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Imre Z. Ruzsa
Imre Z. Ruzsa (born 23 July 1953) is a Hungarian mathematician specializing in number theory. Life He graduated from the Eötvös Loránd University in 1976. Since then he has been at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences. He was awarded the Rollo Davidson Prize in 1988. He was elected corresponding member (1998) and member (2004) of the Hungarian Academy of Sciences. He was invited speaker at the European Congress of Mathematics at Stockholm, 2004, and in the Combinatorics section of the International Congress of Mathematicians in Madrid, 2006. In 2012 he became a fellow of the American Mathematical Society. 0. On the other hand, for every ε > 0 there is an essential component that has at most (log ''x'')1+ε elements up to ''x'', for every ''x''. He gave a new proof to Freiman's theorem. Ruzsa also showed the existence of a Sidon sequence which has at least ''x''0.41 elements up to ''x''. In a result complementing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Budapest
Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by population within city limits and the List of cities and towns on the river Danube, second-largest city on the river Danube. The estimated population of the city in 2025 is 1,782,240. This includes the city's population and surrounding suburban areas, over a land area of about . Budapest, which is both a List of cities and towns of Hungary, city and Counties of Hungary, municipality, forms the centre of the Budapest metropolitan area, which has an area of and a population of 3,019,479. It is a primate city, constituting 33% of the population of Hungary. The history of Budapest began when an early Celts, Celtic settlement transformed into the Ancient Rome, Roman town of Aquincum, the capital of Pannonia Inferior, Lower Pannonia. The Hungarian p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sidon Sequence
In number theory, a Sidon sequence is a sequence A=\ of natural numbers in which all pairwise sums a_i+a_j are different. Sidon sequences are also called Sidon sets; they are named after the Hungarian mathematician Simon Sidon, who introduced the concept in his investigations of Fourier series. The main problem in the study of Sidon sequences, posed by Sidon, is to find the maximum number of elements that a Sidon sequence can contain, up to some bound x. Despite a large body of research, the question has remained unsolved. Early results Paul Erdős and Pál Turán proved that, for every x>0, the number of elements smaller than x in a Sidon sequence is at most \sqrt+O(\sqrt . Several years earlier, James Singer had constructed Sidon sequences with \sqrt(1-o(1)) terms less than ''x''. The upper bound was improved to \sqrt+\sqrt 1 in 1969 and to \sqrt+0.998\sqrt /math> in 2023. In 1994 Erdős offered 500 dollars for a proof or disproof of the bound \sqrt+o(x^\varepsilon). Dense ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Members Of The Hungarian Academy Of Sciences
Member may refer to: * Military jury, referred to as "Members" in military jargon * Element (mathematics), an object that belongs to a mathematical set * In object-oriented programming, a member of a class ** Field (computer science), entries in a database ** Member variable, a variable that is associated with a specific object * Limb (anatomy), an appendage of the human or animal body ** Euphemism for penis * Structural component of a truss, connected by nodes * User (computing), a person making use of a computing service, especially on the Internet * Member (geology), a component of a geological formation * Member of parliament * The Members, a British punk rock band * Meronymy, a semantic relationship in linguistics * Church membership, belonging to a local Christian congregation, a Christian denomination and the universal Church * Member, a participant in a club or learned society A learned society ( ; also scholarly, intellectual, or academic society) is an organizatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century Hungarian Mathematicians
File:1st century collage.png, From top left, clockwise: Jesus is crucified by Roman authorities in Judaea (17th century painting). Four different men (Galba, Otho, Vitellius, and Vespasian) claim the title of Emperor within the span of a year; The Great Fire of Rome (18th-century painting) sees the destruction of two-thirds of the city, precipitating the empire's first persecution against Christians, who are blamed for the disaster; The Roman Colosseum is built and holds its inaugural games; Roman forces besiege Jerusalem during the First Jewish–Roman War (19th-century painting); The Trưng sisters lead a rebellion against the Chinese Han dynasty (anachronistic depiction); Boudica, queen of the British Iceni leads a rebellion against Rome (19th-century statue); Knife-shaped coin of the Xin dynasty., 335px rect 30 30 737 1077 Crucifixion of Jesus rect 767 30 1815 1077 Year of the Four Emperors rect 1846 30 3223 1077 Great Fire of Rome rect 30 1108 1106 2155 Boudican revolt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theorists
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations ( Diophantine geometry). Questions in number theory can often be understood through the study of analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is that it deals wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Purpose: Because living persons may suffer personal harm from inappropriate information, we should watch their articles carefully. By adding an article to this category, it marks them with a notice about sources whenever someone tries to edit them, to remind them of WP:BLP (biographies of living persons) policy that these articles must maintain a neutral point of view, maintain factual accuracy, and be properly sourced. Recent changes to these articles are listed on Special:RecentChangesLinked/Living people. Organization: This category should not be sub-categorized. Entries are generally sorted by family name In many societies, a surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person, although several give .... Maintenance: Individuals of advanced age (over 90), for whom there has been no new documentation in the last ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1953 Births
Events January * January 6 – The Asian Socialist Conference opens in Rangoon, Burma. * January 12 – Estonian émigrés found a government-in-exile in Oslo. * January 14 ** Marshal Josip Broz Tito is chosen President of Yugoslavia. ** The CIA-sponsored Robertson Panel first meets to discuss the UFO phenomenon. * January 15 ** Georg Dertinger, foreign minister of East Germany, is arrested for spying. ** British security forces in West Germany arrest 7 members of the Naumann Circle, a clandestine Neo-Nazi organization. * January 19 – 71.1% of all television sets in the United States are tuned into '' I Love Lucy'', to watch Lucy give birth to Little Ricky, which is more people than those who tune into Dwight Eisenhower's inauguration the next day. This record is never broken. * January 24 ** Mau Mau Uprising: Rebels in Kenya kill the Ruck family (father, mother, and six-year-old son). ** Leader of East Germany Walter Ulbricht announces that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plünnecke–Ruzsa Inequality
In additive combinatorics, the Plünnecke–Ruzsa inequality is an inequality that bounds the size of various sumsets of a set B, given that there is another set A so that A+B is not much larger than A. A slightly weaker version of this inequality was originally proven and published by Helmut Plünnecke (1970). Imre Ruzsa (1989) later published a simpler proof of the current, more general, version of the inequality. The inequality forms a crucial step in the proof of Freiman's theorem. Statement The following sumset notation is standard in additive combinatorics. For subsets A and B of an abelian group and a natural number k, the following are defined: * A+B=\ * A-B=\ * kA=\underbrace_ The set A + B is known as the sumset of A and B. Plünnecke-Ruzsa inequality The most commonly cited version of the statement of the Plünnecke–Ruzsa inequality is the following. This is often used when A = B, in which case the constant K = , 2A, /, A, is known as the doubling constant of A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruzsa Triangle Inequality
In additive combinatorics, the Ruzsa triangle inequality, also known as the Ruzsa difference triangle inequality to differentiate it from some of its variants, bounds the size of the difference of two sets in terms of the sizes of both their differences with a third set. It was proven by Imre Ruzsa (1996), and is so named for its resemblance to the triangle inequality. It is an important lemma in the proof of the Plünnecke-Ruzsa inequality. Statement If A and B are subsets of a group, then the sumset notation A+B is used to denote \. Similarly, A-B denotes \. Then, the Ruzsa triangle inequality states the following. An alternate formulation involves the notion of the ''Ruzsa distance''. Definition. If A and B are finite subsets of a group, then the Ruzsa distance between these two sets, denoted d(A, B), is defined to be :d(A, B) = \log \frac. Then, the Ruzsa triangle inequality has the following equivalent formulation: This formulation resembles the triangle inequalit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometriae Dedicata
''Geometriae Dedicata'' is a mathematical journal, founded in 1972, concentrating on geometry and its relationship to topology, group theory and the theory of dynamical systems. It was created on the initiative of Hans Freudenthal in Utrecht, the Netherlands.. It is published by Springer Netherlands. The Editor-in-Chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The editor-in-chief heads all departments of the organization and is held accoun ... is Richard Alan Wentworth. References External links Springer site Geometry journals Springer Science+Business Media academic journals Algebra journals Dynamical systems journals Topology journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acta Mathematica Hungarica
'' Acta Mathematica Hungarica'' is a peer-reviewed mathematics journal of the Hungarian Academy of Sciences, published by Akadémiai Kiadó and Springer Science+Business Media. The journal was established in 1950 and publishes articles on mathematics related to work by Hungarian mathematicians. Its 2009 MCQ was 0.39, and its 2015 impact factor was 0.469. The editor-in-chief is Imre Bárány, honorary editor is Ákos Császár, the editors are the mathematician members of the Hungarian Academy of Sciences. Abstracting and indexing According to the ''Journal Citation Reports'', the journal had a 2021 impact factor of 0.979. This journal is indexed by the following services: * Science Citation Index * Journal Citation Reports/Science Edition * Scopus * Mathematical Reviews * Zentralblatt Math zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
