" (pine), and "Larix" (larch) are the bark beetles' trees of choice. The most recent spruce bark beetle invasive outbreaks are found mainly in fallen, diseased or damaged Norway spruce. Healthy trees use defenses by producing resin or latex, which might contain several insecticidal and fungicidal compounds that kill or injure attacking insects. However, under outbreak conditions, the beetles can overwhelm the tree's defenses.  Though it specializes on Norway spruce, it is not found throughout the tree's range. It may not be able to persist in the northernmost spruce forests due to inadequate climatic oscillations. Other researchers argue that the beetle populations that have evolved in such regions have an active, directed host searching ability and are not equipped for long-range dispersal.

Impact.

Ecological.

The European spruce bark beetle has a significant impact on both the ecological and economic environment of Norway spruce forests. Together with storm events, bark beetle outbreaks are thought by some to be one of the most important natural disturbances in this region. Some scientists consider this beetle to be a keystone species, in part because it has an unusually high number of relationships with other organisms in the community and because it changes its environment so drastically.  Outbreak species, in general, assist in the renewal of the forest. Spruce beetles are detritivores. They feed on and break down dead plant matter, returning essential nutrients to the ecosystem. Also, they further the evolution of stronger, more resistant trees by instigating a range of adaptations to ward off their attacks.

Economical.

The bark beetles of the Norway spruce forests are associated with various types of fungi, who each have different basic ecological roles. Several fungal pathogens can be transmitted to spruces by the invasive beetles. One of the most damaging is a species of blue stain fungus, "Ophiostoma polonicum", which can kill healthy trees by hindering the upward flow of water, wilting its foliage. It also stains the wood with blue streaks, which destroys its commercial value. The results of such beetle outbreaks could be devastating for the lumber industry in that area because of the amount of time required for natural regression to take place. When this cycle affects the lumber industries by attacking spruce tree farms, they become known as serious pests.

Detection.

Spruce beetles usually infest the lower and middle parts of trunks. Trees that have been attacked are easy to recognize by concentrations of brown dust from bark at the basal areas of stems and trunks. However, sometimes apparently infected trees with green crowns can be without bark because of larval and woodpecker activity. Other common ways that infection can be detected is the presence of red-brown dust (frass) in bark crevices, many round exit holes, or small pitch tubes extruding from the bark. Large populations can be detected from a distance by patches of red foliage.

Conservation.

Interventions for beetle outbreaks are controversial in locations such as the Šumava National Park in the Bohemian Forest of the Czech Republic. Some authorities suggest that outbreaks be allowed to run their course, even at the expense of most of the forest. Others, including the lumber industry, request intervention. Some experts argue that salvage logging tends to have a greater negative effect on the vegetation than the bark beetle outbreak alone. A study of the effects of forestry interventions on the herb and moss layers of infested mountain spruce forests suggest that without intervention the forests do eventually recover. Salvage logging also had negative effects on the composition of species, delaying recovery.

Prevention and control methods.

Several methods have been proposed to prevent the start of beetle outbreaks. Some suggest using “trap trees” at the beginning of each reproductive cycle. This should be done in March, May, and in late June or early July. The trap trees should be debarked when distinct larval galleries with small larvae are found. Another method is clearcutting, removing sections of trees at the first signs of infestation. Pheromone traps can be used. Removal of attractive material, such as logs with bark, weakened trees, and windthrow, may help prevent outbreaks.

The European spruce bark beetle ("Ips typographus"), is a species of beetle in the weevil subfamily Scolytinae, the bark beetles, and is found from Europe to Asia Minor and some parts of Africa.


Characteristics.

The kodkod's fur color ranges from brownish-yellow to grey-brown. It has dark spots, a pale underside and a ringed tail. The ears are black with a white spot, while the dark spots on the shoulders and neck almost merge to form a series of dotted streaks. Melanistic kodkods with spotted black coats are quite common. It has a small head, large feet, and a thick tail. Adult kodkods are in head to body length with a short tail and a shoulder height of about. Weight ranges between.

Distribution and habitat.

The kodkod is strongly associated with mixed temperate rainforests of the southern Andean and coastal ranges, particularly the Valdivian and Araucaria forests of Chile, which is characterized by the presence of bamboo in the understory. It prefers evergreen temperate rainforest habitats to deciduous temperate moist forests, sclerophyllous scrub and coniferous forests. It is tolerant of altered habitats, being found in secondary forest and shrub as well as primary forest, and on the fringes of settled and cultivated areas. It ranges up to the treeline at approximately. In Argentina, it has been recorded from moist montane forest, which has Valdivian temperate rain forest characteristics, including a multi-layered structure with bamboo, and numerous lianas and epiphytes.

Ecology and behavior.

Kodkods are equally active during the day and during the night, although they only venture into open terrain under the cover of darkness. During the day, they rest in dense vegetation in ravines, along streams with heavy cover, and in piles of dead gorse. They are excellent climbers, and easily able to climb trees more than a meter in diameter. They are terrestrial predators of birds, lizards and rodents in the ravines and forested areas, feeding on southern lapwing, austral thrush, chucao tapaculo, huet-huet, domestic geese and chicken.  Male kodkods maintain exclusive territories in size, while females occupy smaller ranges of just.

Reproduction.

The gestation period lasts about 72–78 days. The average litter size is one to three kittens. This species may live to be about 11 years old.

Threats.

The major threat to the kodkod is logging of its temperate moist forest habitat, and the spread of pine forest plantations and agriculture, particularly in central Chile. In 1997 to 1998, two out of five radio-collared kodkods were killed on Chiloé Island while raiding chicken coops.

Taxonomy.

"Felis guigna" was the scientific name used in 1782 by Juan Ignacio Molina who first described a kodkod from Chile. "Felis tigrillo" was the name used in 1844 by Heinrich Rudolf Schinz.  The genus "Leopardus" was proposed in 1842 by John Edward Gray, when he described two spotted cat skins from Central America and two from India in the collection of the Natural History Museum, London. The subgenus "Oncifelis" was proposed in 1851 by Nikolai Severtzov with the Geoffroy's cat as type species. The kodkod was subordinated to "Leopardus" in 1958, and to "Oncifelis" in 1978.  Today, the genus "Leopardus" is widely recognized as valid, with two kodkod subspecies:

The kodkod ("Leopardus guigna") (), also called güiña, is the smallest cat in the Americas. It lives primarily in central and southern Chile and marginally in adjoining areas of Argentina. Its area of distribution is small compared to the other South American cats. Since 2002, it has been listed as Vulnerable on the IUCN Red List as the total effective population may comprise less than 10,000 mature individuals, and is threatened due to persecution and loss of habitat and prey base.


Eastern Church.

Caesaropapism's chief example is the authority that the Byzantine (East Roman) Emperors had over the Church of Constantinople and Eastern Christianity from the 330 consecration of Constantinople through the tenth century. The Byzantine Emperor would typically protect the Eastern Church and manage its administration by presiding over Ecumenical Councils and appointing Patriarchs and setting territorial boundaries for their jurisdiction. The Emperor exercised a strong control over the ecclesiastical hierarchy, and the Patriarch of Constantinople could not hold office if he did not have the Emperor's approval. Such Emperors as Basiliscus, Zeno, Justinian I, Heraclius, and Constans II published several strictly ecclesiastical edicts either on their own without the mediation of church councils, or they exercised their own political influence on the councils to issue the edicts. According to Metropolitan Kallistos Ware, the historical reality of caesaropapism stems from the confusion of the Byzantine Empire with the Kingdom of God and the zeal of the Byzantines "to establish here on earth a living icon of God's government in heaven."  However, Caesaropapism "never became an accepted principle in Byzantium." Several Eastern churchmen such as John Chrysostom, Patriarch of Constantinople and Athanasius, Patriarch of Alexandria, strongly opposed imperial control over the Church, as did Western theologians like Hilary of Poitiers and Hosius, Bishop of Córdoba. Saints, such as Maximus the Confessor, resisted the imperial power as a consequence of their witness to orthodoxy. In addition, at several occasions imperial decrees had to be withdrawn as the people of the Church, both lay people, monks and priests, refused to accept inventions at variance with the Church's customs and beliefs. These events show that power over the Church really was in the hands of the Church itself – not solely with the emperor.  Caesaropapism was most notorious in the Tsardom of Russia when Ivan IV the Terrible assumed the title Czar in 1547 and subordinated the Russian Orthodox Church to the state. This level of caesaropapism far exceeded that of the Byzantine Empire and was taken to a new level in 1721, when Peter the Great replaced the patriarchate with a Holy Synod, making the church a department of his government.  The patriarchate was restored on November 10 (October 28 O.S.), 1917, 3 days after the Bolshevik Revolution, by decision of the All-Russian Local Council.

Western Church.

Justinian I conquered the Italian peninsula in the Gothic War (535–554) and appointed the next three popes, a practice that would be continued by his successors and later be delegated to the Exarchate of Ravenna. The "Byzantine Papacy" was a period of Byzantine domination of the papacy from 537 to 752, when popes required the approval of the Byzantine Emperor for episcopal consecration, and many popes were chosen from the "apocrisiarii" (liaisons from the pope to the emperor) or the inhabitants of Byzantine Greece, Byzantine Syria, or Byzantine Sicily.

Analogue in the Church of England.

During the dispute between Henry VIII and Pope Clement VII over Henry's wish to have his marriage to Catherine of Aragon annulled, the English Parliament passed the Act in Restraint of Appeals (1533). It stated  The next year Parliament passed the First Act of Supremacy (1534) that explicitly tied the head of church to the imperial crown:  The Crown of Ireland Act, passed by the Irish Parliament in 1541 (effective 1542), changed the traditional title used by the Monarchs of England for the reign over Ireland, from Lord of Ireland to King of Ireland and naming Henry head of the Church of Ireland, for similar reasons.  During the reign of Mary I, the First Act of Supremacy was annulled, but during the reign of Elizabeth I the Second Act of Supremacy, with similar wording to the First Act, was passed in 1559. During the English Interregnum the laws were annulled, but the acts which caused the laws to be in abeyance were themselves deemed to be null and void by the Parliaments of the English Restoration.  When Elizabeth I restored royal supremacy, she replaced the title "Supreme Head" with that of "Supreme Governor", a change both conciliatory to English Catholics on a political level and reflecting a shift toward a more metaphysically and theologically modest stance involving only a claim to supreme authority over the Church of England's conduct in temporal matters. Since then, the monarchs of England, of Great Britain, and of the United Kingdom have claimed the "Supreme Governor" status as well as the title of "Defender of the Faith" (which was originally bestowed on Henry VIII by Pope Leo X but later revoked by Pope Paul III, as that was originally an award for Henry's defense of Catholicism).

Caesaropapism is the idea of combining the social and political power of secular government with religious power, or of making secular authority superior to the spiritual authority of the Church; especially concerning the connection of the Church with government. Justus Henning Böhmer (1674–1749) may have originally coined the term "" ("Cäseropapismus"). Max Weber (1864-1920) wrote: "a secular, caesaropapist ruler... exercises supreme authority in ecclesiastic matters by virtue of his autonomous legitimacy". According to Weber, caesaropapism entails "the complete subordination of priests to secular power."


Functional principle.

The high surface tension of water causes droplets to assume a nearly spherical shape, since a sphere has minimal surface area, and this shape therefore minimizes the solid-liquid surface energy. On contact of liquid with a surface, adhesion forces result in wetting of the surface. Either complete or incomplete wetting may occur depending on the structure of the surface and the fluid tension of the droplet. The cause of self-cleaning properties is the hydrophobic water-repellent double structure of the surface. This enables the contact area and the adhesion force between surface and droplet to be significantly reduced, resulting in a self-cleaning process. This hierarchical double structure is formed out of a characteristic epidermis (its outermost layer called the cuticle) and the covering waxes. The epidermis of the lotus plant possesses papillae 10 μm to 20 μm in height and 10 μm to 15 μm in width on which the so-called epicuticular waxes are imposed. These superimposed waxes are hydrophobic and form the second layer of the double structure. This system regenerates. This biochemical property is responsible for the functioning of the water repellency of the surface.  The hydrophobicity of a surface can be measured by its contact angle. The higher the contact angle the higher the hydrophobicity of a surface. Surfaces with a contact angle < 90° are referred to as hydrophilic and those with an angle >90° as hydrophobic. Some plants show contact angles up to 160° and are called ultrahydrophobic, meaning that only 2–3% of the surface of a droplet (of typical size) is in contact. Plants with a double structured surface like the lotus can reach a contact angle of 170°, whereby the droplet's contact area is only 0.6%. All this leads to a self-cleaning effect.  Dirt particles with an extremely reduced contact area are picked up by water droplets and are thus easily cleaned off the surface. If a water droplet rolls across such a contaminated surface the adhesion between the dirt particle, irrespective of its chemistry, and the droplet is higher than between the particle and the surface. This cleaning effect has been demonstrated on common materials such as stainless steel when a superhydrophobic surface is produced. As this self-cleaning effect is based on the high surface tension of water it does not work with organic solvents. Therefore, the hydrophobicity of a surface is no protection against graffiti.  This effect is of a great importance for plants as a protection against pathogens like fungi or algae growth, and also for animals like butterflies, dragonflies and other insects not able to cleanse all their body parts. Another positive effect of self-cleaning is the prevention of contamination of the area of a plant surface exposed to light resulting in reduced photosynthesis.

Technical application.

When it was discovered that the self-cleaning qualities of ultrahydrophobic surfaces come from physical-chemical properties at the microscopic to nanoscopic scale rather than from the specific chemical properties of the leaf surface, the possibility arose of using this effect in manmade surfaces, by mimicking nature in a general way rather than a specific one.  Some nanotechnologists have developed treatments, coatings, paints, roof tiles, fabrics and other surfaces that can stay dry and clean themselves by replicating in a technical manner the self-cleaning properties of plants, such as the lotus plant. This can usually be achieved using special fluorochemical or silicone treatments on structured surfaces or with compositions containing micro-scale particulates.  In addition to chemical surface treatments, which can be removed over time, metals have been sculpted with femtosecond pulse lasers to produce the lotus effect. The materials are uniformly black at any angle, which combined with the self-cleaning properties might produce very low maintenance solar thermal energy collectors, while the high durability of the metals could be used for self-cleaning latrines to reduce disease transmission.  Further applications have been marketed, such as self-cleaning glasses installed in the sensors of traffic control units on German autobahns developed by a cooperation partner (Ferro GmbH). The Swiss companies HeiQ and Schoeller Textil have developed stain-resistant textiles under the brand names "HeiQ Eco Dry" and "nanosphere" respectively. In October 2005, tests of the Hohenstein Research Institute showed that clothes treated with NanoSphere technology allowed tomato sauce, coffee and red wine to be easily washed away even after a few washes. Another possible application is thus with self-cleaning awnings, tarpaulins and sails, which otherwise quickly become dirty and difficult to clean.  Superhydrophobic coatings applied to microwave antennas can significantly reduce rain fade and the buildup of ice and snow. "Easy to clean" products in ads are often mistaken in the name of the self-cleaning properties of hydrophobic or ultrahydrophobic surfaces. Patterned ultrahydrophobic surfaces also show promise for "lab-on-a-chip" microfluidic devices and can greatly improve surface-based bioanalysis.  Superhydrophobic or hydrophobic properties have been used in dew harvesting, or the funneling of water to a basin for use in irrigation. The Groasis Waterboxx has a lid with a microscopic pyramidal structure based on the ultrahydrophobic properties that funnel condensation and rainwater into a basin for release to a growing plant's roots.

Research history.

Although the self-cleaning phenomenon of the lotus was possibly known in Asia long before (reference to the lotus effect is found in the "Bhagavad Gita",) its mechanism was explained only in the early 1970s after the introduction of the scanning electron microscope. Studies were performed with leaves of "Tropaeolum" and lotus ("Nelumbo"). "The Lotus Effect" is a registered trademark of STO SE & CO. KGAA (US Registration No. 2613850). Similar to lotus effect, a recent study has revealed a honeycomb like micro-structures on the taro leaf, which makes the leaf superhydrophobic. The measured contact angle on this leaf in this study is around 148 degrees.

The lotus effect refers to self-cleaning properties that are a result of ultrahydrophobicity as exhibited by the leaves of "Nelumbo" or "lotus flower". Dirt particles are picked up by water droplets due to the micro- and nanoscopic architecture on the surface, which minimizes the droplet's adhesion to that surface. Ultrahydrophobicity and self-cleaning properties are also found in other plants, such as "Tropaeolum" (nasturtium), "Opuntia" (prickly pear), "Alchemilla", cane, and also on the wings of certain insects.


Life.

Jovian was born at Singidunum (today Belgrade in Serbia) in 331 AD, the son of Varronianus, the commander of Constantius II's imperial bodyguards ("comes domesticorum"). He also joined the guards and in this capacity in 361, escorted Constantius' remains to the Church of the Holy Apostles. Jovian was married to Charito and they had two sons, Varronianus, and the other's name is unknown.  Jovian accompanied the Emperor Julian on the Mesopotamian campaign of the same year against Shapur II, the Sasanid king. At the Battle of Samarra, a small but decisive engagement, Julian was mortally wounded, and died on 26 June 363. The next day, after the aged Saturninius Secundus Salutius, praetorian prefect of the Orient, had declined their offer for Emperor, the army elected, despite Julian's reinstitution of paganism, the Christian Jovian, senior officer of the Scholae, as Emperor.

Rule.

On the very morning of his accession, Jovian resumed the retreat begun by Julian. Though harassed by the Sasanids, the army succeeded in reaching the city of Dura on the banks of the Tigris. There the army came to a halt, hoping to cross the Tigris to reach the Empire on the western bank. When the attempt to bridge the river failed, he was forced to sue for a peace treaty on humiliating terms. In exchange for an unhindered retreat to his own territory, he agreed to a thirty-year truce, a withdrawal from the five Roman provinces, Arzamena, Moxoeona, Azbdicena, Rehimena and Corduena, and to allow the Sasanids to occupy the fortresses of Nisibis, Castra Maurorum and Singara. The Romans also surrendered their interests in the Kingdom of Armenia to the Sasanids. The king of Armenia, Arsaces II (Arshak II), was to receive no help from Rome. The treaty was widely seen as a disgrace.  After crossing the Tigris, Jovian sent an embassy to the West to announce his elevation. With the treaty signed, Jovian and his army marched to Nisibis. The populace of Nisibis, devastated by the news their city was to be given to the Sasanids, were given three days to leave.  In September 363 Jovian arrived at Edessa where he issued two edicts. The first, a limitation on the distance a soldier could be sent for straw, was to indicate an end to the war with Sasanid Persia. The second was the restoration of estates of the "res privata" to the Imperial finances following Julian's incorporating them to pagan temples.  Jovian's arrival at Antioch in October 363, was met with an enraged populace. Faced with offensive graffiti and insulting authorless bills ("famosi") throughout the city, he ordered the Library of Antioch to be burned down. Jovian left Antioch in November 363, making his way back to Constantinople. By December 363 Jovian was at Ancyra proclaiming his infant son, Varronianus, consul. While en route from there to Constantinople, Jovian was found dead in his tent at Dadastana, halfway between Ancyra and Nicaea, on 17 February 364. His death, which went uninvestigated, was possibly the result of suffocating on poisonous fumes seeping from the newly painted bedchamber walls by a brazier. Jovian died aged 33 and was buried in the Church of the Holy Apostles in Constantinople, in a porphyry sarcophagus. He was succeeded by two brothers, Valentinian I and Valens, who subsequently divided the empire between them.  Following Jovian's death, Valentinian and Valens removed any threats to their position. Jovian's son Varronianus was blinded to ensure he would never inherit the throne. According to John Chrysostom, Jovian's wife Charito lived in fear the remaining days of her life.

Restoration of Christianity.

Jovian was met at Edessa by a group of bishops, including Athanasius. The Semi-Arian bishops received a poor greeting, but Athanasius, newly returned from exile, delivered a letter to Jovian insisting on the Nicene Creed and the rejection of Arianism. Having restored Athanasius to his episcopal duties, Jovian allowed Athanasius to accompany him to Antioch.  Upon arriving at Antioch, Jovian received a letter from the Synod of Antioch, imploring for Meletius' restoration as bishop of Antioch. By September 363, Jovian reestablished Christianity as the state religion, restored the labarum ("Chi-Rho") as the army's standard, and revoked the edicts of Julian against Christians, but did not close any pagan temples. He issued an edict of toleration, to the effect that his subjects could enjoy full liberty of conscience, but he banned magic and divination. Despite supporting the Nicene doctrines, he passed no edicts against Arians. Philostorgius, an Arian church historian, stated, "The Emperor Jovian restored the churches to their original uses, and set them free from all the vexatious persecutions inflicted on them by the Apostate Julian."

Jovian (; ; 331 – 17 February 364) was Roman Emperor from June 363 to February 364. As part of the imperial bodyguard, he accompanied Emperor Julian on his campaign against the Sasanian Empire and following the latter's death, Jovian was hastily declared Emperor by his soldiers. With the army exhausted, provisions running low, and unable to cross the Tigris, he sought peace with the Sasanids on humiliating terms. After his arrival at Edessa, Jovian was petitioned by bishops over doctrinal issues concerning Christianity and by September 363, he had reestablished Christianity as the state religion. His return to Constantinople would be cut short by his death at Dadastana. Jovian reigned only eight months.


Life.

Gratian was the son of Emperor Valentinian I by Marina Severa, and was born at Sirmium (now Sremska Mitrovica, Serbia) in Pannonia. He was named after his grandfather Gratian the Elder. Gratian was first married to Flavia Maxima Constantia, daughter of Constantius II. His second wife was Laeta. Both marriages remained childless. His stepmother was Empress Justina and his paternal half siblings were Valentinian II, Galla and Justa. Gratian was educated by Ausonius who had praised his pupil for his tolerance.  On 24 August 367 he received from his father the title of "Augustus". When his father died on 17 November 375, Gratian began his actual reign at the age of sixteen. Six days later, Gratian's half brother Valentinian II, Valentinian's four-year old son by his second wife Justina, was also proclaimed Emperor by troops in Pannonia, impelled by the generals Aequitius and Maximinus, two of Valentinian's more unscrupulous ministers.  Gratian prudently acquiesced in their choice; reserving for himself the administration of the Gallic provinces, to command the forces responsible for the frontier, while handing over the peaceful Italy, Illyricum and Africa to Valentinian and his mother, who fixed their residence at Mediolanum. The division, however, was merely nominal, and the real authority even in those provinces remained in the hands of Gratian.  Gratian, with the aid of his capable generals Mallobaudes, a king of the Franks, and Naniemus, completely defeated the Lentienses, the southernmost branch of the Alamanni, in May 378 at the Battle of Argentovaria. Next, Gratian personally led a campaign across the Upper Rhine into the territory of the Lentienses. After initial trouble facing the Lentienses on high ground, Gratian blockaded the enemy instead and received their surrender. The Lentienses were forced to supply young men to be levied into the Roman army, while the remainder were allowed to return home.  Later that year, Gratian's uncle Valens met his death in the Battle of Adrianople against a coalition of hostile Gothic and Hunnic tribes who had rebelled after being settled in Thrace by the eastern emperor. Valens refused to wait for Gratian, who had promised to march to his aid as soon as the Alemanni threat was contained; as a result, two-thirds of Valens men, to the number of 40,000 dead, fell in the battle along with the emperor and some of his top staff. By the time Gratian arrived in the east, the Gothic war had spiraled out of control; the provinces south of the Danube were daily being devastated by barbarians, and Roman authority as well as military prestige was all but annihilated. Hearing that the Germans were planning a new invasion in Gaul now that Gratian had departed from the province, and convinced that one emperor alone was incapable of repelling the inundation of foes on several different fronts, Gratian appointed the Spaniard Theodosius I Augustus on 19 January 379 to govern the east. During the ensuing four years Theodosius would take advantage of the internal discord and disorder of the Goths to destroy the more intractable of the barbarians and settle the rest by a peaceful treaty in the provinces of Thrace and Asia Minor.  For some years Gratian governed the Empire with energy and success, earning the esteem of the army and people by his personal courage and justice, but at length, being deprived by death of some of his abler counselors, the promising young emperor neglected public affairs, and occupied himself chiefly with the hunting. He alienated the army and German auxiliaries by his favoritism towards his Frankish general Merobaudes and a body of Scythian archers whom he made his body-guard and companions in the hunt. On other side his tutor Ausonius which has worked toward religious tolerance, has lost influence with time as bishop Ambrose' influence over Gratian grew. This has resulted with Roman Senate protests and fall of emperor popularity.  By appearing in public in the dress of a Scythian warrior, after the disaster of the Battle of Adrianople, he finally exasperated his army. One of his generals, Magnus Maximus, took advantage of this feeling to raise the standard of revolt in Britain and invaded Gaul with a large army. From Paris, Gratian, having been deserted by his troops, fled to Lyon. There, through the treachery of the governor, Gratian was delivered over to one of the rebel generals, Andragathius, and assassinated on 25 August 383.

Empire and Christianity.

The reign of Gratian forms an important epoch in church history, since during that period Nicene Christianity for the first time became dominant throughout the empire. In his reign, his co-Emperor Theodosius I also published an edict that all their subjects should profess the faith of the bishops of Rome and Alexandria (i.e., the Nicene faith). The move was mainly thrust at the various beliefs that had arisen out of Arianism, but smaller dissident sects, such as the Macedonians, were also prohibited.  Gratian, under the influence of Ambrose, Bishop of Milan, took active steps against pagan worship. This brought to an end a period of widespread religious tolerance that had existed since the death of Julian.  In 382, Gratian appropriated the income of the pagan priests and Vestal Virgins, forbade legacies of real property to them and abolished other privileges belonging to the Vestals and to the pontiffs. He confiscated the personal possessions of the colleges of pagan priests, which also lost all their privileges and immunities. Gratian declared that all of the pagan temples and shrines were to be confiscated by the government and that their revenues were to be joined to the property of the royal treasury. According to Zosimus, Gratian was the first Emperor to reject the insignia of the "Pontifex Maximus" in 381. He ordered another removal of the Altar of Victory from the Senate House at Rome, despite protests of the pagan members of the Senate, and confiscated its revenues.

Gratian (; ; ; 18 April/23 May 359 – 25 August 383) was Roman emperor from 367 to 383. The eldest son of Valentinian I, Gratian accompanied, during his youth, his father on several campaigns along the Rhine and Danube frontiers. Upon the death of Valentinian in 375, Gratian's brother Valentinian II was declared emperor by his father's soldiers. In 378, Gratian's generals won a decisive victory over the Lentienses, a branch of the Alamanni, at the Battle of Argentovaria. Gratian subsequently led a campaign across the Rhine, the last emperor to do so, and attacked the Lentienses, forcing the tribe to surrender. That same year, his uncle Valens was killed in the Battle of Adrianople against the Goths. He favoured Christianity over traditional Roman religion, refusing the office of Pontifex maximus and removing the Altar of Victory from the Roman Senate.


Isomers.

Rotation about the central C−C bond produces two different conformations ("trans" and "gauche") for "n"-butane.

Reactions.

When oxygen is plentiful, butane burns to form carbon dioxide and water vapor; when oxygen is limited, carbon (soot) or carbon monoxide may also be formed. Butane is denser than air.  When there is sufficient oxygen: When oxygen is limited:  The maximum adiabatic flame temperature of butane with air is.  "n"-Butane is the feedstock for DuPont's catalytic process for the preparation of maleic anhydride:  "n"-Butane, like all hydrocarbons, undergoes free radical chlorination providing both 1-chloro- and 2-chlorobutanes, as well as more highly chlorinated derivatives. The relative rates of the chlorination is partially explained by the differing bond dissociation energies, 425 and 411 kJ/mol for the two types of C-H bonds.

Uses.

Normal butane can be used for gasoline blending, as a fuel gas, fragrance extraction solvent, either alone or in a mixture with propane, and as a feedstock for the manufacture of ethylene and butadiene, a key ingredient of synthetic rubber. Isobutane is primarily used by refineries to enhance (increase) the octane number of motor gasoline.  When blended with propane and other hydrocarbons, it may be referred to commercially as LPG, for liquefied petroleum gas. It is used as a petrol component, as a feedstock for the production of base petrochemicals in steam cracking, as fuel for cigarette lighters and as a propellant in aerosol sprays such as deodorants.  Very pure forms of butane, especially isobutane, can be used as refrigerants and have largely replaced the ozone-layer-depleting halomethanes, for instance in household refrigerators and freezers. The system operating pressure for butane is lower than for the halomethanes, such as R-12, so R-12 systems such as in automotive air conditioning systems, when converted to pure butane will not function optimally and therefore a mix of isobutane and propane is used to give cooling system performance comparable to R-12.  Butane is also used as lighter fuel for a common lighter or butane torch and is sold bottled as a fuel for cooking, barbecues and camping stoves. Butane canisters global market is dominated by South Korean manufacturers.  As fuel, it is often mixed with small amounts of hydrogen sulfide and mercaptans which will give the unburned gas an offensive smell easily detected by the human nose. In this way, butane leaks can easily be identified. While hydrogen sulfide and mercaptans are toxic, they are present in levels so low that suffocation and fire hazard by the butane becomes a concern far before toxicity. Most commercially available butane also contains a certain amount of contaminant oil which can be removed through filtration but which will otherwise leave a deposit at the point of ignition and may eventually block the uniform flow of gas. and butane gases can cause gas explosions in poorly ventilated areas if leaks go unnoticed and are ignited by spark or flame.

Effects and health issues.

Inhalation of butane can cause euphoria, drowsiness, unconsciousness, asphyxia, cardiac arrhythmia, fluctuations in blood pressure and temporary memory loss, when abused directly from a highly pressurized container, and can result in death from asphyxiation and ventricular fibrillation. It enters the blood supply and within seconds produces intoxication. Butane is the most commonly abused volatile substance in the UK, and was the cause of 52% of solvent related deaths in 2000. By spraying butane directly into the throat, the jet of fluid can cool rapidly to by expansion, causing prolonged laryngospasm. "Sudden sniffer's death" syndrome, first described by Bass in 1970, is the most common single cause of solvent related death, resulting in 55% of known fatal cases.  A small amount of nitrogen dioxide, a toxic gas, results from burning butane gas, along with any combustion in the earth's atmosphere, and represents a human health hazard from home heaters and stoves.

Butane () or "n"-butane is an alkane with the formula CH. Butane is a gas at room temperature and atmospheric pressure. Butane is highly flammable, colorless, easily liquefied gas that quickly vaporize at room temperature. The name butane comes from the roots but- (from butyric acid, named after the Greek word for butter) and -ane. It was discovered by the chemist Edward Frankland in 1849. It was found dissolved in crude petroleum in 1864 by Edmund Ronalds, who was the first to describe its properties.


Life.

Early life.

Lessing was born into an upper-middle-class assimilated Jewish family. His father was a doctor in Hanover, his mother the daughter of a banker. He remembered his schooldays as unhappy; he was a mediocre student and graduated from Ratsgymnasium Hannover only with great difficulty. In his memoirs he wrote: "This humanistic German gymnasium specialising in patriotism, Latin, and Greek... this institute for the furtherance of stupidification, half of it built on white-collar boundering, the other half on mendacious, platitudinous German nationalism, was not just incredibly irresponsible, it was utterly boring... Nothing, nothing could ever make up for what those fifteen years destroyed in me. Even now, almost every night I dream of the tortures of my schooldays." At the time he was friendly with Ludwig Klages, but this friendship came to an end in 1899 (although whether anti-Semitism was a factor is unclear). Each later maintained that his own adult views had been determined by this shared background.  After his graduation he began studying medicine in Freiburg im Breisgau, Bonn, and finally Munich, where, in greater conformity with his real interests, he turned to literature, philosophy, and psychology. He concluded his study of philosophy with a dissertation on the work of the Russian logician Afrikan Spir.  His plans of habilitation at the University of Dresden were abandoned in the face of continuing public outrage over the influence in academia of Jews, socialists, and feminists. The next few years he spent as a substitute teacher and lecturer. In 1906 he travelled to Göttingen in order to obtain a habilitation under Edmund Husserl. This plan also came to nothing, but resulted briefly in a position as theatre critic for the "Göttinger Zeitung"; his critical notes were later collected in book form as "Nachtkritiken".

Growing renown.

In 1907 he returned to Hanover, where he lectured on philosophy at the "Technische Hochschule", founding the first German anti-noise (noise abatement) society.  In January 1910 he created a literary scandal with a vicious attack on the critic Samuel Lublinski and his "Bilanz der Moderne" (1904), in a piece published in "Die Schaubühne" filled with "Jewish jokes" and gibes about Lublinski's appearance; it drew strong condemnation from Thomas Mann, who returned the insults by calling Lessing a "disgraceful dwarf who should consider himself lucky that the sun shines on him, too."  On the outbreak of World War I Lessing volunteered for medical service. At this time he wrote his famous essay "Geschichte als Sinngebung des Sinnlosen" ("History as Making Sense of the Senseless"). Its publication was delayed by the censor until 1919 on account of its uncompromising anti-war position. After the war he returned to lecturing in Hanover and established the Volkshochschule Hannover-Linden with the help of his second wife, Ada Lessing.

Fame and anti-nationalist polemics.

From 1923 he was highly active in public life, publishing articles and essays in "Prager Tagblatt" and "Dortmunder Generalanzeiger", and quickly became one of the best-known political writers of Weimar Germany. In 1925 he drew attention to the fact that the serial killer Fritz Haarmann had been a spy for the Hanover police, and this resulted in him being excluded from covering the trial. In the same year he wrote an unflattering piece on Paul von Hindenburg, describing him as an intellectually vacuous man who was being used as a front by sinister political forces:  This article earned him the enmity of nationalists, and his lectures were soon disrupted by anti-Semitic protestors. Lessing received only limited support from the public, and even his colleagues argued that he had gone too far. A six-month leave of absence failed to calm the situation. On 7 June nearly a thousand students threatened to move their studies to the Technische Universität Braunschweig unless he was removed, and on 18 June 1926 the Prussian minister Carl Heinrich Becker bowed to public pressure by putting Lessing on indefinite leave on a reduced salary.

Escape from the Nazis and assassination.

On 30 January 1933 the Nazi Party entered government and in February, after the suppression of the "Freie Wort" congress, Lessing started packing his bags. On 1 March he and his wife fled to Marienbad in Czechoslovakia, where he continued to write for German-language newspapers abroad. But in June it was reported in Sudeten newspapers that a reward had been announced for his capture.  On 30 August 1933 he was working in his study when he was shot through the window by assassins. He died the next day at the hospital in Marienbad.

Theodor Lessing (8 February 1872, Hanover – 31 August 1933, Marienbad) was a German Jewish philosopher. He is known for opposing the rise of Hindenburg as president of the Weimar Republic and for his classic on Jewish self-hatred (Der jüdische Selbsthaß), a book which he wrote in 1930, three years before Hitler came to power, in which he tried to explain the phenomenon of Jewish intellectuals who incited anti-Semitism against the Jewish people and who regarded Judaism as the source of evil in the world.


Etymology.

"Ben oni" (בֶּן אוֹנִי) is a Hebrew term meaning "son of my sorrow" (cf. Genesis 35:18) – the name of an 1825 book by Aaron Reinganum about several defenses against the King's Gambit and the Queen's Gambit.

Old Benoni: 1.d4 c5.

The Old Benoni starts with 1.d4 c5. The Old Benoni may transpose to the Czech Benoni, but there are a few independent variations. This form has never attracted serious interest in high-level play, though Alexander Alekhine defeated Efim Bogoljubow with it in one game of their second match, in 1934. The Old Benoni is sometimes called the Blackburne Defense, after Englishman Joseph Henry Blackburne, the first player known to have used it successfully.

Czech Benoni: 1.d4 Nf6 2.c4 c5 3.d5 e5.

In the Czech Benoni, also known as the Hromadka Benoni, after Karel Hromádka, Black plays 1.d4 Nf6 2.c4 c5 3.d5 e5. The Czech Benoni is more than the Modern Benoni, but also more passive. The middlegames arising from this line are characterized by much maneuvering; in most lines, Black will look to break with...b7–b5 or...f7–f5 after due preparation, while White may play Nc3–e4–h3–Bd3–Nf3–g4, in order to gain space on the and prevent...f5.

Modern Benoni: 1.d4 Nf6 2.c4 c5 3.d5 e6.

The Modern Benoni, 1. 2. 3., is the most common form of Benoni apart from the Benko Gambit. Black's intention is to play...exd5 and create a, whose advance will be supported by fianchettoed bishop on g7. The combination of these two features differentiates Black's setup from the other Benoni defenses and the King's Indian Defense, although transpositions between these openings are common. The Modern Benoni is classified under the "ECO" codes A60–A79.

Snake Benoni: 4.Nc3 exd5 5.cxd5 Bd6.

The Snake Benoni refers to a variant of the Modern Benoni where the bishop is developed to d6 rather than g7. This opening was invented in 1982 by Rolf Olav Martens, who gave it its name because of the sinuous movement of the bishop—in Martens's original concept, Black follows up with 6...Bc7 and sometimes...Ba5—and because the Swedish word for "snake", "orm", was an anagram of his initials. Normunds Miezis has been a regular exponent of this variation. Aside from Martens's plan, 6...0-0 intending...Re8,...Bf8 and a potential redeployment of the bishop to g7, has also been tried. White appears to retain the advantage against both setups.

"ECO".

The "Encyclopaedia of Chess Openings" ("ECO") has many codes for the Benoni Defense.  Old Benoni Defense:  Benoni Defense:  Fianchetto Variation:  Modern Benoni:  Taimanov Variation:  Four Pawns Attack:  Classical Benoni:

The Benoni Defense is a chess opening characterized by the moves: Black can then sacrifice a pawn with 3...b5 (the Benko Gambit), otherwise 3...e6 is the most common move (although 3...d6 or 3...g6 are also seen, typically transposing to main lines).


White's third move.

White's two main choices for move three are:  The move 3.Nc3 may transpose to the Four Knights Game or the Three Knights Game. The move 3.Bc4 may lead to the Boden–Kieseritzky Gambit or transpose to the Two Knights Defence. Occasionally seen is the 3.d3.

Classical Variation: 3.Nxe5.

After 3.Nxe5, the Classical Variation, Black should not continue to copy White's moves and try to restore the balance immediately with 3...Nxe4? because after 4.Qe2 White will either win material (4...Nf6 5.Nc6+ wins Black's queen, and after 4...d5 5.d3 Qe7 6.dxe4 Qxe5 7.exd5 Black loses a pawn), or obtain a superior position (4...Qe7 5.Qxe4 d6 6.d4 f6 7.Nc3 dxe5 8.Nd5 Qd6 9.Bf4 Nd7 10.0-0-0 and White has a big advantage). Black usually plays 3...d6 (although 3...Qe7 is also possible). White now must retreat the knight, or sacrifice it.  Most often, White follows the main line 4.Nf3 Nxe4 5.d4 (5.Bd3 is also playable) d5 6.Bd3, where he will try to drive Black's advanced knight from e4 with moves like c4 and Re1. If White achieves this, then he is up two tempi (Nf6-e4-f6, plus the tempo White starts the game with). In practice White is usually able to achieve this, but at some structural cost such as having to play c4, which balances out. White can also force simplification with Lasker's 5.Qe2 Qe7 6.d3. This is generally only good enough for a draw, which Black should be satisfied with. Another possibility, explored by Keres, is 5.c4, known as the Kauffmann Attack.  A completely different approach is to meet 4...Nxe4 with 5.Nc3 Nxc3 6.dxc3, with rapid and castling. For instance, White can plan a quick Be3, Qd2, and 0-0-0, and play for a attack, trusting that his doubled c-pawns will help protect his king, and that his initiative and attacking potential will offset the long term disadvantage of having doubled pawns. In the 5.Nc3 line, Black must avoid 5...Bf5?? 6.Qe2! which wins a piece due to the pin (if 6...Qe7 7.Nd5, forcing 7...Qd7 because of the threat to the c7-pawn. Then 8.d3 wins the piece). Viswanathan Anand resigned after only six moves after falling for this against Alonso Zapata at Biel in 1988.  The Cochrane Gambit, 4.Nxf7, is labeled "speculative but entertaining" by Nick de Firmian. In "Modern Chess Openings–14" he evaluates the position in Veselin Topalov–Vladimir Kramnik, Linares 1999, as offering chances for both sides after 4...Kxf7 5.Nc3 c5!? 6.Bc4+ Be6 7.Bxe6+ Kxe6 8.d4 Kf7 9.dxc5 Nc6.  The Paulsen Variation, 4.Nc4, is labelled "ineffective" by de Firmian in "MCO", but is occasionally seen at grandmaster level. US master Andrew Karklins has experimented with 4.Nd3!?  The Stafford Gambit is 1. e4 e5 2. Nf3 Nf6 3. Nxe5 Nc6.

Steinitz Variation: 3.d4.

The move 3.d4 was favoured by Wilhelm Steinitz, and is sometimes called the Steinitz Variation though it was known earlier. Black can capture either pawn; also possible is 3...d6, transposing into the Philidor Defence.  After 3...exd4 4.e5 (4.Bc4 transposes into the Urusov Gambit) 4...Ne4 (4...Qe7 5.Be2 is better for White) 5.Qxd4 d5 6.exd6 Nxd6 7.Nc3 Nc6 8.Qf4 the game is approximately equal. After the other capture, 3...Nxe4, 4.Bd3 d5 (4...Nc6!? 5.Bxe4 d5, intending 6.Bd3 e4, is also possible) 5.Nxe5, either 5...Nd7 or 5...Bd6 gives roughly equal chances.  A long and complicated tactical sequence which has frequently been seen in master games is 3...Nxe4 4.Bd3 d5 5.Nxe5 Bd6 6.0-0 0-0 7.c4 Bxe5 8.dxe5 Nc6 9.cxd5 Qxd5 10.Qc2 Nb4 11.Bxe4 Nxc2 12.Bxd5 Bf5 13.g4 Bxg4 14.Be4 Nxa1 15.Bf4 f5 16.Bd5+ Kh8 17.Rc1 c6 18.Bg2 Rfd8 19.Nd2 (diagram) and White has the slightly better endgame after either 19...Rxd2 20.Bxd2 Rd8 21.Bc3 Rd1+ 22.Rxd1 Bxd1 or 19...h6 20.h4.

Three Knights Game: 3.Nc3.

The move 3.Nc3 is the Three Knights Game of Petrov's Defence. It can also be reached via 2.Nc3 Nf6 3.Nf3 (the Vienna Game). Commonly, with the move 3...Nc6, the opening transposes to the Four Knights Game. With the reply 3...Bb4 (or some others), it remains the Three Knights Game proper.

Italian Variation: 3.Bc4.

The move 3.Bc4 is the Italian Variation of Petrov's Defence. With the move 3...Nc6, it transposes to the Two Knights Defence.

Boden–Kieseritzky Gambit.

Another possibility is 3.Bc4 Nxe4 4.Nc3, the Boden–Kieseritzky Gambit. It is not considered wholly sound, since Black has several viable options. Black can accept the gambit with 4...Nxc3 5.dxc3 f6, although he must play carefully after 6.0-0 (for example 6...Bc5?? 7.Nxe5! is disastrous; 6...d6 and 6...Nc6 are good). Another more aggressive try is 6.Nh4, where White goes for a quick assault on Black's king, but Black can maintain a small advantage if he plays cautiously via 6...g6 7.f4 Qe7 8.f5 Qg7 9.Qg4 Kd8. Another possibility is returning the gambit pawn with 4...Nxc3 5.dxc3 c6 6.Nxe5 d5, which equalises. A third possibility is transposing to the Italian Four Knights Game with 4...Nc6, and if 5.Nxe4, d5. If 5.Bxf7+?, Kxf7 6.Nxe4 d5 gives Black the and control of the. If 5.0-0, Black plays 5...Nxc3 6.dxc3 and now Black can play 6...Qe7!, after which Bobby Fischer wrote that "White has no compensation for the Pawn", or 6...f6 transposing to the main line of the Boden–Kieseritzky. Black also has lines beginning 6...Be7 and 6...h6.

Petrov's Defence or the Petrov Defence (also called Petroff's Defence, Petrov's Game, Russian Defence, or Russian Game — ) is a chess opening characterised by the following moves:


General considerations.

In the Nimzo-Indian, Black is generally prepared to concede the bishop pair by playing Bxc3. As dynamic compensation, he often doubles White's c-pawns, which represent a static weakness, and gains play against the central light squares d5 and e4, even in those instances where White is able to recapture with a piece after...Bxc3. Black will aim to close the position to reduce the scope of White's bishops. To this end, Black must blockade the white pawn centre from advancing and neutralise White's attacking chances on the. An example of Black's strategy carried out successfully is the game Mikhail Botvinnik–Samuel Reshevsky from the 1948 World Chess Championship, which reached the position in the diagram after White's 24th move.  Earlier in the game, Reshevsky was able to block White's kingside attack by playing...Nf6–h5 and...f7–f5. Now, both White's bishops are reduced to defence, and White's queen is reduced to passivity at the a2-square to defend the pawns on a3 and c4. Without prospects for counterplay, White's game is strategically hopeless, and Black ultimately exchanged queens and won the endgame.

Rubinstein System: 4.e3.

The Rubinstein System (named after Akiba Rubinstein) is White's most common method of combating the Nimzo-Indian. Svetozar Gligorić and Lajos Portisch made great contributions to the theory and practice of this line at top level during their careers. White continues his development before committing to a definite plan of action. In reply, Black has three main moves to choose from: 4...0-0, 4...c5, and 4...b6.  In addition, Black sometimes plays 4...d5 or 4...Nc6. 4...d5 can transpose to lines arising from 4...0-0, but White has the extra option of 5.a3 (known as the Botvinnik Variation). This forces Black to retreat the bishop to e7 or capture on c3, which transposes to a line of the Sämisch Variation long considered good for White because he will undouble his pawns at some point by playing cxd5, eliminating the weak pawn on c4, then prepare the e4 pawn break, backed by the bishop pair (and in some cases with f3, since he hasn't committed the knight to that square yet), which will gain force in the more open type of position which will ensue. 4...Nc6 is the Taimanov Variation, named after Russian GM Mark Taimanov. Black prepares to play...e5, which may be preceded by...d5 and...dxc4, or...d6. The variation was tried several times by the young Bobby Fischer, and has long been favoured by GM Nukhim Rashkovsky.

4...0-0 Main line: 4.e3 0-0 5.Bd3 d5 6.Nf3 c5 7.0-0.

Black's most flexible and frequently played response is 4...0-0. The main line continues 5.Bd3 d5 6.Nf3 c5 7.0-0, reaching the position in the diagram.  White has completed his kingside development, while Black has claimed his share of the centre. At this point, the most important continuations are:  After 7...dxc4 8.Bxc4, Black also has two rare alternatives on his eighth move worth mentioning: 8...Qe7 intending...Rd8 is the Smyslov Variation, invented by former world champion Vasily Smyslov, and 8...Bd7 followed by...Bc6 is the Bronstein Variation, the brainchild of two-time world championship finalist David Bronstein.

4...0-0: lines with Ne2.

In general, the main line of the Rubinstein has held up very well for Black, so since the 1980s White has begun to look elsewhere for chances of obtaining an advantage. In the Rubinstein, White has often resorted to playing Ne2 rather than Nf3 at some point to be able to recapture on c3 with the knight, thus avoiding the doubled pawns. Two lines where White does this (following 4.e3 0-0) are:

4...c5.

Black puts pressure on d4 and leaves open the option of playing...d5, or...d6 and...e5. The game can still transpose to the main line mentioned above after moves such as 5.Bd3 d5 6.Nf3 0-0 7.0-0, but there are two major variations particular to 4...c5:

4...b6.

Favoured by Nimzowitsch, 4...b6 is a move in accordance with the spirit of the Nimzo-Indian: Black fianchettoes his light-squared bishop to increase his control over e4. White usually continues 5.Ne2, avoiding the doubled pawns, or 5.Bd3, continuing his development (5.Nf3 usually transposes to 5.Bd3). The main variations emerging from these moves are:

Classical Variation: 4.Qc2.

The Classical or Capablanca Variation was popular in the early days of the Nimzo-Indian, and though eventually superseded by 4.e3 it was revived in the 1990s; it is now just as popular as the Rubinstein. White aims to acquire the two bishops without compromising his pawn structure. The drawback is that the queen will move at least twice within the opening moves and that White's kingside development is delayed. Thus, even though White possesses the bishop pair, it is usually advisable for Black to open the game quickly to exploit his lead in development. Black has four common replies to 4.Qc2. These include 4...0-0, 4...c5, 4...d5, and 4...Nc6 (4...d6 intending...Nbd7 and...e5 is a rarer fifth option).

Kasparov Variation: 4.Nf3.

4.Nf3 is known as the Kasparov Variation, since Garry Kasparov used it to great effect against Anatoly Karpov in their 1985 World Championship match. Kasparov played 4.Nf3 six times, scoring three wins and three draws. Today as White, this is a favourite weapon of GM Alexei Barsov and former Women's Champion Nona Gaprindashvili.  White develops the knight to a natural square and waits to see Black's reply. 4...d5 transposes to the Ragozin Defence of the Queen's Gambit Declined and 4...b6 5.Bg5 Bb7 transposes to the Nimzo/Queen's Indian hybrid line, so 4...c5 is the most common move that stays within Nimzo-Indian territory. Now 5.e3 transposes to the Rubinstein System, but the main move is 5.g3, which leads to a position that also arises from the Fianchetto Variation. 5.g3 cxd4 6.Nxd4 0-0 7.Bg2 d5 8.cxd5 Nxd5 can be considered the main line. Black has dissolved White's centre, but the bishop on g2 exerts pressure on the black queenside, which White may augment with 9.Qb3.  This line can also arise from the Bogo-Indian Defence (1.d4 Nf6 2.c4 e6 3.Nf3 Bb4+) if White blocks the check with 4.Nc3.

"ECO" codes.

In the "Encyclopaedia of Chess Openings", the Nimzo-Indian Defence has codes E20 to E59. All codes begin with 1.d4 Nf6 2.c4 e6 3.Nc3 Bb4, excluding E20, which also includes alternatives to 3...Bb4 apart from 3...d5 (which would be the Queen's Gambit Declined).

The Nimzo-Indian Defence is a chess opening characterised by the moves: Other move orders, such as 1.c4 e6 2.Nc3 Nf6 3.d4 Bb4, are also feasible. In the "Encyclopaedia of Chess Openings", the Nimzo-Indian is classified as E20–E59.