The Boros-Moll polynomials arise in the evaluation of a quartic integral. The original double summation formula does not imply the fact that the coefficients of these polynomials are positive. Boros and Moll proved the positivity by using Ramanujan’s Master Theorem to reduce the double sum to a single sum. Based on the structure of reluctant functions introduced by Mullin and Rota along with an...

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing one t...

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing to ch...

An alternative analytical approach to calculate the weakly singular free-space static potential integral associated to uniform sources is presented. Arbitrary oriented flat polygons are considered as integration domains. The technique stands out by its mathematical simplicity and it is based on a novel integral transformation. The presented formula is equivalent to others existing in literature...

Let I be a non degenerated non empty multiplicative loop with zero structure and let u be an element of Q(I). Then u1 is an element of I. Then u2 is an element of I. Let I be a non degenerated integral domain-like non empty double loop structure and let u, v be elements of Q(I). The functor u+ v yields an element of Q(I) and is defined by: (Def. 2) u+ v = 〈u1 · v2 + v1 ·u2, u2 · v2〉. Let I be a...

Let n be an ordinal number and let R be a non trivial zero structure. One can verify that there exists a monomial of n, R which is non-zero. Let us observe that there exists a field which is non trivial. Let us note that every left zeroed add-right-cancelable right distributive left unital commutative associative non empty double loop structure which is fieldlike is also integral domain-like. L...

Based on recently proposed non-singular contour-integral representations of single and double layer potentials for 3D surfaces, formulas in the axisymmetric case are derived. They express explicitly the singular layer potentials in terms of elliptic integrals. The presented expressions are non-singular, satisfy exactly very important conservation principles and directly take into account the mu...

A surface integral formulation based on direct boundary integral equation (BIE) was recently proposed for inductance or impedance calculation of 3D electric structures. Though faster than other volume integral methods, this formulation still suffers from as many as 7N unknowns, where N is the number of panels. A mixed surface integral formulation is proposed in this paper, which combines indire...

Lipid-protein interactions in membranes are dynamic, and consequently are well studied by magnetic resonance spectroscopy. More recently, lipids associated with integral membrane proteins have been resolved in crystals by X-ray diffraction, mostly at cryogenic temperatures. The conformation and chain ordering of lipids in crystals of integral proteins are reviewed here and are compared and cont...