On invariant convex cones in simple Lie algebras

This paper is devoted to a study and classification ofG-invariant convex cones ing, whereG is a lie group andg its Lie algebra which is simple. It is proved that any such cone is characterized by its intersection withh-a fixed compact Cartan subalgebra which exists by the very virtue of existence of properG-invariant cones. In fact the pair (g,k) is necessarily Hermitian symmetric.     

On a non-abelian invariant on complex surfaces of general type

In this paper, we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S. Cheung, Bun Wong and Stephen S. T. Yau concerning a local rigidity problem of the tangent bundle over compact surfaces of general type.     

Colored Turaev-Viro invariants of twist knots

In the present paper we give a formula for colored Turaev-Viro invariants of twist knots using special polyhedra derived from (1,1)-decomposition of the knots.     

On the Casson invariant of homology 3-spheres of Mazur type

We compute the Casson invariant for some integral homology 3-spheres. We also show that for every integer n, there exists an integral homology 3-sphere of Mazur type with the Casson invariant 2n.     

On a novel eccentricity-based invariant of a graph

In this paper,for the purpose of measuring the non-self-centrality extent of non-selfcentered graphs,a novel eccentricity-based invariant,named as non-self-centrality number(NSC number for short),of a graph G is defined as follows:N(G)=∑v_i,v_j∈V(G)|e_i-e_j| where the summation goes over all the unordered pairs of vertices in G and e_i is the eccentricity of vertex v_i in G,whereas the invariant will be called third Zagreb eccentricity index if the summation only goes over the adjacent vertex pairs of graph G.In this paper,we determine the lower and upper bounds on N(G) and characterize the corresponding graphs at which the lower and upper bounds are attained.Finally we propose some attractive research topics for this new invariant of graphs.     

On simple modules of Hecke algebras of type Dn

This is a continuation of our previous work. We classify all the simple ?_q(D _n )-modules via an automorphismh defined on the set { λ | D^λ ≠ 0}. Whenf _n(q) ≠ 0, this yields a classification of all the simple ? ^q (D _n)- modules for arbitrary n. In general ( i. e., q arbitrary), if λ⁽¹⁾ = λ⁽²⁾,wegivea necessary and sufficient condition ( in terms of some polynomials ) to ensure that the irreducible ?_q,1(B _n )- module D^λ remains irreducible on restriction to ?_q(D _n ).     

On invariant immersions

Summary Theory of immersions satisfying the condition that tangent spaces to an immersed submanifold are invariant under the curvature transformation.     

On the existence of a finite invariant measure

A necessary and sufficient condition is given for a Borel automorphism on a standard Borel space to admit an invariant probability measure.     

On matrices leaving invariant a nontrivial convex set

A real square matrix A leaves a nontrivial convex set invariant if there exists a convex set C, which is not a linear subspace, such that A(C) ? C. It is shown that this is equivalent to the statement that A has an eigenvalue λ with λ?0 or |λ|?1.     

On families of invariant lines of a Brouwer homeomorphism

ABSTRACT

We present properties of equivalence classes of the codivergency relation defined for a Brouwer homeomorphism for which there exists a family of invariant pairwise disjoint lines covering the plane. In particular, using the codivergency relation we describe the sets of regular and irregular points for such Brouwer homeomorphisms. Moreover, we show that under this assumption the interior of each equivalence class of this relation is invariant and simply connected.     

On compact sets with a certain affine invariant

We give a complete characterization of finite-dimensional compact sets with the following property: all of their images under affine operators are symmetric (that is, have symmetry planes of certain dimensions). We also study the noncompact case; namely, we reveal a class of unbounded closed sets with this property and conjecture that this class is complete.     

On essential conformal groups and a conformal invariant

We show that various conformal groups, including classical conformal diffeomorphism groups are essential. The essentiality is shown to be equivalent to the non-vanishing of a conformal cohomological invariant.