A successful algorithm for the undirected Hamiltonian path problem

In this paper a polynomial algorithm called the Minram algorithm is presented which finds a Hamiltonian Path in an undirected graph with high frequency of success for graphs up to 1000 nodes. It first reintroduces the concept described in [13] and then explains the algorithm. Computational comparison with the algorithm by Posa [10] is given.It is shown that a Hamiltonian Path is a spanning arborescence with zero ramification index. Given an undirected graph, the Minram algorithm starts by finding a spanning tree which defines a unique spanning arborescence. By suitable pivots it locates a locally minimal value of the ramification index. If this local minima corresponds to zero ramification index then the algorithm is considered to have ended successfully, else a failure is reported.Computational performance of the algorithm on randomly generated Hamiltonian graphs is given. The random graphs used as test problems were generated using the procedure explained in Section 6.1. Comparison with our version of the Posa algorithm which we call Posa-ran algorithm [10] is also made.     

Remarks concerning impact-parameter dependent binary encounter approximation

It is pointed out that the velocity of target electron as a function of it's position from the nucleus needed in the impact-parameter version of binary encounter theory of ionization can be obtained from statistical arguments.     

Antimalaria agents II. Synthesis and reactions of 3-([p-(4-nitrophenyl)sulfonyl] phenyl)sydnone

The synthesis and several reactions of a sydnone substituted with strongly electron-withdrawing substituents are described. Infrared evidence for labile open chain iminoanhydride is presented.     

A class of polynomials defined by generalized Rodrigues’ formula

Summary The present paper incorporates a systematic study of linear, bilinear and bilateral generating functions, pure as well as mixed recurrence relations, and the differential equations associated with the class of polynomials {G _n ^α (x, r, p, k)|n=0, 1, 2, ... }, defined by (1.3) below, which evidently provides an elegant generalization of the various recent extensions of the classical Hermite and Laguerre polynomials. This work was supported in part by the National Research Council of Canada under Grant A7353. See also Abstract 71T-B15, Notices Amer. Math. Soc.18 (1971), p. 252. Entrata in Redazione il 16 novembre 1970.     

Highly bacterial resistant silver nanoparticles: synthesis and antibacterial activities

In this article, we describe a simple one-pot rapid synthesis route to produce uniform silver nanoparticles by thermal reduction of AgNO₃ using oleylamine as reducing and capping agent. To enhance the dispersal ability of as-synthesized hydrophobic silver nanoparticles in water, while maintaining their unique properties, a facile phase transfer mechanism has been developed using biocompatible block co-polymer pluronic F-127. Formation of silver nanoparticles is confirmed by X-ray diffraction (XRD), transmission electron microscopy (TEM) and UV–vis spectroscopy. Hydrodynamic size and its distribution are obtained from dynamic light scattering (DLS). Hydrodynamic size and size distribution of as-synthesized and phase transferred silver nanoparticles are 8.2 ± 1.5 nm (σ = 18.3%) and 31.1 ± 4.5 nm (σ = 14.5%), respectively. Antimicrobial activities of hydrophilic silver nanoparticles is tested against two Gram positive (Bacillus megaterium and Staphylococcus aureus), and three Gram negative (Escherichia coli, Proteus vulgaris and Shigella sonnei) bacteria. Minimum inhibitory concentration (MIC) values obtained in the present study for the tested microorganisms are found much better than those reported for commercially available antibacterial agents.     

Carbohydrate-based switch-on molecular sensor for Cu(II) in buffer: absorption and fluorescence study of the selective recognition of Cu(II) ions by galactosyl derivatives in HEPES buffer

[graph: see text] 1-(Beta-D-galactopyranosyl-1'-deoxy-1'-iminomethyl)-2-hydroxynaphthalene (L1), possessing an ONO binding core, was found to be selective for Cu2+ ions in N-[2-hydroxyethyl]piperazine-N'-[2-ethanesulfonic acid] buffer, at concentrations < or = 580 ppb, at physiological pH by eliciting switch-on behavior, whereas the other ions, viz., Mg2+, Ca2+, Mn2+, Fe2+, Co2+, Ni2+, Zn2+, and Cd2+, caused no significant change in the fluorescence. Whereas the binding characteristics were ascertained by absorption spectroscopy, the species formed were shown by Q-TOF ES MS.     

Minimal logarithmic signatures for finite groups of Lie type

A logarithmic signature (LS) for a finite group G is an ordered tuple α =  [A ₁, A ₂, . . . , A _n ] of subsets A _i of G, such that every element ${g \in G}$ can be expressed uniquely as a product g =  a ₁ a ₂ . . . a _n , where ${a_i \in A_i}$ . The length of an LS α is defined to be ${l(\alpha)= \sum^{n}_{i=1}|A_i|}$ . It can be easily seen that for a group G of order ${\prod^k_{j=1}{p_j}^{m_j}}$ , the length of any LS α for G, satisfies, ${l(\alpha) \geq \sum^k_{j=1}m_jp_j}$ . An LS for which this lower bound is achieved is called a minimal logarithmic signature (MLS) (González Vasco et al., Tatra Mt. Math. Publ. 25:2337, 2002). The MLS conjecture states that every finite simple group has an MLS. This paper addresses the MLS conjecture for classical groups of Lie type and is shown to be true for the families PSL _n (q) and PSp _2n (q). Our methods use Singer subgroups and the Levi decomposition of parabolic subgroups for these groups.