Paramagnetic Properties and Moderately RapidConformational Dynamics in the Cobalt(II) Calix[4]arene Complex by NMR

¹H NMR measurements are reported for the CD₂Cl₂/CDCl₃ solutions of the Co(II) calix[4]arenetetraphosphineoxide complex (I). Temperature dependences of the ¹H NMR spectra of I have been analyzed using the line shape analysis, taking into account the temperature variation of paramagnetic chemical shifts, within the frame of the dynamic NMR method. Conformational dynamics of the 2:1 Co(II) calix[4]arene complexes was conditioned by the pinched cone ↔pinched cone interconversion of I (with activation Gibbs energy ΔG^≠(298K) = 40 ± 3 kJ/mol. Due to substantial temperature dependence of paramagnetic shifts, complex I can be used as model compound for designing an NMR thermosensor reagent for local temperature monitoring.     

Characterization and Bioavailability of Vitamin C Nanoliposomes Prepared by Film Evaporation-Dynamic High Pressure Microfluidization

Vitamin C nanoliposomes were prepared by combining a conventional method (film evaporation) with dynamic high pressure microfluidization. Their physicochemical characterizations (antioxidant activity, particle size, entrapment efficiency, morphology, in vitro drug release, and storage stability) and skin permeation behavior were investigated. The results showed that vitamin C nanoliposomes, having equivalent DPPH (2, 2-diphenyl-1-picrylhydrazyl) free radical scavenging capacity of pure vitamin C solution without loss of their biological activity, exhibited better storage stability at 37°C for 24 hours and at 4°C for 60 days, a more excellent sustained drug release as well as higher skin penetration rate than vitamin C liposomes.     

On the usage of NURBS as interface representation in free‐surface flows

When simulating free‐surface flows using the finite element method, there are many cases where the governing equations require information which must be derived from the available discretized geometry. Examples are curvature or normal vectors. The accurate computation of this information directly from the finite element mesh often requires a high degree of refinement—which is not necessarily required to obtain an accurate flow solution. As a remedy and an option to be able to use coarser meshes, the representation of the free surface using non‐uniform rational B‐splines (NURBS) curves or surfaces is investigated in this work. The advantages of a NURBS parameterization in comparison with the standard approach are discussed. In addition, it is explored how the pressure jump resulting from surface tension effects can be handled using doubled interface nodes. Numerical examples include the computation of surface tension in a two‐phase flow as well as the computation of normal vectors as a basis for mesh deformation methods. For these examples, the improvement of the numerical solution compared with the standard approaches on identical meshes is shown. Copyright © 2011 John Wiley & Sons, Ltd.     

伪测度是乘子的条件

设G是LCA群,S(G)是G上的Segal代数。对S(G)的每一个乘子T,已知它对应唯一一个伪测度σ,使得Tf=σ*f,f∈S(G),并且|T|=|σ|又称此σ是乘子。但对许多Segal代数说来,并不是每一个伪测度都是乘子。本文给出了伪测度是Segal代数的乘子的充分条件,此外还研究了Segal代数的最小伪测度集。     

Hulthen势与谱生成代数

本文将Hulthen势场中的S波径向方程作适当的变量变换、使其可用so(2.1)李代数求解;进而通过倾斜变换引入附加参数ω以改善解的收敛性,并给出了迭代求解的全部计算公式。     

The Perturbation of the Interface of the Two-dimensional Diffraction Problem and an Approximating Muskat Modal

ln this paper, a new transformation is found out to straighten the interface Γ_2 x = f(y), f ∈ C^{2+a}([0, a]), f_y|_y =0, δ < f < l-δ,δ > 0,δ,l=constants and a perturbation of the interface is considered for a two dimensional diffraction problem. And the existence, uniqueness and regularity of an appeoximating Muskat model are proved.     

On Linear Representations of Analytic Moufang Loops

Mathematical Notes -     

Symmetry of the Barochronous Motions of a Gas

We study the system of nonlinear differential equations which expresses the constancy of the algebraic invariants of the Jacobian matrix for smooth vector fields in three-dimensional space. This system is equivalent to the equations of gas dynamics which describe the barochronous motions of a gas (the pressure and density depend only on the time). We present the results of computation of the admissible local Lie group and construction of the general solution of the system. We mention a few new problems that arise here.     

Bivariate Free Knot Splines

We consider the least squares approximation of gridded 2D data by tensor product splines with free knots. The smoothing functional to be minimized—a generalization of the univariate Schoenberg functional—is chosen in such a way that the solution of the bivariate problem separates into the solution of a sequence of univariate problems in case of fixed knots. The resulting optimization problem is a constrained separable least squares problem with tensor product structure. Based on some ideas developed by the authors for the univariate case, an efficient method for solving the specially structured 2D problem is proposed, analyzed and tested on hand of some examples from the literature.