Integral currents ${\rm mod}$ $2$

Mod 2 and Mod 5 Icosahedral Representations

We shall call a simple abelian variety A/Q modular if it is isogenous (over Q) to a factor of the Jacobian of a modular curve. In this paper we shall call a representation ρ̄ : GQ→GL2(F̄l) modular if there is a modular abelian variety A/Q, a number field F/Q of degree equal to dimA, an embedding OF ↪→ End(A/Q) and a homomorphism θ : OF→F̄l such that ρ̄ is equivalent to the action of GQ on the ker θ...

Topological superconductor in quasi-one-dimensional ${\rm Tl}_{2-x}{\rm Mo}_6{\rm Se}_6$

(2 Mod 4)-cycles

For two integers k(> 0) and s(≥ 0), a cycle of length l is called an (s mod k)-cycle if l ≡ s mod k. In this paper, the following conjecture of Chen, Dean, and Shreve [5] is proved: Every 2-connected graph with at least six vertices and minimum degree at least three contains a (2 mod 4)-cycle.

The ( mod , integral and exclusive ) sum number of graph

In this paper, we developed some new formulae for exclusive sum number of the complete bipartite graph , n m K . Also we show that for     , 2 2 , 6 n n K E n K n    2 4, 2 6, 3 n n n          and 2 4 n   .

Flat Norm Decomposition of Integral Currents

Currents represent generalized surfaces studied in geometric measure theory. They range from relatively tame integral currents representing oriented compact manifolds with boundary and integer multiplicities, to arbitrary elements of the dual space of differential forms. The flat norm provides a natural distance in the space of currents, and works by decomposing a d-dimensional current into dan...