Related papers: A refined determinantal inequality for correlation…
We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and…
We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These…
The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].
In recent work Simkin shows that bounds on an exponent occurring in the famous $n$-queens problem can be evaluated by solving convex optimization problems, allowing him to find bounds far tighter than previously known. In this note we use…
We give the first known bound for orders of differentiations in differential Nullstellensatz for both partial and ordinary algebraic differential equations. This problem was previously addressed by A. Seidenberg but no complete solution was…
We provide a simple algorithm for finding the optimal upper bound for sums of products of matrix entries of the form S_pi(N) := sum_{j_1, ..., j_2m = 1}^N t^1_{j_1 j_2} t^2_{j_3 j_4} ... t^m_{j_2m-1 j_2m} where some of the summation indices…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
M. Aouchiche and P. Hansen proposed the distance Laplacian and the distance signless Laplacian of a connected graph [Two Laplacians for the distance matrix of a graph, LAA 439 (2013) 21{33]. In this paper, we obtain three theorems on the…
Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…
Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We…
An important yet challenging problem in numerical linear algebra is finding a principal submatrix with maximum determinant from a given symmetric positive semidefinite matrix. This problem arises in experimental design, statistics, and…
For minimally $k$-connected graphs on $n$ vertices, Mader proved a tight lower bound for the number $|V_k|$ of vertices of degree $k$ in dependence on $n$ and $k$. Oxley observed 1981 that in many cases a considerably better bound can be…
We give an $O(\log^2 n)$-query algorithm for finding a Tarski fixed point over the $4$-dimensional lattice $[n]^4$, matching the $\Omega(\log^2 n)$ lower bound of [EPRY20]. Additionally, our algorithm yields an ${O(\log^{\lceil…
An inequality, recently proposed by Franson [Phys. Rev. A 54, 3808 (1996)] is analyzed and improved. The inequality connects the change of the expectation value of an observable with the uncertainty of this observable. A strict bound on the…
This paper is concerned with the problem of approximating the determinant of A for a large sparse symmetric positive definite matrix A. It is shown that an efficient solution of this problem is obtained by using a sparse approximate inverse…
We prove new borderline regularity results for solutions to fully nonlinear elliptic equations together with pointwise gradient potential estimates.
We present new algorithms for computing the log-determinant of symmetric, diagonally dominant matrices. Existing algorithms run with cubic complexity with respect to the size of the matrix in the worst case. Our algorithm computes an…
In this paper we improve the bounds of the third order Hankel determinant for two classes of univalent functions with bounded turning. The bounds are not sharp, but the sharp ones are conjectured.
An exact expression for the determinant of the splitting matrix is derived: it allows us to analyze the asympotic behaviour needed to amend the large angles theorem proposed in Ann. Inst. H. Poincar\'e, B-60, 1, 1994. The asymptotic…
Using an approach of Bergh, we give an alternate proof of Bennett's result on lower bounds for non-negative matrices acting on non-increasing non-negative sequences in $l^p$ when $p \geq 1$ and its dual version, the upper bounds when $0<p…