Critically indecomposable graphs

An undirected graph G=(V,E) with a specific subset X⊂V is called X-critical if G and G(X), induced subgraph on X, are indecomposable but G(V−{w}) is decomposable for every w∈V−X. This is a generalization of critically indecomposable graphs studied by Schmerl and Trotter [J.H. Schmerl, W.T. Trotter, Critically indecomposable partially ordered sets, graphs, tournaments and other binary relational structures, Discrete Mathematics 113 (1993) 191-205] and Bonizzoni [P. Bonizzoni, Primitive 2-structures with the (n−2)-property, Theoretical Computer Science 132 (1994) 151-178], who deal with the case where X is empty.We present several structural results for this class of graphs and show that in every X-critical graph the vertices of V−X can be partitioned into pairs (a₁,b₁),(a₂,b₂),…,(a_m,b_m) such that G(V−{a_j1,b_j1,…,a_jk,b_jk}) is also an X-critical graph for arbitrary set of indices {j₁,…,j_k}. These vertex pairs are called commutative elimination sequence. If G is an arbitrary indecomposable graph with an indecomposable induced subgraph G(X), then the above result establishes the existence of an indecomposability preserving sequence of vertex pairs (x₁,y₁),…,(x_t,y_t) such that x_i,y_i∈V−X. As an application of the commutative elimination sequence of an X-critical graph we present algorithms to extend a 3-coloring (similarly, 1-factor) of G(X) to entire G.     

Modeling the survival of a resource-dependent population: Effects of toxicants (pollutants) emitted from external sources as well as formed by its precursors

In this paper, a nonlinear mathematical model is proposed and analyzed to study the survival of a resource-dependent population. It is assumed that this population and its resource are affected simultaneously by a toxicant (pollutant) emitted into the environment from external sources as well as formed by precursors of this population. It is shown that as the cumulative rates of emission and formation of the toxicant into the environment increase, the densities of population and its resource settle down to lower equilibria than their initial carrying capacities, and their magnitudes decrease as rates of emission and formation of the toxicant increase. On comparing different cases, it is noted that when population is not affected directly by the toxicant but only its resource is affected, the possibility of its survival is greater than the case when both are affected simultaneously. But for large emission rate of toxicant, the affected resource may be driven to extinction under certain conditions and the population which wholly depends on it may not survive for long even if it is not affected directly by the toxicant.     

Synthesis of α‐Benzylthiobenzimidazoleacetonitriles and Their Chemoselective Reduction of the Double Bond with NaBH4

Condensation of 2‐((1H‐benzimidazol‐2‐yl)thio)acetonitre 1 with aromatic aldehydes in methanol containing piperidine gave the corresponding 2‐((1H‐benzimidazol‐2‐yl)thio)‐3‐arylacrylonitrile 2 , which on treatment with NaBH₄ in ethanol unexpectedly and chemoselectively gave 2‐((1H‐benzimidazol‐2‐yl)thio)‐3‐arylpropanenitrile 3 by the reduction of the double bond of 2 . 3 on methylation with dimethyl sulfate containing K₂CO₃ as a base and tetrabutylammonium bromide as PTC gave 2‐((1‐methylbenzimidazol‐2‐yl)thio)‐3‐arylpropanenitrile 6 . The latter could also be prepared in an alternative way by reaction of 1 with dimethyl sulfate giving the intermediary 2‐((1‐methylbenzimidazol‐2‐yl)thio)acetonitrile 4 , followed by condensation with aromatic aldehydes yielding 5 and subsequent reduction of 5 with NaBH₄ in methanol. 6 could be directly synthesized by treatment of 4 with benzyl chloride in DMF and triethylamine as a base at 60°C for 5 h.     

Synthesis,spectroscopic characterization and crystal structure of 5-bromo-1-(2-cyano-pyridin-4-yl)-1H-indazole-3-carboxylic acid diethylamide

The title compound 5-bromo-1-(2-cyano-pyridin-4-yl)-1H-indazole-3-carboxylic acid diethylamide, C₁₈H₁₆BrN₅O, is prepared from 5-bromoindazole-3-carboxylic acid methylester. N ¹-arylation is carried out with 4-chloro-2-cyanopyridine and the resulting product is converted to diethylamide by reacting with thionyl chloride and diethylamine. The structure is identified from its FT-IR, ¹H NMR, ¹³C NMR spectroscopy, elemental analysis data and unambiguously confirmed by single crystal X-ray diffraction studies. There are two symmetry independent molecules in the asymmetric unit with no significant differences in bond lengths and angles. The title compound crystallizes in the triclinic system, space group \(P\bar 1\) , with a = 11.2330(2); b = 11.6130(2); c = 15.4710(3) Å, α = 92.515(1)°; β = 109.956(1)°; γ = 107.199(1)°; V = 1788.45(6)ų and z = 4. An intramolecular C-H…N hydrogen bond forms an S(6) ring motif in one of the unique molecules. In the crystal, two molecules are linked about a center of inversion by C-H…O hydrogen bonded dimers generating an R ₂ ² (16) ring motif. The crystal packing is stabilized by C-H…N, C-H…O hydrogen bonds and π…π stacking interactions.     

Ionic liquid catalyzed synthesis of 7-phenyl-1,4,6,7-tetrahydro-thiazolo[5,4-d]pyrimidine-2,5-diones

A simple, green and catalyst free one pot synthesis of 7-phenyl-1,4,6,7-tetrahydro-thiazolo[5,4-d]pyrimidine-2,5-diones via a multicomponent reaction between thiazolidine-2, 4-dione (TZD), aromatic aldehyde and urea analogues is described. The ionic liquid has been used as a solvent as well as catalyst for this reaction. This reaction proceeded smoothly in good to excellent yields and offered several other advantages including short reaction time, simple experimental workup procedure and no by-products.     

Direct observation of phenylalanine orientations in statherin bound to hydroxyapatite surfaces

Extracellular biomineralization proteins such as salivary statherin control the growth of hydroxyapatite (HAP), the principal component of teeth and bones. Despite the important role that statherin plays in the regulation of hard tissue formation in humans, the surface recognition mechanisms involved are poorly understood. The protein-surface interaction likely involves very specific contacts between the surface atoms and the key protein side chains. This study demonstrates for the first time the power of combining near-edge X-ray absorption fine structure (NEXAFS) spectroscopy with element labeling to quantify the orientation of individual side chains. In this work, the 15 amino acid N-terminal binding domain of statherin has been adsorbed onto HAP surfaces, and the orientations of phenylalanine rings F7 and F14 have been determined using NEXAFS analysis and fluorine labels at individual phenylalanine sites. The NEXAFS-derived phenylalanine tilt angles have been verified with sum frequency generation spectroscopy.     

Unraveling the Rationale Behind Organic Solvent Stability of Lipases

Organic solvent-stable lipases have pronounced impact on industrial economy as they are involved in synthesis by esterification, interesterification, and transesterification. However, very few of such natural lipases have been isolated till date. A study of the recent past provided few pillars to rely on for this work. The three-dimensional structure, inclusive of the surface and active site, of 29 organic solvent-stable lipases was analyzed by subfamily classification and protein solvent molecular docking based on fast Fourier transform correlation approach. The observations revealed that organic solvent stability of lipases is their intrinsic property and unique with respect to each lipase. In this paper, factors like surface distribution of charged, hydrophobic, and neutral residues, interaction of solvents with catalytically immutable residues, and residues interacting with essential water molecules required for lipase activity, synergistically and by mutualism contribute to render a stable lipase organic solvent. The propensity of surface charge in relation to stability in organic solvents by establishing repulsive forces to exclude solvent molecules from interacting with the surface and prohibiting the same from gaining entry to the protein core, thus stabilizing the active conformation, is a new finding. It was also interesting to note that lipases having equivalent surface-exposed positive and negative residues were stable in a wide range of organic solvents, irrespective of their LogP values.     

Validated high-performance liquid chromatographic enantioseparation of selenomethionine using isothiocyanate based chiral derivatizing reagents

A high-performance liquid chromatographic (HPLC) method for enantioseparation of selenomethionine (SeMet) was developed using two isothiocyanate-based chiral derivatizing reagents [(R)-methyl benzyl isothiocyanate (MBIC) and (S)-1-(1-naphthyl) ethyl isothiocyanate (NEIC)] and UV detection. Diastereomers of selenomethionine were synthesized either via stirring (using MBIC) or by microwave irradiation (using NEIC). Derivatization conditions were optimized and the synthesized diastereomers were successfully resolved using triethyl ammonium phosphate buffer and acetonitrile on a reversed-phase column. The method was validated for accuracy, precision and limit of detection. The mechanism of separation is also discussed.     

Simultaneous optimization of multiple quality characteristics in laser cutting of titanium alloy sheet

Titanium and its alloys have high demand in different industries due to their superior properties. The conventional cutting methods face difficulties for cutting these alloys due to their poor thermal conductivity, low elastic modulus and high chemical affinity at elevated temperatures. Laser cutting may be used for quality cuts by proper control of different process parameters. The aim of present research is to simultaneously optimize kerf taper and surface roughness in the laser cutting of Titanium alloy sheet (grade 5). The developed regression models for kerf taper and surface roughness have been taken as objective functions for the genetic algorithm based multi-objective optimization. The paper presents optimal solutions and improvements in different quality characteristics thereof. The significant control factors have been found with further discussion of their effect on two important quality characteristics kerf taper and surface roughness.     

Application of Atanassov’s I-fuzzy set theory to matrix games with fuzzy goals and fuzzy payoffs

We aim to extend some results in [6, 7, 8, 2] on two person zero sum matrix games (TPZSMG) with fuzzy goals and fuzzy payoffs to I-fuzzy scenario. Because the payoffs of the matrix game are fuzzy numbers, the aspiration levels of the players are fuzzy as well. It is reasonable to believe that there is some indeterminacy in estimating the aspiration levels of both players from their respective expected pay offs. This situation is modeled in the game using Atanassov??s I-fuzzy set theory. A new solution concept is proposed for such games and a procedure is outlined to obtain the degrees of suitability of the aspiration levels for each of the two players.