We study the Cauchy problem associated with the system of two conservation laws arising in isothermal gas dynamics, in which the pressure and the density are related by the γ-law equation p(ρ) ∼ ρ with γ = 1. Our results complete those obtained earlier for γ > 1. We prove the global existence and compactness of entropy solutions generated by the vanishing viscosity method. The proof relies on c...

Let A be a Banach algebra with bounded approximate identity by 1. Two new topologies ?so and ?wo are introduced on A. We study these compare them each other the norm topology. The properties of then studied further we pay attention to group L1(G) locally compact G. Various necessary sufficient conditions found for G finite.

Two distributions over n-bit strings are (k, δ)-wise indistinguishable if no statistical test that observes k of the n bits can tell the two distributions apart with advantage better than δ. Motivated by secret sharing and cryptographic leakage resilience, we study the existence of pairs of distributions that are (k, δ)-wise indistinguishable, but can be distinguished by some function f of suit...

We consider weakly convergent sequences of approximate H-surface maps defined in the plane with their tension fields bounded in Lp for p > 4/3, and establish an energy quantization that accounts for the loss of their energies by the sum of energies over finitely many nontrivial bubbles maps on R2. As a direct consequence, we establish the energy identity at finite singular time to their H-surfa...

Let S be a locally compact topological foundation semigroup with identity and Ma(S) be its semigroup algebra. In this paper, we give necessary and sufficient conditions to have abounded approximate identity in closed codimension one ideals of the semigroup algebra $M_a(S)$ of a locally compact topological foundationsemigroup with identity.

We survey the recent investigations on (bounded, sequential) approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We will discuss the core problems concerning these notions and address the signicance of any solutions to them to the development of the eld.

We investigate the stability of generalizedderivations on Banach algebras with a bounded central approximateidentity. We show that every approximate generalized derivation inthe sense of Rassias, is an exact generalized derivation. Also thestability problem of generalized derivations on the faithful Banachalgebras is investigated.

We prove that, for every extension of Banach algebras 0 → B → A → D → 0 such that B has a left or right bounded approximate identity, the existence of an associated long exact sequence of Banach simplicial or cyclic cohomology groups is equivalent to the existence of one for homology groups. It follows from the continuous version of a result of Wodzicki that associated long exact sequences exis...