The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.

In this paper, the wear resistance and antifriction of epsilon phase layer and diffusion layer of gas nitrided D2 steel and M2 steel have been studied. The changes m wear mechanism of epsilon phase under the load from 20N to 200N are analysed. When the load is lighter than 100N, it is mainly oxidizing wear on friction surface. The adhesion, peeling off and abrasive wear appear on friction surfa...

In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible ...

This paper studies some existence results for generalized epsilon-vector equilibrium problems and generalized epsilon-vector variational inequalities. The existence results for solutions are derived by using the celebrated KKM theorem. The results achieved in this paper generalize and improve the works of many authors in references.

In this study, a series of interaction coefficients of the Brønsted-Guggenheim-Scatchard specific interaction theory (SIT) have been estimated up to 200 degrees C and 400 bars. The interaction coefficients involving Cl- estimated include epsilon(H+, Cl-), epsilon(Na+, Cl-), epsilon(Ag+, Cl-), epsilon(Na+, AgCl2 -), epsilon(Mg2+, Cl-), epsilon(Ca2+, Cl-), epsilon(Sr2+, Cl-), epsilon(Ba2+, Cl-), ...

BACKGROUND To determine the interaction effect between APOE polymorphism and lipid concentrations and alcohol use on spontaneous deep intracerebral hemorrhage (SDICH) risks. METHODS We enrolled 217 SDICH patients and 280 controls. Anthropometrics, personal history, and concentrations of total cholesterol (TC), high-density lipoprotein cholesterol, low-density lipoprotein cholesterol (LDL-c), ...

designing and producing a proper fusion construction is the most important problem of producing large quantities of a properly folded functional protein. this construction should have all necessary components of a real gene. a good designed fusion gene construction could be cloned into a good and suitable host. clostridium perfringens is an important pathogen of humans and livestock and produce...

The use of random samples to approximate properties of geometric configurations has been an influential idea for both combinatorial and algorithmic purposes. This chapter considers two related notions—ǫ-approximations and ǫ-nets—that capture the most important quantitative properties that one would expect from a random sample with respect to an underlying geometric configuration. An example pro...

We give a $(1+\epsilon)$-approximate distance oracle with $O(1)$ query time for an undirected planar graph $G$ with $n$ vertices and non-negative edge lengths. For $\epsilon>0$ and any two vertices $u$ and $v$ in $G$, our oracle gives a distance $\tilde{d}(u,v)$ with stretch $(1+\epsilon)$ in $O(1)$ time. The oracle has size $O(n\log n ((\log n)/\epsilon+f(\epsilon)))$ and pre-processing time $...

We developed a method to estimate genotype-specific average relative mortality risk, R, from genotype distributions in cross-sectional studies of people belonging to different age-groups, and applied the method to new data from a study of apolipoprotein E genotypes (apoE) in 177 Danish centenarians and data from a study of 40-year-old Danish men. Twenty-one percent of the centenarians were epsi...