A portmanteau or portmanteau word is a linguistic blend of words, in which parts of multiple words or their phones are combined into a new word, as in smog, coined by blending smoke and fog, or motel, from motor and hotel. In linguistics, a portmanteau is defined as a single morph; the definition overlaps with the grammatical term contraction, but contractions are formed from words that would otherwise appear together in sequence, such as do and not to make don't, whereas a portmanteau word is formed by combining two or more existing words that all relate to a singular concept. A portmanteau differs from a compound, which does not involve the truncation of parts of the stems of the blended words. For instance, starfish is not a portmanteau, of star and fish; the word portmanteau was first used in this sense by Lewis Carroll in the book Through the Looking-Glass, in which Humpty Dumpty explains to Alice the coinage of the unusual words in "Jabberwocky", where slithy means "slimy and lithe" and mimsy is "miserable and flimsy".
Humpty Dumpty explains to Alice the practice of combining words in various ways: You see it's like a portmanteau—there are two meanings packed up into one word. In his introduction to The Hunting of the Snark, Carroll uses portmanteau when discussing lexical selection: Humpty Dumpty's theory, of two meanings packed into one word like a portmanteau, seems to me the right explanation for all. For instance, take the two words "fuming" and "furious." Make up your mind that you will say both words, but leave it unsettled which you will say first … if you have the rarest of gifts, a balanced mind, you will say "frumious." In then-contemporary English, a portmanteau was a suitcase. The etymology of the word is the French porte-manteau, from porter, "to carry", manteau, "cloak". In modern French, a porte-manteau is a clothes valet, a coat-tree or similar article of furniture for hanging up jackets, hats and the like. An occasional synonym for "portmanteau word" is frankenword, an autological word exemplifying the phenomenon it describes, blending "Frankenstein" and "word".
Many neologisms are examples of blends. In Punch in 1896, the word brunch was introduced as a "portmanteau word." In 1964, the newly independent African republic of Tanganyika and Zanzibar chose the portmanteau word Tanzania as its name. Eurasia is a portmanteau of Europe and Asia; some city names are portmanteaus of the border regions they straddle: Texarkana spreads across the Texas-Arkansas border, while Calexico and Mexicali are the American and Mexican sides of a single conurbation. A scientific example is a liger, a cross between a male lion and a female tiger. Many company or brand names are portmanteaus, including Microsoft, a portmanteau of microcomputer and software. "Jeoportmanteau!" is a recurring category on the American television quiz show Jeopardy!. The category's name is itself a portmanteau of the words "Jeopardy" and "portmanteau." Responses in the category are portmanteaus constructed by fitting two words together. Portmanteau words may be produced by joining together proper nouns with common nouns, such as "gerrymandering", which refers to the scheme of Massachusetts Governor Elbridge Gerry for politically contrived redistricting.
The term gerrymander has itself contributed to portmanteau terms playmander. Oxbridge is a common portmanteau for the UK's two oldest universities, those of Oxford and Cambridge. In 2016, Britain's planned exit from the European Union became known as "Brexit". David Beckham's English mansion Rowneybury House was nicknamed "Beckingham Palace", a portmanteau of his surname and Buckingham Palace. Many portmanteau words do not appear in all dictionaries. For example, a spork is an eating utensil, a combination of a spoon and a fork, a skort is an item of clothing, part skirt, part shorts. On the other hand, turducken, a dish made by inserting a chicken into a duck, the duck into a turkey, was added to the Oxford English Dictionary in 2010; the word refudiate was first used by Sarah Palin when she misspoke, conflating the words refute and repudiate. Though a gaffe, the word was recognized as the New Oxford American Dictionary's "Word of the Year" in 2010; the business lexicon is replete with newly coined portmanteau words like "permalance", "advertainment", "advertorial", "infotainment", "infomercial".
A company name may be portmanteau as well as a product name. Two proper names can be used in creating a portmanteau word in r
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though most classify up to homotopy equivalence. Although algebraic topology uses algebra to study topological problems, using topology to solve algebraic problems is sometimes possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. Below are some of the main areas studied in algebraic topology: In mathematics, homotopy groups are used in algebraic topology to classify topological spaces; the first and simplest homotopy group is the fundamental group, which records information about loops in a space. Intuitively, homotopy groups record information about the basic shape, or holes, of a topological space. In algebraic topology and abstract algebra, homology is a certain general procedure to associate a sequence of abelian groups or modules with a given mathematical object such as a topological space or a group.
In homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain complex. That is, cohomology is defined as the abstract study of cochains and coboundaries. Cohomology can be viewed as a method of assigning algebraic invariants to a topological space that has a more refined algebraic structure than does homology. Cohomology arises from the algebraic dualization of the construction of homology. In less abstract language, cochains in the fundamental sense should assign'quantities' to the chains of homology theory. A manifold is a topological space. Examples include the plane, the sphere, the torus, which can all be realized in three dimensions, but the Klein bottle and real projective plane which cannot be realized in three dimensions, but can be realized in four dimensions. Results in algebraic topology focus on global, non-differentiable aspects of manifolds. Knot theory is the study of mathematical knots. While inspired by knots that appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone.
In precise mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R 3. Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R 3 upon itself. A simplicial complex is a topological space of a certain kind, constructed by "gluing together" points, line segments and their n-dimensional counterparts. Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory; the purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex. A CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory; this class of spaces is broader and has some better categorical properties than simplicial complexes, but still retains a combinatorial nature that allows for computation. An older name for the subject was combinatorial topology, implying an emphasis on how a space X was constructed from simpler ones.
In the 1920s and 1930s, there was growing emphasis on investigating topological spaces by finding correspondences from them to algebraic groups, which led to the change of name to algebraic topology. The combinatorial topology name is still sometimes used to emphasize an algorithmic approach based on decomposition of spaces. In the algebraic approach, one finds a correspondence between spaces and groups that respects the relation of homeomorphism of spaces; this allows one to recast statements about topological spaces into statements about groups, which have a great deal of manageable structure making these statement easier to prove. Two major ways in which this can be done are through fundamental groups, or more homotopy theory, through homology and cohomology groups; the fundamental groups give us basic information about the structure of a topological space, but they are nonabelian and can be difficult to work with. The fundamental group of a simplicial complex does have a finite presentation.
Homology and cohomology groups, on the other hand, are abelian and in many important cases finitely generated. Finitely generated abelian groups are classified and are easy to work with. In general, all constructions of algebraic topology are functorial. Fundamental groups and homology and cohomology groups are not only invariants of the underlying topological space, in the sense that two topological spaces which are homeomorphic have the same associated groups, but their associated morphisms correspond — a continuous mapping of spaces induces a group homomorphism on the associated groups, these homomorphisms can be used to show non-existence of mappings. One of the first mathematicians to work with different types of cohomology was Georges de Rham. One can use the differential structure of smooth manifolds via de Rham cohomology, or Čech or sheaf co
In set theory, a Cartesian product is a mathematical operation that returns a set from multiple sets. That is, for sets A and B, the Cartesian product A × B is the set of all ordered pairs where a ∈ A and b ∈ B. Products can be specified using e.g.. A × B =. A table can be created by taking the Cartesian product of a set of columns. If the Cartesian product rows × columns is taken, the cells of the table contain ordered pairs of the form. More a Cartesian product of n sets known as an n-fold Cartesian product, can be represented by an array of n dimensions, where each element is an n-tuple. An ordered pair is a couple; the Cartesian product is named after René Descartes, whose formulation of analytic geometry gave rise to the concept, further generalized in terms of direct product. An illustrative example is the standard 52-card deck; the standard playing card ranks form a 13-element set. The card suits form a four-element set; the Cartesian product of these sets returns a 52-element set consisting of 52 ordered pairs, which correspond to all 52 possible playing cards.
Ranks × Suits returns a set of the form. Suits × Ranks returns a set of the form. Both sets are distinct disjoint; the main historical example is the Cartesian plane in analytic geometry. In order to represent geometrical shapes in a numerical way and extract numerical information from shapes' numerical representations, René Descartes assigned to each point in the plane a pair of real numbers, called its coordinates; such a pair's first and second components are called its x and y coordinates, respectively. The set of all such pairs is thus assigned to the set of all points in the plane. A formal definition of the Cartesian product from set-theoretical principles follows from a definition of ordered pair; the most common definition of ordered pairs, the Kuratowski definition, is =. Under this definition, is an element of P, X × Y is a subset of that set, where P represents the power set operator. Therefore, the existence of the Cartesian product of any two sets in ZFC follows from the axioms of pairing, power set, specification.
Since functions are defined as a special case of relations, relations are defined as subsets of the Cartesian product, the definition of the two-set Cartesian product is prior to most other definitions. Let A, B, C, D be sets; the Cartesian product A × B is not commutative, A × B ≠ B × A, because the ordered pairs are reversed unless at least one of the following conditions is satisfied: A is equal to B, or A or B is the empty set. For example: A =. × C ≠ A × If for example A = × A = ≠ = A ×. The Cartesian product behaves nicely with respect to intersections. × = ∩. × ≠ ∪ In fact, we have that: ∪ = ∪ ∪ [ ( B
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra. It consists of a set equipped with two binary operations that generalize the arithmetic operations of addition and multiplication. Through this generalization, theorems from arithmetic are extended to non-numerical objects such as polynomials, series and functions. A ring is an abelian group with a second binary operation, associative, is distributive over the abelian group operation, has an identity element. By extension from the integers, the abelian group operation is called addition and the second binary operation is called multiplication. Whether a ring is commutative or not has profound implications on its behavior as an abstract object; as a result, commutative ring theory known as commutative algebra, is a key topic in ring theory. Its development has been influenced by problems and ideas occurring in algebraic number theory and algebraic geometry. Examples of commutative rings include the set of integers equipped with the addition and multiplication operations, the set of polynomials equipped with their addition and multiplication, the coordinate ring of an affine algebraic variety, the ring of integers of a number field.
Examples of noncommutative rings include the ring of n × n real square matrices with n ≥ 2, group rings in representation theory, operator algebras in functional analysis, rings of differential operators in the theory of differential operators, the cohomology ring of a topological space in topology. The conceptualization of rings was completed in the 1920s. Key contributors include Dedekind, Hilbert and Noether. Rings were first formalized as a generalization of Dedekind domains that occur in number theory, of polynomial rings and rings of invariants that occur in algebraic geometry and invariant theory. Afterward, they proved to be useful in other branches of mathematics such as geometry and mathematical analysis; the most familiar example of a ring is the set of all integers, Z, consisting of the numbers …, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, …The familiar properties for addition and multiplication of integers serve as a model for the axioms for rings. A ring is a set R equipped with two binary operations + and · satisfying the following three sets of axioms, called the ring axioms R is an abelian group under addition, meaning that: + c = a + for all a, b, c in R. a + b = b + a for all a, b in R.
There is an element 0 in R such that a + 0 = a for all a in R. For each a in R there exists −a in R such that a + = 0. R is a monoid under multiplication, meaning that: · c = a · for all a, b, c in R. There is an element 1 in R such that a · 1 = a and 1 · a = a for all a in R. Multiplication is distributive with respect to addition, meaning that: a ⋅ = + for all a, b, c in R. · a = + for all a, b, c in R. As explained in § History below, many authors follow an alternative convention in which a ring is not defined to have a multiplicative identity; this article adopts the convention that, unless otherwise stated, a ring is assumed to have such an identity. A structure satisfying all the axioms except the requirement that there exists a multiplicative identity element is called a rng. For example, the set of integers with the usual + and ⋅ is a rng, but not a ring; the operations + and ⋅ are called multiplication, respectively. The multiplication symbol ⋅ is omitted, so the juxtaposition of ring elements is interpreted as multiplication.
For example, xy means x ⋅ y. Although ring addition is commutative, ring multiplication is not required to be commutative: ab need not equal ba. Rings that satisfy commutativity for multiplication are called commutative rings. Books on commutative algebra or algebraic geometry adopt the convention that ring means commutative ring, to simplify terminology. In a ring, multiplication does not have to have an inverse. A commutative ring such; the additive group of a ring is the ring equipped just with the structure of addition. Although the definition assumes that the additive group is abelian, this can be inferred from the other ring axioms; some basic properties of a ring follow from the axioms: The additive identity, the additive inverse of each element, the multiplicative identity are unique. For any element x in a ring R, one has x0 = 0 = 0x and x = –x. If 0 = 1 in a ring R R has only one element, is called the zero ring; the binomial formula holds for any commuting pair of elements. Equip the set Z 4 = with the following operat
Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to
Pierre René, Viscount Deligne is a Belgian mathematician. He is known for work on the Weil conjectures, leading to a complete proof in 1973, he is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, 1978 Fields Medal. Deligne was born in Etterbeek, attended school at Athénée Adolphe Max and studied at the Université libre de Bruxelles, writing a dissertation titled Théorème de Lefschetz et critères de dégénérescence de suites spectrales, he completed his doctorate at the University of Paris-Sud in Orsay 1972 under the supervision of Alexander Grothendieck, with a thesis titled Théorie de Hodge. Starting in 1972, Deligne worked with Grothendieck at the Institut des Hautes Études Scientifiques near Paris on the generalization within scheme theory of Zariski's main theorem. In 1968, he worked with Jean-Pierre Serre. Deligne's focused on topics in Hodge theory, he tested them on objects in complex geometry. He collaborated with David Mumford on a new description of the moduli spaces for curves.
Their work came to be seen as an introduction to one form of the theory of algebraic stacks, has been applied to questions arising from string theory. Deligne's most famous contribution was his proof of the third and last of the Weil conjectures; this proof completed a programme initiated and developed by Alexander Grothendieck. As a corollary he proved the celebrated Ramanujan–Petersson conjecture for modular forms of weight greater than one. Deligne's 1974 paper contains the first proof of the Weil conjectures, Deligne's contribution being to supply the estimate of the eigenvalues of the Frobenius endomorphism, considered the geometric analogue of the Riemann hypothesis. Deligne's 1980 paper contains a much more general version of the Riemann hypothesis. From 1970 until 1984, Deligne was a permanent member of the IHÉS staff. During this time he did much important work outside of his work on algebraic geometry. In joint work with George Lusztig, Deligne applied étale cohomology to construct representations of finite groups of Lie type.
He received a Fields Medal in 1978. In 1984, Deligne moved to the Institute for Advanced Study in Princeton. In terms of the completion of some of the underlying Grothendieck program of research, he defined absolute Hodge cycles, as a surrogate for the missing and still conjectural theory of motives; this idea allows one to get around the lack of knowledge of the Hodge conjecture, for some applications. He reworked the Tannakian category theory in his 1990 paper for the Grothendieck Festschrift, employing Beck's theorem – the Tannakian category concept being the categorical expression of the linearity of the theory of motives as the ultimate Weil cohomology. All this is part of the yoga of uniting Hodge theory and the l-adic Galois representations; the Shimura variety theory is related, by the idea that such varieties should parametrize not just good families of Hodge structures, but actual motives. This theory is not yet a finished product, more recent trends have used K-theory approaches, he was awarded the Fields Medal in 1978, the Crafoord Prize in 1988, the Balzan Prize in 2004, the Wolf Prize in 2008, the Abel Prize in 2013.
In 2006 he was ennobled by the Belgian king as viscount. In 2009, Deligne was elected a foreign member of the Royal Swedish Academy of Sciences, he is a member of the Norwegian Academy of Letters. Deligne, Pierre. "La conjecture de Weil: I". Publications Mathématiques de l'IHÉS. 43: 273–307. Doi:10.1007/bf02684373. Deligne, Pierre. "La conjecture de Weil: II". Publications Mathématiques de l'IHÉS. 52: 137–252. Doi:10.1007/BF02684780. Deligne, Pierre. "Catégories tannakiennes". Grothendieck Festschrift vol II. Progress in Mathematics. 87: 111–195. Deligne, Pierre. "Real homotopy theory of Kähler manifolds". Inventiones Mathematicae. 29: 245–274. Doi:10.1007/BF01389853. MR 0382702. Deligne, Pierre. Commensurabilities among Lattices in PU. Princeton, N. J.: Princeton University Press. ISBN 0-691-00096-4. Quantum fields and strings: a course for mathematicians. Vols. 1, 2. Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997. Edited by Pierre Deligne, Pavel Etingof, Daniel S. Freed, Lisa C.
Jeffrey, David Kazhdan, John W. Morgan, David R. Morrison and Edward Witten. American Mathematical Society, Providence, RI. Vol. 1: xxii+723 pp.. ISBN 0-8218-1198-3. Deligne wrote multiple hand-written letters to other mathematicians in the 1970s; these include "Deligne's letter to Piatetskii-Shapiro". Archived from the original on 7 December 2012. Retrieved 15 December 2012. "Deligne's letter to Jean-Pierre Serre". 2012-12-15. "Deligne's letter to Looijenga". Retrieved 15 December 2012; the following mathematical concepts are named after Deligne: Deligne–Lusztig theory Deligne–Mumford moduli space of curves Deligne–Mumford stacks Fourier–Deligne transform Deligne cohomology Deligne motive Deligne tensor product of abelian categories Langlands–Deligne local constantAdditionally, many different conjectures in mathematics have been called the De
The 1990s was a decade of the Gregorian calendar that began on January 1, 1990, ended on December 31, 1999. Culturally, the 1990s are characterized by the rise of multiculturalism and alternative media, which continued into the 2000s and 2010s. Movements such as grunge, the rave scene and hip hop spread around the world to young people during that decade, aided by then-new technology such as cable television and the World Wide Web. In the absence of world communism, which collapsed in the first two years of the decade, the 1990s was politically defined by a movement towards the right-wing, including increase in support for far-right parties in Europe as well as the advent of the Hindu nationalist Bharatiya Janata Party and cuts in social spending in the United States, New Zealand, the UK; the United States saw a massive revival in the use of the death penalty in the 1990s, which reversed in the early 21st century. During the 1990s the character of the European Union and Euro were codified in treaties.
A combination of factors, including the continued mass mobilization of capital markets through neo-liberalism, the thawing of the decades-long Cold War, the beginning of the widespread proliferation of new media such as the Internet from the middle of the decade onwards, increasing skepticism towards government, the dissolution of the Soviet Union led to a realignment and reconsolidation of economic and political power across the world and within countries. The dot-com bubble of 1997–2000 brought wealth to some entrepreneurs before its crash between 2000 and 2001; the 1990s saw extreme advances in technology, with the World Wide Web, the first gene therapy trial, the first designer babies all emerging in 1990 and being improved and built upon throughout the decade. New ethnic conflicts emerged in Africa, the Balkans, the Caucasus, the former two which led to the Rwandan and Bosnian genocides, respectively. Signs of any resolution of tensions between Israel and the Arab world remained elusive despite the progress of the Oslo Accords, though The Troubles in Northern Ireland came to a standstill in 1998 with the Good Friday Agreement after 30 years of violence.
The most prominent armed conflicts of the decade include: The Congo wars break out in the 1990s: The First Congo War takes place in Zaire from 1996 to 1997, resulting in Zairian dictator Mobutu Sese Seko being overthrown from power on 16 May 1997, ending 32 years of his rule. Zaire is renamed the Democratic Republic of the Congo; the Second Congo War starts in 1998 in central Africa and includes 50 different cultures and 7 different nations. It continued until 2003; the Gulf War – Iraq was left in severe debt after the 1980s war with Iran. President Saddam Hussein accused Kuwait of driving down prices; as a result, on 2 August 1990, Iraqi forces conquered Kuwait. The UN condemned the action, a coalition force led by the United States was sent to the Persian Gulf. Aerial bombing of Iraq began in January 1991, a month the UN forces drove the Iraqi army from Kuwait in just four days. In the aftermath of the war, the Kurds in the north of Iraq and the Shiites in the south rose up in revolt, Saddam Hussein managed to hold onto power.
Until the US invasion in 2003, Iraq was cut off from much of the world. The Chechen wars break out in the 1990s: The First Chechen War – the conflict was fought between the Russian Federation and the Chechen Republic of Ichkeria. After the initial campaign of 1994–1995, culminating in the devastating Battle of Grozny, Russian federal forces attempted to seize control of the mountainous area of Chechnya but were set back by Chechen guerrilla warfare and raids on the flatlands in spite of Russia's overwhelming manpower and air support; the resulting widespread demoralization of federal forces, the universal opposition of the Russian public to the conflict, led Boris Yeltsin's government to declare a ceasefire in 1996 and sign a peace treaty a year later. The Second Chechen War – the war was launched by the Russian Federation starting 26 August 1999, in response to the Invasion of Dagestan and the Russian apartment bombings which were blamed on the Chechens. During the war Russian forces recaptured the separatist region of Chechnya.
The campaign reversed the outcome of the First Chechen War, in which the region gained de facto independence as the Chechen Republic of Ichkeria. The Kargil War – In May 1999, Pakistan sent troops covertly to occupy strategic peaks in Kashmir. A month the Kargil War with India results in a political fiasco for Prime Minister Nawaz Sharif, followed by a Pakistani military withdrawal to the Line of Control; the incident leads to a military coup in October, in which Sharif is ousted by Army Chief Pervez Musharraf. This conflict remains; the Yugoslav Wars – The breakup of Yugoslavia beginning on 25 June 1991 after the republics of Croatia and Slovenia declared independence from Yugoslavia, followed by the subsequent Yugoslav wars. The Yugoslav Wars would become notorious for numerous war crimes and human rights violations such as ethnic cleansing and genocide committed by all sides. Ten-Day War – a brief military conflict between Slovenian TO and the Yugoslav People's Army following Slovenia's declaration of independence.
Croatian War of Independence – the war fought in hegh town Croatia between the Croatian government, having declared independence from the Socialist Federal Republic of Yugoslavia, both the Yugoslav People's Army and Serb forces, who established