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Glen E. Baxter
Glen Earl Baxter (March 19, 1930 – March 30, 1983) was an American mathematician. Baxter's fields of research include probability theory, combinatorial analysis, statistical mechanics and functional analysis. He is known for the Baxter's strong limit theorem., Baxter strong limit theorem. Lately, his 1960 work on the derivation of a specific operator identity that later bore his name, the Rota–Baxter algebra, Rota–Baxter identity, and emanated from some of the fundamental results of the famous probabilist Frank Spitzer in random walk theory has received attention in fields as remote as renormalization theory in perturbative quantum field theory. In 1983 the Glen E. Baxter Memorial Fund was established by family and friends at Purdue University.Purdue University (Department of Statistics): Recipients of the Baxter Award' See also * Baxter permutation References External links * {{DEFAULTSORT:Baxter, Glen E 1930 births 1983 deaths 20th-century American ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minneapolis, Minnesota
Minneapolis () is the largest city in Minnesota, United States, and the county seat of Hennepin County. The city is abundant in water, with thirteen lakes, wetlands, the Mississippi River, creeks and waterfalls. Minneapolis has its origins in timber and as the flour milling capital of the world. It occupies both banks of the Mississippi River and adjoins Saint Paul, the state capital of Minnesota. Prior to European settlement, the site of Minneapolis was inhabited by Dakota people. The settlement was founded along Saint Anthony Falls on a section of land north of Fort Snelling; its growth is attributed to its proximity to the fort and the falls providing power for industrial activity. , the city has an estimated 425,336 inhabitants. It is the most populous city in the state and the 46th-most-populous city in the United States. Minneapolis, Saint Paul and the surrounding area are collectively known as the Twin Cities. Minneapolis has one of the most extensive public ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baxter's Strong Limit Theorem
Baxters Food Group Limited, also known as Baxters of Speyside or Baxters, is a food processing company, based in Fochabers, Scotland. It produces foods such as canned soups, canned meat products, sour pickles, sauces, vinegars, Antipasto, anti-pasti, chutneys, fruit preserves and salad and meat condiments. Products are sold under the Baxters brand as well as a variety of brands owned, or Brand licensing, licensed, to the group. Baxters has remained a Privately held company, private family company for four generations, during which time it has expanded significantly by acquiring other business within the United Kingdom and internationally. Baxters holds a Royal Warrant of Appointment (United Kingdom), Royal Warrant from Elizabeth II of the United Kingdom, Her Majesty the Queen as purveyors of Scottish specialities. The company was known as W.A. Baxter & Sons Ltd. prior to 21 December 2006. History Origins and early to mid 20th century Baxters was founded in 1868 by 25 year ol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1930 Births
Year 193 ( CXCIII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Sosius and Ericius (or, less frequently, year 946 ''Ab urbe condita''). The denomination 193 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * January 1 – Year of the Five Emperors: The Roman Senate chooses Publius Helvius Pertinax, against his will, to succeed the late Commodus as Emperor. Pertinax is forced to reorganize the handling of finances, which were wrecked under Commodus, to reestablish discipline in the Roman army, and to suspend the food programs established by Trajan, provoking the ire of the Praetorian Guard. * March 28 – Pertinax is assassinated by members of the Praetorian Guard, who storm the imperial palace. The Empire is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baxter Permutation
In combinatorial mathematics, a Baxter permutation is a permutation \sigma \in S_n which satisfies the following generalized pattern avoidance property: * There are no indices ''i'' < ''j'' < ''k'' such that ''σ''(''j'' + 1) < ''σ''(''i'') < ''σ''(''k'') < ''σ''(''j'') or ''σ''(''j'') < ''σ''(''k'') < ''σ''(''i'') < ''σ''(''j'' + 1). Equivalently, using the notation for vincular patterns, a Baxter permutation is one that avoids the two dashed patterns 2-41-3 and 3-14-2. For example, the permutation ''σ'' = 2413 in ''S''4 (written in ) is ''not'' a Baxter permutation because, taking ''i'' = 1, ''j'' = 2 and ''k'' = 4, this permutation violates the first condition. These permutations ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirk Kreimer
Dirk Kreimer (born 12 July 1960) is a German physicist who pioneered the Hopf-algebraic approach to perturbative quantum field theory with Alain Connes and other co-authors. He is currently Humboldt professor at the department of mathematics of Humboldt University in Berlin Berlin is Capital of Germany, the capital and largest city of Germany, both by area and List of cities in Germany by population, by population. Its more than 3.85 million inhabitants make it the European Union's List of cities in the European U ..., where he teaches the courses of ''Quantum Field Theory'' (I and II) and ''Hopf Algebras and the Renormalization Group''. References External links * * Living people 1960 births 21st-century German physicists Boston University faculty Academic staff of the Humboldt University of Berlin {{Germany-physicist-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory in quantum mechanics. History Quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its devel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Renormalization
Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of these quantities to compensate for effects of their self-interactions. But even if no infinities arose in loop diagrams in quantum field theory, it could be shown that it would be necessary to renormalize the mass and fields appearing in the original Lagrangian. For example, an electron theory may begin by postulating an electron with an initial mass and charge. In quantum field theory a cloud of virtual particles, such as photons, positrons, and others surrounds and interacts with the initial electron. Accounting for the interactions of the surrounding particles (e.g. collisions at different energies) shows that the electron-system behaves as if it had a different mass and charge than initially postulated. Renormalization, in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Walk Theory
In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line \mathbb Z which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler. Random walks have applications to engineering and many scientific fields including ecology, psychology, computer science, physics, chemistry, biology, economics, and sociology. The term ''random walk'' was first introduced by Karl Pearson in 1905. Lattice random walk A popular random walk model is that of a random walk on a regular lattice, where at each step the location jumps to another site according to some probability distribution. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank Spitzer
Frank Ludvig Spitzer (July 24, 1926 – February 1, 1992) was an Austrian-born American mathematician who made fundamental contributions to probability theory, including the theory of random walks, fluctuation theory, percolation theory, the Wiener sausage, and especially the theory of interacting particle systems. Rare among mathematicians, he chose to focus broadly on "phenomena", rather than any one of the many specific theorems that might help to articulate a given phenomenon. His book ''Principles of Random Walk'', first published in 1964, remains a well-cited classic. Spitzer was born into a Jewish family in Vienna, Austria, and by the time he was twelve years old, the Nazi threat in Austria was evident. His parents were able to send him to a summer camp for Jewish children in Sweden, and, as a result, Spitzer spent all of the war years in Sweden. He lived with two Swedish families, learned Swedish, graduated from high school, and for one year attended Teknis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rota–Baxter Algebra
In mathematics, a Rota–Baxter algebra is an associative algebra, together with a particular linear map R which satisfies the Rota–Baxter identity. It appeared first in the work of the American mathematician Glen E. Baxter in the realm of probability theory. Baxter's work was further explored from different angles by Gian-Carlo Rota, Pierre Cartier, and Frederic V. Atkinson, among others. Baxter’s derivation of this identity that later bore his name emanated from some of the fundamental results of the famous probabilist Frank Spitzer in random walk theory. In the 1980s, the Rota-Baxter operator of weight 0 in the context of Lie algebras was rediscovered as the operator form of the classical Yang–Baxter equation, named after the well-known physicists Chen-Ning Yang and Rodney Baxter. The study of Rota–Baxter algebras experienced a renaissance this century, beginning with several developments, in the algebraic approach to renormalization of perturbative quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations. The usage of the word '' functional'' as a noun goes back to the calculus of variations, implying a function whose argument is a function. The term was first used in Hadamard's 1910 book on that subject. However, the general concept of a functional had previously been introduced in 1887 by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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