Let J% exp(-PQf(t) dt = F(P) P > 0 where b > 0 is a given number. We give a formula for f (t) in terms of F (p) , p > 0. The object of this Letter is to give a formula for the inverse Laplace transform in which the data used are given on the semi-axis p > 0 only. Let P>O where b > 0 is a fixed number. We have (1, formula 4.14.1) where Jo is a Bessel function. It follows from (1) and (2) that s,...

The Rydberg formula is emblematic of atomic spectroscopy. We review here the personal background, research accomplishments, and academic career of its discoverer, Janne Rydberg. Although his formula is often introduced as a generalization of the hydrogenic Balmer formula, Rydberg s work was independent of Balmer s, and displayed great ingenuity and a rare ability to recognize hidden patterns in...

Many medicinal, nutraceutical, and botanic extracts have been used as cytoprotective agents in liver disease. This article explains the mechanisms of action, pertinent pharmacokinetics, side effects, and clinical indications for the use of S-adenosylmethionine, N-acetylcysteine, ursodeoxycholic acid, silymarin, and vitamin E. The literature pertaining to in vitro studies, laboratory animal mode...

Taking inspiration from a recent paper by Bergounioux et al., we study the Riemann-Liouville fractional Sobolev space \begin{document}$ W^{s, p}_{RL, a+}(I) $\end{document}, for id="M2">\begin{document}$ I = (a, b) $\end{document} some id="M3">\begin{document}$ a, b \in \mathbb...

A monadic formula ψ(Y ) is a selector for a monadic formula φ(Y ) in a structure M if ψ defines inM a unique subset P of the domain and this P also satisfies φ inM. If C is a class of structures and φ is a selector for ψ in everyM ∈ C, we say that φ is a selector for φ over C. For a monadic formula φ(X, Y ) and ordinals α ≤ ω1 and δ < ω , we decide whether there exists a monadic formula ψ(X, Y ...

First we prove that if a separable Banach space X X contains an isometric copy of infinite-dimensional A left-parenthesis upper S right...

In this paper, an ischemia detector is presented based on the analysis of QRS-derived angles. The detector has been developed by modeling ischemic effects on the QRS angles as a gradual change with a certain transition time and assuming a Laplacian additive modeling error contaminating the angle series. Both standard and non-standard leads were used for analysis. Non-standard leads were obtaine...

Let G V, E be a simple graph. A set S ⊆ V is a dominating set of G, if every vertex in V \S is adjacent to at least one vertex in S. Let Pi n be the family of all dominating sets of a path Pn with cardinality i, and let d Pn, j |P n|. In this paper, we construct Pi n, and obtain a recursive formula for d Pn, i . Using this recursive formula, we consider the polynomialD Pn, x ∑n i n/3 d Pn, i x ...

Let G = (V,E) be a simple graph. A set S ⊆ V is a dominating set of G, if every vertex in V \S is adjacent to at least one vertex in S. Let C n be the family of dominating sets of a cycle Cn with cardinality i, and let d(Cn, i) = |C i n|. In this paper, we construct C i n, and obtain a recursive formula for d(Cn, i). Using this recursive formula, we consider the polynomial D(Cn, x) = ∑n i=⌈n 3 ...

this formula defines a Schwartz function, and hence the solution u = uf ∈ S also, and the mapping f 7→ uf is continuous in the sense that if fn is a sequence of Schwartz functions such that ‖fn − f‖α,β → 0 for every Schwartz semi-norm ‖ · ‖α,β , then also ‖un − u‖α,β → 0 for every Schwartz semi-norm, where un = ufn , u = uf . In fact the formula above extends to define a distributional solution...