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Biography
Misir Mardanov
Misir Jumayil oglu Mardanov (Azerbaijani: Misir Mərdanov Cumayıl oğlu; born October 3, 1946) is an Azerbaijani academic and politician who is director of the institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, former Minister of Education of Azerbaijan Republic, Corr.-member of ANAS, doctor of physico-mathematical sciences, professor. Misir Mardanov wa
  • 2.4K
  • 26 Dec 2022
Topic Review
Journal Axioms
Axioms (ISSN 2075-1680) is an international, peer-reviewed, open access journal of mathematics, mathematical logic and mathematical physics, published quarterly online by MDPI. It's now indexed within SCIE (Web of Science), Scopus, dblp, and other databases.
  • 2.3K
  • 26 Sep 2021
Topic Review
Hybrid Number
A hybrid number is a generalization of complex numbers [math]\displaystyle{ \left(a+\mathbf{i}b, \mathbf{i}^{2}=-1\right) }[/math], split-complex numbers (or "hyperbolic number") [math]\displaystyle{ \left(a+\mathbf{h}b, \mathbf{h}^2=1\right) }[/math] and dual numbers [math]\displaystyle{ \left(a+\mathbf{\varepsilon} b, \mathbf{\varepsilon}^2 = 0\right) }[/math]. Hybrid numbers form a noncommutative ring. Complex, hyperbolic and dual numbers are well known two-dimensional number systems. It is well known that, the set of complex numbers, hyperbolic numbers and dual numbers are respectively. The algebra of hybrid numbers is a noncommutative algebra which unifies all three number systems calls them hybrid numbers., , . A hybrid number is a number created with any combination of the complex, hyperbolic and dual numbers satisfying the relation Because these numbers are a composition of dual, complex and hyperbolic numbers, Ozdemir calls them hybrid numbers . A commutative two-dimensional unital algebra generated by a 2 by 2 matrix is isomorphic to either complex, dual or hyperbolic numbers . Due to the set of hybrid numbers is a two-dimensional commutative algebra spanned by 1 and [math]\displaystyle{ \mathbf{i}b+c\mathbf{\varepsilon }+d\mathbf{h} }[/math], it is isomorphic to one of the complex, dual or hyperbolic numbers. Especially in the last century, a lot of researchers deal with the geometric and physical applications of these numbers. Just as the geometry of the Euclidean plane can be described with complex numbers, the geometry of the Minkowski plane and Galilean plane can be described with hyperbolic numbers. The group of Euclidean rotations SO(2) is isomorphic to the group U(1) of unit complex numbers. The geometrical meaning of multiplying by [math]\displaystyle{ e^{\mathbf{i}\theta}=\cos \theta +\mathbf{i}\sin \theta }[/math] means a rotation of the plane. , . The group of Lorentzian rotations [math]\displaystyle{ SO(1,1) }[/math] is isomorphic to the group of unit spacelike hyperbolic numbers. This rotation can be viewed as hyperbolic rotation. Thus, multiplying by [math]\displaystyle{ e^{\mathbf{h}\theta }=\cosh \theta +\mathbf{h} \sinh \theta }[/math] means a map of hyperbolic numbers into itself which preserves the Lorentzian metric. , , , The Galilean rotations can be interpreted with dual numbers. The concept of a rotation in the dual number plane is equivalent to a vertical shear mapping since [math]\displaystyle{ \left( 1+x\mathbf{\varepsilon }\right) \left( 1+y\mathbf{\varepsilon }\right) =1+\left( x+y\right) \mathbf{\varepsilon } }[/math]. The Euler formula for dual numbers is [math]\displaystyle{ e^{\mathbf{\varepsilon }\theta }=1+\mathbf{\varepsilon }\theta }[/math]. Multiplying by [math]\displaystyle{ e^{\mathbf{\varepsilon \theta }} }[/math] is a map of dual numbers into itself which preserves the Galilean metric. This rotation can be named as parabolic rotation , , , , , . File:Planar rotations.tif In abstract algebra, the complex, the hyperbolic and the dual numbers can be described as the quotient of the polynomial ring [math]\displaystyle{ \mathbb{R}[x] }[/math] by the ideal generated by the polynomials [math]\displaystyle{ x^2+1, }[/math], [math]\displaystyle{ x^2-1 }[/math] and [math]\displaystyle{ x^{2} }[/math] respectively. That is, Matrix represantations of the units [math]\displaystyle{ \mathbf{i} }[/math], [math]\displaystyle{ \mathbf{\varepsilon } }[/math], [math]\displaystyle{ \mathbf{h} }[/math] are respectively.
  • 2.0K
  • 08 Nov 2022
Topic Review
König's Lemma
König's lemma or Kőnig's infinity lemma is a theorem in graph theory due to Dénes Kőnig (1927). It gives a sufficient condition for an infinite graph to have an infinitely long path. The computability aspects of this theorem have been thoroughly investigated by researchers in mathematical logic, especially in computability theory. This theorem also has important roles in constructive mathematics and proof theory.
  • 2.0K
  • 31 Oct 2022
Biography
Daina Taimina
Daina Taimiņa (born August 19, 1954)[1] is a Latvian mathematician, currently adjunct associate professor at Cornell University, known for crocheting objects to illustrate hyperbolic space. Taimina received all her formal education in Riga, Latvia, where in 1977 she graduated summa cum laude from the University of Latvia and completed her graduate work in theoretical computer science (superv
  • 1.9K
  • 16 Dec 2022
Topic Review Video
K-Center Problem
This entry is adapted from the peer-reviewed paper 10.1109/ACCESS.2019.2933875 K-center problems are particular cases of the facility location problem, where a set of optimal centers are to be found given a set of constraints. In a nutshell, a k-center problem usually seeks a set of at most k centers that minimize the distance a client must travel to its nearest center. Namely, their objective function is often a minmax one. Naturally, these problems are well suited for modeling real location problems. Although many different problems fit within the description of a k-center problem, the most popular of these is the vertex k-center problem, where the input is a simple graph and an integer k, and the goal is to find at most k vertices whose distance to the remaining vertices is minimal.
  • 1.8K
  • 30 Nov 2023
Biography
Thomas Little Heath
Sir Thomas Little Heath KCB KCVO FRS FBA (/hiːθ/; 5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer. He was educated at Clifton College. Heath translated works of Euclid of Alexandria, Apollonius of Perga, Aristarchus of Samos, and Archimedes of Syracuse into English. Heath was
  • 1.7K
  • 18 Nov 2022
Biography
Slavik Jablan
After a long and brave battle with a serious illness, our dear friend and colleague Slavik Jablan passed away on 26 February 2015. The world is deprived of a remarkable mathematician, a great artist, a wonderful man and a dear friend. He made significant contributions to many areas of mathematics: geometry, group theory, mathematical crystallography, the theory of symmetry, antisymmetry, color
  • 1.7K
  • 26 Sep 2022
Biography
Alexander Dewdney
Alexander Keewatin Dewdney (born August 5, 1941) is a Canadian mathematician, computer scientist, author, filmmaker, and conspiracy theorist. Dewdney is the son of Canadian artist and author Selwyn Dewdney, and brother of poet Christopher Dewdney. He was born in London, Ontario. In his student days, Dewdney made a number of influential experimental films, including Malanga, on the poet Gerald
  • 1.5K
  • 12 Dec 2022
Biography
Pierre Deligne
Pierre René, Viscount Deligne (French: [dəliɲ]; born 3 October 1944) 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, and 1978 Fields Medal. Deligne was born in Etterbeek, attended school at Athénée Adolphe Max and studied at the Université libre
  • 1.4K
  • 08 Dec 2022
Biography
Ezra A. (Bud) Brown
Ezra A. Brown (born January 22, 1944 in Reading, PA) is an American mathematician active in combinatorics, algebraic number theory, elliptic curves, graph theory, expository mathematics and cryptography. He spent most of his career at Virginia Tech where he is now Alumni Distinguished Professor Emeritus of Mathematics.[1] Brown earned a B.A. at Rice University in 1965.[2] He then studied math
  • 1.4K
  • 15 Dec 2022
Topic Review
Facility Location and Vehicle-Routing Problem in Reverse Logistics
The concept of reverse logistics (RL) was put forward in 1992, whose essence was to transfer end-of-life (EOL) products from the consumer to the producer for processing.
  • 1.4K
  • 13 Jan 2023
Biography
John Pell
John Pell (1 March 1611 – 12 December 1685) was an English mathematician and political agent abroad. He was born at Southwick in Sussex. His father, also named John Pell, was from Southwick, and his mother was Mary Holland, from Halden in Kent. The second of two sons, Pell's older brother was Thomas Pell. By the time he was six, they were orphans, their father dying in 1616 and their mother
  • 1.4K
  • 06 Dec 2022
Topic Review
Lebesgue Constant (Interpolation)
In mathematics, the Lebesgue constants (depending on a set of nodes and of its size) give an idea of how good the interpolant of a function (at the given nodes) is in comparison with the best polynomial approximation of the function (the degree of the polynomials are obviously fixed). The Lebesgue constant for polynomials of degree at most n and for the set of n + 1 nodes T is generally denoted by Λn(T ). These constants are named after Henri Lebesgue.
  • 1.4K
  • 01 Dec 2022
Topic Review
Moser–De Bruijn Sequence
In number theory, the Moser–De Bruijn sequence is an integer sequence named after Leo Moser and Nicolaas Govert de Bruijn, consisting of the sums of distinct powers of 4, or equivalently the numbers whose binary representations are nonzero only in even positions. These numbers grow in proportion to the square numbers, and are the squares for a modified form of arithmetic without carrying. No two doubled sequence members differ by a square, and every non-negative integer has a unique representation as the sum of a sequence member and a doubled sequence member. This decomposition into sums can be used to define a bijection between the integers and pairs of integers, to define coordinates for the Z-order curve, and to construct inverse pairs of transcendental numbers with simple decimal representations. A simple recurrence relation allows values of the Moser–De Bruijn sequence to be calculated from earlier values, and can be used to prove that the Moser–De Bruijn sequence is a 2-regular sequence.
  • 1.3K
  • 10 Oct 2022
Biography
Mary Eleanor Spear
Mary Eleanor Hunt Spear (March 4, 1897 – January 22, 1986) was an American data visualization specialist, graphic analyst and author, who pioneered development of the bar chart and box plot. Spear was born in Jonesboro, Indiana, the daughter of Amos Zophar Hunt and Mabel Elizabeth Ewry Hunt.[1] She attended Peabody Elementary School, Washington D.C.,[2] followed by Eastern High School.[2] S
  • 1.3K
  • 16 Nov 2022
Topic Review
Birkhoff's Representation Theorem
In mathematics, Birkhoff's representation theorem for distributive lattices states that the elements of any finite distributive lattice can be represented as finite sets, in such a way that the lattice operations correspond to unions and intersections of sets. The theorem can be interpreted as providing a one-to-one correspondence between distributive lattices and partial orders, between quasi-ordinal knowledge spaces and preorders, or between finite topological spaces and preorders. It is named after Garrett Birkhoff, who published a proof of it in 1937. The name “Birkhoff's representation theorem” has also been applied to two other results of Birkhoff, one from 1935 on the representation of Boolean algebras as families of sets closed under union, intersection, and complement (so-called fields of sets, closely related to the rings of sets used by Birkhoff to represent distributive lattices), and Birkhoff's HSP theorem representing algebras as products of irreducible algebras. Birkhoff's representation theorem has also been called the fundamental theorem for finite distributive lattices.
  • 1.3K
  • 10 Oct 2022
Topic Review
Deformation Theory
In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions Pε, where ε is a small number, or vector of small quantities. The infinitesimal conditions are therefore the result of applying the approach of differential calculus to solving a problem with constraints. One might think, in analogy, of a structure that is not completely rigid, and that deforms slightly to accommodate forces applied from the outside; this explains the name. Some characteristic phenomena are: the derivation of first-order equations by treating the ε quantities as having negligible squares; the possibility of isolated solutions, in that varying a solution may not be possible, or does not bring anything new; and the question of whether the infinitesimal constraints actually 'integrate', so that their solution does provide small variations. In some form these considerations have a history of centuries in mathematics, but also in physics and engineering. For example, in the geometry of numbers a class of results called isolation theorems was recognised, with the topological interpretation of an open orbit (of a group action) around a given solution. Perturbation theory also looks at deformations, in general of operators.
  • 1.3K
  • 02 Dec 2022
Biography
William Minicozzi II
William Philip Minicozzi II is an United States mathematician. He was born in Bryn Mawr, Pennsylvania, in 1967. Minicozzi graduated from Princeton University in 1990 and received his Ph.D. from Stanford University in 1994 under the direction of Richard Schoen. After graduating he spent a year at the Courant Institute of New York University as a visiting member where he began working with Tobi
  • 1.3K
  • 12 Dec 2022
Biography
Mark Krasnosel'skii
Mark Alexandrovich Krasnosel'skii (Russian: Ма́рк Алекса́ндрович Красносе́льский) (April 27, 1920, Starokostiantyniv – February 13, 1997, Moscow) was a Soviet, Russia n and Ukraine mathematician renowned for his work on nonlinear functional analysis and its applications. Mark Krasnosel'skii was born in the town of Starokostiantyniv in Ukraine on the 27 Ap
  • 1.3K
  • 03 Jan 2023
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