Related papers: New upper bound for a class of vertex Folkman numb…
We survey recent developments on the Restriction conjecture.
For a graph $G$ the expression $G \overset{v}{\rightarrow} (a_1, ..., a_s)$ means that for any $s$-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 improve constants in the Rademacher-Menchov inequality.
We investigate the possibility of proving upper bounds on Hadwiger's number of a graph with partial information, mirroring several known upper bounds for the chromatic number. For each such bound we determine whether the corresponding bound…
The aim of this paper is to give a proof of improving of Zalcman's lemma.
Some occurrences of $n$ can be replaced by $n-1$ in a special case of the Shapley-Folkman lemma.
We obtain some new inequalities of Chebyshev Type.
We obtain an improved lower bound for the regularity of the binomial edge ideals of trees. We prove an upper bound for the regularity of the binomial edge ideals of certain subclass of block-graphs. As a consequence we obtain sharp upper…
We obtain upper bounds on the number of finite sets $\mathcal S$ of primes below a given bound for which various $2$ variable $\mathcal S$-unit equations have a solution.
Suppose X is any finite complex with vanishing L^2 Betti number. We prove upper bounds on the Betti numbers for regular coverings of X, sublinear in the order of covering. The bounds are sensitive to the Novikov-Shubin invariants of X, and…
In this paper, we establish a new estimate (including lower and upper bounds) for an important quantity involved in the convergence analysis of smoothed aggregation algebraic multigrid methods. The new upper bound improves the existing…
We prove a tight lower bound on the Betti numbers of tree and forest ideals and a tight upper bound on certain graded Betti numbers of squarefree monomial ideals.
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
Some new Frobenius norm bounds of the unique solution to certain structured Sylvester equation are derived. Based on the derived norm upper bounds, new multiplicative perturbation bounds are provided both for subunitary polar factors and…
We give a new lower bound on the expansion coefficient of an edge-vertex graph of a $d$-regular graph. As a consequence, we obtain an improvement on the lower bound on relative minimum distance of the expander codes constructed by Sipser…
We establish sharp upper bounds for the $2k$th moment of the Riemann zeta function on the critical line, for all real $0 \leqslant k \leqslant 2$. This improves on earlier work of Ramachandra, Heath-Brown and Bettin-Chandee-Radziwi\l\l
An inequality proved firstly by Remak and then generalized by Friedman shows that there are only finitely many number fields with a fixed signature and whose regulator is less than a prescribed bound. Using this inequality, Astudillo, Diaz…
A new error bound which is better than the current exponential-type error bound is presented in this paper.
We obtain new lower and upper bounds for probabilities of unions of events.These bounds are sharp. They are stronger than earlier ones. General bounds maybe applied in arbitrary measurable spaces.We have improved the method that has been…
We obtain a good upper bound on the number of solutions of a diophantine equation arising from a strictly convex sequences of real numbers.