Related papers: Weighted energy problem on the unit circle
In this paper, we investigate the energy problem in general relativity using approximate Lie symmetry methods for differential equations. This procedure is applied to Bardeen model (the regular black hole solution). Here we are forced to…
In this paper we consider the problem of connected edge searching of weighted trees. It is shown that there exists a polynomial-time algorithm for finding optimal connected search strategy for bounded degree trees with arbitrary weights on…
We present a unified approach to the problems of reconstruction of large-scale structure distribution in the universe and determination of the underlying power spectrum. These have often been treated as two separate problems and different…
We consider several non-standard discrete and continuous Green energy problems in the complex plane and study the asymptotic relations between their solutions. In the discrete setting, we consider two problems; one with variable particle…
We consider a heat equation and a wave equation in a spatial interval over a time interval. This article deals with inverse problems of determining sizes of spatial intervals by extra boundary data of solutions of the governing equations.…
After a systematic introduction of some formulae for the energy radiated by localized electric charges and currents, one considers the multipole radiation and the reduction of the multipole tensors to the symmetric traceless ones.
We give an improved polynomial bound on the complexity of the equation solvability problem, or more generally, of finding the value sets of polynomials over finite nilpotent rings. Our proof depends on a result in additive combinatorics,…
We calculate the self-energy and self-force for an electrically charged particle at rest in the background of Gott-Hiscock cosmic string space-time. We found the general expression for the self-energy which is expressed in terms of the $S$…
The tensor self energy is computed at one loop order in a model in which a vector and tensor interact in a way that eliminates all tensor degrees of freedom. Divergencies arise which cannot be eliminated without introducing a kinetic term…
We introduce a synthetic approach to global pluripotential theory, covering in particular the case of a compact K\"ahler manifold and that of a projective Berkovich space over a non-Archimedean field. We define and study the space of…
We extend the problem of $(1+1)$ circular dilaton gravity to include charged particles. We examine the two (charged) particle case in detail and find an exact equilibrium solution. We then extend this to $N-$particles and obtain a solution…
We present here the extended-object approach for the explanation and calculation of the self-force phenomenon. In this approach, one considers a charged extended object of a finite size $\epsilon$ that accelerates in a nontrivial manner,…
We study wave equations with energy dependent potentials. Simple analytical models are found useful to illustrate difficulties encountered with the calculation and interpretation of observables. A formal analysis shows under which…
Using the variational approach and the critical point theory, we established several criteria for the existence of at least one nontrivial solution for a discrete elliptic boundary value problem with a weight $p(\cdot, \cdot)$ and depending…
In this paper we consider the problem of packing a fixed number of identical circles inside the unit circle container, where the packing is complicated by the presence of fixed size circular prohibited areas. Here the objective is to…
We consider a one-dimensional singularly perturbed 4th order problem with the additional feature of a shift term. An expansion into a smooth term, boundary layers and an inner layer yields a formal solution decomposition, and together with…
An analytical expression for the relativistic corrections to the energy spectra of particles completely confined in an one-dimensional limited length in real space is given, based upon the wave property of particles, the relativistic…
The Dark Energy problem is forcing us to re-examine our models and our understanding of relativity and space-time. Here a novel idea of Fundamental Forces is introduced. This allows us to perceive the General Theory of Relativity and…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
We study the problem of self-energy of pointlike charges in higher dimensional static spacetimes. Their energy, as a functional of the spacetime metric, is invariant under a specific continuous transformation of the metric. We show that the…