A bstract We study the near horizon 2d gravity theory which captures extremal thermodynamics of Kerr black holes where a linear combination excess angular momentum δJ and mass δM is held fixed. These correspond to processes both momenta are perturbed leaving them extremal. For AdS 4 we hold $$ \delta J-\mathcal{L}\delta M=0 δJ</m...

Abstract Let X X be a compact Riemann surface of genus g ≥ 2 g\ge 2 and ℳ ( E 6 ) {\mathcal{ {\mathcal M} }}\left({E}_{6}) the mo...

The dynamics of nonlinear flip-flop quantum walk with amplitude-dependent phase shifts pertubing potential barrier is investigated. Through the adjustment between uniform local perturbations and a Kerr-like nonlinearity medium we find rich set dynamic profiles. We will show existence different Hadamard walking regimes, including those mobile soliton-like structures or self-trapped states. latte...

In this paper, we prove that for any Kähler metrics $$\omega _0$$ and $$\chi $$ on M, there exists a metric _\varphi =\omega _0+\sqrt{-1}\partial {\bar{\partial }}\varphi >0$$ satisfying the J-equation $${\mathrm {tr}}_{\omega }\chi =c$$ if only $$(M,[\omega _0],[\chi ])$$ is uniformly J-stable. As corollary, find sufficient condition existence of constant scalar curvature with $$c_1<0$$ . Usin...

Abstract In a first-order theory $\varTheta $, the decision problem for class of formulae $\varPhi $ is solvable if there an algorithmic procedure that can assess whether or not existential closure $\varphi ^{\exists }$ belongs to any \in \varPhi $. 1988, Parlamento and Policriti already showed how tailor arguments à la Gödel very weak axiomatic set theory, referring them $\varSigma _{1}$-formu...

Let X be a locally compact Hausdorff topological space, let V = ( v n , k ) ∈ N $\mathcal {V}=(v_{n,k})_{n,k\in {\mathbb {N}}}$ system of positive continuous functions on and φ self-map X. The composition operators C : f ↦ ∘ $C_\varphi f\mapsto \ f\,\circ\, \varphi$ the weighted function (LF)-spaces {V}C(X)$ 0 {V}_0C(X)$ resp.) (PLB)-spaces A {A}C(X)$ {A}_0C(X)$ are studied. We characterize whe...

Let $\Re$ and $\Re'$ unital $2$,$3$-torsion free alternative rings $\varphi: \Re \rightarrow \Re'$ be a surjective Lie multiplicative map that preserves idempotents. Assume has nontrivial Under certain assumptions on $\Re$, we prove $\varphi$ is of the form $\psi + \tau$, where $\psi$ either an isomorphism or negative anti-isomorphism onto $\tau$ additive mapping into centre which maps commutat...

Let A and B be C*-algebras $$\varphi :A\rightarrow B$$ a $$*$$ -homomorphism. We discuss the properties of kernel (co-)image induced map $$\mathrm {K}_{0}(\varphi ):\mathrm {K}_{0}(A) \rightarrow \mathrm {K}_{0}(B)$$ on level K-theory. In particular, we are interested in case that co-image is torsion free, show it holds when commutative unital, has real rank zero, $$ unital injective. also embe...

We give a characterization of complete interpolating sequences for the Fock spaces $\mathcal{F}^p_\varphi,\ 1\leq p<\infty$, where $\varphi(z)=\alpha\left(\log^+|z|\right)^2,\ \alpha>0$. Our results are {analogous} to classical Kadets-Ingham's $1/4-$Theorem on perturbation Riesz bases complex exponentials, and they answer question asked by A. Baranov, Dumont, Hartmann K. Kellay in \cite[page 31...

It is proved that if $\varphi\colon A\to B$ a local homomorphism of commutative noetherian rings, nonzero finitely generated $B$-module $N$ whose flat dimension over $A$ at most $\mathrm{edim}\, A - \mathrm{edim}\, B$, free $B$, and $\varphi$ special type complete intersection. This result motivated by "patching method" developed Taylor Wiles, conjecture de Smit, the first author, dealing with ...