Let Γ denote a finite, connected, simple graph. For an edge e of let n(e) the number girth cycles containing e. vertex v {e1, e2, …, ek} be set edges incident to ordered such that n(e1) ≤ n(e2) … n(ek). Then (n(e1),n(e2),…,n(ek)) is called signature v. The graph said girth-biregular if it bipartite, and all its vertices belonging same bipartition have signature. with g = 2d signatures (a1,a2,…,...

In this paper, we prove that for any positive integers k, n with k ≥ 2, the graph P k n is a divisor graph if and only if n ≤ 2k + 2, where P k n is the k power of the path Pn. For powers of cycles we show that C n is a divisor graph when n ≤ 2k + 2, but is not a divisor graph when n ≥ 2k + bk2 c+ 3, where C k n is the k th power of the cycle Cn. Moreover, for odd n with 2k + 2 < n < 2k + bk2 c...

We develop a technique to compute asymptotic expansions for recurrent sequences of the form an+1 = f(an), where f(x) = x − axα + bxβ + o(xβ) as x → 0, for some real numbers α, β, a, and b satisfying a > 0, 1 < α < β. We prove a result which summarizes the present stage of our investigation, generalizing the expansions in [Amer. Math Monthly, Problem E 3034[1984, 58], Solution [1986, 739]]. One ...

Human adenylate kinase isoenzyme 1 (AK1) is the key enzyme in maintaining the cellular energy homeostasis. The catalysis-associated conformational changes of AK1 involve large-amplitude rearrangements. To decipher the conformational changes of AK1 at the single-molecule level, we tagged AK1 with two identical fluorophores, one near the substrate-binding site and the other at the boundary of the...

The maize (Zea mays) brittle stalk2 (bk2) is a recessive mutant, the aerial parts of which are easily broken. The bk2 phenotype is developmentally regulated and appears 4 weeks after planting, at about the fifth-leaf stage. Before this time, mutants are indistinguishable from wild-type siblings. Afterward, all organs of the bk2 mutants turn brittle, even the preexisting ones, and they remain br...

University of Florida funds to purchase a pyrolysis mass spectrometer (to W.V.). Abstract The maize brittle stalk2 (bk2) is a recessive mutant, the aerial parts of which are easily broken. The bk2 phenotype is developmentally regulated and appears four weeks after planting, at about the fifth-leaf stage. Before this time, mutants are indistinguishable from wild-type siblings. Afterwards, all or...

Deletion of the major adenylate kinase AK1 isoform, which catalyzes adenine nucleotide exchange, disrupts cellular energetic economy and compromises metabolic signal transduction. However, the consequences of deleting the AK1 gene on cardiac energetic dynamics and performance in the setting of ischemia-reperfusion have not been determined. Here, at the onset of ischemia, AK1 knockout mice heart...

Abnormally hyperphosphorylated tau is often caused by tau kinases, such as GSK3β and Cdk5. Such occurrence leads to neurofibrillary tangle formation and neuronal degeneration in tauopathy, including Alzheimer's disease (AD). However, little is known about the signaling cascade underlying the pathologic phosphorylation of tau by Aβ(42). In this study, we show that adenylate kinase 1 (AK1) is a n...

Background: Previous studies suggest that adenylate kinase locus 1 (Ak1) has an important role in the control of blood glucose level and in the glycation of structural and functional proteins in type 2 diabetes and in the balanced development of fetoplacental unit in healthy puerperae (HP). In this study, an attempt was made to investigate the relationship of Ak1 with maternal and neonatal para...