Related papers: New upper bound for a class of vertex Folkman numb…

We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.

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 give an upper bound for the number elliptic Carmichael numbers $n \le x$ that have recently been introduced by J. H. Silverman. We also discuss several possible ways for further improvements.

We study the number of degree $n$ number fields with discriminant bounded by $X$. In this article, we improve an upper bound due to Schmidt on the number of such fields that was previously the best known upper bound for $6 \leq n \leq 94$.

In the paper, some lower bounds for polygamma functions are refined.

New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths.…

We obtain a new upper bound for binary sums with multiplicative characters over variables belong to some sets, having small additive doubling.

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.

We fix an error in the bound obtained in [13] for the crossing number of wrapped butterflies. The new bound finer than the one provided earlier.

We prove explicit upper bounds for weighted sums over prime numbers in arithmetic progressions with slowly varying weight functions. The results generalize the well-known Brun-Titchmarsh inequality.

Olkin [3] obtained a neat upper bound for the determinant of a correlation matrix. In this note, we present an extension and improvement of his result.

An approach to constructing an upper bound for the Riemann-Farey sum is described.

We give an upper bound on the number of extensions of a fixed number field of prescribed degree and discriminant less than X; these bounds improve on work of Schmidt. We also prove various related results, such as lower bounds for the…

We establish upper bounds for moments of zeta sums using results on shifted moments of the Riemann zeta function under the Riemann hypothesis.

In this paper we study upper and lower bounds on the Bregman divergence $\Delta_{\mathcal{F}}^{\xi}(y,x):=\mathcal{F}(y)-\mathcal{F}(x)-\langle \xi, y-x\rangle $ for some convex functional $\mathcal{F}$ on a normed space $\mathcal{X}$, with…

Lower bounds for some explicit decision problems over the complex numbers are given.

For a graph $G$ the expression $G \overset{v}{\rightarrow} (a_1, ..., a_s)$ means that for every $s$-coloring of the vertices of $G$ there exists $i \in \{1, ..., s\}$ such that there is a monochromatic $a_i$-clique of color $i$. The vertex…

We use some properties of orthogonal polynomials to provide a class of upper/lower variance bounds for a function $g(X)$ of an absolutely continuous random variable $X$, in terms of the derivatives of $g$ up to some order. The new bounds…

In this short note we derive, for bounded domains, an upper bound for a Friedrichs type constant in a weighted Friedrichs type inequality. This upper bound generalizes a well known upper bound of the Friedrichs constant. This upper bound is…

In this paper, new relations between the derivatives of the Legendre polynomials are obtained, and by these relations, new upper bounds for the Legendre coefficients of differentiable functions are presented. These upper bounds are sharp…