We study sharp growth conditions for the boundedness of Hardy-Littlewood maximal function in generalized Orlicz spaces. assume that \(\phi(x,t)\) satisfies standard continuity properties (A0), (A1) and (A2). show if is bounded from space to itself then \(\phi(x,t)/t^p\) almost increasing large \(t\) some \(p>1\). Moreover we \(L^\phi(\mathbb{R}^n)\) only \(\phi\) weakly equivalent a \(\psi\)...

In this paper we study the concept of ph-biatness ofa Banach algebra A, where ph is a continuous homomorphism on A.We prove that if ph is a continuous epimorphism on A and A hasa bounded approximate identity and A is ph- biat, then A is ph-amenable. In the case where ph is an isomorphism on A we showthat the ph- amenability of A implies its ph-biatness.

We extend the definition of involutivity to non-Lipschitz tangent subbundles using generalized functions. prove Frobenius Theorem with sharp regularity estimate when subbundle is log-Lipschitz: if $${\mathcal {V}}$$ a log-Lipschitz involutive rank r, then for any $$\varepsilon >0$$ , locally there homeomorphism $$\Phi (u,v)$$ such that ,\frac{\partial \Phi }{\partial u^1},\dots u^r}\in C^{0,1-\...

In this paper, we study the $$L^{1}$$ boundedness of Fourier integral operator $$T_{\phi ,a}$$ with rough symbol $$a\in L^{\infty }S^{m}_{\rho }$$ and a new class phase $$\phi $$ . class, extend $$L^{\infty }\Phi ^{2}$$ non-degeneracy conditions to some generalized derivative estimation measure condition respectively. Our main result substantially extends improves known results about operator. ...

Direct-phi perception elicited by a reverse-phi (i.e. reversed-polarity) stimulus may well be accounted for, if the front-end filters of a classical Reichardt unit are full-wave rectifiers. It is shown that reverse-phi perception is progressively replaced by direct-phi perception when either the spatial or the temporal modulation of the reversed-polarity stimuli are decreased. Reverse-phi perce...

BACKGROUND Since it was first defined in 1995, Public Health Informatics (PHI) has become a recognized discipline, with a research agenda, defined domain-specific competencies and a specialized corpus of technical knowledge. Information systems form a cornerstone of PHI research and implementation, representing significant progress for the nascent field. However, PHI does not advocate or incorp...

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...

In this paper, we study $(G,\chi_{\phi})$-equivariant $\phi$-coordinated quasi modules for nonlocal vertex algebras. Among the main results, establish several conceptual including a generalized commutator formula and general construction of weak quantum algebras their modules. As an application, also construct (equivariant) lattice by using Lepowsky's work on twisted operators.

In the present paper, we introduced concept of generalized multi-valued contraction mappings, via class functions \(\Phi\) and \(\Psi\) Also proved some fixed point results for (\(\phi\),\(\mathfrak{F}\))- mappings on cone b-metric spaces over Banach algebra \(\mathfrak{V}\). The conditions existence uniqueness are investigated. We give an example to support our main result.