Complement activation by sulfonated poly(ethylene glycol)-acrylate copolymers through alternative pathway

Previously, novel poly(ethylene glycol) (PEG) and sulfonated PEG acrylate (PEG-SO₃A/OA) copolymers were prepared as coating and/or blending materials for biomedical applications. Surfaces modified with copolymers exhibited increased anti-coagulation properties and decreased plasma adsorption level due to increased hydrophilic properties and reorientation characteristics of PEG/PEG-SO₃A chains in water phase. As continuation study, anti-complement effects of PEG-SO₃/OA copolymers were investigated in vitro, and compared with those of low-density polyethylene (LDPE) and PEG/OA. C3 activation by PEG-SO₃/OA samples was lower than that by PEG/OA samples, which was attributed to decreased surface nucleophile level of samples. PEG-SO₃/OA samples increased inhibition of Bb production, resulting in decreased C5 activation. Owing to reduced activations of C3 and C5, PEG-SO₃/OA samples markedly decreased SC5b-9 levels in plasma.     

Extending framework based on the linear coordination polymers: Alternative chains containing lanthanum ion and acrylic acid ligand

One-dimensional alternative chains of two lanthanum complexes: [La(L¹)₃(CH₃OH)(H₂O)₂]·5H₂O (L¹=anion of α-cyano-4-hydroxycinnamic acid ) 1 and [La(L²)₃(H₂O)₂]·3H₂O (L²=anion of trans-3-(4-methyl-benzoyl)-acrylic acid) 2 were synthesized and structurally characterized by single-crystal X-ray diffraction, element analysis, IR and thermogravimetric analysis. The crystal structure data are as follows for 1: C₃₁H₃₆LaN₃O₁₇, triclinic, P-1, , , , α=72.7960(10)°, β=83.3820(10)°, γ=67.1650(10)º, Z=2, R₁=0.0377, wR₂=0.0746; for 2: C₃₃H₃₇LaO₁₄, triclinic, P-1, , , , α=81.145(2)°, β=87.591(2)°, γ=67.345(5)°, Z=2, R₁=0.0869, wR₂=0.220. 1 is a rare example of the alternative chain constructed by syn-syn and anti-syn coordination mode of carboxylato ligand arranged along the chain alternatively. La(III) ions in 2 are linked by two η³-O bridges and four bridges (two η²-O and two η³-O) alternatively. Both of the linear coordination polymers grow into two- and three-dimensional networks by packing through extending hydrogen-bond network directed by ligands.     

The Knoevenagel reaction: analysis and recycling of the ionic liquid medium

A study involving the scope of substrate in the Knoevenagel reaction in an IL medium has been conducted. Reactivity trends favor formation of the condensation product using electron deficient aryl aldehydes. Use of electron rich aldehydes and ketones lead to lower levels of conversion and no measurable amounts of condensation products, respectively. A recycling study confirmed that the reaction medium could be used multiple times affording, with each run, the desired condensation product 1a in excess of 90% conversion. Post-run analyses of the IL documented that the IL medium was unaltered upon reuse.     

Einstein-aether theory with a Maxwell field: General formalism

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.     

HOMOTOPY PERTURBATION SOLUTION AND PERIODICITY ANALYSIS OF NONLINEAR VIBRATION OF THIN RECTANGULAR FUNCTIONALLY GRADED PLATES

In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing＇s equation. The homotopy perturbation solution of generated Duffing＇s equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green＇s function and Schauder＇s fixed point theorem.     

Invex nonsmooth alternative theorem and applications *

An invex constrained nonsmooth optimization problem is considered, in which the presence of an abstract constraint set is possibly allowed. Necessary and sufficient conditions of optimality are provided and weak and strong duality results established. Following Geoffrion’s approach an invex nonsmooth alternative theorem of Gordan type is then derived. Subsequently, some applications on multiobjective programming are then pursued     

Positive solutions of second-order differential systems with nonhomogeneous boundary conditions

This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder fixed point theorem and fixed point index theory, under certain conditions, it is proved that there exist appropriate regions of parameters in which the problem has at least two, at least one or no positive solution.     

Gaps and Fatou theorems for series in Schauder basis of holomorphic functions

We prove a gap theorem and the “Fatou change-of-sign theorem” [Fatou, P., 1906, Sèries trigonométriques e séries de Taylor. Acta Mathematica, 39, 335–400] for expansions in common Schauder basis of holomorphic functions.     

多复变中一个带Haseman位移及共轭值的非线性边值问题

研究多复变中一个带Haseman位移及共轭值的非线性边值问题.利用积分方程方法和Schauder不动点原理给出问题解的存在性和积分表示,并用压缩映象原理证明了线性问题解的唯一性.