A class of antimagic join graphs

A labeling f of a graph G is a bijection from its edge set E(G) to the set {1, 2, . . . , |E(G)|}, which is antimagic if for any distinct vertices x and y, the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y. A graph G is antimagic if G has an f which is antimagic. Hartsfield and Ringel conjectured in 1990 that every connected graph other than K 2 is antimagic. In this paper, we show that if G 1 is an n-vertex graph with minimum degree at least r, and G 2 is an m-vertex graph with maximum degree at most 2r-1 (m ≥ n), then G1 ∨ G2 is antimagic.     

In Silico Prediction,Molecular Docking and Dynamics Studies of Steroidal Alkaloids of Holarrhena pubescens Wall. ex G. Don to Guanylyl Cyclase C: Implications in Designing of Novel Antidiarrheal Therapeutic Strategies

The binding of heat stable enterotoxin (STa) secreted by enterotoxigenic Escherichia coli (ETEC) to the extracellular domain of guanylyl cyclase c (ECD_GC-C) causes activation of a signaling cascade, which ultimately results in watery diarrhea. We carried out this study with the objective of finding ligands that would interfere with the binding of STa on ECD_GC-C. With this view in mind, we tested the biological activity of a alkaloid rich fraction of Holarrhena pubescens against ETEC under in vitro conditions. Since this fraction showed significant antibacterial activity against ETEC, we decided to test the screen binding affinity of nine compounds of steroidal alkaloid type from Holarrhena pubescens against extracellular domain (ECD) by molecular docking and identified three compounds with significant binding energy. Molecular dynamics simulations were performed for all the three lead compounds to establish the stability of their interaction with the target protein. Pharmacokinetics and toxicity profiling of these leads demonstrated that they possessed good drug-like properties. Furthermore, the ability of these leads to inhibit the binding of STa to ECD was evaluated. This was first done by identifying amino acid residues of ECD_GC-C binding to STa by protein–protein docking. The results were matched with our molecular docking results. We report here that holadysenterine, one of the lead compounds that showed a strong affinity for the amino acid residues on ECD_GC-C, also binds to STa. This suggests that holadysenterine has the potential to inhibit binding of STa on ECD and can be considered for future study, involving its validation through in vitro assays and animal model studies.     

t-Spread strongly stable monomial ideals*

We introduce the concept of t-spread monomials and t-spread strongly stable ideals. These concepts are a natural generalization of strongly stable and squarefree strongly stable ideals. For the study of this class of ideals we use the t-fold stretching operator. It is shown that t-spread strongly stable ideals are componentwise linear. Their height, their graded Betti numbers and their generic initial ideal are determined. We also consider the toric rings whose generators come from t-spread principal Borel ideals.     

A new proof of the stable manifold theorem for hyperbolic fixed points on surfaces

We introduce a new technique for proving the classical stable manifold theorem for hyperbolic fixed points. This method is much more geometrical than the standard approaches which rely on abstract fixed point theorems. It is based on the convergence of a canonical sequence of “finite time local stable manifolds” which are related to the dynamics of a finite number of iterations.     

Some Analytical Properties of the Model for Stochastic Evolutionary Games in Finite Populations with Non-uniform Interaction Rate

Traditional evolutionary games assume uniform interaction rate, which means that the rate at which individuals meet and interact is independent of their strategies. But in some systems, especially biological systems, the players interact with each other discriminately. Taylor and Nowak (2006) were the first to establish the corresponding non-uniform interaction rate model by allowing the interaction rates to depend on strategies. Their model is based on replicator dynamics which assumes an infinite size population. But in reality, the number of individuals in the population is always finite, and there will be some random interference in the individuals' strategy selection process. Therefore, it is more practical to establish the corresponding stochastic evolutionary model in finite populations. In fact, the analysis of evolutionary games in a finite size population is more difficult. Just as Taylor and Nowak said in the outlook section of their paper, "The analysis of non-uniform interaction rates should be extended to stochastic game dynamics of finite populations." In this paper, we are exactly doing this work. We extend Taylor and Nowak's model from infinite to finite case, especially focusing on the influence of non-uniform connection characteristics on the evolutionary stable state of the system. We model the strategy evolutionary process of the population by a continuous ergodic Markov process. Based on the limit distribution of the process, we can give the evolutionary stable state of the system. We make a complete classification of the symmetric 2×2 games. For each case game, the corresponding limit distribution of the Markov-based process is given when noise intensity is small enough. In contrast with most literatures in evolutionary games using the simulation method, all our results obtained are analytical. Especially, in the dominant-case game, coexistence of the two strategies may become evolutionary stable states in our model. This result can be used to explain the emergence of cooperation in the Prisoner is Dilemma Games to some extent. Some specific examples are given to illustrate our results.     

Electronic Bands of the BeOH and BeOD

The electronic bands appearing in the region 300–330 nm were produced in a low-pressure DC are with beryllium electrodes. The bands were obtained in the atmosphere of ordinary water vapour and heavy water vapour. From isotope shift studies, experimental conditions and the similarity with the bands of isoelectronic BeF, the emitting molecules were identified as BeOH and BeOD, respectively.     

Vibrational Assignment of N-Phenylphthalimide and 15N-Phenylphthalimide

Abstract

The i.r. spectra of N-phenylphthalimide and ¹⁵N-phenylphthalimide have been measured in 4000–100 cm^?1 frequency range as KBr and polyethylene pellets and as chloroform solutions. The Raman spectra (4000–50) cm^?1 of microcrystalline powder of the of the same compounds have also been investigated.

A detailed assignment of most of the observed frequencies has been proposed on the basis of the group vibrational concept, isotopic shift data and analogies with the spectra of related molecules. Some literature data have been discussed and some frequencies are reassigned.