相关论文: Totally real Thue inequalities over imaginary quad…

We establish a new improvement of the classical $L^p$-Hardy inequality on the multidimensional Euclidean space in the supercritical case. Recently, in [14], there has been a new kind of development of the one dimensional Hardy inequality.…

We give a new proof of a classical theorem on approximation of continuous functions on totally real sets

We appeal to a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultra-distributions we are able to show that the q-Gaussian distribution can be…

We prove finite-field analogs of Bourgain's projection theorem in higher dimensions. In particular, for a certain range of parameters we improve on an exceptional set estimate by Chen in all dimensions and codimensions.

Main goal of this paper is to generalize Hadamard's real part theorem and invariant forms of Borel-Carath\'eodory's theorem from complex analysis to solutions of the Riesz system in the three-dimensional Euclidean space in the framework of…

We establish large sieve inequalities for power moduli in imaginary quadratic number fields, extending earlier work of Baier and Bansal for the Gaussian field.

A generalization of the affine-geometric Wirtinger inequality for curves to hypersurfaces is given.

To numerically evolve the full Einstein equations (or modifications thereof), simulations of cosmological spacetimes must rely on a particular formulation of the field equations combined with a specific gauge/frame choice. Yet truly…

We study the two-dimensional affine Toda field equations for affine Lie algebra $\hat{\mathfrak{g}}$ modified by a conformal transformation and the associated linear equations. In the conformal limit, the associated linear problem reduces…

We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.

Based on M. Hall's theorem we prove a simple result dealing with real numbers which admit exact approximations by rationals.

We introduce totally nonnegative Grassmannians over finite fields where an element of a finite field is nonnegative if it is a square of an element of the finite field. Explicit point counts are given in some special cases where we find new…

Using the Thue-Siegel method, we obtain effective improvements on Liouville's irrationality measure for certain one-parameter families of algebraic numbers, defined by equations of the type $(t-a)Q(t)+P(t)=0$. We apply these to some…

We show that a problem by Yau can not be true in general. The counterexamples are constructed based on the recent work of Wu and Zheng.

We prove a self-improvement property regarding quadratic forms on arbitrary vector spaces. We discuss several consequences of this result, in particular those concerning dimension-free L^p estimates of certain singular integral operators…

In this paper, we establish a version of the large sieve with square moduli for imaginary quadratic extensions of rational function fields of odd characteristics.

Certain new inequalities for the sums of factorials are presented.

We show that classical U(infinity) gauge theories can be obtained from the dimensional reduction of a certain class of higher-derivative theories. In general, the exact symmetry is attained in the limit of degenerate metric; otherwise, the…

We study the linear problem associated with modified affine Toda field equation for the Langlands dual $\hat{\mathfrak{g}}^\vee$, where $\hat{\mathfrak{g}}$ is an untwisted affine Lie algebra. The connection coefficients for the asymptotic…

We discuss integrating out matter fields and integrating in matter fields in four dimensional supersymmetric gauge theories. Highly nontrivial exact superpotentials can be easily obtained by starting from a known theory and integrating in…