Near-Kerr black hole initial datasets are constructed by applying either the parabolic-hyperbolic or algebraic-hyperbolic form of constraints. In both cases, strongly and weakly asymptotically flat with desirable falloff rates produced controlling only monopole part one freely specifiable variables. The viability applied method is verified numerically integrating evolutionary forms constraint e...

We have measured the force between a weakly charged micron-sized colloidal particle and flat substrate in the presence of highly charged nanoparticles of the same sign under solution conditions such that the nanoparticles physically adsorb to the colloidal particle and substrate. The objective was to investigate the net effect on the force profile between the microparticle and flat substrate ar...

I outline some nonperturbative relativistic effects that arise from gravitational corrections to the Boltzmann equations. These may be important for the study of CMB temperature anisotropies, particularly their interpretation. These terms are not included in the canonical treatment as they arise from the exact equations. Here a weakly nonlinear investigation of these effects is defined and inve...

Let $R$ be a commutative ring. The purpose of this article is to introduce a new class of ideals of R called weakly irreducible ideals. This class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. The relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...

The pressure gradient along the ultrasonic beam results in medium streaming. Following Nyborg's analysis of the Navier-Stokes equation, Wu and Du developed an approximate solution for the streaming velocity generated by flat and weakly focused transducers. We have modified their solution of the Poisson equation by directly deriving the Dirichlet boundary conditions to be applied for this type o...

We discuss the impact of special relativistic effects on the observed light curves and variability duty cycles of radio-loud active galactic nuclei (AGNs). We model the properties of AGN light curves at radio wavelengths using a simulated shot noise process in which the occurrence of major flaring events in a relativistic jet is governed by Poisson statistics. We show that flaring sources whose...

For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.