Approximate First Integrals of Weakly Nonlinear,Damped-Driven Oscillators with One Degree of Freedom

First-order approximate symmetries of weaklynonlinear, damped-driven oscillators have been determined.First-order approximate first integrals have been obtained byemploying an approximate version of Noether's theorem for the conservativecase. Furthermore, approximate first integrals of the damped case have been obtained based on the first integrals of the conservative case.Approximate first integrals enabled us to identify three types of genericbifurcations. Analytical results have been verified by numerical experiments.     

Preferential Solvation in Mixed Solvents X. Completely Miscible Aqueous Co-Solvent Binary Mixtures at 298.15 K

Summary.  The Kirkwood-Buff integrals for 18 completely miscible aqueous co-solvent binary mixtures have been recalculated from thermodynamic data, and the volume-corrected preferential solvation parameters derived from them are presented. Also presented are these latter quantities for 15 additional such mixtures, for which the volume correction has not been applied previously. The self-interaction of the water, the mutual interaction of the water and the co-solvent, and the self-interaction of the co-solvent at infinite dilution derived from these integrals and parameters are then discussed. The systems studied include aqueous hydrogen peroxide, methanol, ethanol, 1- and 2-propanol, 2-methyl-2-propanol, 2,2,2-trifluoroethanol, 1,1,1,3,3,3-hexafluoro-2-propanol, ethane-1,2-diol, glycerol, 2-methoxyethanol (at 313 and 343 K), 2-ethoxyethanol, 2-butoxyethanol, 2-aminoethanol, N-methyl- and N,N-dimethyl-2-aminoethanol, tetrahydrofuran, 1,4-dioxane, acetone, formic, acetic, and propanoic acids, piperidine, pyridine, acetonitrile, formamide, N-methyl- and N,N-dimethylformamide, N-methylacetamide, N-methylpyrrolidin-2-one (at 303 K), hexamethyl phosphoric triamide, dimethylsulfoxide, and tetramethylenesulfone (at 303 K). Received January 10, 2001. Accepted (revised) February 20, 2001     

Single-mass-scale diagrams: construction of a basis for the -expansion

Exploring the idea of Broadhurst on the “sixth root of unity” we present an ansatz for construction of a basis of transcendental numbers for the -expansion of single mass scale diagrams with two particle massive cut. As example, several new two- and three-loop master integrals are calculated.     

On Information Processes in Statistical Experiments with Distributed Observations

Using stochastic integration theory in topological vector spaces general formulas for the Hellinger processes are derived. Feynman–Kac type formulas are obtained for the related Hellinger integrals in terms of the Hellinger processes and the geometric mean measures. The expected logarithmic utility from data, characterized as the Shannon information, is also considered.     

一类含参变量积分的常差分方程计算方法

首次利用常差分方程方法计算了一类形如∫0πa+co bs cnoxs xdx(n∈N,a,b∈R)的含非负整数参数n与实数a,b的积分,且得到了完整的积分公式.     

Inequalities for the generalized elliptic integrals and modular functions

In this paper, the authors study monotonicity and convexity of the generalized elliptic integrals and certain combinations of these special functions, such as ma(r) and μa(r). Making use of these results, the authors obtain some sharp inequalities for the so-called Ramanujan's generalized modular functions.     

Numerical evaluation of hypersingular integrals

Boundary integral equations which employ integrals which exist only if defined in the Cauchy principal value sense or as the Hadamard finite part are currently used with success to solve many two- and three-dimensional problems of applied mechanics. We will recall definitions and main properties of these integrals, examine some numerical approaches for their evaluation and present several new results.