Related papers: Multiple-Order Singularity Expansion Method
A variant of Siu's analyticity theorem is proved for relative types of plurisubharmonic functions. Some results on propagation of plurisubharmonic singularities and maximality of pluricomplex Green functions with analytic singularities are…
We investigate a system of harmonically coupled identical nonlinear constituents subject to noise in different spatial arrangements. For global coupling we find for infinitely many constituents the coexistence of several ergodic components…
The CEGM formalism offers a general framework for scattering amplitudes, which rests on Grassmannians, moduli spaces and tropical geometry. The physical implications of this generalization are still to be understood. Conventional wisdom…
The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems…
Across many areas of physics, multipole expansions are used to simplify problems, solve differential equations, calculate integrals, and process experimental data. Spherical harmonics are the commonly used basis functions for a multipole…
We generalize the Hamilton-Jacobi formulation for higher order singular systems and obtain the equations of motion as total differential equations. To do this we first study the constraint structure present in such systems.
Orders in an algebraic number field form a class of rings which are of special historical interest to the field of factorization theory. One of the primary tools used to study factorization is elasticity - a measure of how badly unique…
Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper we…
We study the spectral form factor (SFF) for hydrodynamic systems with a sound pole, a large class including any fluid with momentum conservation and energy conservation, or any extended system with spontaneously broken continuous symmetry.…
In this paper, we introduce and investigate two new subclasses of analytic functions in the open unit disk in the complex plane. Several interesting properties of the functions belonging to these classes are examined. Here, sufficient, and…
A mono-component is a real-valued signal of finite energy that has non-negative instantaneous frequencies, which may be defined as the derivative of the phase function of the given real-valued signal through the approach of canonical…
The scalar difference equation $x_{n+1}=f_{n}(x_{n},x_{n-1},...,x_{n-k})$ may exhibit symmetries in its form that allow for reduction of order through substitution or a change of variables. Such form symmetries can be defined generally…
The atomic cluster expansion (ACE) (Drautz, 2019) yields a highly efficient and intepretable parameterisation of symmetric polynomials that has achieved great success in modelling properties of many-particle systems. In the present work we…
In the paper, the author studies properties of three functions relating to the exponential function and the existence of partitions of unity, including accurate and explicit computation of their derivatives, analyticity, complete…
In Physics, we are generally interested in real solutions involving natural phenomena, where knowledge of real functions of real variables is sufficient to obtain physically relevant results. However, the complexity of phenomena associated…
This text provides very easy and short proofs of some basic properties of complex power series (addition, subtraction, multiplication, division, rearrangement, composition, differentiation, uniqueness, Taylor's series, Principle of…
The phenomenon of removable singularity is studied for overedetermined systems of differential equations. We show that the dimension of the characteristic variety plays a key role in the problem.
Potential resonances are usually investigated either directly in the complex energy plane or indirectly in the complex angular momentum plane. Another formulation complementing these two is presented in this work. It is an indirect method…
It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and…
The standard Bloch oscillation normally refers to the oscillatory tunneling dynamics of quantum particles in a periodic lattice plus a linear gradient. In this work we theoretically investigate the generalized form of the Bloch oscillation…