In [6–8] Murskii studied probability in algebra. He showed, for example, that the probability that a random groupoid is simple is 1 and that the probability that it has no idempotent element (one that satisfies a = a) is 1/e. To make these statements precise, define a groupoid table on the set {0, 1, . . . , n− 1} to be an n by n matrix with entries from {0, 1, . . . , n− 1}. Of course, each gr...

In this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid G(n). Also we show that G(n) contains commuting regular subsemigroup and give a necessary and sufficient condition for the groupoid G(n) to be commuting regular.

By a 2-group we mean a groupoid equipped with a weakened group structure. It is called split when it is equivalent to the semidirect product of a discrete 2-group and a oneobject 2-group. By a permutation 2-group we mean the 2-group Sym(G) of self-equivalences of a groupoid G and natural isomorphisms between them, with the product given by composition of self-equivalences. These generalize the ...

For any body-time manifold [Formula: see text] there exists a groupoid, called the material encoding all properties of evolution. A smooth distribution, is constructed to deal with case in which groupoid not Lie groupoid. This new tool provides unified framework general non-uniform

Post-Occupancy Evaluation (POE) has become increasingly accepted and influential among client organizations responsible for large building management and construction programs. Managers and administrators look to POE to provide answers to· important facilities questions. This increased focus on decision-making has resulted in a number of changes to the way in which POEs are conducted, including...

X iv :0 80 3. 04 72 v1 [ m at h. R A ] 4 M ar 2 00 8 On decomposition of commutative Moufang groupoids B.V.Novikov It is well-known that the multiplicative groupoid of an alternative/Jordan algebra satisfies Moufang identities [1, 4]. Therefore it seems interesting to study the structure of such groupoids. In this note we apply to Moufang groupoids an approach which is widespread in Semigroup T...

In this paper we study Poisson actions of complete Poisson groups, without any connectivity assumption or requiring the existence of a momentum map. For any complete Poisson group G with dual G⋆ we obtain a suitably connected integrating symplectic double groupoid S. As a consequence, the cotangent lift of a Poisson action on an integrable Poisson manifold P can be integrated to a Poisson actio...

We introduce the concept of vague ideals in a distributive implication groupoid and investigate their properties. The vague ideals of a distributive implication groupoid are also characterized.

Correct authenticated decryption requires the receiver to buffer the decrypted message until the authenticity check has been performed. In high-speed networks, which must handle large message frames at low latency, this behavior becomes practically infeasible. This paper proposes CCA-secure on-line ciphers as a practical alternative to AE schemes since the former provide some defense against ma...

The retention behavior on poly(oxyethylene) (POE) chemically-bonded stationary phases was investigated in ion-exchange, reversed-phase (RP) and hydrophilic interaction (HILIC) modes in capillary liquid chromatography. The eluent cations fixed on the oxygen atoms of the POE chains by ion-dipole interaction worked as the anion-exchange sites for the separation of inorganic anions. Nonpolar analyt...