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.     

Classification of (16,6,2)-designs by ovals

Using the triangular graph T(6) it is shown that up to isomorphism any (16,6,2)-design is uniquely determined by the number of ovals in it, which is 12, 28 or 60. It is shown that the (16,6,2)-design with precisely 60 ovals is embeddable in a 3-(22,6,1)-design. As a consequence the uniqueness of the 3-(22,6,1)-design is obtained.     

Auxiliary sets of matrices with new step parameter sequences

Constructions are given for auxiliary sets of matrices which have the previously unknown step parameter sequences (3,11,3), (2,2,8,11), (2,2,8,13), (2,2,9,11). As a consequence one obtains a projective Hjelmslev plane for each of the preceding four step parameter sequences.     

Evaluation of Successive Fractions for Optimum Quantification of Bergenin and Gallic Acid in Three Industrially Important Bergenia species by High-Performance Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC -     

Surface chemical modification of TEOS based silica aerogels synthesized by two step (acid-base) sol-gel process

The present paper describes the comparative studies on the hydrophobic and physical properties of the tetraethoxysilane (TEOS) based silica aerogels prepared by two step sol-gel process followed by supercritical drying. Silica alcogels were prepared by keeping the molar ratio of TEOS:methanol (MeOH):H₂O (acidic):H₂O (basic) constant at 1:33:3.5:3.5 with oxalic acid and ammonium hydroxide concentrations fixed at 0.001 and 1 M, respectively. In all, nine different co-precursors (CP) of the type R_nSiX_4 − n, have been used. The aerogels have been characterized by density, porosity, percentage of volume shrinkage, optical transmission, contact angle and thermal conductivity measurements. The surface chemical modification of silica aerogels was confirmed by the presence of CH and SiC peaks at 2900, 1450 and 840 cm⁻¹, respectively, from the Fourier transform-infrared spectroscopy (FT-IR). The microstructure of the aerogels was studied using transmission electron microscopy (TEM) and scanning electron microscopy (SEM) techniques. In addition to these studies, the stability of the hydrophobic aerogels against an organic impurity (methanol, in the present studies) in water has also been studied.     

Maximal arcs in designs

An (α,n)-arc in a 2-design is a set ofn points of the design such that any block intersects it in at most α points. For such an arc,n is bounded by 1+(r(α−1)/λ), with equality if and only if every block meets the arc in either 0 or α points. An (α,n) arc with equality in above is said to be maximal. A maximal block arc can be dually defined. This generalizes the notion of an oval (α=2) in a symmetric design due to Asmus and van Lint. The aim of this paper is to study the infinite family of possibly extendable symmetric designs other than the Hadamard design family and their related designs using maximal arcs. It is shown that the extendability corresponds to the existence of a proper family of maximal arcs. A natural duality between point and block arcs is established, which among other things implies a result of Cameron and van Lint that extendability of a given design in this family is equivalent to extendability of its dual. Similar results are proved for other related designs.     

Kinetic investigations on interaction of carbon monoxide with RuIICl2(PPh3)3 in mixed aqueous medium

Kinetics, equilibrium and thermodynamics of interaction of CO with RuCl₂(PPh₃)₃ (1) have been investigated in 1:1(v/v) water — 1,4-dioxan mixture in which 1 dissociates to RuCl₂(PPh₃)₂ (1a), by losing a coordinated PPh₃. The kinetics of complexation of (1a) with CO to form RuCl₂(CO)(PPh₃)₂ (2) indicated first order dependence in [1a] and [CO]. The thermodynamic parameters for the formation of 2 were determined.This revised version was published online in December 2005 with corrections to the Cover Date.     

A Model for Tracking Fronts of Stress-Induced Permeability Enhancement

Using an analogy to the classical Stefan problem, we construct evolution equations for the fluid pore pressure on both sides of a propagating stress-induced damage front. Closed form expressions are derived for the position of the damage front as a function of time for the cases of thermally-induced damage as well as damage induced by over-pressure. We derive expressions for the flow rate during constant pressure fluid injection from the surface corresponding to a spherically shaped subsurface damage front. Finally, our model results suggest an interpretation of field data obtained during constant pressure fluid injection over the course of 16 days at an injection site near Desert Peak, NV.     

A highly efficient stereoselective synthesis of β-lactams

An efficient strategy for a one-pot, single step synthesis of β-lactams employing an imidazolidinone based chiral auxiliary with various aldimines via asymmetric Mannich-type reaction has been described.     

Enantioselective synthesis of (R)-(+)-α-lipoic acid via proline-catalyzed sequential α-aminoxylation and HWE olefination of aldehyde

An efficient enantioselective synthesis of (R)-(+)-α-lipoic acid is described, in high optical purity (>97% ee), using l-proline-catalyzed sequential α-aminoxylation and Horner-Wadsworth-Emmons olefination of aldehyde as the key step.