Related papers: Symmetry problem
Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…
I will sketchily illustrate how the theory of symmetry helps in determining solutions of (deterministic) differential equations, both ODEs and PDEs, staying within the classical theory. I will then present a quick discussion of some more…
In this paper, we show that under certain conditions on the coefficients and initial values, solutions of two different Bernoulli initial-value problems are symmetric to each other either with respect to the t-axis, or the y-axis, or the…
We survey some principal results and open problems related to colorings of algebraic and geometric objects endowed with symmetries.
In this note we obtain a new convergence result for the Adomian decomposition method.
We establish symmetry results for two categories of overdetermined obstacle problems: a Serrin-type problem and a two-phase problem under the overdetermination that the interface serves as a level surface of the solution. The first proof…
We review the motivation for Gauge-Mediated Supersymmetry Breaking and discuss some recent advances.
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
We obtain symmetry results for solutions of an elliptic system of equation possessing a cooperative structure. The domain in which the problem is set may possess "holes" or "small vacancies" (measured in terms of capacity) along which the…
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
We consider an overdetermined problem arising in potential theory for the capacitary potential and we prove a radial symmetry result.
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.
We consider 1D quantum scattering problem for a Hamiltonian with symmetries. We show that the proper treatment of symmetries in the spirit of homological algebra leads to new objects, generalizing the well known T- and K-matrices.…
We prove an improved form of an expectation of Polya and discuss several related questions
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
We prove some symmetric $q$-congruences.
A newly-generalized problem from a problem initially thought for the Mathematical Olympiad and the methods to solve it.
In this paper we prove some new symmetry results for the extremals of the Caffarelli-Kohn-Nirenberg inequalities, in any dimension larger or equal than two.
A static axisymmetric solution with an additional cylindrical symmetry is considered and that the matter consists in a cosmological and a dust term.
We prove a new cross theorem for separately holomorphic functions.