Scattering by interstellar dust grains can produce time variable X-ray halos around gamma-ray bursts (GRB). In particular, an X-ray expanding ring is expected when a short pulse of X-ray radiation is scattered by a narrow layer of dust in our Galaxy. We present a new method to detect and analyze dust scattering expanding rings around gamma-ray bursts, using as an example XMM-Newton data of GRB ...

In this article, we give several differentiation and integrability formulas of special and composite functions including the trigonometric function, the hyperbolic function and the polynomial function [3]. For simplicity, we adopt the following rules: r, x, a, b denote real numbers, n, m denote elements of N, A denotes a closed-interval subset of R, and Z denotes an open subset of R. One can pr...

We consider the problem of reconstruction of entire functions of exponential type τ that are elements of certain weighted Lp(μ)-spaces from their values and the values of their derivatives up to order ν. In this paper we extend the interpolation results of [24] in which the case ν = 1 was solved. Using the theory of de Branges spaces we find a discrete set Tτ,ν of points on the real line and a ...

Let λ = (λ1, λ2, . . . , λl), λ1 ≥ λ2 ≥ . . . ≥ λl > 0, be a partition of n, λ ⊢ n, and let [λ] = {(i, j) ∈ Z : 1 ≤ i ≤ l, 1 ≤ j ≤ λi} be the corresponding Young diagram. The conjugate partition λ is defined by λj = max{i : λi ≥ j}. We will freely use implications such as i ≤ j ⇒ λi ≥ λj. The hook Hz ⊆ [λ] is the set of squares weakly to the right and below of z = (i, j) ∈ [λ], and the hook len...

We show that the SATISFIABILITY (SAT) problem for CNF formulas with β-acyclic hypergraphs can be solved in polynomial time by using a special type of Davis-Putnam resolution where each resolvent is a subset of a parent clause. We extend this class to CNF formulas for which this type of Davis-Putnam resolution still applies and show that testing membership in this class is NP-complete. We compar...

The papers [11], [13], [14], [1], [8], [10], [2], [4], [7], [5], [6], [9], [15], [3], and [12] provide the notation and terminology for this paper. For simplicity, we use the following convention: x, a denote real numbers, n denotes a natural number, Z denotes an open subset of R, and f , f1, f2 denote partial functions from R to R. One can prove the following propositions: (1) If a > 0, then e...

Through minimal-model semantics, three-valued logics provide an interesting formalism for capturing reasoning from inconsistent information. However, the resulting paraconsistent logics lack so far a uniform implementation platform. Here, we address this and specifically provide a translation of two such paraconsistent logics into the language of quantified Boolean formulas (QBFs). These formul...

A formula is said to have unique-normal proof property and unique-normal proof property ii it has a unique-normal proof and a-normal proof in NJ, respectively. In this report a condition of implicational minimal formulas in the intuitionistic logic for unique-normal proof property is presented making use of unique-normal proof property for negatively non-duplicated formulas. It is shown that th...

Arbitrary Arrow Update Logic with Common Knowledge (AAULC) is a dynamic epistemic logic with (i) an arrow update operator, which represents a particular type of information change and (ii) an arbitrary arrow update operator, which quantifies over arrow updates. By encoding the execution of a Turing machine in AAULC, we show that neither the valid formulas nor the satisfiable formulas of AAULC a...

This paper deals with: (i) the theory ID # 1 which results from c ID 1 by restricting induction on the natural numbers to formulas which are positive in the xed point constants, (ii) the theory BON() plus various forms of positive induction, and (iii) a subtheory of Peano arithmetic with ordinals in which induction on the natural numbers is restricted to formulas which are in the ordinals. We s...