Related papers: Symmetry problems 2
We study compactness of solutions to the Yamabe problem on Riemannian manifolds which are not locally conformally flat.
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
We report the recent progress in understanding of symmetries which can be implemented in the scalar sector of electroweak symmetry breaking models with several Higgs doublets. In particular we present the list of finite reparametrization…
The simplest consequences of the common E_{11} symmetry of the eleven dimensional, IIA and IIB theories are derived and are shown to imply the known relations between these three theories.
The problem of shadow is solved. It is equivalent to condition for point is in generalized convex hull of a family of compact sets.
We present a symmetry result to solutions of equations involving the fractional Laplacian in a domain with at least two perpendicular symmetries. We show that if the solution is continuous, bounded, and odd in one direction such that it has…
Errors quoted on results are often given in asymmetric form. An account is given of the two ways these can arise in an analysis, and the combination of asymmetric errors is discussed. It is shown that the usual method has no basis and is…
H\"older estimates for second derivatives are proved for solutions of fully nonlinear parabolic equations in two space variables. Related techniques extend the regularity theory for fully nonlinear parabolic equations in higher dimensions.
A list of open problems on holomorphic symplectic, contact and Poisson manifolds.
We consider the Dirichlet problem for two types of degenerate elliptic Hessian equations . New results about solvability of the equations in the $C^{1,1}$ space are provided.
The study of recently introduced Fedosov supermanifolds is continued. Using normal coordinates, properties of even and odd symplectic supermanifolds endowed with a symmetric connection respecting given sympletic structure are studied.
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
The one-mode and the two-mode multiboson systems with sl(2,R) symmetry are investigated.Hamiltonians of these systems are integrated using the theory of orthogonal polynomials. The coherent state representation for these systems is…
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
Some aspects of $Q$-conditional symmetry and of its connections with reduction and compatibility are discussed.
The issue of symmetry and symmetry breaking is fundamental in all areas of science. Symmetry is often assimilated to order and beauty while symmetry breaking is the source of many interesting phenomena such as phase transitions,…
Nonlinear ODEs invariant under the group SL(2,R) are solved numerically. We show that solution methods incorporating the Lie point symmetries provide better results than standard methods.
A closed-form solution for the boundary of the flat state of an orthogonal cross section of contiguous surface geometry formed by the intersection of two cylinders of equal radii oriented in dual directions of rotation about their…