This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

We examine the regularity of weak solutions of quasi-geostrophic (QG) type equations with supercritical (α < 1/2) dissipation (−∆). This study is motivated by a recent work of Caffarelli and Vasseur, in which they study the global regularity issue for the critical (α = 1/2) QG equation [2]. Their approach successively increases the regularity levels of Leray-Hopf weak solutions: from L to L∞, f...

in this paper an approach based on evolutionary algorithms to find pareto optimal pair of state and control for multi-objective optimal control problems (moocp)'s is introduced‎. ‎in this approach‎, ‎first a discretized form of the time-control space is considered and then‎, ‎a piecewise linear control and a piecewise linear trajectory are obtained from the discretized time-control space using ...

In this paper we will prove that if $L$ is a continuous symmetric n-linear form on a Hilbert space and $widehat{L}$ is the associated continuous n-homogeneous polynomial, then $||L||=||widehat{L}||$. For the proof we are using a classical generalized  inequality due to S. Bernstein for entire functions of exponential type. Furthermore we study the case that if X is a Banach space then we have t...

We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...

background decentralisation aims to bring services closer to the community and has been advocated in the health sector to improve quality, access and equity, and to empower local agencies, increase innovation and efficiency and bring healthcare and decision-making as close as possible to where people live and work. fiji has attempted two approaches to decentralisation. the current approach refl...

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We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.