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Bernstein problem for affine maximal type hypersurfaces has been a core problem in affine geometry. A conjecture proposed firstly by Chern (Proc. Japan-United States Sem., Tokyo, 1977, 17-30) for enti...
We elaborate the theory of the stable Bernstein center of a p-adic group G, and apply it to state a general conjecture on test functions for Shimura varieties due to the author and R. Kottwitz. This...
Let G be an unrami ed group over a p-adic eld. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for G and proves the corresponding base ...
A first-order theory T has the Schr╫der-Bernstein (SB) property if any pair of elementarily bi-embeddable models are isomorphic. We prove that T has an expansion by constants with the SB property if...
For a countable, weakly minimal theory T, we show that the SchröderBernstein property (any two elementarily bi-embeddable models are isomorphic) is equivalent to each of the following: 1. For ...
A first-order theory T has the Schr\"oder-Bernstein (SB) property if any pair of elementarily bi-embeddable models are isomorphic. We prove that T has an expansion by constants that has the SB propert...
A direct almost Bernstein operational matrix of integration is used to propose a stable algorithm for numerical inversion of the generalized Abel integral equation. The applicability of the earlier pr...
Abstract: We show somewhat unexpectedly that whenever a general Bernstein-type maximal inequality holds for partial sums of a sequence of random variables, a maximal form of the inequality is also val...
In this paper, we discuss rates of convergence for the Lupa¸s q-analogue of Bernstein polynomials Rn,q. We prove a quantitative variant of Voronovskaja’s theorem for Rn,q.
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and different...
Let G be an unramified group over a p-adic field. This article intro-duces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for G and proves the corresponding bas...
For a nonzero ideal I ⊳C[x1, . . . , xn], with 0 ∈ supp I, a (general-ized) conjecture of Igusa–Denef–Loeser predicts that every pole of its topologi-cal zeta function is a root of its Bernstein...
Recently, T. Kim([4]) introduced q-Bernstein polynomials which are different q-Bernstein polynomials of Phillips([12]). In this paper, we give p-adic q-integral representation for Kim’s q-Bernstein po...
Recently, T. Kim([5]) introduced q-Bernstein polynomials which are different q-Bernstein polynomials of Phillips q-Bernstein polynomials([11, 12]). The purpose of this paper is to study some propertie...

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