Linear Volterra Integral Equations

The Kurzweil-Henstock integral formalism is applied to establish the existence of solutions to the linear integral equations of Volterra-typewhere the functions are Banach-space valued. Special theorems on existence of solutions concerning the Lebesgu3 integral setting are obtained. These sharpen earlier results.     

Traces of harmonic functions,capacities, and traces of symmetric Markov processes

We derive explicit isomorphism formulas between weighted Dirichlet integrals for harmonic functions and boundary Dirichlet forms. Applications yield results on traces of Markov processes and convergence quasieverywhere of harmonic functions.     

含余割核奇异积分修改的反演问题

针对含余害核奇异积分反演问题在指κ＜0时一般无解的情况，本文提出并求解两种修改的反演问题，而后一种修改反演问题的提法与此前类似问题颇不相同，由于运用了推广的留数定理和Bertrand型换序公式使本问题及类似问题解法得以简化。     

Two-Temperature Transport Coefficients in Argon–Hydrogen Plasmas—I: Elastic Processes and Collision Integrals

The calculation of two-temperature transport coefficients in an argon–hydrogen plasma at atmospheric pressure is performed using a new theory of two-temperature transport properties recently presented. The latter takes into account the coupling between electrons and heavy species, coupling neglected in the already existing theories of Devoto and Bonnefoi. Transport coefficients are calculated at two-temperatures, the kinetic temperature of electrons T_e being different from that of heavy species T_h. This paper is divided into two parts. The first one is related to elastic processes and its aim is to compare the results obtained with this new theory for viscosity , translational thermal conductivities ^tr _e and ^tr _h and electrical conductivity with the previous results of Bonnefoi. The composition is calculated with the modified equilibrium constant of van de Sanden et al. and the most recent interaction potential are discussed. As it could be expected the electron translational thermal conductivity and the electrical conductivity calculated when taking into account or not the coupling between electrons and heavy species show non-negligible discrepancies. Besides this comparison, the results also show the drastic influence of the non-equilibrium parameter =T_e/T_h on the values of , , ^tr _e, and ^tr _h.     

Multipole expansion of diatomic overlap

A systematic extension of Ruedenberg's expansion formula is applied to evaluate two-electron integrals occurring in calculations on molecular structure. Minimum STO basis sets are used for all SCF-calculations within the framework of the MEDO-method (Multipole Expansion of Diatomic Overlap). The errors due to this approximation scheme are almost negligible compared to those introduced by the truncated basis set: LiH, Li₂ and N₂ are chosen as examples.     

Ab initio molecular orbital calculations on large lattice cluster models: Use of translational symmetry

Summary Translational symmetry has been shown to be useful in the calculation of electronic structures of large lattice models. The number of unique integrals has been derived for cases of different dimensionality. For the unique integrals zero screening and approximation methods are described. The method has been applied to arrays of hydrogen atoms and to a zincblende surface model. When the size of the system is increased the translationally unique integrals are shown to become either zero or they can be calculated by simple coulombic approximations.     

Using ordinary differential equations system to solve isoconversional problems in non-isothermal kinetic analysis

The mathematical evaluation of the activation energy, E, of non-isothermal degradation reactions is usually made using the Ozawa/Flynn–Wall isoconversion principle and involves the numerical resolution of a set of integrals without closed form solution, which are solved by polynomial approximation or by numeric integration. In the present work, the isoconversion principle, originally described and maintained until now as an algebraic problem, was written as a set of ordinary differential equations (ODEs). The individual ODEs obtained are integrated by numeric methods and are used to estimate the activation energy of simulated examples. A least square error (LSE) objective function using the introduced ODEs was written to deal with multiple heating rate CaCO₃ thermal decomposition TG experiments.     

Exploiting non-abelian point group symmetry in direct two-electron integral transformations

Summary A simple and general scheme to exploit any discrete point group symmetry in two-electron integral transformations is introduced. It has been implemented together with integral pre-screening techniques in direct two-electron integral transformations. Its application has also been extended to subsequent MO integral processing steps like MP2 or solution of the coupled-perturbed Hartree-Fock equations (CPHF). Timings for representative applications are presented.     

On the complete solution of ∈y″=y 3

In Ref. 1, the author claimed that the problem y=y ³ is soluble only for a certain range of the parameter . An analytic approach, as adopted in the following contribution, reveals that a unique solution exists for any positive value of . The solution is given in closed form by means of Jacobian elliptic functions, which can be numerically computed very efficiently. In the limit 0+, the solutions exhibit boundary-layer behavior at both endpoints. An easily interpretable approximate solution for small is obtained using a three-variable approach.     

Estimating the complexity of a class of path-following methods for solving linear programs by curvature integrals

In this paper we study a particular class of primal-dual path-following methods which try to follow a trajectory of interior feasible solutions in primal-dual space toward an optimal solution to the primal and dual problem. The methods investigated are so-called first-order methods: each iteration consists of a long step along the tangent of the trajectory, followed by explicit recentering steps to get close to the trajectory again. It is shown that the complexity of these methods, which can be measured by the number of points close to the trajectory which have to be computed in order to achieve a desired gain in accuracy, is bounded by an integral along the trajectory. The integrand is a suitably weighted measure of the second derivative of the trajectory with respect to a distinguished path parameter, so the integral may be loosely called a curvature integral.