Related papers: Angular integrals with three denominators via IBP,…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
Loop diagram calculations typically rely on reduction to a finite set of master integrals in $4 - 2\epsilon$ dimensions. It has been shown that for any problem, the masters can be chosen so that their coefficients are finite as $\epsilon…
A novel perturbative method, proposed by Panda {\it et al.} [1] to solve the Helmholtz equation in two dimensions, is extended to three dimensions for general boundary surfaces. Although a few numerical works are available in the literature…
Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals…
New method of calculation of master integrals using differential equations and asymptotical expansion is presented. This method leads to the results exact in space-time dimension $D$ having the form of the convergent power series. As an…
We study equations with infinitely many derivatives. Equations of this type form a new class of equations in mathematical physics. These equations originally appeared in p-adic and later in fermionic string theories and their investigation…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
We present a simplified variant of the integrand reduction algorithm for multiloop scattering amplitudes in $d = 4 - 2\epsilon$ dimensions, which exploits the decomposition of the integration momenta in parallel and orthogonal subspaces,…
In this note we elaborate on the reduction of four dimensional Seiberg duality with adjoint matter to three dimensions. We use the exact formulation of the superconformal index and of the partition function as instruments to test this…
We describe an elementary method for bounding a one-dimensional oscillatory integral in terms of an associated non-oscillatory integral. The bounds obtained are efficient in an appropriate sense and behave well under perturbations of the…
Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial…
Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum…
A recently developed linear algebraic method for the computation of perturbation expansion coefficients to large order is applied to the problem of a hydrogenic atom in a magnetic field. We take as the zeroth order approximation the $D…
In this note, we are concerned with the asymptotic approximation of a class of double integrals which can be represented as an angular spectrum superposition. These double integrals typically appear in electromagnetic scattering problems.…
Under the formalism of annealed averaging of the partition function, a type of random multifractal measures with their multipliers satisfying exponentially distributed is investigated in detail. Branching emerges in the curve of generalized…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…
In this note, by using the result in one variable, we obtain asymptotic expansions of oscillatory integrals for certain multivariable phase functions with {\bf degenerate} singular points. Moreover by using this result, we have asymptotic…
We introduce a quantum volume operator $K$ in three--dimensional Quantum Gravity by taking into account a symmetrical coupling scheme of three SU(2) angular momenta. The spectrum of $K$ is discrete and defines a complete set of eigenvectors…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…