Consider the non-autonomous logistic model ∆xn = pnxn 1− xn−kn 1− λxn−kn , n = 0, 1, 2, · · ·, where {pn} is a sequence of positive real numbers, {kn} a sequence of nonnegative integers satisfying limn→∞(n−kn) = ∞, λ ∈ [0, 1). We obtain new sufficient conditions for the attractivity of equilibrium x = 1 of the model, which improve and generalize some recent results established by Chen and Yu [4...

We address Bass’ question, on whether Kn(R) = Kn(R[t]) implies Kn(R) = Kn(R[t1, t2]). In a companion paper, we establish a positive answer to this question when R is of finite type over a field of infinite transcendence degree over the rationals. Here we provide an example of an isolated surface singularity over a number field for which the answer the Bass’ question is “no” when n = 0.

We study direct limits (G,K) = lim −→ (Gn, Kn) of Gelfand pairs of the form Gn = Nn Kn with Nn nilpotent, in other words pairs (Gn, Kn) for which Gn/Kn is a commutative nilmanifold. First, we extend the criterion of [W4] for a direct limit representation to be multiplicity free. Then we study direct limits G/K = lim −→ Gn/Kn of commutative nilmanifolds and look to see when the regular represent...

A Hamiltonian embedding of Kn is an embedding of Kn in a surface, which may be orientable or non-orientable, in such a way that the boundary of each face is a Hamiltonian cycle. Ellingham and Stephens recently established the existence of such embeddings in non-orientable surfaces for n = 4 and n 6. Here we present an entirely new construction which produces Hamiltonian embeddings of Kn from tr...

In this paper we examine the classes of graphs whose Kn-complements are trees or quasi-threshold graphs and derive formulas for their number of spanning trees; for a subgraph H of Kn, the Kn-complement of H is the graph Kn H which is obtained from Kn by removing the edges of H . Our proofs are based on the complement spanning-tree matrix theorem, which expresses the number of spanning trees of ...

A graph G is said to be F-residual if for every point u in G, the graph obtained by removing the closed neighborhood of u from G is isomorphic to F. Similarly, if the remove of m consecutive closed neighborhoods yields Kn, then G is called m-Kn-residual graph. Erdös determine the minimum order of the m-Kn-residual graph for all m and n, the minimum order of the connected Kn-residual graph is fo...

Crop productivity continues to decline due to a wide array of biotic and abiotic stresses. Salinity is one of the worst abiotic stresses, as it causes huge losses to crop yield each year. Kinetin (Kn) has been reported as plant growth regulator since long, but its role in improving plant growth and food quality under saline conditions through mediating phytohormonal cross-talk is poorly studied...

Ca(+)/calmodulin-dependent protein kinase II (CaM kinase II) has been implicated in the regulation of smooth muscle contractility. The goals of this study were to determine: 1) to what extent CaM kinase II is activated by contractile stimuli in intact arterial smooth muscle, and 2) the effect of a CaM kinase II inhibitor (KN-93) on CaM kinase II activation, phosphorylation of myosin regulatory ...

Denote Sn(p)=kn−1∑i=1knlog(Xn+1−i,n∕Xn−kn,n)p, where p>0, kn≤n is a sequence of integers such that kn→∞ and kn∕n→0, X1,n≤⋯≤Xn,n are the order statistics iid random variables X1,…,Xn with regularly varying upper tail index 1∕γ. The estimator γ̂(n)=(Sn(p)∕Γ(p+1))1∕p an extension Hill estimator. We investigate asymptotic properties Sn(p) γ̂(n) both for fixed p>0 p=pn→∞. prove consistency limit theor...

It has been conjectured that for knots K and K′ in S3, w(K#K′) = w(K)+w(K′)−2. In [7], Scharlemann and Thompson proposed potential counterexamples to this conjecture. For every n, they proposed a family of knots {Kn i } for which they conjectured that w(Bn#Kn i ) = w(Kn i ) where Bn is a bridge number n knot. We show that for n > 2 none of the knots in {Kn i } produces such counterexamples.