We prove that every separable tracial von Neumann algebra embeds into a II1 factor with property (T) which can be taken to have trivial outer automorphism and fundamental groups. also establish an analogous result for the extension over non-atomic probability space of countable p.m.p. equivalence relation. In addition, we obtain two new results concerning structure infinitely generic factors. T...

The study of simply definable equivalence relations, and in particular of Borei and analytic ones, on Polish spaces, has attracted a lot of attention in descriptive set theory since 1970, when the first fundamental result in the subject, Silver's theorem, was proved. One motivation has certainly been the conjecture of Vaught in model theory, one of the oldest still open problems in mathematical...

Morita equivalence is a widely used tool for rings with identity. (Two rings are said to be Morita equivalent if the categories of unitary modules over them are equivalent.) For monoids, this notion is not really useful: in most cases it reduces to isomorphism. As the theory of Morita equivalence could be developed for the more general case of rings with local units, and then for idempotent rin...

An equivalence relation in the symmetric group , where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described. n S 2 n3 n

Isospectrality of the planar domains which are obtained by successive unfolding of a fundamental building block is studied in relation to iso-length spectrality of the corresponding domains. Although an explicit and exact trace formula such as Poisson’s summation formula or Selberg’s trace formula is not known to exist for such planar domains, equivalence between isospectrality and iso-length s...

The fundamental notion of bisimulation has inspired various notions of system equivalences in concurrency theory. Many notions of bisimulation for various discrete systems have been recently unified in the abstract category theoretical formulation of bisimulation due to Joyal, Nielsen and Winskel. In this paper, we adopt their framework and unify the notions of bisimulation equivalences for dis...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measure-preserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac ...

It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. Some basic operations on functions such as the inverse and composition are applicable to binary relations as well. Depending on the domain or range or both are fuzzy value fuzzy set, i...

The notion of pseudomonotone operator in the sense of Karamardian has been studied for 35 years and has found many applications in variational inequalities and economics. The purpose of this survey paper is to present the most fundamental results in this field, starting from the earliest developments and reaching the latest results and some open questions. The exposition includes: the relation ...