In this paper, we prove the Hyers-Ulam stability in$beta$-homogeneous probabilistic modular spaces via fixed point method for the functional equation[f(x+ky)+f(x-ky)=f(x+y)+f(x-y)+frac{2(k+1)}{k}f(ky)-2(k+1)f(y)]for fixed integers $k$ with $kneq 0,pm1.$

in this paper, we derive rst some results on the shannon entropyin order statistics and their concomitants arising from a sequence of f(xi; yi): i = 1; 2; :::g independent and identically distributed (iid) random variablesfrom the bivariate normal distribution and extend our results to a collectionc(x; y ) = f(xr1:n; y[r1:n]); (xr2:n; y[r2:n]); :::; (xrk:n; y[rk:n])g of order sta-tistics and t...

abstract bowel obstruction is a known complication after bariatric surgery especially roux-en-y gastric bypass. the known etiologies include internal hernia, jejunojejunostomy stricture, ileus, intussusceptions, superior mesenteric artery syndrome, incarcerated port site hernia, and adhesions. blood clot is a rare cause of small intestinal obstruction after laparoscopic roux-en-y gastric bypass...

‎this paper deals with the singular sturm-liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of sturm-liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...

A new family of Y(4)/M(2) and Y(5)/M heterobimetallic rare-earth-metal/d-block-transition-metal-polyhydride complexes has been synthesized. The reactions of the tetranuclear yttrium-octahydride complex [{Cp''Y(μ-H)(2)}(4)(thf)(4)] (Cp'' = C(5)Me(4)H, 1-C(5)Me(4)H) with one equivalent of Group-6-metal-pentahydride complexes [Cp*M(PMe(3))H(5)] (M = Mo, W; Cp* = C(5)Me(5)) afforded pentanuclear he...

Numerous bulk crystalline materials exhibit attractive nonlinear and luminescent properties for classical and quantum optical applications. A chip-scale platform for high quality factor optical nanocavities in these materials will enable new optoelectronic devices and quantum light-matter interfaces. In this article, photonic crystal nanobeam resonators fabricated using focused ion beam milling...

for suitable banach spaces $x$ and $y$ with schauder decompositions and‎ ‎a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$‎, ‎it is shown that the strong banach-saks-ness of all evaluation‎ ‎operators on ${mathcal m}$ is a sufficient condition for the weak‎ ‎banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in‎ ‎y^*$‎, ‎the evaluation op...

Chiral alkyl or amido yttrium complexes were prepared from N-silyl- or N-cyclopentyl-substituted binaphthylamido ligands. According to the synthetic procedure, these complexes could be obtained in their neutral form or as heterobimetallic complexes in the presence of 1 equiv. LiCl. These new species were characterized by IR and NMR spectroscopies, elemental analyses and some of them by X-ray di...