相关论文: Polar decomposition and Brion's theorem

Baryogenesis via leptogenesis provides an appealing mechanism to explain the observed baryon asymmetry of the Universe. Recent refinements in the understanding of the dynamics of leptogenesis include detailed studies of the effects of…

We obtain the exact nontopological soliton lattice solutions of the Associated Lam\'e equation in different parameter regimes and compute the corresponding energy for each of these solutions. We show that in specific limits these solutions…

For a given complete lattice L, we investigate whether L can be decomposed as a direct product of directly indecomposable lattices. We prove that this is the case if every element of L is a join of join-irreducible elements and dually, thus…

Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…

Leveraging tools from convex analysis and incorporating additional singular value information of matrices, we completely resolve the problem of establishing perturbation bounds for the Frobenius norm of subunitary and positive polar…

In this paper we formulate an integrable model on the simple cubic lattice. The $N$ -- valued spin variables of the model belong to edges of the lattice. The Boltzmann weights of the model obey the vertex type Tetrahedron Equation. In the…

Structured optimization uses a prescribed set of atoms to assemble a solution that fits a model to data. Polarity, which extends the familiar notion of orthogonality from linear sets to general convex sets, plays a special role in a simple…

We describe and analyze a new construction that produces new Eulerian lattices from old ones. It specializes to a construction that produces new strongly regular cellular spheres (whose face lattices are Eulerian). The construction does not…

We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this non-classical elasticity…

The decomposition theorem is deduced from local purity.

Calculations of the polarization of $\Lambda$ and $\bar{\Lambda}$ particles after fragmentation of a polarized quark produced in processes like $Z$-decay and deep inelastic polarized lepton scattering must include $\Lambda$ and…

We study the PBW filtration on irreducible finite--dimensional representations for the Lie algebra of type $\tt B_n$. We prove in several cases, including all multiples of the adjoint representation and all irreducible finite--dimensional…

In the present work we study non-thermal leptogenesis and baryon asymmetry in the universe in different neutrino mass models discussed recently. For each model we obtain a formula relating the reheating temperature after inflation to the…

We present a much simplified proof of Dehn's theorem on the infinitesimal rigidity of convex polytopes. Our approach is based on the ideas of Trushkina and Schramm.

We introduce the PBW degeneration for basic classical Lie superalgebras and construct for all type I, $\mathfrak{osp}(1,2n)$ and exceptional Lie superalgebras new monomial bases. These bases are parametrized by lattice points in convex…

We derive the proper form of Virial theorem for a system of rotating self-gravitating Brownian particles. We show that, in the two-dimensional case, it takes a very simple form that can be used to obtain general results about the dynamics…

Area and orientation preserving diffeomorphisms of the standard 2-disc, referred to as symplectomorphisms of $\mathbb{D}^{2}$, allow decompositions in terms of positive twist diffeomorphisms. Using the latter decomposition we utilize the…

For a d-dimensional convex lattice polytope P, a formula for the boundary volume is derived in terms of the number of boundary lattice points on the first $\floor{d/2}$ dilations of P. As an application we give a necessary and sufficient…

We obtain exact, simple and very compact expressions for the linearization coefficients of the products of orthogonal polynomials; both the conventional Clebsch-Gordan-type and the modified version. The expressions are general depending…

We present a concise proof for the supporting hyperplane theorem. We then observe that the proof not only establishes the supporting hyperplane theorem but also extends it to a hyperplane separation theorem for certain non-convex sets. The…