Corners of self-conjugate (s,s + 1)-cores and (s‾,s+1‾)-cores

In this paper, we describe a result on self-conjugate $(s,s+1)$-core partitions with the fixed number of corners. We also define shifted corners of a distinct partition and find formulas for the number of $(\stackrel{￣}{s},\stackrel{￣}{s+1})$-core partitions and the number of $(s,s+1)$-core shifted Young diagrams with the fixed number of shifted corners.     

Hardy和Littlewood的一个三角和

本文对Hardy和Littlewood考虑的一个有限三角和做了进一步地研究.通过充分运用Chebyshev多项式和M?bius函数的性质,建立了该有限三角和的一个有趣的恒等式,并得到了一个精确的渐近公式.     

The connected partition lattice of a graph and the reconstruction conjecture

Previously we showed that many invariants of a graph can be computed from its abstract induced subgraph poset, which is the isomorphism class of the induced subgraph poset, suitably weighted by subgraph counting numbers. In this paper, we study the abstract bond lattice of a graph, which is the isomorphism class of the lattice of distinct unlabelled connected partitions of a graph, suitably weighted by subgraph counting numbers. We show that these two abstract posets can be constructed from each other except in a few trivial cases. The constructions rely on certain generalisations of a lemma of Kocay in graph reconstruction theory to abstract induced subgraph posets. As a corollary, trees are reconstructible from their abstract bond lattice. We show that the chromatic symmetric function and the symmetric Tutte polynomial of a graph can be computed from its abstract induced subgraph poset. Stanley has asked if every tree is determined up to isomorphism by its chromatic symmetric function. We prove a counting lemma, and indicate future directions for a study of Stanley's question.     

Commuting traces of multilinear maps on invertible elements

Let R be a unital simple ring. Under some technical restrictions, we characterize m-linear mappings G:R^m→R satisfying [G(u,…,u),u]?=?0 for all unit u∈R.     

Physicochemical investigation of sulfonamide-derived compounds interacting with conventional cationic surfactants in aqueous media

The sulfonamide core in compounds is effective synthons, which offer exciting perspectives in chemotherapeutic and pharmacological research. In this study, we investigated the molecular interaction of potent sulfonamide derivatives (SDs), 2-benzenesulfonamido-3-methylbutyric acid (BSB) and tetraaquabis{3-methyl-2-[(phenylsulfonyl)amino]butanoate}copper(II) (Cu-BSB), with cationic surfactants, cetyltrimethyl ammonium bromide (CTAB) and ethylhexadecyl dimethyl ammonium bromide (EHDAB), using UV-visible spectroscopy and steady-state fluorescence measurements. Various mathematical models were applied to quantify the effect of cationic surfactants on physicochemical characteristics of BSB and Cu-BSB. These interactions were confirmed by estimating the partition coefficient (K_x), binding capacities (K_b), Stern-Volmer quenching constant (K_sv), and related Gibbs free energies (ΔG_b). The in-depth mechanism revealed that the binding mode in SD–surfactants combinational system is spontaneous and quenching exists in static mode initiated by ground-state complex formation. We believe that the true knowledge of host–guest interaction mechanisms concerning model membrane with entrapped moiety can help in better understanding of molecular recognition in related phospholipid membrane models.