We show how methods of continuum perturbation theory can be used to simplify perturbative lattice calculations. We use the technique of asymptotic expansions to expand lattice loop integrals around the continuum limit. After the expansion, all nontrivial dependence on momenta and masses is encoded in continuum loop integrals and the only genuine lattice integrals left are tadpole integrals. Usi...

This paper may be regarded as a new numerical method for the analysis of triangular thin plates using the natural area coordinates. Previous studies on the solution of triangular plates with different boundary conditions are mostly based on the Rayleigh-Ritz principle which is performed in the Cartesian coordinates. Consequently, manipulation of the geometry and numerical calculation of the int...

A bstract We consider a class of differential equations for multi-loop Feynman integrals which can be solved to all orders in dimensional regularisation terms iterated meromorphic modular forms. show that the subgroup under forms transform naturally identified with monodromy group certain second-order operator. provide an explicit decomposition spaces into direct sum total derivatives and basis...

This is a brief survey of product-integration for biostatisticians. 1 Product-Integration Product-integration was introduced more than 110 years ago by the Italian mathematician Vito Volterra, as a tool in the solution of a certain class of differential equations. It was studied intensively by mathematicians for half a century, but finally the subject became unfashionable and lapsed into obscur...

A half-numeric algorithm for the evaluation of effective core potential integrals over Cartesian Gaussian functions is described. Local and semilocal integrals are separated into two-dimensional angular and one-dimensional radial integrals. The angular integrals are evaluated analytically using a general approach that has no limitation for the l-quantum number. The radial integrals are calculat...

Formulae connecting the multiple Stratonovich integrals with single Ogawa and Stratonovich integrals are derived. Multiple Riemann-Stieltjes integrals with respect to certain smooth approximations of the Wiener process are considered and it is shown that these integrals converge to multiple Stratonovich integrals as the approximation converges to the Wiener process.

In this paper, we generalize the definition of Sugeno integrals by utilizing the so-called median operations, which are a special kind of aggregation operations. The generalized integrals, which we call median integrals, possess almost all common properties of Sugeno integrals. The properties of median integrals are investigated and their significance is discussed.

In this paper, the Poincar e (or hyperbolic) metric and the associated distance are investigated for a plane domain based on the detailed properties of those for the particular domain C n f0; 1g: In particular, another proof of a recent result of Gardiner and Lakic [7] is given with explicit constant. This and some other constants in this paper involve particular values of complete elliptic int...

In this paper, we establish some new versions of Hermite–Hadamard type inequalities for co-ordinated convex functions via q1,q2-integrals. Since the are newly proved, therefore consider examples and show their validity particular choices q1,q2∈(0,1). We hope that readers interest in these results.