This paper presents a hybrid numerical method to solve efficiently a class of highly anisotropic elliptic problems. The anisotropy is aligned with one coordinateaxis and its strength is described by a parameter ε ∈ (0, 1], which can largely vary in the study domain. Our hybrid model is based on asymptotic techniques and couples (spatially) an Asymptotic-Preserving model with its asymptotic Limi...

The Gel'fand-Yaglom theorem has been used to calculate the one-loop effective action in quantum field theory by means of "partial-wave-cutoff method". This method works well for a wide class background fields and is essentially exact. However, its implementation semi-analytical so far since it involves solving non-linear ordinary differential equation which solutions are general unknown. Within...

This paper presents a fixed-end two-mass system (TMS) with end constraints that permits uncoupled solutions for different masses. The coupled nonlinear models for the present fixed-end TMS were solved using the continuous piecewise linearization method (CPLM) and detailed investigation on the effect of mass-ratio on the TMS response was conducted. The investigations showed that increased mass-r...

There has been much work on the following question: given n, how large can a subset of {1, . . . , n} be that has no arithmetic progressions of length 3. We call such sets 3-free. Most of the work has been asymptotic. In this paper we sketch applications of large 3-free sets, present techniques to find large 3-free sets of {1, . . . , n} for n ≤ 250, and give empirical results obtained by codin...

Both direct and indirect techniques have been used for many years to determine nuclear reaction rates at astrophysical energies. A number of problems have been encountered which limit measurements by direct techniques, including very low cross sections, the importance of subthreshold states and the need for radioactive targets. Over the past decade, new indirect techniques have been developed t...

We consider the distribution of cycle counts in a random regular graph, which is closely linked to the graph’s spectral properties. We broaden the asymptotic regime in which the cycle counts are known to be approximately Poisson, and we give an explicit bound in total variation distance for the approximation. Using this result, we calculate limiting distributions of linear eigenvalue statistics...