We show that the operator \[ T_{K,s_1,s_2}f(z) := \int_{\mathbb{R}^n} A_{K,s_1,s_2}(z_1,z_2) f(z_2)\, dz_2 \] is a Calderon-Zygmund operator. Here for $K \in L^\infty(\mathbb{R}^n \times \mathbb{R}^n)$, and $s,s_1,s_2 (0,1)$ with $s_1+s_2 = 2s$ we have \frac{K(x,y) \left (|x-z_1|^{s_1-n} -|y-z_1|^{s_1-n} \right )\, (|x-z_2|^{s_2-n} -|y-z_2|^{s_2-n}\right )}{|x-y|^{n+2s}}\, dx\, dy. This motivat...

<abstract><p>Consider the problem of finding maximal nonpositive solvent $ \varPhi quadratic matrix equation (QME) X^2 + BX C = 0 with B being a nonsingular M $-matrix and an such that B^{-1}C\ge $. Such QME arises from overdamped vibrating system. Recently, under condition - I is $-matrix, Yu et al. (<italic>Appl. Math. Comput.</italic>, 218 (2011): 3303–3310) proved \r...

Abstract The research determined the resistance to compression and low velocity impact of wood-based sandwich panels, face sheet made high-density fiber board, high pressure laminate, while its auxetic lattice core was by 3D printing using LayWood bio-composite filament. core's property (i.e. exhibiting negative Poisson's ratio) observed within planes parallel facings. ability particular types ...

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...