Extending the Balas-Yu bounds on the number of maximal independent sets in graphs to hypergraphs and lattices

A result of Balas and Yu (1989) states that the number of maximal independent sets of a graph G is at most ^p+1, where is the number of pairs of vertices in G at distance 2, and p is the cardinality of a maximum induced matching in G. In this paper, we give an analogue of this result for hypergraphs and, more generally, for subsets of vectors in the product of n lattices =₁××_n, where the notion of an induced matching in G is replaced by a certain binary tree each internal node of which is mapped into . We show that our bounds may be nearly sharp for arbitrarily large hypergraphs and lattices. As an application, we prove that the number of maximal infeasible vectors x=₁××_n for a system of polymatroid inequalities does not exceed max{Q,^logt/c(2Q,)}, where is the number of minimal feasible vectors for the system, , , and c(,) is the unique positive root of the equation 2^c(^c/log–1)=1. This bound is nearly sharp for the Boolean case ={0,1}ⁿ, and it allows for the efficient generation of all minimal feasible sets to a given system of polymatroid inequalities with quasi-polynomially bounded right-hand sides . This research was supported by the National Science Foundation (Grant IIS-0118635), and by the Office of Naval Research (Grant N00014-92-J-1375). The second and third authors are also grateful for the partial support by DIMACS, the National Science Foundation's Center for Discrete Mathematics and Theoretical Computer Science.Mathematics Subject Classification (2000):20E28, 20G40, 20C20     

Similarity solutions for hydromagnetic simultaneous heat and mass transfer by natural convection from an inclined plate with internal heat generation or absorption

 The problem of coupled heat and mass transfer by natural convection from a semi-infinite inclined flat plate in the presence of an external magnetic field and internal heat generation or absorption effects is formulated. The plate surface has a power-law variation of both wall temperature and concentration and is permeable to allow for possible fluid wall suction or blowing. The resulting governing equations are transformed using a similarity transformation and then solved numerically by an implicit, iterative, finite-difference scheme. Comparisons with previously published work are performed and good agreement is obtained. A parametric study of all involved parameters is conducted and a representative set of numerical results for the velocity and temperature profiles as well as the skin-friction parameter, average Nusselt number, and the average Sherwood number is illustrated graphically to show typical trends of the solutions. Received on 26 October 1998     

Resolution approach for multi-objective problems with uncertain demands

The job-shop scheduling problem (JSP) is one of the hardest problems (NP-complete problem). In a lot of cases, the combination of goals and resource exponentially increases search space. The objective of resolution of such a problem is generally, to maximize the production with a lower cost and makespan. In this paper, we explain how to modify the objective function of genetic algorithms to treat the multi-objective problem and to generate a set of diversified “optimal” solutions in order to help decision maker. We are interested in one of the problems occurring in the production workshops where the list of demands is split into firm (certain) jobs and predicted jobs. One wishes to maximize the produced quantity, while minimizing as well as possible the makespan and the production costs. Genetic algorithms are used to find the scheduling solution of the firm jobs because they are well adapted to the treatment of the multi-objective optimization problems. The predicted jobs will be inserted in the real solutions (given by genetic algorithms). The solutions proposed by our approach are compared to the lower bound of the cost and makespan in order to prove the quality and robustness of our proposed approach.     

Unravelling the anticancer potency of 1,2,4-triazole-N-arylamide hybrids through inhibition of STAT3: synthesis and in silico mechanistic studies

Molecular Diversity - The discovery of potent STAT3 inhibitors has gained noteworthy impetus in the last decade. In line with this trend, considering the proven biological importance of...     

Synthesis and crystal structure of some 3,5-pyrazolidinediones

Syntheses of various derivatives of 3,5-pyrazolidenedione are reported. This includes 4-arylidene (alkylidene or aralkylidene)-3,5-pyrazolidinediones, which on epoxidation gave unreported oxiranes. The syntheses of these derivatives were based on either the Knoevenagel reaction of carbonyl derivatives with 3,4-pyrazolidinedione or cyclization of arylidene (alkylidene) malonic acid hydrazide with glacial acetic acid. 4-Arylazo-3,5-pyrazolidinedione derivatives were also prepared by coupling of aryldiazonium salts with 3,5-pyrazolidinedione or cyclization of arylazomalonic acid hydrazide. Reduction of 4-benzylidene derivatives gave the corresponding benzyl derivatives. The structure of the new products was confirmed by elemental and spectral analyses and X-ray crystallography.     

Étude structurale de britholite au césium Sr7La2Cs(PO4)5(SiO4)F2

Several studies demonstrated the ability of britholites to retain radionuclides such as the caesium and actinides. Therefore, three compounds with formulas Sr₈LaCs(PO₄)₆F₂, Sr₇La₂Cs(PO₄)₅(SiO₄)F₂ and Sr₂La₇Cs(SiO₄)₆F₂, were prepared by solid state reaction. However, it seems that only the mono-silicated composition was obtained in a pure state. In this present work, the X-ray diffraction and magnetic nuclear resonance have been used to investigate the structure for this composition. The results showed that in fact this phase was not pure, but it was mixed with a secondary phase, SrLaCs(PO₄)₂. The refinement by the Rietveld method allowed also to precise the distribution of La³⁺ and Cs⁺ ions between the two cationic sites of the apatite.     

Lead-nano-dopings effects on the structural,microstructural, vibrational and thermal properties of Bi2−xPbxSrV2O9 layered perovskite

The sample with in the general formula Bi_2-xPb_xSrV₂O₉, where x = 0.0, 0.05, 0.1, 0.2, 0.3, and 0.6 mol were synthesized by the high temperature solid state reaction and firing method. The X-ray diffractograms confirmed the formation of single phased layered perovskite in all samples. TGA and DTA thermal analyses on the green samples included steps of thermal analysis of strontium carbonate, bismuth carbonate, ammonium vanadate, lead oxide and finally on the high temperature solid state formation. The effect of lead dopings on the sintering, structural and micro-structure, properties of 212BiSrV-ceramics were investigated. The infrared absorption spectra show a series of vibrational modes within the range of 400–1600 cm^?1.     

New concept of failure of thin organic films

A critical (steady state) value of the thermal expansion coefficients of different coatings was determined by a nondestructive technique (NDT) known as laser shearography. The behavior of organic coatings, i.e., ACE premium-grey enamel, a yellow acrylic lacquer, and a gold nail polish on a metallic alloy, i.e., a carbon steel, was investigated over a temperature range of 20–60 °C. The value of the thermal expansion coefficients of coatings was derived from the slope of the plot of the thermal deformation (strain) versus the applied temperature. The integrity of the coatings with respect to time was assessed by comparison the measured coefficients of thermal expansion (CTE) to the critical (steady state) or asymptotic value of CTE. By shearography, measurement of coating properties could be performed independent of parameters such as UV exposure, humidity, presence of chemical species, and other parameters which may normally interfere with conventional methods of the assessing of the integrity of coatings. Therefore, one may measure CTE of coatings, regardless of the history of the coating, in order to assess the integrity of coatings. Also, the obtained shearography data were found to be in a reasonable trend with the data of electrochemical impedance spectroscopy (EIS) in 3%NaCl solution.