Abstract We prove implications among the conditions in title for general $\text C^*$-inclusions $A\subseteq B$, and we also relate this to several other properties case $B$ is a crossed product an action of group, inverse semigroup, or étale groupoid on $A$. show that if C^*$-inclusion aperiodic it has unique pseudo-expectations, if, addition, pseudo-expectation faithful, then $A$ supports sens...

this paper aims to investigate the presence of quantifier phrase and classifier phrase in the dp of sarhadi dialect of the baluchi language. to reach this goal, pseudo partitive constructions and their characteristics in different languages are introduced and then it is shown that determiner phrases containing a classifier in baluchi are examples of juxtaposed pseudo partitive constructions in ...

We prove that if $R$ is a commutative Noetherian ring, then every countably generated flat $R$-module quite flat, i.e., direct summand of transfinite extension localizations in countable multiplicative subsets. also show the spectrum cardinality less than $\kappa$, where $\kappa$ an uncountable regular cardinal, modules with generators. This provides alternative proof fact over ring spectrum, a...

The real closed valuation rings, i.e., convex subrings of real closed fields, form a proper subclass of the class of real closed domains. It is shown how one can recognize whether a real closed domain is a valuation ring. This leads to a characterization of the totally ordered domains whose real closure is a valuation ring. Real closures of totally ordered factor rings of coordinate rings of re...

Abstract We introduce the notion of approximation type for partial, and in certain cases total description extensions a given valuation from field K to rational function ( x ). To every extension, unique over is associated, while may be limit many pseudo Cauchy sequences. Approximation types also provide information where are not immediate, we prove that they correspond bijectively when algebra...

By means of the exponential dichotomy method and the properties of the weighted pseudo almost periodic functions, sufficient conditions are obtained for the existence of weighted pseudo almost periodic solutions of functional differential equations with finite delay.

Face anti-spoofing (FAS) plays an important role in protecting face recognition systems from representation attacks. Many recent studies FAS have approached this problem with domain generalization technique. Domain aims to increase performance better detect various types of attacks and unseen However, previous area defined each simply as datasets focused on developing learning techniques. In pa...