Extremal perfect graphs for a bound on the domination number

We examine classes of extremal graphs for the inequality γ(G)?|V|-max{d(v)+β_v(G)}, where γ(G) is the domination number of graph G, d(v) is the degree of vertex v, and β_v(G) is the size of a largest matching in the subgraph of G induced by the non-neighbours of v. This inequality improves on the classical upper bound |V|-maxd(v) due to Claude Berge. We give a characterization of the bipartite graphs and of the chordal graphs that achieve equality in the inequality. The characterization implies that the extremal bipartite graphs can be recognized in polynomial time, while the corresponding problem remains NP-complete for the extremal chordal graphs.     

Object-motion measurements using pulse-echo acoustical speckle and two-dimensional correlation

A basic theory of acoustical speckle and cross-correlation is described which utilizes the ubiquitous wave characteristics in ultrasonics. A computer-based pulse-echo system has been developed. It is interfaced to a VAX11/780 computer which operates the system and performs the data analysis. Data from three tests using specimens of steel, aluminum and Plexiglas are discussed. On each specimen, a pulse-echo scan of a scattering surface is made over some area which represents reference configuration. After the surface is displaced, a pulse-echo scan is made over the same area. A small region of the displaced configuration is correlated with the reference as a measure of object motion.     

Comparison of three hypothesis testing approaches for the selection of the appropriate number of clusters of variables

Within the scope of cluster analysis of variables, the selection of the appropriate number of clusters is of paramount interest. The strategy of determination of the appropriate number of clusters adopted herein is based on a hypothesis testing approach. It consists in testing whether the variation of a partition quality criterion between two consecutive partitions is far removed from the expected variation under the null-hypothesis stipulating a lack of structure. Three hypothesis testing strategies are detailed and compared in the scope of clustering of variables: Gap, Weighted Gap and a statistic associated with CLV methodology. Finally, an illustration is presented based on data from a preference study.     

Integer extended ABS algorithms and possible control of intermediate results for linear Diophantine systems

We present a new class of integer extended ABS algorithms for solving linear Diophantine systems. The proposed class contains the integer ABS (the so-called EMAS and our proposed MEMAS) algorithms and the generalized Rosser’s algorithm as its members. After an application of each member of the class a particular solution of the system and an integer basis for the null space of the coefficient matrix are at hand. We show that effective algorithms exist within this class by appropriately setting the parameters of the members of the new class to control the growth of intermediate results. Finally, we propose two effective heuristic rules for selecting certain parameters in the new class of integer extended ABS algorithms.      

A parity digraph has a kernel

We show that every digraph has a kernel (i.e. an absorbing and independent set) under the following parity condition: For every pair of verticesx, y x ≠ y all minimal directed paths betweenx andy have the same length parity.     

Ethanol oxidation at metal–zeolite-modified electrodes in alkaline medium. Part 2: palladium–zeolite-modified graphite electrode

Impregnated Pd–zeolite graphite (PdZG) electrodes have been tested for ethanol oxidation in 0.5 M NaOH. The results obtained have been compared with that of Pd electrode. Cyclic voltammetric and chronoamperometric measurements indicated the activity of PdZG electrode toward ethanol oxidation and poisoning tolerance. The influence of zeolite loading as well as impregnation time in Pd²⁺ solution has been examined. Scan rate effect and ethanol concentration dependency indicated that ethanol oxidation at PdZG electrode was governed by diffusion control.     

Blends of carbon blacks and multiwall carbon nanotubes as reinforcing fillers for hydrocarbon rubbers

The reinforcement of a styrene‐butadiene rubber (SBR) by single fillers—carbon black (CB) or multiwall carbon nanotubes (MWNTs)—or by mixtures of CB and MWNTs, is investigated. The morphologies, mechanical and electrical properties of the composites, are analyzed. A significant improvement in the tensile properties is observed for samples containing a dual phase. Using atomic force (AFM) and transmission electron (TEM) microscopies, we demonstrate that the double loading improves the dispersion of the nanotubes in SBR. Electrical measurements show lower resistivity and a lower percolation threshhold for composites containing blends of fillers, which provides further evidence of better dispersion. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 46: 1939–1951, 2008     

Topological KKM theorems and generalized vector equilibria on G-convex spaces with applications

In the present paper, slightly modifying the topological KKM Theorem of Park and Kim (1996), we obtain a new existence theorem for generalized vector equilibrium problems related to an admissible multifunction. We work here under the general framework of G-convex space which does not have any linear structure. Also, we give applications to greatest element, fixed point and vector saddle point problems. The results presented in this paper extend and unify many results in the literature by relaxing the compactness, the closedness and the convexity conditions.

     

Ruthenium(II) 2-hydroxybenzophenone N(4)-substituted thiosemicarbazone complexes

New ruthenium(II) complexes with 2-hydroxybenzophenone N(4)-substituted (Me, Ph and/or piperidyl) thiosemicarbazones have been prepared and characterised by elemental analysis, molar conductivity, thermal analysis, spectroscopy (i.r., ¹H-n.m.r. and u.v.–vis.) and by cyclic voltammetry. The thiosemicarbazones coordinate to ruthenium(II) as mononegative tridentate ligands via the deprotonated hydroxyl group, N¹ nitrogen and thione sulphur centres. The redox properties, nature of the electrode processes and the stability of the complexes towards oxidation in CH₂Cl₂ are discussed. The change in the E _1/2 values of the complexes can be related to the basicity of the N(4)-substituents. All the complexes display an irreversible one-electron charge-transfer couple in the potential range studied. This revised version was published online in June 2006 with corrections to the Cover Date.     

Synthesis of 3,3′-methylenebis(4-hydroxyquinolin-2(1H)-ones) of prospective anti-COVID-19 drugs

Molecular Diversity - During formylation of 2-quinolones by DMF/Et3N mixture, the unexpected 3,3′-methylenebis(4-hydroxyquinolin-2(1H)-ones) were formed. The discussed mechanism was proved as...