Multiplicative bounds for L 1-norms of exponential sums

This paper is a sequel to the author's papers [1–8] devoted to lower multiplicative bounds on L ₁ norms and their applications. Now we give estimates for L ₁ norms of exponential sums and prove the result announced in [8]. __________ Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 25, Theory of Functions, 2007.     

Estimates for L p -norms of simple partial fractions

We obtain estimates for L _p -norms of simple partial fractions in terms of their L _r -norms on bounded and unbounded segments of the real axis for various p > 1 and r > 1 (S. M. Nikolskii type inequalities). We adduce examples and remarks concerning sharpness of the inequalities and area of their application.     

On lower bounds for theL 2-Wasserstein metric in a Hilbert space

We provide two families of lower bounds for theL ²-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.Research partially supported by the Spanish DGICYT under grants PB91-0306-02-00, 01 and 02.     

Upper bounds for Ramsey numbers

The Ramsey number R(G₁,G₂,…,G_k) is the least integer p so that for any k-edge coloring of the complete graph K_p, there is a monochromatic copy of G_i of color i. In this paper, we derive upper bounds of R(G₁,G₂,…,G_k) for certain graphs G_i. In particular, these bounds show that R(9,9)6588 and R(10,10)23556 improving the previous best bounds of 6625 and 23854.     

Upper bounds for harmonious colorings

A harmonious coloring of a simple graph G is a coloring of the vertices such that adjacent vertices receive distinct colors and each pair of colors appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colors in such a coloring. We improve an upper bound on h(G) due to Lee and Mitchem, and give upper bounds for related quantities.     

Upper bounds for Gaussian stochastic programs

We present a construction which gives deterministic upper bounds for stochastic programs in which the randomness appears on the right–hand–side and has a multivariate Gaussian distribution. Computation of these bounds requires the solution of only as many linear programs as the problem has variables. Received December 2, 1997 / Revised version received January 5, 1999? Published online May 12, 1999     

Upper bounds for parent-identifying set systems

We derive new upper bounds on the size set families having the c-identifiable parent property (c-IPP) and the c-traceability property (c-TA) and compare these bounds to similar results on parent-identifying codes. An earlier version of this paper appeared in [4]. Sandia National Laboratories—This is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.     

Upper bounds of topologies

The topology of a space (X, ) homeomorphic to a non--compact separable Borel set is equal to the upper bound of two topologies of the Hilbert cube. In particular, (X, ) condenses to a compact space. The topology of a complete zero-dimensional metric space is the upper bound of two compact topologies. In particular, it dominates a compact Hausdorff topology.Translated from Matematicheskie Zametki, Vol. 20, No. 4, pp. 489–500, October, 1976.     

Upper eigenvalue bounds for pencils of matrices

Eigenvalue bounds are obtained for pencils of matrices A ? vB where A is a Stieltjes matrix and B is positive definite, under assumptions suitable for the estimation of asymptotic convergence rates of factorization iterative methods, where B represents the approximate factorization of A. The upper bounds obtained depend on the “connectivity” structure of the matrices involved, which enters through matrix graph considerations; in addition, a more classical argument is used to obtain a lower bound. Potential applications of these results include a partial confirmation of Gustafsson's conjecture concerning the nonnecessity of Axelsson's perturbations.     

Upper bounds for eigenvalues of Cauchy-Hankel tensors

We present upper bounds of eigenvalues for finite and infinite dimensional Cauchy-Hankel tensors. It is proved that an m-order infinite dimensional Cauchy-Hankel tensor defines a bounded and positively (m－1)-homogeneous operator from l¹ into l^p (1<p<∞); and two upper bounds of corresponding positively homogeneous operator norms are given. Moreover, for a fourth-order real partially symmetric Cauchy-Hankel tensor, suffcient and necessary conditions of M-positive definiteness are obtained, and an upper bound of M-eigenvalue is also shown.     

Upper bounds for edge-antipodal and subequilateral polytopes

A polytope in a finite-dimensional normed space is subequilateral if the length in the norm of each of its edges equals its diameter. Subequilateral polytopes occur in the study of two unrelated subjects: surface energy minimizing cones and edge-antipodal polytopes. We show that the number of vertices of a subequilateral polytope in any d-dimensional normed space is bounded above by (d / 2 + 1) ^d for any d ≥ 2. The same upper bound then follows for the number of vertices of the edge-antipodal polytopes introduced by I. Talata [19]. This is a constructive improvement to the result of A. Pór (to appear) that for each dimension d there exists an upper bound f(d) for the number of vertices of an edge-antipodal d-polytopes. We also show that in d-dimensional Euclidean space the only subequilateral polytopes are equilateral simplices. This material is based upon work supported by the South African National Research Foundation under Grant number 2053752.     

Upper bounds of Schubert polynomials

Science China Mathematics - Let w be a permutation of {1, 2, …, n}, and let D(w) be the Rothe diagram of w. The Schubert polynomial ${\mathfrak{S}_w}\left(x \right)$ can be realized as the...     

Upper bounds for dominant dimensions of gendo-symmetric algebras

The famous Nakayama conjecture states that the dominant dimension of a non-selfinjective finite dimensional algebra is finite. Yamagata (Frobenius algebras handbook of algebra, vol 1. Elsevier/North-Holland, Amsterdam, pp 841–887, 1996) stated the stronger conjecture that the dominant dimension of a non-selfinjective finite dimensional algebra is bounded by a function depending on the number of simple modules of that algebra. With a view towards those conjectures, new bounds on dominant dimensions seem desirable. We give a new approach to bounds on the dominant dimension of gendo-symmetric algebras via counting non-isomorphic indecomposable summands of rigid modules in the module category of those algebras. On the other hand, by Mueller’s theorem, the calculation of dominant dimensions is directly related to the calculation of certain Ext-groups. Motivated by this connection we also give new results for showing the non-vanishing of \(Ext^{1}(M,M)\) for certain modules in local symmetric algebras, which specializes to show that blocks of category \(\mathcal {O}\) and 1-quasi-hereditary algebras with a special duality have dominant dimension exactly 2.