In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

A new London-Eyring-Polanyi-Sato (LEPS) potential energy surface (PES) is used in the O + CH(4) --> OH + CH(3) reaction via the quasiclassical trajectory method (QCT). Comparing with the experiments and the former ab initio calculations, the new LEPS PES describes the actual potential energy surface of the O + CH(4) reaction successfully. The four polarization dependent "generalized" differenti...

Abstract Given $$E_0, E_1, E, F$$ E 0 , 1 F rearrangement invariant spaces, $$a, \mathrm {b}, {b}_0, {b}_1$$ a b slowly varying functions and $$0\le \theta _0<...

We consider minimal graphs $$u = u(x,y) > 0$$ over unbounded domains $$D \subset R^2$$ bounded by a Jordan arc $$\gamma $$ on which . prove sort of reverse Phragmén-Lindelöf theorem showing that if D contains sector $$\begin{aligned} S_{\lambda }=\{(r,\theta )=\{-\lambda /2<\theta<\lambda /2\},\quad \pi <\lambda \le 2\pi , \end{aligned}$$ then the rate growth is at most $$r^{\pi /\lambda }$$

We have obtained the exact-order estimates for some approximative characteristics of Sobolev classes $$ {\mathbbm{W}}_{p,\alpha}^r and Nikоl’skii–Besov {\mathbbm{B}}_{p,\theta}^r periodic functions one several variables in norm space B∞,1. Properties linear operators realizing orders best approximation {\mathbbm{B}}_{\infty, \theta}^r this by trigonometric polynomials generated a set harmonics ...

The hydrostatic equilibrium is a prominent topic in fluid dynamics and astrophysics. Understanding the stability of perturbations near Boussinesq systems helps gain insight into certain weather phenomena. 2D system focused here anisotropic involves only horizontal dissipation thermal diffusion. Due to lack vertical dissipation, precise large-time behavior problem difficult. When spatial domain ...

An “automatic continuity” question has naturally occurred since Roger Howe established the local theta correspondence over R: Does the algebraic version of local theta correspondence over R agree with the smooth version? We show that the answer is yes, at least when the concerning dual pair has no quaternionic type I irreducible factor.