In this paper our purpose is to extend some results known in the literature for ordinary difference (single) to difference double sequences of real numbers.Quite recently, Esi [1] defined the statistical analogue for double difference sequences x = (xk,l) as follows: A real double sequence x = (xk,l) is said to be P-statistically ∆− convergent to L provided that for each ε > 0 P − lim m,n 1 mn ...

We revisit the Near Equidiffusional Flames (NEF) model introduced by Matkowsky and Sivashinsky in 1979 and consider a simplified, quasisteady version of it. This simplification allows, near the planar front, an explicit derivation of the front equation. The latter is a pseudodifferential fully nonlinear parabolic equation of the fourth-order. First, we study the (orbital) stability of the null ...

A new and powerful indentation hardness (H) approach to evaluating the true stress (σ)-true plastic strain (ε), σ(ε), constitutive behavior of materials is described. Since measurements of H intrinsically probe a wide-range of ε (up to ≈0.5) , accurate assessment of the corresponding yield (σy) stress and strain hardening [σsh(ε)] pose a significant challenge. Extensive elastic-plastic finite ...

The ε subunit from bacterial ATP synthases functions as an ATP sensor, preventing ATPase activity when the ATP concentration in bacterial cells crosses a certain threshold. The R103A/R115A double mutant of the ε subunit from thermophilic Bacillus PS3 has been shown to bind ATP two orders of magnitude stronger than the wild type protein. We use molecular dynamics simulations and free energy calc...

Let U ′′ = 2 be arbitrary. In [1], the main result was the derivation of multiply linear isomorphisms. We show that sM is countably negative definite and extrinsic. In [1], the authors described projective planes. It is well known that 0×N > { limB ( 1 0 , 0−2 ) , ε ≤ ∅ ∫ I′′ exp (G ′(χ) + 1) dm, ‖d(c)‖ ⊃ I .

In this paper we are interested in a rigorous derivation of the Kuramoto-Sivashinsky equation (K–S) in a Free Boundary Problem. As a paradigm, we consider a two-dimensional Stefan problem in a strip, a simplified version of a solid-liquid interface model. Near the instability threshold, we introduce a small parameter ε and define rescaled variables accordingly. At fixed ε, our method is based o...

and objectives In tutorial 2, we demonstrated the basic steps for deriving the direct boundary integral equation. In this tutorial we will explain, with more examples, the derivation of the direct boundary integral equation for systems of partial differential equations. We will consider two examples: elasticity problems and shear-deformable plate bending problems. 1 Elasticity equations In this...

We are interested in a rigorous derivation of the Kuramoto–Sivashinsky (K-S) equation from a free boundary problem. As a paradigm, we consider a two-dimensional Stefan problem in a strip, a simplified version of a solid-liquid interface model. Near the instability threshold, we introduce a small parameter ε and define rescaled variables accordingly. At fixed ε, our method is based on: definitio...