The objective of reconstructive integral geometry is to recover a function from its integrals over a set of subvarieties. A parametrix is a method of reconstruction of a function from its integral data up to a smoothing operator. In the simplest case, a parametrix recovers a function with a jump singularity along a curve (surface) up to a continuous function, which can be quite informative in m...

MKT0000528 › With recent improvements in the efficiency of integral equation solutions it is now possible to combine the integral equation procedure with the finite element method (FEM) in a hybrid Finite Element Boundary Integral approach (FEBI) [1]. In electromagnetics the FEM is a general purpose technique that solves for volumetric electric fields and can be used to accurately characterize ...

A collocation method is formulated and justified for numerical solution of the Fredholm second-kind integral equations. As an application the Lippmann-Schwinger equation is considered. The results obtained provide an error estimate and a justification of the limiting procedure used in the earlier papers by the author, dealing with many-body scattering problems in the case of small scatterers, a...

In this article, we consider the nonlinear Duffing-van der Pol-type oscillator system by means of the first integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly, we apply the Division Theorem for two variables in the comple...

This paper introduces an exact algorithm for solving integer programs, neither using cutting planes nor enumeration techniques. It is a primal augmentation algorithm that relies on iteratively substituting one column by columns that correspond to irreducible solutions of certain linear diophantine inequalities. We prove that our algorithm is finite and demonstrate its potential by testing it on...

Homotopy type of partially ordered sets (poset for short) play a crucial role in algebraic topology. In fact, every space is weakly equivalent to a simplicial complex which, of course, can be considered as a poset. Posets also arise in more specific contexts as homological decompositions [10, 6, 16, 20] and subgroups complexes associated to finite groups [7, 26, 4]. The easy structure of a pose...

We study the cohomology and hence K-theory of the aperiodic tilings formed by the so called ‘cut and project’ method, i.e., patterns in d dimensional Euclidean space which arise as sections of higher dimensional, periodic structures. They form one of the key families of patterns used in quasicrystal physics, where their topological invariants carry quantum mechanical information. Our work devel...

We introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows to calculate spectra and wave functions, in particular at strong fields and semiclassical values of the magnetic length. The method is presented for interior and exterior problems with general boundary conditions. We explain why the magnetic analogues of the field-free...

We describe a path integral approach for data assimilation. It is based on the generalized hybrid Monte Carlo sampling scheme. Since it makes no assumptions on linearity in the dynamics, or on Gaussianity in the statistics, it permits consideration of very general estimation problems. The method can be used for such tasks as computing a smoother solution, parameter estimation, and data/model in...

The integral simplex method for set partitioning problems allows only pivots-on-one to be made, which results in a primal all-integer method. In this technical note we outline how to tailor the column generation principle to this method. Because of the restriction to pivots-onone, only local optimality can be guaranteed, and to ensure global optimality we consider the use of implicit enumeratio...