Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

1. A complex Banach algebra A is a compact (weakly compact) algebra if its left and right regular representations consist of compact (weakly compact) operators. Let E be any subset of A and denote by Ei and Er the left and right annihilators of E. A is an annihilator algebra if A¡= (0) —Ar, Ir^{fS) for each proper closed left ideal / and Ji t¿ (0) for each proper closed right ideal /. In [6, Th...

Let κ be an uncountable regular cardinal. Call an equivalence relation on functions from κ into 2 Σ11-definable over H(κ) if there is a first order sentence φ and a parameter R ⊆ H(κ) such that functions f, g ∈ κ2 are equivalent iff for some h ∈ κ2, the structure 〈H(κ),∈, R, f, g, h〉 satisfies φ, where ∈, R, f , g, and h are interpretations of the symbols appearing in φ. All the values μ, 1 ≤ μ...

Using the lottery preparation, we prove that any strongly unfoldable cardinal κ can be made indestructible by all <κ-closed κ+-preserving forcing. This degree of indestructibility, we prove, is the best possible from this hypothesis within the class of <κ-closed forcing. From a stronger hypothesis, however, we prove that the strong unfoldability of κ can be made indestructible by all <κ-closed ...

It is a well-known phenomenon in set theory that problems in infinite combinatorics involving singular cardinals and their successors tend to be harder than the parallel problems for regular cardinals. Examples include the behaviour of cardinal exponentiation, the extent of the tree property, the extent of stationary reflection, and the existence of non-free almost-free abelian groups. The expl...

Using results announced by Stevo Todorcevic we establish that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. Modulo the large cardinal, this answers a question of S. Watson. We also solve a problem raised by the second author, proving that it is consistent with ZFC that every first countable hered...

Say that κ’s measurability is destructible if there exists a <κ-closed forcing adding a new subset of κ which destroys κ’s measurability. For any δ, let λδ =df The least beth fixed point above δ. Suppose that κ is indestructibly supercompact and there is a measurable cardinal λ > κ. It then follows that A1 = {δ < κ | δ is measurable, δ is not a limit of measurable cardinals, δ is not δ+ strongl...