‎in this paper some properties of weak regular injectivity for $s$-posets‎, ‎where $s$ is a pomonoid‎, ‎are studied‎. ‎the behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎also‎, ‎some‎ ‎characterizations of pomonoids over which all $s$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎further‎, ‎we‎ ‎giv...

The modern study of singular integral operators on curves in the plane began 1970s. Since then, there has been a vast array work done boundedness defined lower dimensional sets Euclidean spaces. In recent years, mathematicians have attempted to push these results into more general metric setting particularly case and graphs Carnot groups. Suppose $$X = Y^*$$ for separable Banach space Y. Any ca...

The focus of this paper is on Ahlfors Q-regular compact sets $$E\subset \mathbb {R}^n$$ such that, for each $$Q-2<\alpha \le 0$$ , the weighted measure $$\mu _{\alpha }$$ given by integrating density $$\omega (x)=\text {dist}(x, E)^\alpha $$ yields a Muckenhoupt $$\mathcal {A}_p$$ -weight in ball B containing E. For E we show existence bounded linear trace operator acting from $$W^{1,p}(B,...

We construct a large class of explicit, asymptotically flat and regular wormhole solutions in higher order scalar tensor theories. The are vacuum theory no matter (exotic or regular) is introduced to support them. They constructed via general disformal transformation seed black hole solution. belong particular Horndeski which requires the presence all extended Galileons has dimensional Lovelock...

&#x0D; Assume that \(f\) lies in the class of starlike functions order \(\alpha\in[0,1)\), is, which are regular and univalent for \(|z|&lt;1\) such that&#x0D; Re\(\left(\frac{zf'(z)}{f(z)}\right)&gt;\alpha\) \(|z|&lt;1.\)&#x0D; In this paper we show each following sharp inequality holds:&#x0D; \(|f(re^{i\theta})|^{-1}\int_{0}^{r}|f'(ue^{i\theta})|\,du\leq\frac{\Gamma(\frac{1}{2})\Gamma(2-\alph...

Two classes of distributions that are widely used in the analysis of Bayesian auctions are the Monotone Hazard Rate (MHR) and Regular distributions. They can both be characterized in terms of the rate of change of the associated virtual value functions: for MHR distributions the condition is that for values v < v, φ(v) − φ(v) ≥ v − v, and for regular distributions, φ(v) − φ(v) ≥ 0. Cole and Rou...