Some Grüss type inequalities for two sequences of vectors in terms of the forward difference are given. An application for the Jensen inequality for convex functions defined on inner product spaces is also pointed out. 2000 Mathematics Subject Classification: 26D15, 47A05, 46A05.

In this paper, we propose a general framework to incorporate semantic knowledge into the popular data-driven learning process of word embeddings to improve the quality of them. Under this framework, we represent semantic knowledge as many ordinal ranking inequalities and formulate the learning of semantic word embeddings (SWE) as a constrained optimization problem, where the data-derived object...

We consider pairwise multiple comparisons and multiple comparisons with a control among mean vectors for high-dimensional data under the multivariate normality. For such cases, the statistics based on Dempster trace criterion are given, and also their approximate upper percentiles are derived by using Bonferroni’s inequality. Finally, the accuracy of their approximate values is evaluated by Monte

transportation is by people and for them. it is a process of providing mobility and accessibility for people both as passengers and as consumers of the goods. therefore it is true when today there is an emphasis on the considering transportation the most influential development in every society. regional development cannot properly be happened without enough transportation infrastructure and qu...

A novel method for clustering computational fluid dynamics (CFD) solution vectors with the goal of building efficient local reduced-order models (ROMs) is proposed. In this method, the clustering process is accelerated through the introduction of triangle-inequality bounds to avoid unnecessary computation during K-Means, and the accuracy of the resulting ROM simulation is improved through the i...

and D dimensional vectors, it takes O (D) operations to compute this distance. For a set of N vectors, computing the nearest neighbour to q would take then O (DN) operations. For large datasets this can be prohibitively expensive. Is there a way to avoid calculating all the distances? This is a large research area (see [2] for a review) and we will focus here on first methods that make use of t...

In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing non-null normal vectors of the feasible set. In particular, two conceptual algorithms are proposed and each of them has three different variants which are related to modified extragradient algorithms. Our analysis contains two main parts: The first part contains two differ...

A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures include random variables with densities proportional to e−|t| p and symmetric p-stable random variables, where p ∈ (0, 2]. We obtain various sharp moment an...

This paper shows what are called Welch bound equality (WBE) sequences by the signal processing community are precisely the isometric/equal norm/normalized/uniform tight frames which are currently being investigated for a number of applications, and in the real case are the spherical 2–designs of combinatorics. Recent applications include wavelet expansions, Grassmannian frames, frames robust to...

The purpose of this note– inspired by and using a number of properties from Barbara and Jackson [2] – is to characterize the Pareto dominance relation. The set-up and interpretation is completely analogous to [2]. In particular, situations are considered where different actions are to be compared on the basis of their consequences, which are described by vectors of real numbers. Ranking actions...