Some general formulas for double Laplace transformations

Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions

We consider a process (X (α) t )t∈[0,T ) given by the SDE dX (α) t = αb(t)X (α) t dt+σ(t) dBt, t ∈ [0, T ), with initial condition X 0 = 0, where T ∈ (0,∞], α ∈ R, (Bt)t∈[0,T ) is a standard Wiener process, b : [0, T ) → R \ {0} and σ : [0, T ) → (0,∞) are continuously differentiable functions. Assuming d dt ( b(t) σ(t)2 ) = −2K b(t) 2 σ(t)2 , t ∈ [0, T ), with some K ∈ R, we derive an explicit...

Model-based transformations for quantified boolean formulas

Numerical accuracy of real inversion formulas for the Laplace transform

In this paper we investigate and compare a number of real inversion formulas for the Laplace transform. The focus is on the accuracy and applicability of the formulas for numerical inversion. In this contribution, we study the performance of the formulas for measures concentrated on a positive half-line to continue with measures on an arbitrary half-line.

Range Restriction for General Formulas

Deductive databases need general formulas in rule bodies, not only conjuctions of literals. This is well known since the work of Lloyd and Topor about extended logic programming. Of course, formulas must be restricted in such a way that they can be effectively evaluated in finite time, and produce only a finite number of new tuples (in each iteration of the TP -operator: the fixpoint can still ...

Some New Formulas for π

We show how to find series expansions for π of the form π = ∞ n=0 S(n) mn pn a n , where S(n) is some polynomial in n (depending on m, p, a). We prove that there exist such expansions for m = 8k, p = 4k, a = (−4) k , for any k, and give explicit examples for such expansions for small values of m, p and a.