Coxeter Transformation and Quasiquivers

Mathematical Notes -     

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {X_n, n≥1} be a strictly stationary sequence of random variables, whichare either associated or negatively associated, f(·) be their common density. In this paper,the author shows a central limit theorem for a kernel estimate of f(·) under certain regularconditions.     

Structural properties of charged diblock copolymer solutions

Aqueous micellar solutions of ionic/neutral block copolymers have been studied by light scattering, small angle neutron scattering and small angle X-ray scattering. We made use of a polymer comprised of a short hydrophobic block (polyethylene-propylene) PEP and of a long polyelectrolytic block (polystyrene-sulfonate) PSSNa which has been shown previously to micellize in water. The apparent polydispersity of these micelles is studied in detail, showing the existence of a few large aggregates coexisting with the population of micelles. Solutions of micelles are found to order above some threshold in polymer concentration. The order is liquid-like, as demonstrated by the evolution with concentration of the peak observed in the structure factor (), and the degree of order is found to be identical over a large range of concentrations (up to 20 wt%). Consistent values of the aggregation number of the micelles are found by independent methods. The effect of salt addition on the order is found to be weak. Received: 19 June 1997 / Received in final form: 4 September 1997 / Accepted: 9 October 1997     

Thermodynamics of molecular interactions in ethyl iodide+toluene mixtures

The excess Gibb's free energy of mixing, G^E, for ethyl iodide+toluene at 25°C have been obtained from the measured vapor pressuure data. The H^E and G^E values for ethyl iodide+toluene are positive throughout the ethyl iodide concentration range and G^E>H^E. The results have been analyzed in terms of Flory and ideal associated model theory of nonelectrolyte solutions. It has been observed that the ideal associated model approach which assumes the presence of AN and A₂B molecular species describes well (within±10 J-mol^–1 in the worst case) the general dependence of H^E on X_A (mole fraction of ethyl iodide) over the whole composition range for ethyl iodide+toluene mixtures. The equilibrium constants for A+A AB and 2A+BA₂B reactions along with the enthalpies of formation of AB and A₂B molecular species have been calculated.     

Effect of cooperativity on the O-H stretching force constant in associated water species

CNDO/force calculations have been employed to calculate the O-H stretching force constants for various structures of associated water species such as water-dimethylether, water-acetonitrile, water-lithium fluoride, linear and cyclic water polymers. The variation in the O-H stretching force constant in A_m… O-H… D_n species where A_m and D_n represent, respectively,m number of electron-acceptor andn number of electron-donor molecules, is explained on the basis of the cooperativity effect. With increasing electron-acceptor power of A and electron-donor power of D, the hydrogen-bonded O-H stretching force constant is significantly reduced. The results obtained in these studies are in general agreement with experimental observations reported earlier.     

Synthesis of tumor-associated glycopeptide antigens for the development of tumor-selective vaccines

In contrast to normal cells, the glycoprotein profile on epithelial tumor cells is distinctly altered. Due to an incomplete formation of the glycan side-chains resulting from a premature sialylation, additional peptide epitopes become accessible to the immune system in mucin-type glycoproteins on tumor cells. These tumor-associated structure alterations constitute the basis for a selective immunological attack on cancer cells. For the construction of immunostimulating antigens, glycopeptide partial structures from the mucins MUC1 and MUC4 carrying the tumor-associated sialyl-T(N), alpha2,6-sialyl-T and alpha2,3-sialyl-T antigens have been synthesized. Employing different linkers such as the allylic HYCRON or the fluoride-sensitive PTMSEL anchor, the antigenic glycopeptide structures were constructed on the solid phase utilizing pre-assembled glycosyl amino acid building blocks prepared in solution by convergent chemical or chemoenzymatic strategies. The proliferation of cytotoxic T cells has been induced applying a construct composed of a sialyl-T(N) MUC1-glycopeptide conjugated with a tetanus toxin T cell peptide epitope.     

Complete Moment Convergence for the Dependent Linear Processes with Random Coefficients

In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form     

Membranes,peptides, and disease: Unraveling the mechanisms of viral proteins with solid state nuclear magnetic resonance spectroscopy

The interplay between peptides and lipid bilayers drives crucial biological processes. For example, a critical step in the replication cycle of enveloped viruses is the fusion of the viral membrane and host cell endosomal membrane, and these fusion events are controlled by viral fusion peptides. Thus such membrane-interacting peptides are of considerable interest as potential pharmacological targets. Deeper insight is needed into the mechanisms by which fusion peptides and other viral peptides modulate their surrounding membrane environment, and also how the particular membrane environment modulates the structure and activity of these peptides. An important step toward understanding these processes is to characterize the structure of viral peptides in environments that are as biologically relevant as possible. Solid state nuclear magnetic resonance (ssNMR) is uniquely well suited to provide atomic level information on the structure and dynamics of both membrane-associated peptides as well as the lipid bilayer itself; further ssNMR can delineate the contribution of specific membrane components, such as cholesterol, or changing cellular conditions, such as a decrease in pH on membrane-associating peptides. This paper highlights recent advances in the study of three types of membrane associated viral peptides by ssNMR to illustrate the more general power of ssNMR in addressing important biological questions involving membrane proteins.     

Numerical simulations of negatively buoyant jets in an immiscible fluid using the Particle Finite Element Method

Negatively buoyant jets consist in a dense fluid injected vertically upward into a lighter ambient fluid. The numerical simulation of this kind of buoyancy‐driven flows is challenging as it involves multiple fluids with different physical properties. In the case of immiscible fluids, it requires, in addition, to track the motion of the interface between fluids and accurately represent the discontinuities of the flow variables. In this paper, we investigate numerically the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid using the Particle Finite Element Method and compare the two‐dimensional numerical results with experiments on the injection of a jet of dyed water through a nozzle in the base of a cylindrical tank containing rapeseed oil. In both simulations and experiments, the fountain inlet flow velocity and nozzle diameter have been varied to cover a wide range of Froude Fr and Reynolds Re numbers ( 0.1 < Fr < 30, 8 < Re < 1350), reproducing both weak and strong laminar fountains. The flow behaviors observed for the different numerical simulations fit in the regime map based on the Re and Fr values of the experiments, and the maximum fountain height is in good agreement with the experimental observations, suggesting that particle finite element method is a useful tool for the study of immiscible two‐fluid systems. Copyright © 2011 John Wiley & Sons, Ltd.     

扩张环上的$\Sigma$-相伴素理想

作为对相伴素理想与幂零相伴素理想的推广,我们在本文中引进了$\Sigma$-相伴素理想的定义,探讨了$\Sigma$-相伴素理想的基本性质,证明了Ore扩张环$R[x;\alpha,\delta]$、斜洛朗多项式环$R[x,x^{-1};\alpha]$及斜幂级数环$R[[x;\alpha]]$的$\Sigma$-相伴素理想都分别可以用环$R$的$\Sigma$-相伴素理想来刻画,从而将相伴素理想与幂零相伴素理想的一些已有结论推广到更一般的情形.