On the speed of a cookie random walk

We consider the model of the one-dimensional cookie random walk when the initial cookie distribution is spatially uniform and the number of cookies per site is finite. We give a criterion to decide whether the limiting speed of the walk is non-zero. In particular, we show that a positive speed may be obtained for just three cookies per site. We also prove a result on the continuity of the speed with respect to the initial cookie distribution.      

Detection of copper(II) sulfate’s uniformity and its thermal behavior in flammability of cotton fabric

Blue vitriol (copper(II) sulfate pentahydrate), CuSO₄·5H₂O has been chosen and investigated for its effectiveness as a flame-retardant, when impregnated into cotton fabric (cotton with a plain structure; woven 180 g m⁻², with 22 numbers of yarns per 10 mm). Using the vertical flame test, the extent of resistance to burning of the specimens has been determined. The impregnation was accomplished via dipping and stirring of bone-dried, weighed fabrics into the individual and suitable concentrations of the salt at room temperature. Afterwards the samples were squeeze rolled and dried horizontally at 110°C for 30 min in an oven and cooled in a desiccator and reweighed with an analytical precision. They were then kept under ordinary conditions overnight prior the fulfillment of the vertical flame test. The efficient quantities of the aforesaid salt expressed in g per 100 g dry fabric have been determined in an average figure of 12.75%. Estimation of uniformity in a selected sample was carried out via a spectrophotometer and results are in favor of the heterogeneous distribution of the salt in the fabric’s middle sectors. However initial and final parts of specimen showed to be rather uniformed. Thermogravimetric analysis of the pure cotton and the treated ones with insufficient and effective amounts of the salt were fulfilled and their thermograms were compared and commented. The results obtained for the effect of copper(II) sulfate comply with ‘The Dust or Wall Effect Theory’. This action is also assigned to the condensed phase retardation.     

A complete class for linear estimation in a general linear model

Summary It is shown that in linear estimation both unbiased and biased, all unique (up to equivalence with respect to risk) locally best estimators and their limits constitute a complete class.     

A UNIVERSAL APPROACH FOR CONTINUOUS OR DISCRETE NONLINEAR PROGRAMMINGS WITH MULTIPLE VARIABLES AND CONSTRAINTS

IntroductionExtensive research works have been published for solving nonlinear mathematicprogramming problems.Nonetheless,it is still difficult to find an effective and universalapproach for general programming problems with multiple design variables and …     

Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

Prediction of retention indices. VI: Isothermal and temperature-programmed retention indices,methylene value,functionality constant,electronic and steric effects

The Kováts retention index system with n-alkanes as reference standards has properties not fully explored when single, isolated or stand-alone analytes are analyzed by isothermal gas chromatography. When a homologous series of analytes are analyzed by either linear or non-linear temperature-programmed gas chromatography, the retention data of the entire series can be treated systematically to produce an I vs. Z plot that is linear, thereby giving insight into the relationship between chemical structure and retention index. Dead time t_M is both instrument and temperature dependent. With no dead time t_M adjustment, the retention indices of analytes calculated from experimental retention times by the method of either linear or logarithmic interpolation give statistically identical values. Linear regression analysis of the data shows the slope as methylene value (A) and intercept as functionality constant or group retention factor (GRF) of the homologous series. The A and (GRF) values vary with chemical structures, intermolecular electronic and steric interactions, and polarity of column liquid phases, and can link gas chromatographic retention index to chemical structure. Examples of the influence of molecular electronic effects and steric effects on retention index are given and discussed.     

Exploring the mechanisms of renoprotection against progressive glomerulosclerosis

In this review, I introduce the strategy developed by our laboratory to explore the mechanisms of renoprotection against progressive glomerulosclerosis leading to renal death. First, I describe the experimental rat model in which disturbances of vascular regeneration and glomerular hemodynamics lead to irreversible glomerulosclerosis. Second, I discuss the possible mechanisms determining the progression of glomerulosclerosis and introduce a new imaging system based on intravital confocal laser scanning microscopy. Third, I provide an in-depth review of the regulatory glomerular hemodynamics at the cellular and molecular levels while focusing on the pivotal role of Ca(2+)-dependent gap junctional intercellular communication in coordinating the behavior of mesangial cells. Last, I show that local delivery of renoprotective agents, in combination with diagnostic imaging of the renal microvasculature, allows the evaluation of the therapeutic effects of angiotensin II receptor and cyclooxygenase activity local blockade on the progression of glomerulosclerosis, which would otherwise lead to renal death.     

Improved blowup results for the Euler and Euler–Poisson equations with repulsive forces

Some results are presented on the formation of singularities in the solutions of the radially-symmetric N-dimensional Euler or Euler–Poisson equations with repulsive forces. Based on the integration method of M.W. Yuen, we generalize the blowup results with constant compact radius R   of solutions to the case with general compact radius R(t)$R(t)$ and to the case with no compact support restriction.