Let R be a right GF -closed ring with finite left and right Gorenstein global dimension. We prove that if I is an ideal of R such that R/I is a semi-simple ring, then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein injective dimension of R/I as a left R-module are identical. In particular, we show that for a simple module S over a commutative Gorenstein ring R, the G...

We study positive solutions to the fractional semi-linear elliptic equation $${\left( { - \Delta } \right)^\sigma }u = K\left( x \right){u^{{{n + 2\sigma \over {n }}\,}}\,\,\,{\rm{in}}\,{B_2}\backslash \left\{ 0 \right\}$$ with an isolated singularity at origin, where K is a function on B2, punctured ball B2 {0} ⊂ ℝn n ⩾ 2, σ ∈ (0, 1), and (−Δ)σ Laplacian. In lower dimensions, we show that for ...

We present a theoretical study of electromagnetic surface waves localized at an interface separating a conventional uniform medium and a semi-infinite 1-D photonic crystal made of alternate left-handed metamaterial and right-handed material which we refer to as left-handed photonic crystal. We find novel type of surface mode’s structure, the so-called surface Tamm states and demonstrate that th...

We study the second-harmonic generation in left-handed metamaterials with a quadratic nonlinear response. We demonstrate a novel type of the exact phase matching between the backward propagating wave of the fundamental frequency and the forward propagating wave of the second harmonics. We show that this novel parametric process can convert a surface of the left-handed metamaterial into an effec...

We study one-dimensional cellular automata (CA) with values 0 and 1. We assume that such CA are started from semi-infinite configurations (those that have 0’s to the left of some site), and we focus on the identification of robust periodic solutions (RPS), which, when observed from the left edge of the light cone, advance into any environment with positive velocity. We then utilize RPS and rela...

the polynomial interpolation in one dimensional space r is an important method to approximate the functions. the lagrange and newton methods are two well known types of interpolations. in this work, we describe the semi inherited interpolation for approximating the values of a function. in this case, the interpolation matrix has the semi inherited lu factorization.

INTRODUCTION The human functional connectome is a graphical representation, consisting of nodes connected by edges, of the inter-relationships of blood oxygenation-level dependent (BOLD) time-series measured by MRI from regions encompassing the cerebral cortices and, often, the cerebellum. Semi-metric analysis of the weighted, undirected connectome distinguishes an edge as either direct (metric...

Cardiovascular CT is considered the diagnostic standard for establishing the presence of a functional and dynamic imaging system. It is difficult, however, to estimate the ventricular motion and volumes that are processed using hundreds and thousands of CT images, in a few moments.The main concept and design of our work are two fold - the development of effective semi-automatic tools for measur...

Let $A$ be a positive (semidefinite) operator on complex Hilbert space $\mathcal{H}$ and let $\mathbb{A}=\left(\begin{array}{cc} A & O O A \end{array}\right).$ We obtain upper lower bounds for the $A$-Davis-Wielandt radius of semi-Hilbertian operators, which generalize improve existing ones. also $\mathbb{A}$-Davis-Wielandt $2 \times 2$ matrices. Finally, we determine exact value two matr...

In the survey of the activity of the kidneys by nuclear medical imaging, determining the region of interest (ROI) by the operator is an important factor. The current study aimed to obtain an automatic method to determine the ROI of kidney to reduce the error of manual method of the operator. In this survey, the equations obtained through the thresholding method are performed to semi-automation ...