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     

近非临界相位匹配温度调谐MgO：LiNbO3OPO

通过对MgO:LiNbO3参量过程温度相位匹配及走离角，允许参量等运转参数的理论计算与分析，确定了晶体的切割角度θ=82℃，以近非临界相位匹配（NCPM）取代NCPM，将温度调节范围控制在较低的温度上，研制了532nm泵浦的MgO:LiNbO3温度调谐脉冲光学参数振荡器（OPO），在800～1700nm波段实现连续调谐输出。参量泵浦功率密度阈值为57.3MW/cm^2，泵浦能量约2倍阈值处，单谐振（SRO）参量转换效率为11%以上。     

长脉冲激光沉积原位生成YBaCuO超导膜

用长脉冲激光(脉冲宽度150μs,波长1.06μm)辐照高温烧结的YBa_2Cu_3O_(7-x)靶,在6Pa的氧气压强下,巳在(100)YSZ单晶衬底上原位生成YBa_2Cu_(?)O_(7-x)超导膜。衬底置于750℃的加热器上,衬底与靶之间的距离5cm,用该法制得的薄膜光亮坚实,正常态呈金属性,零电阻温度为84.7K。用XRD和SEM对薄膜进行了分析研究。     

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     

Skein related links in 3-manifolds

This paper addresses two problems in the skein theory of homotopy spheres first posed by P. Traczyk. Solutions to both problems are obtained for a large class of manifolds and, since one of the basic techniques used requires the first homology group of the ambient manifold to be torsion free, the extent to which this hypothesis is actually necessary is further explored.     

Deciding Frattini is NP-complete

We show that it is a NP-complete problem to decide whether a finite poset arises as the (Birkhoff) dual of the Frattini sublattice of some finite distributive lattice.This work was supported in part by Swiss NSF grant 20-32644.91.     

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.