This paper investigates algebraic objects equipped with an operator, such as operated monoids, algebras etc. Various free object functors in these contexts are explicitly constructed. For whose operator satisfies a set $\Phi$ of relations (usually called polynomial identities (aka. OPIs)), Guo defined objects, $\Phi$-algebras, via universal algebra. Free $\Phi$-algebras over studied details. A ...

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. ...

We study the boundedness of Riesz transforms in L for p > 2 on a doubling metric measure space endowed with a gradient operator and an injective, ω-accretive operator L satisfying Davies-Gaffney estimates. If L is non-negative self-adjoint, we show that under a reverse Hölder inequality, the Riesz transform is always bounded on L for p in some interval [2, 2 + ε), and that L gradient estimates ...

A new three-step iterative algorithm for approximating the zero point of the sum of an infinite family ofm-accretive mappings and an infinite family ofμi-inversely strongly accretive mappings in a real q-uniformly smooth and uniformly convex Banach space is presented. The computational error in each step is being considered. A strong convergence theorem is proved by means of some new techniques...

Measurements of the low-shear viscosity eta(o) with a Zimm-Crothers viscometer for dispersions of colloidal hard spheres are reported as a function of volume fraction phi up to 0.56. Nonequilibrium theories based on solutions to the two-particle Smoluchoski equation or ideal mode coupling approximations do not capture the divergence. However, the nonhydrodynamic contribution to the relative vis...

In this paper, we give simple characterization of binormal weighted composition operators $C_{\psi, \phi}$ on the Fock space over $\mathbb{C}$ where weight function is form $\psi(\zeta) = e^{\langle \zeta, c \rangle}$ for some $c \in \mathbb{C}$. We derive conditions $C_{\phi}$ to be such that $C^*_{\phi}C_{\phi}$ and $C^*_{\phi} + C_{\phi}$ commute. Finally operator complex symmetric.

and Applied Analysis 3 proving: 1 a fixed point theorem for an asymptotically pseudocontractive mapping that is also uniformly L-Lipschitzian and uniformly asymptotically regular, 2 that the set of fixed points of T is closed and convex, and 3 the strong convergence of a CQ-iterative method. The literature on asymptotical-type mappings is very wide see, 7–15 . In 1967, Browder 16 and Kato 17 , ...

We study port-Hamiltonian systems on a family of intervals and characterize all boundary conditions leading to m-accretive realizations the operator thus generators contractive semigroups. The proofs are based structural observation that can be transformed derivative familiy reference by suitable congruence relations, allowing for studying simpler case transport equation. Moreover, we provide w...