Related papers: Exponential bases on multi-rectangles in $\mathbb{…

We study mutually unbiased maximally entangled bases (MUMEB's) in bipartite system $\mathbb{C}^d\otimes\mathbb{C}^d (d \geq 3)$. We generalize the method to construct MUMEB's given in [16], by using any commutative ring $R$ with $d$…

We announce the folowing result: Any finitely generated non virtually solvable linear group over a field of characteristic zero has uniform exponential growth.

In the 1990's exponential-type error bounds appeared in the theory of radial basis functions. This kind of error bounds is very powerful. However it only measures the difference between the approximant and approximand. Mathematicians and…

We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal polynomials on the surface of quadratic surfaces of revolution,…

This paper concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights $w:=\exp(-Q)$ with finite moments and with smooth external fields $Q:\mathbb R\to [0,\infty)$, with varying…

Finite dimensional subspaces spanned by exponential functions in the space of square integrable functions on a finite interval of the real line are considered. Their limiting positions are studied and described in terms of expo-polynomials.

In terms of the number of triangles, it is known that there are more than exponentially many triangulations of surfaces, but only exponentially many triangulations of surfaces with bounded genus. In this paper we provide a first geometric…

We prove that hypersurfaces defined by irreducible square-free polynomials have rational singularities. As an easy consequence, we deduce that certain (possibly non-square-free) polynomials associated to pairs of square-free polynomials…

We construct maximal $\Lambda(p)$-subsets on a large class of curved manifolds, in an optimal range of Lebesgue exponents $p$. Our arguments combine restriction estimates and decoupling with old and new probabilistic estimates.

After obtaining some useful identities, we prove an additional functional relation for $q$ exponentials with reversed order of multiplication, as well as the well known direct one in a completely rigorous manner.

We develop the theory of Gr\"obner bases for ideals in a polynomial ring with countably infinite variables over a field. As an application we reconstruct some of the one-one correspondences among various sets of partitions by using division…

In this paper we propose a method for proving some exponential inequalities based on power series expansion and analysis of derivations of the corresponding functions. Our approach provides a simple proof and generates a new class of…

By employing an accelerated weighting method, we establish arbitrary polynomial and exponential pointwise convergence for multiple ergodic averages under general balancing conditions in both discrete and continuous settings, including…

We obtain new upper bounds on the number of distinct roots of lacunary polynomials over finite fields. Our focus will be on polynomials for which there is a large gap between consecutive exponents in the monomial expansion.

We study the topology of the real algebraic hypersurfaces in $\mathbb{P}^n$ that can be constructed via combinatorial patchworking using triangulations that are dilations by two of other triangulations. By examining the real critical points…

We provide an asymptotic estimate for the number of rational points of bounded height on a non-singular conic over the rationals. The estimate is uniform in the coefficients of the underlying quadratic form.

In this paper, we construct geometrically finite rational maps with buried critical points on the boundaries of some hyperbolic components by using the pinching and plumbing deformations.

In this paper, some particular rational maps P_n ---> P_n+1, called quadratic congruences, are studied. They appear in the theory of exceptional vector bundles on projective spaces.

This note (which makes no claim to novelty) presents a proof of the separable rational connectedness of smooth cubic hypersurfaces, in any characteristic, by showing how to explicitly construct very free curves (of degree 3) on them. -----…

For central simple algebras of exponent $2$ over fields of characteristic $2$ and $2$-cohomological dimension equal to $2$, we study the adapted decomposition to some multiquadratic extensions of the base field. Several remarkable…