Related papers: A Convenient Alternative for Series Manipulation v…
Partial transpose is an important operation for quantifying the entanglement, here we study the (partial) transpose of any single (two-mode) operators. Using the Fock-basis expansion, it is found that the transposed operator of an arbitrary…
We use the method of similar operators to study a mixed problem for a differential equation with an involution and an operator-valued potential function. The differential operator defined by the equation is transformed into a similar…
We show how series expansions of functions of bosonic number operators are naturally derived from finite-difference calculus. The scheme employs Newton series rather than Taylor series known from differential calculus, and also works in…
The standard perturbative weak-coupling expansions in lattice models are asymptotic. The reason for this is hidden in the incorrect interchange of the summation and integration. However, substituting the Gaussian initial approximation of…
Poly-infix operators and operator families are introduced as an alternative for working modulo associativity and the corresponding bracket deletion convention. Poly-infix operators represent the basic intuition of repetitively connecting an…
We consider a class of linear integral operators with impulse responses varying regularly in time or space. These operators appear in a large number of applications ranging from signal/image processing to biology. Evaluating their action on…
In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbitrary characteristic and illustrate the proposed approach…
Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by…
We present a method of solving master equations which may describe, in their most general form, phase sensitive processes such as decay and amplification. We make use of the superoperator technique.
As was initially shown by Brent, exponentials of truncated power series can be computed using a constant number of polynomial multiplications. This note gives a relatively simple algorithm with a low constant factor.
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…
One may obtain, using operator transformations, algebraic relations between the Fourier transforms of the causal propagators of different exactly solvable potentials. These relations are derived for the shape invariant potentials. Also,…
This paper derives a way to express differentiable complex-valued functions as the sum of powers of $(1-e^{\lambda x})$, where $\lambda\in\mathbb{R}$, with an explicit formula for the remainder. This formulation is then used to associate an…
Formal Laurent-Puiseux series are important in many branches of mathematics. This paper presents a {\it Mathematica} implementation of algorithms developed by the author for converting between certain classes of functions and their…
We introduce an exact functor defined on multigraded modules which we call the expansion functor and study its homological properties. The expansion functor applied to a monomial ideal amounts to substitute the variables by monomial prime…
We consider the problem of modularizing control flow in a generic abstract interpretation framework. A generic abstract interpretation framework is not truly flexible if it does not allow interpreting with different path- and…
To improve accuracy in calculating QCD effects, we propose a method for renormalon subtraction in the context of the operator-product expansion. The method enables subtracting renormalons of various powers in $\Lambda_{\rm QCD}$ efficiently…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
This work introduces a methodology for generating linear operators that approximately represent nonlinear systems of perturbed ordinary differential equations. This is done through the application of classical perturbation theory via the…
The letter proposes an adaptive model reduction approach based on tensor decomposition to speed up time-domain power system simulation. Taylor series expansion of a power system dynamic model is calculated around multiple equilibria…