A periodic Schrödinger operator on a noncompact Riemannian manifold M such that H1(M, R) = 0 endowed with a properly discontinuous cocompact isometric action of a discrete group are considered. Under some additional conditions on the magnetic field existence of an arbitrary large number of gaps in the spectrum of such an operator in the semiclassical limit is established. The proofs are based o...

in this paper, we nd the relationships between module contractibility of abanach algebra and its ideals. we also prove that module contractibility ofa banach algebra is equivalent to module contractibility of its module uniti-zation. finally, we show that when a maximal group homomorphic image ofan inverse semigroup s with the set of idempotents e is nite, the moduleprojective tensor product ...

In a previous paper, we proved that quasi-isometric map $$f:X\rightarrow Y$$ between two pinched Hadamard manifolds X and Y is within bounded distance from unique harmonic map. We extend this result to maps $$f:\Gamma \backslash X\rightarrow , where $$\Gamma $$ convex cocompact discrete group of isometries f locally at infinity.

Let $X$ be a Banach space of $dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $tau : B(X)to FI$ vanishing at commutators $[A, B]$ for all $A, Bin B(X)$ such that $L = D + tau$.

let r be a ring, m a right r-module and (s,≤) a strictly ordered monoid. in this paper we will show that if (s,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ s, then the module [[ms,≤]] of generalized power series is a uniserial right [[rs,≤]] ]]-module if and only if m is a simple right r-module and s is a chain monoid.

‎we determine the‎ ‎form of polynomially bounded solutions to the loewner differential ‎equation that is satisfied by univalent subordination chains of the‎ ‎form $f(z,t)=e^{int_0^t a(tau){rm d}tau}z+cdots$‎, ‎where‎ ‎$a:[0,infty]rightarrow l(mathbb{c}^n,mathbb{c}^n)$ is a locally‎ ‎lebesgue integrable mapping and satisfying the condition‎ ‎$$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t‎ ‎[a(tau)...

Let $A$ be a Banach algebra and $E$ be a Banach $A$-bimodule then $S = A oplus E$, the $l^1$-direct sum of $A$ and $E$ becomes a module extension Banach algebra when equipped with the algebras product $(a,x).(a^prime,x^prime)= (aa^prime, a.x^prime+ x.a^prime)$. In this paper, we investigate $triangle$-amenability for these Banach algebras and we show that for discrete inverse semigroup $S$ with...

the concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. the notion of free fuzzy modules was introducedby muganda as an extension of free modules in the fuzzy context. zahedi and ameriintroduced the concept of projective and injective l-modules. in this paper we give analternate definition for projective l-modules. we prove that e...

Although tau is a cytoplasmic protein, it is also found in brain extracellular fluids, e.g., CSF. Recent findings suggest that aggregated tau can be transferred between cells and extracellular tau aggregates might mediate spread of tau pathology. Despite these data, details of whether tau is normally released into the brain interstitial fluid (ISF), its concentration in ISF in relation to CSF, ...

Mess deduces this result as part of a general theory of domains of dependence in constant curvature Lorentzian 3-manifolds. We give an alternate proof, using an invariant introduced by Margulis [18, 19] and Teichmüller theory. We thank Scott Wolpert for helpful conversations concerning Teichmüller theory. We also wish to thank Paul Igodt and the Algebra Research Group at the Katholieke Universi...