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Topic Review
Sound Source Localization and Detection Methods
Many acoustic detection and localization methods have been developed. However, all of the methods require capturing the audio signal. Therefore, any method’s essential element and requirement is using an acoustic sensor. In addition to converting sound waves into an electrical signal, they also perform other functions, such as: reducing ambient noise, or capturing sounds with frequencies beyond the hearing range of the human ear. Classic methods have stood the test of time and are still widely used due to their simplicity, reliability, and effectiveness. There are three main mathematical methods for determining the sound source. These include triangulation, trilateration, and multilateration
  • 1.3K
  • 28 Dec 2023
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
  • 1.3K
  • 26 Sep 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
  • 1.2K
  • 16 Dec 2022
Topic Review
Right Triangle
A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). The relation between the sides and angles of a right triangle is the basis for trigonometry. The side opposite the right angle is called the hypotenuse (side c in the figure). The sides adjacent to the right angle are called legs (or catheti, singular: cathetus). Side a may be identified as the side adjacent to angle B and opposed to (or opposite) angle A, while side b is the side adjacent to angle A and opposed to angle B. If the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple.
  • 1.1K
  • 17 Oct 2022
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
  • 1.1K
  • 18 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.
  • 1.0K
  • 31 Oct 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.
  • 1.0K
  • 30 Nov 2023
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
  • 1.0K
  • 12 Dec 2022
Topic Review
Design and Experience of Mobile Applications
With the tremendous growth in mobile phones, mobile application development is an important emerging arena. Moreover, various applications fail to serve the purpose of getting the attention of the intended users, which is determined by their User Interface (UI) and User Experience (UX). As a result, developers often find it challenging to meet the users’ expectations. Various aspects of design and the experience of mobile applications using UX/UI are explored. 
  • 985
  • 20 Jul 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
  • 973
  • 15 Dec 2022
Topic Review
Mersenne Conjectures
In mathematics, the Mersenne conjectures concern the characterization of prime numbers of a form called Mersenne primes, meaning prime numbers that are a power of two minus one.
  • 954
  • 10 Oct 2022
Topic Review
Oscillation of Solutions for Fractional Difference Equations
Oscillation is one of the important branches in applied mathematics and can be induced or destroyed by the introduction of nonlinearity, delay, or a stochastic term. The oscillation of differential and difference equations contributes to many realistic applications, such as torsional oscillations, the oscillation of heart beats, sinusoidal oscillation, voltage-controlled neuron models, and harmonic oscillation with damping. 
  • 952
  • 29 Apr 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
  • 951
  • 16 Nov 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
  • 950
  • 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
  • 930
  • 03 Jan 2023
Topic Review
Technology for Science Education
The COVID-19 confinement has represented both opportunities and losses for education. Rarely before has any other period moved the human spirit into such discipline or submission—depending on one’s personal and emotional points of view. Both extremes have been widely influenced by external factors on each individual’s life path. Education in the sciences and engineering has encountered more issues than other disciplines due to specialized mathematical handwriting, experimental demonstrations, abstract complexity, and lab practices. 
  • 921
  • 22 Sep 2021
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.
  • 913
  • 10 Oct 2022
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
  • 907
  • 06 Dec 2022
Biography
Beatrice Aitchison
Beatrice Aitchison (July 18, 1908 – September 22, 1997) was an American mathematician, statistician, and transportation economist who directed the Transport Economics Division of the United States Department of Commerce,[1] and later became the top woman in the United States Postal Service and the first policy-level appointee there.[2] Aitchison's mother was a musician and her father, Clyde
  • 905
  • 01 Dec 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.
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  • 02 Dec 2022
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