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Book
Current Trends in Symmetric Polynomials with Their Applications Ⅱ
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Year: 2021 Publisher: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute

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Abstract

The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.

Keywords

Research & information: general --- Mathematics & science --- OWA operator --- RIM quantifier --- maximum entropy --- minimax ratio --- generating function --- minimal variability --- minimax disparity --- solution equivalence --- fuzzy sets --- extended minimax disparity --- OWA model --- RIM quantifier problem --- extended degenerate r-central factorial numbers of the second kind --- extended degenerate r-central bell polynomials --- type 2 Bernoulli polynomials --- type 2 Euler polynomials --- identities of symmetry --- Laplace distribution --- Fibonacci polynomials --- Lucas polynomials --- sums of powers --- divisible properties --- R. S. Melham's conjectures --- degenerate Bernoulli polynomials --- degenerate Bernstein operators --- extended r-central complete bell polynomials --- extended r-central incomplete bell polynomials --- complete r-Bell polynomials --- incomplete r-bell polynomials --- Fibonacci numbers --- Lucas numbers --- Chebyshev polynomials --- Legendre polynomials --- Jacobi polynomials --- Gegenbauer polynomials --- convolution formula --- Bernoulli polynomials --- random variables --- p-adic invariant integral on Zp --- integer power sums polynomials --- Stirling polynomials of the second kind --- degenerate Stirling polynomials of the second kind --- type 2 degenerate q-Bernoulli polynomials --- p-adic q-integral --- balancing numbers --- balancing polynomials --- combinatorial methods --- symmetry sums --- Chebyshev polynomials of the first kind --- power series --- polynomial identities --- polynomial inequalities --- Waring-Goldbach problem --- circle method --- exceptional set --- symmetric form --- type 2 degenerate Bernoulli polynomials of the second kind --- degenerate central factorial numbers of the second kind --- degenerate poly-Bernoulli polynomials --- degenerate poly-Genocchi polynomials --- stirling numbers --- Erdős-Ko-Rado theorem --- intersecting families --- polynomial method --- polylogarithm functions --- poly-Genocchi polynomials --- unipoly functions --- unipoly Genocchi polynomials --- OWA operator --- RIM quantifier --- maximum entropy --- minimax ratio --- generating function --- minimal variability --- minimax disparity --- solution equivalence --- fuzzy sets --- extended minimax disparity --- OWA model --- RIM quantifier problem --- extended degenerate r-central factorial numbers of the second kind --- extended degenerate r-central bell polynomials --- type 2 Bernoulli polynomials --- type 2 Euler polynomials --- identities of symmetry --- Laplace distribution --- Fibonacci polynomials --- Lucas polynomials --- sums of powers --- divisible properties --- R. S. Melham's conjectures --- degenerate Bernoulli polynomials --- degenerate Bernstein operators --- extended r-central complete bell polynomials --- extended r-central incomplete bell polynomials --- complete r-Bell polynomials --- incomplete r-bell polynomials --- Fibonacci numbers --- Lucas numbers --- Chebyshev polynomials --- Legendre polynomials --- Jacobi polynomials --- Gegenbauer polynomials --- convolution formula --- Bernoulli polynomials --- random variables --- p-adic invariant integral on Zp --- integer power sums polynomials --- Stirling polynomials of the second kind --- degenerate Stirling polynomials of the second kind --- type 2 degenerate q-Bernoulli polynomials --- p-adic q-integral --- balancing numbers --- balancing polynomials --- combinatorial methods --- symmetry sums --- Chebyshev polynomials of the first kind --- power series --- polynomial identities --- polynomial inequalities --- Waring-Goldbach problem --- circle method --- exceptional set --- symmetric form --- type 2 degenerate Bernoulli polynomials of the second kind --- degenerate central factorial numbers of the second kind --- degenerate poly-Bernoulli polynomials --- degenerate poly-Genocchi polynomials --- stirling numbers --- Erdős-Ko-Rado theorem --- intersecting families --- polynomial method --- polylogarithm functions --- poly-Genocchi polynomials --- unipoly functions --- unipoly Genocchi polynomials


Book
Arithmetic and Geometry : Ten Years in Alpbach (AMS-202)
Authors: ---
ISBN: 0691197547 Year: 2019 Publisher: Princeton, NJ : Princeton University Press,

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Abstract

Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures-which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria-provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings height and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach.The first course, taught by Peter Scholze, contains his recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces; in others, one has to use Scholze's perfectoid spaces.The second course, taught by Umberto Zannier, addresses the famous Pell equation-not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians.The third course, taught by Shou-Wu Zhang, originates in the Chowla-Selberg formula, which was taken up by Gross and Zagier to relate values of the L-function for elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross-Zagier formula on Shimura curves and verify the Colmez conjecture on average.

Keywords

Arithmetical algebraic geometry. --- Algebraic geometry, Arithmetical --- Arithmetic algebraic geometry --- Diophantine geometry --- Geometry, Arithmetical algebraic --- Geometry, Diophantine --- Number theory --- Abelian variety. --- Algebraic geometry. --- Algebraic independence. --- Algebraic space. --- Analytic number theory. --- Arbitrarily large. --- Automorphic form. --- Automorphism. --- Base change. --- Big O notation. --- Class number formula. --- Cohomology. --- Complex multiplication. --- Computation. --- Conjecture. --- Conjugacy class. --- Continued fraction. --- Cusp form. --- Diagram (category theory). --- Dimension. --- Diophantine equation. --- Diophantine geometry. --- Discriminant. --- Divisible group. --- Double coset. --- Eisenstein series. --- Endomorphism. --- Equation. --- Existential quantification. --- Exponential map (Riemannian geometry). --- Fiber bundle. --- Floor and ceiling functions. --- Formal group. --- Formal power series. --- Formal scheme. --- Fundamental group. --- Geometric Langlands correspondence. --- Geometry. --- Heegner point. --- Hodge structure. --- Hodge theory. --- Homomorphism. --- I0. --- Integer. --- Intersection number. --- Irreducible component. --- Isogeny. --- Isomorphism class. --- Jacobian variety. --- L-function. --- Langlands dual group. --- Laurent series. --- Linear combination. --- Local system. --- Logarithmic derivative. --- Logarithmic form. --- Mathematics. --- Modular form. --- Moduli space. --- Monotonic function. --- Natural topology. --- P-adic analysis. --- P-adic number. --- Pell's equation. --- Perverse sheaf. --- Polylogarithm. --- Polynomial. --- Power series. --- Presheaf (category theory). --- Prime number. --- Projective space. --- Quaternion algebra. --- Rational point. --- Real number. --- Reductive group. --- Rigid analytic space. --- Roth's theorem. --- Series expansion. --- Shafarevich conjecture. --- Sheaf (mathematics). --- Shimura variety. --- Siegel zero. --- Special case. --- Stack (mathematics). --- Subset. --- Summation. --- Szpiro's conjecture. --- Tate conjecture. --- Tate module. --- Taylor series. --- Theorem. --- Theta function. --- Topological ring. --- Topology. --- Torsor (algebraic geometry). --- Upper and lower bounds. --- Vector bundle. --- Weil group. --- Witt vector. --- Zariski topology.


Book
Current Trends in Symmetric Polynomials with Their Applications Ⅱ
Author:
Year: 2021 Publisher: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute

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Export citation

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Bookmark

Abstract

The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.

Keywords

Research & information: general --- Mathematics & science --- OWA operator --- RIM quantifier --- maximum entropy --- minimax ratio --- generating function --- minimal variability --- minimax disparity --- solution equivalence --- fuzzy sets --- extended minimax disparity --- OWA model --- RIM quantifier problem --- extended degenerate r-central factorial numbers of the second kind --- extended degenerate r-central bell polynomials --- type 2 Bernoulli polynomials --- type 2 Euler polynomials --- identities of symmetry --- Laplace distribution --- Fibonacci polynomials --- Lucas polynomials --- sums of powers --- divisible properties --- R. S. Melham’s conjectures --- degenerate Bernoulli polynomials --- degenerate Bernstein operators --- extended r-central complete bell polynomials --- extended r-central incomplete bell polynomials --- complete r-Bell polynomials --- incomplete r-bell polynomials --- Fibonacci numbers --- Lucas numbers --- Chebyshev polynomials --- Legendre polynomials --- Jacobi polynomials --- Gegenbauer polynomials --- convolution formula --- Bernoulli polynomials --- random variables --- p-adic invariant integral on Zp --- integer power sums polynomials --- Stirling polynomials of the second kind --- degenerate Stirling polynomials of the second kind --- type 2 degenerate q-Bernoulli polynomials --- p-adic q-integral --- balancing numbers --- balancing polynomials --- combinatorial methods --- symmetry sums --- Chebyshev polynomials of the first kind --- power series --- polynomial identities --- polynomial inequalities --- Waring–Goldbach problem --- circle method --- exceptional set --- symmetric form --- type 2 degenerate Bernoulli polynomials of the second kind --- degenerate central factorial numbers of the second kind --- degenerate poly-Bernoulli polynomials --- degenerate poly-Genocchi polynomials --- stirling numbers --- Erdős-Ko-Rado theorem --- intersecting families --- polynomial method --- n/a --- polylogarithm functions --- poly-Genocchi polynomials --- unipoly functions --- unipoly Genocchi polynomials --- R. S. Melham's conjectures --- Waring-Goldbach problem --- Erdős-Ko-Rado theorem


Book
Current Trends in Symmetric Polynomials with Their Applications Ⅱ
Author:
Year: 2021 Publisher: Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute

Loading...
Export citation

Choose an application

Bookmark

Abstract

The special issue contains research papers with various topics in many different branches of mathematics, applied mathematics, and mathematical physics. Each paper presents mathematical theory, methods, and their application based on current and recent developing symmetric polynomials. Also, each one aims to provide the full understanding of current research problems, theories, and applications on the chosen topics and contains the most recent advances made in the area of symmetric functions and polynomials.

Keywords

OWA operator --- RIM quantifier --- maximum entropy --- minimax ratio --- generating function --- minimal variability --- minimax disparity --- solution equivalence --- fuzzy sets --- extended minimax disparity --- OWA model --- RIM quantifier problem --- extended degenerate r-central factorial numbers of the second kind --- extended degenerate r-central bell polynomials --- type 2 Bernoulli polynomials --- type 2 Euler polynomials --- identities of symmetry --- Laplace distribution --- Fibonacci polynomials --- Lucas polynomials --- sums of powers --- divisible properties --- R. S. Melham’s conjectures --- degenerate Bernoulli polynomials --- degenerate Bernstein operators --- extended r-central complete bell polynomials --- extended r-central incomplete bell polynomials --- complete r-Bell polynomials --- incomplete r-bell polynomials --- Fibonacci numbers --- Lucas numbers --- Chebyshev polynomials --- Legendre polynomials --- Jacobi polynomials --- Gegenbauer polynomials --- convolution formula --- Bernoulli polynomials --- random variables --- p-adic invariant integral on Zp --- integer power sums polynomials --- Stirling polynomials of the second kind --- degenerate Stirling polynomials of the second kind --- type 2 degenerate q-Bernoulli polynomials --- p-adic q-integral --- balancing numbers --- balancing polynomials --- combinatorial methods --- symmetry sums --- Chebyshev polynomials of the first kind --- power series --- polynomial identities --- polynomial inequalities --- Waring–Goldbach problem --- circle method --- exceptional set --- symmetric form --- type 2 degenerate Bernoulli polynomials of the second kind --- degenerate central factorial numbers of the second kind --- degenerate poly-Bernoulli polynomials --- degenerate poly-Genocchi polynomials --- stirling numbers --- Erdős-Ko-Rado theorem --- intersecting families --- polynomial method --- n/a --- polylogarithm functions --- poly-Genocchi polynomials --- unipoly functions --- unipoly Genocchi polynomials --- R. S. Melham's conjectures --- Waring-Goldbach problem --- Erdős-Ko-Rado theorem

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