Some new integral inequalities of Bellman–Bihari type with delay for discontinuous functions

In this article we investigate some integral functional inequalities of Bellman–Bihari type for piecewise-continuous functions with some fixed points of discontinuity. We also prove a new analogy and generalization of results which were obtained by Bellman and Bihari to integro-sum inequalities with delay and discontinuities that do not belong to Lipschitz’s type.     

Continuous time collocation methods for Volterra-Fredholm integral equations

Summary Integral equations of mixed Volterra-Fredholm type arise in various physical and biological problems. In the present paper we study continuous time collocation, time discretization and their global and discrete convergence properties.     

Bipyridinophane‐containing conjugated polymers modulated with an intramolecular aromatic C?H/π interaction

Bipyridinophane–fluorene conjugated copolymers have been synthesized via Suzuki and Heck coupling reactions from 5,8‐dibromo‐2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane and suitable fluorene precursors. Poly[2,7‐(9,9‐dihexylfluorene)‐co‐alt‐5,8‐(2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane)] ( P7 ) exhibits large absorption and emission redshifts of 20 and 34 nm, respectively, with respect to its planar reference polymer Poly[2,7‐(9,9‐dihexylfluorene)‐co‐alt‐1,4‐(2,5‐dimethylbenzene)] ( P11 ), which bears the same polymer backbone as P7 . These spectral shifts originate from intramolecular aromatic C? H/π interactions, which are evidenced by ultraviolet–visible and ¹H NMR spectra as well as X‐ray single‐crystal structural analysis. However, the effect of the intramolecular aromatic C? H/π interactions on the spectral shift in poly[9,9‐dihexylfluorene‐2,7‐yleneethynylene‐co‐alt‐5,8‐(2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane)] ( P10 ) is much weaker. Most interestingly, the quenching behaviors of these two conjugated polymers are largely dependent on the polymer backbone. For example, the fluorescence of P7 is efficiently quenched by Cu²⁺, Co²⁺, Ni²⁺, Zn²⁺, Mn²⁺, and Ag⁺ ions. In contrast, only Cu²⁺, Co²⁺, and Ni²⁺ ions can partially quench the fluorescence of P10 , but much less efficiently than the fluorescence of P7 . The static Stern–Volmer quenching constants of Cu²⁺, Co²⁺, and Ni²⁺ ions toward P7 are of the order of 10⁶ M^?1, being 1300, 2500, and 37,300 times larger than those of P10 , respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4154–4164, 2006     

Codiameters of 3‐connected 3‐domination critical graphs

A graph G is 3‐domination critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Let G be a 3‐connected 3‐domination critical graph of order n. In this paper, we show that there is a path of length at least n?2 between any two distinct vertices in G and the lower bound is sharp. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 76–85, 2002     

A numerical study of an unsteady laminar flow in a doubly constricted 3D vessel

Unsteady flow dynamics in doubly constricted 3D vessels have been investigated under pulsatile flow conditions for a full cycle of period T. The coupled non‐linear partial differential equations governing the mass and momentum of a viscous incompressible fluid has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of non‐linear terms and the pseudo‐compressibility technique employed in the current numerical scheme makes it robust both in space and time. Computational experiments are carried out to assess the influence of Reynolds' number and the spacing between two mild constrictions on the pressure drop across the constrictions. The study reveals that the pressure drop across a series of mild constrictions can get physiologically critical and is also found to be sensitive both to the spacing between the constrictions and the oscillatory nature of the inflow profile. The flow separation zone on the downstream constriction is seen to detach from the diverging wall of the constriction leading to vortex shedding with 3D features earlier than that on the wall in the spacing between the two constrictions. Copyright © 2002 John Wiley & Sons, Ltd.     

Dibutyltin-3-hydroxyflavone titrates a dissociable component (cofactor) of mitochondrial ATP synthase: An energy-transfer component linked to the ubiquinone pool

Dibutyltin-3-hydroxyflavone, Bu₂Sn(of), is a new fluorescence probe inhibitor of F₁F₀-ATPase and oxidative phosphorylation which inhibits by titration of an unidentified component of F₀. Its site of action is closely related to that of the trialkyltins and of venturicidin. This F₀ component is part of a pool of this component which is present in the heart mitochondrial inner membrane at levels of 5–7 nmol (mg protein)^?1 [18 ± 3 Bu₂Sn(of) sites per mol F₁F₀-ATPase]. However, ATPase activity in submitochondrial particles is near maximally inhibited by titration of approx. three Bu₂Sn(of) sites per mol F₁F₀-ATPase. Over 60% (60–80%) of the Bu₂Sn(of) interaction sites can be lost during the purification of F₁F₀-ATPase from submitochondrial particles. The number of Bu₂Sn(of) interaction sites in various F₁F₀-ATPase preparations is variable. The high numbers of Bu₂Sn(of) sites per mol F₁F₀-ATPase for heart mitochondria (18–21) and submitochondrial particles (15–19.5) decline in ATP synthase (11–15) to the low values obtained in Complex V (7–10.5) and the minimal values observed in highly purified F₁F₀?ATPase (3.5–5.6), thus indicating a variable dissociable component or cofactor of ATP synthase. The Bu₂Sn(of) interaction site, a component of ATP synthase, is responsive to the redox status of the respiratory chain and the interaction with Bu₂Sn(of) is with the reduced form of this component. Fluorescence titration studies show that this component is in redox equilibrium with the ubiquinone pool of the respiratory chain. It is proposed that this redox component serves as an inhibitor titratable cofactor pool which cycles through an F₀ interaction site (or sites) via a system which serves as an energy-transfer link between the respiratory chain and ATP synthase.     

Synthesis of functional polymers—Vinylidene fluoride based fluorinated copolymers and terpolymers bearing bromoaromatic side‐group

The radical co‐ and terpolymerization of 4‐[(α,β,β‐trifluorovinyl)oxy]bromo benzene (TFVOBB) with 1,1‐difluoroethylene (or vinylidene fluoride, VDF, or VF₂), hexafluoropropene (HFP), perfluoromethyl vinyl ether (PMVE), and chlorotrifluroroethylene (CTFE) is presented. Although TFVOBB could be thermocyclodimerized, it could not homopolymerize under radical initiation. TFVOBB could be copolymerized in solution under a radical initiator with VDF or CTFE comonomers, while its copolymerization with HFP or PMVE were unsuccessful. The terpolymerization of TFVOBB with VDF and HFP, or VDF and PMVE, or VDF and CTFE also led to original fluorinated terpolymers bearing bromoaromatic side‐groups. The conditions of co‐ and terpolymerization were optimized in terms of the nature of the radical initiators, and of the nature of solvents (fluorinated or nonhalogenated). Various monomer concentrations in the co‐ and terpolymers were assessed by ¹⁹F and ¹H‐NMR spectroscopy. The thermal and physico chemical properties were also studied. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5077–5097, 2004     

Enlarged symmetry groups of finite-size clusters with periodic noundary conditions

Any system that approximates an infinite lattice by a family of finite clusters (with periodic boundary conditions) passes through an intermediate region with enlarged (hidden) symmetry as the system size is increased. The hidden symmetry allows for extra degeneracies and level crossings and has application to exact-diagonalization studies, Monte Carlo simulations, lattice gauge theories, and renormalization group calculations.     

Synthesis and copolymerization of new phosphorus‐containing acrylates

Two phosphorus‐containing acrylate monomers were synthesized from the reaction of ethyl α‐chloromethyl acrylate and t‐butyl α‐bromomethyl acrylate with triethyl phosphite. The selective hydrolysis of the ethyl ester monomer with trimethylsilyl bromide (TMSBr) gave a phosphonic acid monomer. The attempted bulk polymerizations of the monomers at 57–60 °C with 2,2′‐azobisisobutyronitrile (AIBN) were unsuccessful; however, the monomers were copolymerized with methyl methacrylate (MMA) in bulk at 60 °C with AIBN. The resulting copolymers produced chars on burning, showing potential as flame‐retardant materials. Additionally, α‐(chloromethyl)acryloyl chloride (CMAC) was reacted with diethyl (hydroxymethyl)phosphonate to obtain a new monomer with identical ester and ether moieties. This monomer was hydrolyzed with TMSBr, homopolymerized, and copolymerized with MMA. The thermal stabilities of the copolymers increased with increasing amounts of the phosphonate monomer in the copolymers. A new route to highly reactive phosphorus‐containing acrylate monomers was developed. A new derivative of CMAC with mixed ester and ether groups was synthesized by substitution, first with diethyl (hydroxymethyl)phosphonate and then with sodium acetate. This monomer showed the highest reactivity and gave a crosslinked polymer. The incorporation of an ester group increased the rate of polymerization. The relative reactivities of the synthesized monomers in photopolymerizations were determined and compared with those of the other phosphorous‐containing acrylate monomers. Changing the monomer structure allowed control of the polymerization reactivity so that new phosphorus‐containing polymers with desirable properties could be obtained. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2207–2217, 2003     

Synthesis and characterization of poly(vinyl alcohol)‐graft‐[poly(D,L‐lactide)/poly(D,L‐lactide‐co‐glycolide)] hydrogels

Poly(D ,L ‐lactide) and poly(D ,L ‐lactide‐co‐glycolide) with various composition and with one methacrylate and one carboxylate end group were synthesized and grafted onto poly(vinyl alcohol) (PVA) via the carboxylate group. The graft copolymers were crosslinked via the methacrylate groups using a free radical initiator. The polymer networks were characterized by means of NMR and studied qualitatively by means of IR spectroscopy. The influence of the glycolide content in the polyester grafts and of the number of ester units in the grafts on thermal properties and swellability were studied as well. The high swellability in water is characteristic of all hydrogels. Differential scanning calorimetry (DSC) showed a single glass transition temperature that occurs in the range between 51 and 69 °C. Thermogravimetric analysis (TGA) of the networks showed the main loss in weight in the temperature range between 290 and 370 °C. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4536–4544, 2007