Dual Convergences of Iteration Processes for Nonexpansive Mappings in Banach Spaces

In this paper we establish a dual weak convergence theorem for the Ishikawa iteration process for nonexpansive mappings in a reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, and then apply this result to study the problem of the weak convergence of the iteration process.     

DNA binding and topoisomerase II inhibitory activity of water-soluble ruthenium(II) and rhodium(III) complexes

Water-soluble piano-stool arene ruthenium complexes based on 1-(4-cyanophenyl)imidazole (CPI) and 4-cyanopyridine (CNPy) with the formulas [(eta6-arene)RuCl2(L)] (L = CPI, eta6-arene = benzene (1), p-cymene (2), hexamethylbenzene (3); L = CNPy, eta6-arene = benzene (4), p-cymene (5), hexamethylbenzene (6)) have been prepared by our earlier methods. The molecular structure of [(eta6-C6Me6)RuCl2(CNPy)] (6) has been determined crystallographically. Analogous rhodium(III) complex [(eta5-C5Me5)RhCl2(CPI)] (7) has also been prepared and characterized. DNA interaction with the arene ruthenium complexes and the rhodium complex has been examined by spectroscopic and gel mobility shift assay; condensation of DNA and B-->Z transition have also been described. Arene ruthenium(II) and EPh3 (E = P, As)-containing arene ruthenium(II) complexes exhibited strong binding behavior, however, rhodium(III) complexes were found to be Topo II inhibitors with an inhibition percentage of 70% (7) and 30% (7a). Furthermore, arene ruthenium complexes containing polypyridyl ligands also act as mild Topo II inhibitors (10%, 3c and 40%, 3d) in contrast to their precursor complexes. Complexes 4-6 also show significant inhibition of beta-hematin/hemozoin formation activity.     

Berge’s theorem for the maximum charge problem

In 1957 Berge [C. Berge, Two theorems in graph theory, Proceedings of the National Academy of Sciences 43 (1957) 842–844] established that a matching is maximum if and only if there are no augmenting paths in the graph. In this paper we prove Berge’s result for a generalization of the matching problem—the maximum charge problem with capacity constraints. We show that a charge is maximum if and only if there is no alternating path, or lasso, along which the charge can be augmented.     

Interaction of MEV atomic ions with molecular solids: Ion track structure and sputtering phenomena

Recent results obtained in our research groups from studies of the interactions of swift, heavy atomic ions with molecular solids are concisely outlined. The focus is on material ejection (sputtering) and surface track formation. The experimental techniques employed include time-of-flight mass spectrometry, energy analysis, collection and analysis of sputtered material, and scanning force microscopy. Characteristics of the sputtering process probed include the sputtering yield, radial and axial velocity distributions, angular distributions, and surface track morphology. Besides reviewing and correlating experimental results, we also emphasize the common quasi-thermal origin of pressure-pulse/hydrodynamic and evaporative spike sputtering models.     

Heteroleptic dipyrrinato complexes containing 5-ferrocenyldipyrromethene and dithiocarbamates as coligands: selective chromogenic and redox probes

Six heteroleptic dipyrrinato complexes [Ni(fcdpm)(dedtc)] (1), [Ni(fcdpm)(dipdtc)] (2), [Ni(fcdpm)(dbdtc)] (3), [Pd(fcdpm)(dedtc)] (4), [Pd(fcdpm)(dipdtc)] (5), and [Pd(fcdpm)(dbdtc)] (6) (fcdpm = 5-ferrocenyldipyrromethene; dedtc = diethyldithiocarbamate; dipdtc = diisopropyldithiocarbamate; dbdtc = dibutyldithiocarbamate) have been synthesized and characterized by elemental analyses and spectral (ESI-MS, IR, (1)H, (13)C NMR, UV-vis) and electrochemical studies. Crystal structures of 1, 2, 4, and 5 have been authenticated by X-ray single-crystal analyses. Nickel-based complexes 1-3 display selective chromogenic and redox sensing for Hg(2+) and Pb(2+) ions, while palladium complexes 4-6 display selective chromogenic and redox sensing only for Hg(2+). Electronic absorption, ESI-MS, and electrochemical studies indicated that sensing arises from interaction between 1-3 and Hg(2+)/Pb(2+) through sulfur of the coordinated dithiocarbamates, while it arises from the pyrrolic nitrogen of fcdpm and dithiocarbamate sulfur from 4-6 and Hg(2+). Different modes of binding between Ni and Pd complexes have further been supported by theoretical studies. The receptor-cation binding constants (K(a)) and stoichiometry between probes and Hg(2+)/Pb(2+) have been estimated by the Benesi-Hildebrand method and Job's plot analysis. Detection limits for 1-3 toward Hg(2+)/Pb(2+) and 4-6 for Hg(2+) have been found to be reasonably high.     

Routing vehicles to minimize fuel consumption

We consider a generalization of the capacitated vehicle routing problem known as the cumulative vehicle routing problem in the literature. Cumulative VRPs are known to be a simple model for fuel consumption in VRPs. We examine four variants of the problem, and give constant factor approximation algorithms. Our results are based on a well-known heuristic of partitioning the traveling salesman tours and the use of the averaging argument.     

Steady-state and flow-injection response of a metallic silver electrode for potentiometric detection of metal cyanide complex formartion

A metallic silver electrode provides a potentiometric response to Ag(I), Hg(II), Fe(III), Cu(II), Zn(II), Co(II) and Ni(II) ions, and large changes in the electrode potential of up to 400 mV are observed when these ions are injected into a 0.29 mM soulution of cyanide ion. Injection 10-μl aliquots into a reagent stream with a cyanide concentration of 0.1 mM is shown to give the expected sigmoidal-shaped response curve for peak height as a function of metal ion concentration. Sub-nanomole quantities of metal ions are detectable with a peak height of ca. 20 mV, depending on the cyanide concentration.     

Ruthenium(II) polypyridyl complexes: potential precursors, metalloligands, and topo II inhibitors

Neutral and cationic mononuclear complexes containing both group 15 and polypyridyl ligands [Ru(kappa3-tptz)(PPh3)Cl2] [1; tptz=2,4,6-tris(2-pyridyl)-1,3,5-triazine], [Ru(kappa3-tptz)(kappa2-dppm)Cl]BF4 [2; dppm=bis(diphenylphosphino)methane], [Ru(kappa3-tptz)(PPh3)(pa)]Cl (3; pa=phenylalanine), [Ru(kappa3-tptz)(PPh3)(dtc)]Cl (4; dtc=diethyldithiocarbamate), [Ru(kappa3-tptz)(PPh3)(SCN)2] (5) and [Ru(kappa3-tptz)(PPh3)(N3)2] (6) have been synthesized. Complex 1 has been used as a metalloligand in the synthesis of homo- and heterodinuclear complexes [Cl2(PPh3)Ru(micro-tptz)Ru(eta6-C6H6)Cl]BF4 (7), [Cl2(PPh3)Ru(mu-tptz)Ru(eta6-C10H14)Cl]PF6 (8), and [Cl2(PPh3)Ru(micro-tptz)Rh(eta5-C5Me5)Cl]BF4 (9). Complexes 7-9 present examples of homo- and heterodinuclear complexes in which a typical organometallic moiety [(eta6-C6H6)RuCl]+, [(eta6-C10H14)RuCl]+, or [(eta5-C5Me5)RhCl]+ is bonded to a ruthenium(II) polypyridine moiety. The complexes have been fully characterized by elemental analyses, fast-atom-bombardment mass spectroscopy, NMR (1H and 31P), and electronic spectral studies. Molecular structures of 1-3, 8, and 9 have been determined by single-crystal X-ray diffraction analyses. Complex 1 functions as a good precursor in the synthesis of other ruthenium(II) complexes and as a metalloligand. All of the complexes under study exhibit inhibitory effects on the Topoisomerase II-DNA activity of filarial parasite Setaria cervi and beta-hematin/hemozoin formation in the presence of Plasmodium yoelii lysate.     

Self-duality of bounded monotone boolean functions and related problems

In this paper we examine the problem of determining the self-duality of a monotone boolean function in disjunctive normal form (DNF). We show that the self-duality of monotone boolean functions with n disjuncts such that each disjunct has at most k literals can be determined in O(2^k2k²n) time. This implies an O(n²logn) algorithm for determining the self-duality of -DNF functions. We also consider the version where any two disjuncts have at most c literals in common. For this case we give an O(n^4(c+1)) algorithm for determining self-duality.     

Pressure dependence of the superconducting state parameters of metallic glass superconductor Mg70Zn30

Explicit expressions have been derived for the volume dependence of electron-phonon coupling strength (λ) and the Coulomb pseudopotential (μ^*) considering the variation of Fermi momentum (κ _F) and Debye temperature (θ _D) with volume. Ashcroft’s model pseudopotential and RPA form of dielectric screening have been used for obtaining pressure dependence of transition temperature (T _C) and the logarithmic volume derivative (Φ) of the effective interaction strength (N ₀ V) for metallic glass superconductor Mg₇₀Zn₃₀. It has been observed that T _C of the metallic glass Mg₇₀Zn₃₀ decreases rapidly with increase of pressure and the superconducting phase disappears at about 30% decrease of volume, for which the μ^* curve shows a minimum and an elbow is formed in the Φ graph.