It is already well-understood that many delay differential equations with only a single constant exhibit change in stability according to the value of relation critical value. Finding formula for important understanding dynamics delayed systems and often simple obtain when system has delay. However, if we consider multiple delays, there no known way such determines what values delays occurs. In...

We apply improved Taylor expansion method which is one of the variational schemes to Ising model in two-dimensions. It enables us to evaluate free energy and magnetization at strong coupling regions from weak coupling expansion even in the presence of the phase transition. We determine approximated transition point in this scheme. In the presence of external magnetic field we can see not only s...

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...

We show that, given an ordinary lambda-term and a normal resource lambda-term which appears in the normal form of its Taylor expansion, the unique resource term of the Taylor expansion of the ordinary lambda-term reducing to this normal resource term can be obtained by running a version of the Krivine abstract machine.

Each Multiplicative Exponential Linear Logic (MELL) proof-net can be expanded into a differential net, which is its Taylor expansion. We prove that two different MELL proof-nets have two different Taylor expansions. As a corollary, we prove a completeness result for MELL: We show that the relational model is injective for MELL proof-nets, i.e. the equality between MELL proof-nets in the relatio...