We develop the basic elements of a Cauchy theory on the complex Levi-Civita field, which constitutes the smallest algebraically closed nonArchimedean extension of the complex numbers. We introduce a concept of analyticity based on differentiation, and show that it leads to local expandability in power series. We show that analytic functions can be integrated over suitable piecewise smooths path...

A bstract We present new computations for Feynman integrals relevant to Higgs plus jet production at three loops, including first results a non-planar class of integrals. The are expressed in terms generalised polylogarithms up transcendental weight six. also provide the full canonical differential equations, which allows us make structural observations on answer. In particular, we find counter...

We consider a class of Hamiltonian systems in 3 degrees freedom, with particular type quadratic integral and which includes the rational Calogero-Moser system as case. For general class, we introduce separation coordinates to find separable (and therefore Liouville integrable) system, two integrals. This gives coupling large potentials, generalising series potentials are parabolic coordinates. ...

In this paper, using the definition of functions (h,m,s)-convex modified second type, various extensions classic Hermite-Hadamard Inequality are obtained Katugampola integrals. addition, we show that several results known particular cases ours.

In this paper, we give new Simpson’s type integral inequalities for the class of functions whose derivatives absolute values are s-convex via generalized proportional fractional integrals. Some results in literature particular cases our results.

Recently, we have developed an efficient recursive approach for analytically calculating the short-time expansion of the propagator to extremely high orders for a general many-body quantum system. Here we give brief overview of this approach and then demonstrate application of this technique by numerically studying the thermodynamical properties of a rotating ideal Bose gas of Rb atoms in an an...

The connection between Feynman integrals and GKZ $A$-hypergeometric systems has been a topic of recent interest with advances in mathematical techniques computational tools opening new possibilities; this paper we continue to explore connection. To each such hypergeometric system there is an associated toric ideal, prove that the latter Cohen-Macaulay property for two large families integrals. ...

an inversion procedure is used to obtain from the extended principle of corresponding - states the pair interaction potentials for argon, krypton and its mixture over a tetnperature range from absolute zero to the onset of ionization. the experimentally-reduced viscosity collision integrals obtained from the corresponding - states correlation have been inverted directly to give the reduced-inte...

In this paper, we address the general fractional integrals and derivatives with Sonine kernels on spaces of functions an integrable singularity at point zero. First, their important special classes particular cases are discussed. particular, introduce a class that possess power function type For from class, two fundamental theorems calculus proved. Then, construct n-fold study properties.

In this paper, we will consider hypersingular integrals as they arise by transforming elliptic boundary value problems into boundary integral equations. First, local representations of these integrals will be derived. These representations contain so-called finite-part integrals. In the second step, these integrals are reformulated as improper integrals. We will show that these integrals can be...