In this paper, we study a class of critical Choquard equations with axisymmetric potentials, $$\begin{aligned} -\Delta u+ V(|x'|,x'')u =\Big (|x|^{-4}*|u|^{2}\Big )u\text{ in } \mathbb {R}^6, \end{aligned}$$ where $$(x',x'')\in {R}^2\times {R}^{4}$$ , $$V(|x'|, x'')$$ is bounded nonnegative function $$\mathbb {R}^{+}\times and $$*$$ stands for the standard convolution. The equation sense Hardy-...

let $r$ be an infinite ring. here we prove that if $0_r$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin x}$ for every infinite subset $x$ of $r$, then $r$ satisfies the polynomial identity $x^n=0$. also we prove that if $0_r$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in x}$ for every infinite subset $x$ of $r$, then $x^n=x$ for all $xin r$.

We construct and check by explicit Feynman diagram calculations the BRST Ward identities for N = 2 rigid super Yang-Mills theory and N = 2 extended supergravity in four-dimensional Euclidean space without auxiliary fields. We use the Batalin-Vilkovisky formalism. In the supergravity case we need one new contractible pair of complex spinor fields to obtain the usual gauge-fixing term and corresp...

sybil attacks pose a serious threat for wireless sensor networks (wsn) security. they can create problems in routing, voting schemes, decision making, distributed storage and sensor re-programming. in a sybil attack,the attacker masquerades as multiple sensor identities, that are actually controlled by one or a few existing attacker nodes. sybil identities are fabricated out of stolen keys, obt...

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

In recent years, many commentators have stressed that cultural diversity and immigration are integral features of British history (e.g. see Hall 2000; Kushner 1992; Merriman 1997; Ramdin 1999; Walker 1997). Furthermore, ‘four nations’ histories of ‘the Isles’ have highlighted the fault lines of an internally divided series of cultures, which are emphatically hybrid and riddled with conflict (Sa...

The preservation of your identity is a fundamental right. In many situations, you need to claim your identity and this claim needs to be verified somehow. The technology called biometrics may help. But, what if a deliberate impostor claims your identity? Will this forgery be always detected? Biometric identity verification is imperfect. This presentation will review some of the techniques that ...

This study explores the rich spatial-cultural phenomena of street skateboarding and graffiti in Jakarta. The enduring appeal both activities lies their ability to inspire creativity, foster subcultural identities, leave a lasting impact on culture. Through interviews detailed observations by first author, an active skateboarder, research investigates motivations, challenges, cultural significan...