Related papers: Note on Prime Gaps and Zero Spacings
The existence of strictly positive lower bounds on voltage magnitude is taken for granted in optimal power flow problems. Nevertheless, it is not possible to rely on such bounds for a variety of real-world network optimization problems.…
We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of…
We study certain obstacle type problems involving standard and nonlocal minimal surfaces. We obtain optimal regularity of the solution and a characterization of the free boundary.
We present some new ideas on important problems related to primes. The topics of our discussion are: simple formulae for primes, twin primes, Sophie Germain primes, prime tuples less than or equal to a predefined number, and their…
In this paper, we study estimates for eigenvalues of the clamped plate problem. A sharp upper bound for eigenvalues is given and the lower bound for eigenvalues in [10] is improved.
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…
In the present work we investigate the largest possible gaps between consecutive numbers which can be written as the difference of two primes. The best known upper bounds are the same as those concerning the largest possible difference of…
Assuming that there exist (infinitely many) Siegel zeros, we show that the (Rosser-)Jurkat-Richert bounds in the linear sieve cannot be improved, and similarly look at Iwaniec's lower bound on Jacobsthal's problem, as well as minor…
In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.
We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.
This note further addresses the global optimization problem for max-plus linear systems considered in [Automatica 119 (2020) 109104]. Firstly, the operations between infinity elemens and real numbers involved in the formulas of solving…
This paper is a survey of recent advances as well as open problems in the study of face numbers of centrally symmetric simplicial polytopes and spheres. The topics discussed range from neighborliness of centrally symmetric polytopes and the…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
In this paper, we obtain the upper and lower bounds for two inequalities related to the range statistics. The first one is concerning the one-variable case and the second one is about the bivariate case.
The isoperimetric problem asks for the maximum area of a region of given perimeter. It is natural to consider other measurements of a region, such as the diameter and width, and ask for the extreme value of one when another is fixed. The…
In a recent joint work with D.A. Goldston and C.Y. Yildirim we just missed by a hairbreadth a proof that bounded gaps between primes occur infinitely often. In the present work it is shown that adding to the primes a much thinner set,…
In this article, a relation between a gap $d_{k}$ and divisors of composite numbers between $p_{k}$ and $p_{k+1}$ is established.
We study the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem aims at locating p facilities on the vertices (of the network) so as to maximise coverage, considering that the…
We generalise Zhang's and Pintz recent results on bounded prime gaps to give a lower bound for the the number of prime pairs bounded by 6*10^7 in the short interval $[x,x+x (\log x)^{-A}]$. Our result follows only by analysing Zhang's proof…
We propose the formula for the number of pairs of consecutive primes $p_n, p_{n+1}<x$ separated by gap $d=p_{n+1}-p_n$ expressed directly by the number of all primes $<x$, i.e. by $\pi(x)$. As the application of this formula we formulate 7…