Related papers: Improvement of graph theory Wei`s inequality

In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.

The main result of this paper supports a conjecture by C. P\'erez and E. Rela about a very recent result of theirs on self-improving theory. Also, we extend the conclusions of their theorem to the range $p<1$. As an application of our…

Despite enormous successful applications of graph neural networks (GNNs), theoretical understanding of their generalization ability, especially for node-level tasks where data are not independent and identically-distributed (IID), has been…

In this paper, we prove a generalization of Reilly's formula in \cite{Reilly}. We apply such general Reilly's formula to give alternative proofs of the Alexandrov's Theorem and the Heintze-Karcher inequality in the hemisphere and in the…

In this paper we extend the known results of analytic connectivity to non-uniform hypergraphs. We prove a modified Cheeger's inequality and also give a bound on analytic connectivity with respect to the degree sequence and diameter of a…

We introduce a modification of the Tur\'an density of ordered graphs and investigate this graph parameter.

In this paper, we study the support vector machine and introduced the notion of generalized support vector machine for classification of data. We show that the problem of generalized support vector machine is equivalent to the problem of…

Proposed as a general framework, Liu and Yu(Discrete Math. 231 (2001) 311-320) introduced $(n,k,d)$-graphs to unify the concepts of deficiency of matchings, $n$-factor-criticality and $k$-extendability. Let $G$ be a graph and let $n,k$ and…

We give a sheaf-theoretic version of the universal coefficient theorem.

Graph neural networks are widely used tools for graph prediction tasks. Motivated by their empirical performance, prior works have developed generalization bounds for graph neural networks, which scale with graph structures in terms of the…

We generalize the enhanced power graph by replacing elements with classes under automorphisms. We show that the connectivity and diameter of this graph is similar to that of the enhanced power graph. We consider the universal vertices of…

We generalize Jacod's condition and introduce a new type sufficient condition for the uniform integrability of the general stochastic exponential.

In this note, we present a refinement of the well-known AM-GM inequality. We use this improved inequalty to establish corresponding inequalities on Hilbert space. We also give some refinements of the Kantorovich inequality.

We present an example of a result in graph theory that is used to obtain a result in another branch of mathematics. More precisely, we show that the isomorphism of certain directed graphs implies that some trinomials over finite fields have…

We generalize the property that Riemann sums of a continuous function corresponding to equidistant subdivision of an interval converge to the integral of that function, and we give some applications of this generalization.

We use the definition of a fractional integral, recently proposed by Katugampola, to establish a generalization of the reverse Minkowski's inequality. We show two new theorems associated with this inequality, as well as state and show other…

Recently, it has been shown by Ighachanea and Akkouchia \cite{0.1} that using binomial coefficients, one can derive some new refinements of Holder's inequalities. This inequalities then can be applied to a wide class of special functions…

We present, to the best of the authors' knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph…

We extend a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality.

We improve using elementary means an explicit bound on the divisor function due to Friedlander and Iwaniec. Consequently we modestly improve a result regarding a sieving inequality for Gaussian sequences.