Related papers: Multiple-Order Singularity Expansion Method
We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately…
Factorization of quantum mechanical Hamiltonians has been a useful technique for some time. This procedure has been given an elegant description by supersymmetric quantum mechanics, and the subject has become well-developed. We demonstrate…
Factorization properties of one-loop gauge theory amplitudes have been used as checks on explicitly computed amplitudes and in the construction of ansatze for higher-point ones. In massless theories, such as QCD at high energies, infrared…
To study the dynamical behaviour of the engineering and physical systems, we often need to capture their continuous behaviour, which is modeled using differential equations, and perform the frequency-domain analysis of these systems.…
The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory and analysis of algorithms. The aim of this…
We extend a factorization due to Krein to arbitrary analytic functions from the upper half-plane to itself. The factorization represents every such function as a product of fractional linear factors times a function which, generally, has…
Recent studies of transport phenomena with complex potentials are explained by generic square root singularities of spectrum and eigenfunctions of non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that such…
The extension problem asks whether positive semi-definite functions on a symmetric unital subset of a discrete group can be extended to positive semi-definite functions on the whole group. It has been known at least since the work of Rudin…
We discuss the structure of infrared singularities in on-shell QCD amplitudes at two-loop order. We present a general factorization formula that controls all the $\ep$-poles of the dimensionally regularized amplitudes. The dependence on the…
The original purpose of component-based development was to provide techniques to master complex software, through composition, reuse and parametrisation. However, such systems are rapidly moving towards a level in which software becomes…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. Firstly derived in the static case, the result is generalized to the dynamic one.…
We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…
Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as…
We introduce an upper semi-continuous function that stratifies the highest multiplicity locus of a hypersurface in arbitrary characteristic (over a perfect field). The blow-up along the maximum stratum defined by this function leads to a…
We discuss and illustrate the behaviour of the continued fraction expansion of a formal power series under specialisation of parameters or their reduction modulo $p$ and sketch some applications of the reduction theorem here proved.
In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
In this article, we consider some generalizations of polynomial and exponential B-splines. Firstly, the extension from integral to complex orders is reviewed and presented. The second generalization involves the construction of uncountable…
Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more…
Partition function zeros provide alternative approach to study phase structure of finite density QCD. The structure of the Lee-Yang edge singularities associated with the zeros in the complex chemical potential plane has a strong influence…