Let X be an infinite compact metric space with finite covering dimension and let h : X → X be a minimal homeomorphism. We show that the associated crossed product C*-algebra A = C∗(Z, X, h) has tracial rank zero whenever the image of K0(A) in Aff(T (A)) is dense. As a consequence, we show that these crossed product C*-algebras are in fact simple AH algebras with real rank zero. When X is connec...

This paper establishes a set of theorems that describe the diameter of a zero-divisor graph for a finite direct product R1 × R2 × · · · × Rn with respect to the diameters of the zero-divisor graphs of R1, R2, · · · , Rn−1 and Rn(n > 2).

A graph G is an odd-circuit tree if every block of G is an odd length circuit. It is proved in this paper that the product of every pair of graphs G and H admits a nowhere-zero 3-flow unless G is an odd-circuit tree and H has a bridge. This theorem is a partial result to the Tutte’s 3-flow conjecture and generalizes a result by Imrich and Skrekovski [7] that the product of two bipartite graphs ...

In functional encryption (FE) schemes, ciphertexts and private keys are associated with attributes and decryption is possible whenever key and ciphertext attributes are suitably related. It is known that expressive realizations can be obtained from a simple functional encryption flavor called inner product encryption (IPE), where decryption is allowed whenever ciphertext and key attributes form...

Let A be a unital separable simple C∗-algebra with TR(A) ≤ 1 and α be an automorphism. We show that if α satisfies the tracially cyclic Rokhlin property then TR(A ⋊α Z) ≤ 1. We also show that whenever A has a unique tracial state and αm is uniformly outer for each m and αr is approximately inner for some r > 0, α satisfies the tracial cyclic Rokhlin property. By applying the classification theo...

In this lecture we will discuss 2-player zero sum games. Such games are completely competitive , where whatever one player wins, the other must lose. Examples of such games include chess, checkers, backgammon, etc. We will show that in such games: • An equilibrium always exists; • All equilibrium points yield the same payoff for all players; • The set of equilibrium points is actually the carte...

We show that the symmetric product of a flat affine scheme over a commutative ring can be embedded into the quotient by the general linear group of the scheme of commuting matrices. We also prove that the symmetric product of the affine space is isomorphic to the above quotient when the base ring is a characteristic zero field. Over an infinite field of arbitrary characteristic the quotient of ...

The angular distributions of the products of dissociative recombination of diatomic molecular ions are derived. The distributions are determined by the dominant partial waves of the captured electrons. For a single dominant wave, the neutral product distribution is described by the same spherical harmonic that describes the electron partial wave. The derived distributions take into account both...

The zero-divisor graph of a commutative semigroup with zero is the graph whose vertices are the nonzero zero-divisors of the semigroup, with two distinct vertices adjacent if the product of the corresponding elements is zero. New criteria to identify zerodivisor graphs are derived using both graph-theoretic and algebraic methods. We find the lowest bound on the number of edges necessary to guar...