For measuring families of curves, or, more generally, measures, $M_p$-modulus is traditionally used. More recent studies use so-called plans on measures. In their fundamental paper \cite{ADS}, Ambrosio, Di Marino and Savar\'e proved that these two approaches are in some sense equivalent within $1<p<\infty$. We consider the limiting case $p=1$ show $AM$-modulus can be obtained alternatively by p...

Factoring an integer is equivalent to express the integer as the difference of two squares. We test that for any odd modulus, in the corresponding ring of remainders, any element can be realized as the difference of two quadratic residues, and also that, for a fixed remainder value, the map assigning to each modulus the number of ways to express the remainder as difference of quadratic residues...

In this note, we introduce the Durrmeyer variant of Stancu operators that preserve the constant functions depending on non-negative parameters. We give a global approximation theorem in terms of the Ditzian-Totik modulus of smoothness, a Voronovskaja type theorem and a local approximation theorem by means of second order modulus of continuity. Also, we obtain the rate of approximation for absol...

i.e., if every fER attains its maximum modulus on C. As a matter of convenience, we shall, in this paper, abbreviate "maximum modulus algebra on K" to "ilf-algebra." Examples of Af-algebras which come to mind immediately are (a) the algebra ft consisting of all functions which are continuous on K and analytic in U, (b) any subalgebra of ft, (c) any algebra (B which is equivalent to an algebra o...

Board-level package is a complicated multi-components structure. It can be simulated by an equivalent Finite Element Analysis (FEA) model of the board-level package, in which detailed layer structure of the Print Circuit Board (PCB), signal wires and through-holes were ignored. For this purpose, it is necessary to obtain the equivalent material properties of the board-level package. In this wor...

This paper describes a model for the spatial variation of the elastic modulus of parallel strand lumber PSL that is based on bending experiments and also describes a validated stochastic computational model that incorporates orthotropic elasticity and uncertainty in strand geometry and material properties. The PSL exhibits significant variability both within members and between members, but thi...

Many instruments used to measure viscoelastic properties are only capable of subjecting a sample to a limited range of loading frequencies. For thermorheologically simple materials, it is assumed that a change in temperature is equivalent to a shift of the viscoelastic behavior on the log frequency or time axis. For many materials, time–temperature superposition appears to work well for modulus...