We produce skew loops—loops having no pair of parallel tangent lines—homotopic to any loop in a flat torus or other quotient of Rn . The interesting case here is n = 3 . More subtly for any n , we characterize the homotopy classes that will contain a skew loop having a specified loop τ ⊂ S as tangent indicatrix.

We produce skew loops—loops having no pair of parallel tangent lines—homotopic to any loop in a flat torus or other quotient of Rn . The interesting case here is n = 3 . More subtly for any n , we characterize the homotopy classes that will contain a skew loop having a specified loop τ ⊂ S as tangent indicatrix.

The ground field k is algebraically closed and of characteristic zero. Let g be a reductive algebraic Lie algebra over k and σ an involutory automorphism of g. Then g = g0 ⊕ g1 is the direct sum of σ-eigenspaces. Here g0 is a reductive subalgebra and g1 is a g0-module. Let G be the adjoint group of g and G0 ⊂ G a connected subgroup with LieG0 = g0. The commuting variety of (g, g0) is the follow...

This paper is about three classes of objects: Leonard pairs, Leonard triples, and the modules for a certain algebra A. Let K denote an algebraically closed field of characteristic zero. Let V denote a vector space over K with finite positive dimension. A Leonard pair on V is an ordered pair of linear transformations in End(V ) such that, for each of these transformations, there exists a basis f...

Let K denote a field, and let V denote a vector space over K with finite positive dimension. By a Leonard pair on V we mean an ordered pair of linear transformations A : V → V and A∗ : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A∗ is diagonal. (ii) There ex...

An “automatic continuity” question has naturally occurred since Roger Howe established the local theta correspondence over R: Does the algebraic version of local theta correspondence over R agree with the smooth version? We show that the answer is yes, at least when the concerning dual pair has no quaternionic type I irreducible factor.

In the symplectic Lagrangian framework we newly embed an irreducible massive vector-tensor theory into a gauge invariant system, which has become reducible, by extending the configuration space to include an additional pair of scalar and vector fields, which give the desired Wess-Zumino action. A comparision with the BFT Hamiltonian embedding approach is also done. PACS: 11.10.Ef, 11.30.Ly, 11....

In this paper, we study the approximability of the capacitated network design problem (Cap-NDP) on undirected graphs: GivenG = (V,E) with non-negative costs c and capacities u on its edges, sourcesink pairs (si, ti) with demand ri, the goal is to find the minimum cost subgraph where the minimum (si, ti) cut with u-capacities is at least ri. When u ≡ 1, we get usual SNDP for which Jain gave a 2-...

the concept of right (left) quotient (or residual) of an ideal η by anideal ν of an l-subring μ of a ring r is introduced. the right (left) quotients areshown to be ideals of μ . it is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an l-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . most of the results pertaining to the notion of quotients(or residual) of ...

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respec...