‎let $omega$ be a class of unital‎ ‎$c^*$-algebras‎. ‎we introduce the notion of a local tracial $omega$-algebra‎. ‎let $a$ be an $alpha$-simple unital local tracial $omega$-algebra‎. ‎suppose that $alpha:gto $aut($a$) is an action of a finite group $g$ on $a$‎ ‎which has a certain non-simple tracial rokhlin property‎. ‎then the crossed product algebra‎ ‎$c^*(g,a,alpha)$ is a unital local traci...

Inspired by the recent work of Bekka, we study two reasonable analogues of property (T ) for not necessarily unital C∗-algebras. The stronger one of the two is called “property (T )” and the weaker one is called “property (Te)”. It is shown that all non-unital C*-algebras do not have property (T ) (neither do their unitalizations). Moreover, all non-unital σ-unital C*-algebras do not have prope...

ly, ← T may be characterized as the largest theory system of I ≤-included in the theory family T . Proposition 2.2 Suppose that I = 〈Sign, SEN, C〉 is a π-institution and T a theory family of I. Then ← T is the largest theory system of I that is ≤-included in T . P r o o f. Suppose that T ′ is a theory system of I, such that T ′ ≤ T . Let Σ ∈ |Sign|, and φ ∈ SEN(Σ), such that φ ∈ T ′ Σ. Therefor...

Since the 1960s, when Stokoe (1960) demonstrated that sign languages are linguistic systems with typical behavior of natural languages, sign languages began to be studied as complex structural linguistic systems, even if their visual modality differs from the auditive modality of spoken languages. After Stokoe (1960) proved that American Sign Language (ASL) has minimal sign pairs, research on s...

We study a problem of secure data storage in a recently introduced Limited Communication Model. We propose a new cryptographic primitive that we call a Forward-Secure Storage (FSS). This primitive is a special kind of an encryption scheme, which produces huge (5 GB, say) ciphertexts, even from small plaintexts, and has the following non-standard security property. Suppose an adversary gets acce...

In this paper, we show how the process notation of Communicating Sequential Processes (CSP) may be used to describe a lazy caching protocol. We then show that the traces model for CSP can be used to specify the property of sequential consistency. The model-based approach of CSP allows us to demonstrate that the protocol description satisses the speci-cation, thus verifying that the lazy caching...

We represent a computer cluster as a multi-server queue with some arbitrary bipartite graph of compatibilities between jobs and servers. Each server processes its jobs sequentially in FCFS order. The service rate of a job at any given time is the sum of the service rates of all servers processing this job. We show that the corresponding queue is quasi-reversible and use this property to design ...