We present certain results on the direct and inverse spectral theory of Jacobi operator with complex periodic coefficients. For instance, we show that any $N$-th degree polynomial whose leading coefficient is $(-1)^N$ Hill discriminant finitely many discrete $N$-periodic Schrödinger operators (Theorem 1). Also, in case where spectrum a closed interval prove result 2) which analog Borg's Theorem...

Let Th be the complete binary tree of height h. Let M be the infinite grid graph with vertexset Z, where two vertices (x1,y1) and (x2,y2) of M are adjacent if and only if|x1-x2| + |y1-y2| = 1. Suppose that T is a tree which is a subdivision of Th and is also isomorphicto a subgraph of M. Motivated by issues in optimal VLSI design, we show that the point expansionration(T)<lb...

Let P (z) be a formal power series in z = (z1, · · · , zn) with o(P (z)) ≥ 2 and t a formal parameter which commutes with z. We say P (z) is HN (Hessian nilpotent) if its Hessian matrix HesP (z) = ( ∂ 2 P ∂zi∂zj ) is nilpotent. The deformed inversion pair Qt(z) of P (z) by definition is the unique Qt(z) ∈ C[[z, t]] with o(Qt(z)) ≥ 2 such that the formal maps Gt(z) = z + t∇Q(z) and Ft(z) = z − t...

We study (1 + 2v)-constacyclic codes over R + vR and their Gray images, where v + v = 0 and R is a finite chain ring with maximal ideal  and nilpotency index e. It is proved that the Gray map images of a (1 + 2v)-constacyclic codes of length n over R + vR are distance-invariant linear cyclic codes of length 2n over R. The generator polynomials of this kind of codes for length n are determined,...

We show how to gauge the set of raising and lowering generators of an arbitrary Lie algebra. We consider SU(N) as an example. The nilpotency of the BRST charge requires constraints on the ghosts associated to the raising and lowering generators. To remove these constraints we add further ghosts and we need a second BRST charge to obtain nontrivial cohomology. The second BRST operator yields a g...

We consider the nonlinear n-th order boundary value problem Lu=u(n)=f(t,u(t),u′(t),…,u(n−1)(t))=Nu given arbitrary bounded linear functional conditions Bi(u)=0, i=1,…,n and develop a method that allows us to study all such resonance problems of one, as well implementing more general constructive for deriving existence criteria in framework coincidence degree Mawhin. demonstrate applicability fo...

In this paper some results on the structure of finite-dimensional Lie algebras are obtained by means of the concept of maximal abelian dimension. More concretely, a sufficient condition is given for the solvability in finite-dimensional Lie algebras by using maximal abelian dimensions. Besides, a necessary condition for the nilpotency is also stated for such Lie algebras. Finally, the maximal a...

BACKGROUND Therapeutic hypothermia (TH) is an established treatment after cardiac arrest and growing evidence supports its use as neuroprotective treatment in stroke. Only few and heterogeneous studies exist on the effect of hypothermia in subarachnoid hemorrhage (SAH). A novel approach of early and prolonged TH and its influence on key complications in poor-grade SAH, vasospasm and delayed cer...