the distribution pattern of pest population is one of the factors not only effects on sampling program and data analysis method, but also can be used to measure the density of pests and their natural enemies. thus, the spatial distribution pattern of the pea aphid, acyrthosiphon pisum harris (hem.: aphididae) and its two major predators, hippodamia variegata goeze (col.: coccinellidae) and cocc...

We produce formulas, permiting to find the coefficients of Taylor–series expanded of some important solution of the Gelfand-Dikii hierarchy. By the Witten conjecture these coefficients are numbers of intersection of Mumford-Morita-Muller stable cohomological classes of moduli space of n-spin bundles on Riemann surfaces with punctures .

A new type of Taylor series based 2-D finite difference approximation is presented, and it is shown that the coefficients of these approximations are not unique. Explicit formulas are presented for one of the possible sets of coefficients for an arbitrary order, by extending the previously presented 1-D approximations. These coefficients are implemented as maximally linear 2-D FIR digital diffe...

Formulas for the Riemann sums over lattice polytopes determined by the lattice points in the polytopes are often called Euler-Maclaurin formulas. An asymptotic Euler-Maclaurin formula, by which we mean an asymptotic expansion formula for Riemann sums over lattice polytopes, was first obtained by Guillemin-Sternberg [GS]. Then, the problem is to find a concrete formula for the each term of the e...

We present a framework for the verification of the numerical algorithms used in Ariadne, a tool for analysis of nonlinear hybrid system. In particular, in Ariadne, smooth functions are approximated by Taylor models based on sparse polynomials. We use the Coq theorem prover for developing Taylor models as sparse polynomials with floatingpoint coefficients. This development is based on the formal...

In this talk we extend the Polyakov-quark-meson model to N f = 2 + 1 quark flavors and study its bulk thermodynamics at finite temperatures in mean-field approximation. Three different Polyakov-loop potentials are considered. Our findings are confronted to recent QCD lattice simulations of the RBC-Bielefeld and HotQCD collaborations. Furthermore, the finite chemical potential expansion of the q...

In this article, we have investigate a Taylor collocation method, which is based on collocation method for solving fractional pantograph equation. This method is based on first taking the truncated fractional Taylor expansions of the solution function in the mathematical model and then substituting their matrix forms into the equation. Using the collocation points, we have the system of nonline...

X iv :m at hph /0 40 80 59 v1 3 0 A ug 2 00 4 Taylor expansion for an operator function Ioan Sturzu Center for Computational Nanoscience, Ball State University, Muncie, IN 47306 A simple version for the extension of the Taylor theorem to the operator functions was found. The expansion was done with respect to a value given by a diagonal matrix for the non-commutative case, and the coefficients ...

We report about recent progress in computing four-loop massive correlators. The expansion of these correlators in the external momentum leads to vacuum integrals. The calculation of these vacuum integrals can be used to determine Taylor expansion coefficients of the vacuum polarization function and decoupling functions in pertur-bative Quantum chromodynamics. New results at four-loop order for ...

By a Taylor expansion of a generating function, we mean that the remainder of the expansion is a functional of the generating function itself. In this paper, we consider the Taylor expansion for the generating function Bm(t) of them-Catalan numbers. In order to give combinatorial interpretations of the coefficients of these expansions, we study a new collection of partial Grand Dyck paths, that...