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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On polynomial method and its application（III）
多项式方法 多项式划分 关联几何
2023/5/10
We will introduce the polynomial partitioning method which has wide applications in incidence geometry, geometric measure theory, and harmonic analysis. In the first course, we will present some basic...
It is well known that the real cohomology of a compact Riemannian manifold
M is isomorphic to the algebra of its harmonic forms. When M is a fiat
Riemannian manifold, i.e. a Euclidean manifold, a ...
A generalization of The Dress construction for a Tambara functor, and polynomial Tambara functors
A generalization Dress construction Tambara functor polynomial Tambara functors
2011/1/19
For a finite group G, (semi-)Mackey functors and (semi-)Tambara functors are regarded as G-bivariant analogs of (semi-)groups and (semi-)rings respectively. In fact if G is trivial, they agree with th...
Generalization of the Bollobás-Riordan polynomial for tensor graphs
(multivariate) topological graph polynomials group eld theory
2011/1/19
Tensor models are used nowadays for implementing a fundamental theory of quan-tum gravity. We de ne here a polynomial T encoding the supplementary topological information.
Tate properties, polynomial-count varieties, and monodromy of hyperplane arrangements
hyperplane arrangement Milnor fiber monodromy polynomial-count
2011/1/19
A necessary and sufficient condition for the triviality of the Milnor monodromy of a central hyperplane arrangement is given. This is a consequence of a Thom-Sebastiani type result, where the sum of h...
Analysis of Riemann Zeta Function Zeros using Pochhammer Polynomial Expansions
Riemann Zeta function Riemann Hypothesis Entire functions Real zeros
2010/12/7
The Riemann Zeta function ζ(s) can be expressed in terms of the entire function ξ(s)which has an integral representation characteristic of a general class of entire functions symmetric
around s = &fr...
Ratio Vectors of Polynomial-Like Functions
Polynomial Real roots Ratio vector Critical points
2010/1/22
Let be a hyperbolic polynomial-like function of the form where are given positive real numbers and . Let be the critical points of lying in . Define the ratios We prove that . These boun...
Approximation, Numerical Differentiation and Integration Based on Taylor Polynomial
Degree of approximation Taylor polynomial $P_n$-simple functionals least concave majorant of $omega(f,cdot)$
2010/1/22
We represent new estimates of errors of quadrature formula, formula of numerical differentiation and approximation using Taylor polynomial. To measure the errors we apply representation of the remaind...
$L_p$ Inequalities for the Polar Derivative of a Polynomial
$L_p$ inequalities Polar derivatives Polynomials
2010/1/25
Let denote the polar derivative of a polynomial of degree with respect to real or complex number . If does not vanish in ![]()
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Polynomial hulls and H-infinity control for a hypoconvex constraint
Polynomial hulls H-infinity control hypoconvex constraint
2010/10/29
We say that a subset of C^n is hypoconvex if its complement is the union of complex hyperplanes. Let D be the closed unit disk in C, T the unit circle. We prove two conjectures of Helton and Marshall...
Let $p(z)$ be a monic polynomial of degree $n$, with complex coefficients, and let $q(z)$ be its monic factor. We prove an asymptotically sharp inequality of the form $\|q\|_{E} \le C^n \|p\|_E$, whe...