locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

Let $A_1$ be any spectrum in the class of finite spectra whose mod-2 cohomology is isomorphic to $\mathcal{A}(1)$ as a module over subalgebra Steenrod algebra; let $tmf$ connective topological modular forms. In this paper, we prove that $tmf$-Hurewicz image surjective.

Abstract We consider the semilinear heat equation with Sobolev subcritical power nonlinearity in dimension $N=2$, and $u(x,t)$ a solution that blows up finite time $T$. Given non-isolated blow-up point $a$, we assume Taylor expansion of near $(a,T)$ obeys some degenerate situation labeled by even integer $m(a)\ge 4$. If have sequence $a_n \to a$ as $n\to \infty $, show after change coordinates ...

We show that if \(A=\{a_1< a_2< \ldots < a_k\}\) is a set of real numbers such the differences consecutive elements are distinct, then for and finite \(B \subset \mathbb {R}\), $$ |A+B|\gg |A|^{1/2}|B|. $$ The bound tight up to constant.

In this paper, we give bounds on the dichromatic number $\vec{\chi}(\Sigma)$ of a surface $\Sigma$, which is maximum an oriented graph embeddable $\Sigma$. We determine asymptotic behaviour by showing that there exist constants $a_1$ and $a_2$ such that, $ a_1\frac{\sqrt{-c}}{\log(-c)} \leq \vec{\chi}(\Sigma) a_2 \frac{\sqrt{-c}}{\log(-c)} for every $\Sigma$ with Euler characteristic $c\leq -2$...

We prove an $\mathbb F_p$-Selberg integral formula of type $A_n$, in which the is element finite field F_p$ with odd prime number $p$ elements. The motivated by analogy between multidimensional hypergeometric solutions KZ equations and polynomial same reduced modulo $p$. For $A_1$ was proved a previous paper authors.

Using a recently proposed gauge covariant diagonalization of $\pi a_1$-mixing we show that the low energy theorem $F^{\pi}=e f_\pi^2 F^{3\pi}$ current algebra, relating anomalous form factor $F_{\gamma \to \pi^+\pi^0\pi^-} = and neutral pion $F_{\pi^0 \gamma\gamma}=F^\pi$, is fulfilled in framework Nambu-Jona-Lasinio (NJL) model, solving long standing problem encountered extension including vec...

Abstract Let $$A=\{a_0,\ldots ,a_{n-1}\}$$ A = { a 0 , … n - 1 } be a finite set of $$n\ge 4$$...