Let E be an elliptic curve defined over ℚ, and let ρ :Gal(ℚ ¯/ℚ)→GL(2,ℤ ^) the adelic representation associated to natural action of Galois on torsion points E(ℚ ¯). By a theorem Serre, image is open, but always index at least 2 in GL(2,ℤ due certain quadratic entanglement amongst division fields. In this paper, we study other types abelian entanglements. More concretely, classify curves E/ℚ, p...

let $g = (v, e)$ be a simple graph. denote by $d(g)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $a(g)$ the adjacency matrix of $g$. the  signless laplacianmatrix of $g$ is $q(g) = d(g) + a(g)$ and the $k-$th signless laplacian spectral moment of  graph $g$ is defined as $t_k(g)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

Suppose that the conditional distributions of x˜ (resp. y˜) can be ranked according to m-th n-th) risk order. Increasing their statistical concordance increases (m,n) degree riskiness (x˜,y˜), i.e., it reduces expected utility for all bivariate functions whose sign cross-derivative is (?1)m+n+1. This means in particular this increase risks induces a m+n x˜+y˜. On basis these general results, I ...

In this paper, it is pointed out that the Berry’s phase is a good index of degree of no-commutativity of the quantum statistical model. Intrinsic relations between the ‘complex structure’ of the Hilbert space and Berry’s phase is also discussed.

Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient commutativity conditions for commutativity of second-order linear time-varying systems with non-zero initial conditions. It has appeared interesting that the second r...

Careful pe r iodon ta l d o c u m e n t a t i o n and su b seq u en t histological examina t ion of 46 h u m a n tee th wi th varying degrees of per iodonta l i nvo lvemen t showed that their pulps r ema ined wi th in normal limits regardless of the severi ty of the pe r iodon ta l disease. Fur the rmore , it was obse rved that ve ry deep caries or extensive corona l res tora t ions were associ...

We study the topological centers of $nth$ dual of Banach $mathcal{A}$-modules and we extend some propositions from Lau and "{U}lger into $n-th$ dual of Banach $mathcal{A}-modules$ where $ngeq 0$ is even number. Let   $mathcal{B}$   be a Banach  $mathcal{A}-bimodule$. By using some new conditions, we show that $ Z^ell_{mathcal{A}^{(n)}}(mathcal{B}^{(n)})=mathcal{B}^{(n)}$ and $ Z^ell_{mathcal{B}...

A formula is obtained for the dimension a(n; m) of the space of degree m invariants of the regular representation of the n-th order cyclic group. This formula implies in particular that a(n; m) = a(m; n). Moreover, the automorphism group of the multiplicative semigroup generated by invariant monomials of the cyclic group in that representation is determined.