Asymptotic exponential cones of Metzler matrices and their use in the solution of an algebraic problem

The aim of this paper is that of investigating the asymptotic exponential cone of a single Metzler matrix, introduced in [23], and of defining and analysing the new concept of asymptotic exponential cone of a family of Metzler matrices (along a certain direction). These results will provide necessary and/or sufficient conditions for the solvability of an interesting algebraic problem that arises in the context of continuous-time positive switched systems and, specifically, in the investigation of the reachability property [21,22,25].     

Conformation dependence of DNA electrophoretic mobility in a converging channel

The electrophoresis of λ‐DNA is observed in a microscale converging channel where the center‐of‐masses trajectories of DNA molecules are tracked to measure instantaneous electrophoretic (EP) mobilities of DNA molecules of various stretch lengths and conformations. Contrary to the usual assumption that DNA mobility is a constant, independent of field and DNA length in free solution, we find DNA EP mobility varies along the axis in the contracting geometry. We correlate this mobility variation with the local stretch and conformational changes of the DNA, which are induced by the electric field gradient produced by the contraction. A “shish‐kebab” model of a rigid polymer segment is developed, which consists of aligned spheres acting as charge and drag centers. The EP mobility of the shish‐kebab is obtained by determining the electrohydrodynamic interactions of aligned spheres driven by the electric field. Multiple shish‐kebabs are then connected end‐to‐end to form a freely jointed chain model for a flexible DNA chain. DNA EP mobility is finally obtained as an ensemble average over the shish‐kebab orientations that are biased to match the overall stretch of the DNA chain. Using physically reasonable parameters, the model agrees well with experimental results for the dependence of EP mobility on stretch and conformation. We find that the magnitude of the EP mobility increases with DNA stretch, and that this increase is more pronounced for folded conformations.     

Asymptotics of the regression quantile basic solution under misspecification

We consider the asymptotic distribution of covariate values in the quantile regression basic solution under weak assumptions. A diagnostic procedure for assessing homogeneity of the conditional densities is also proposed. The research for this paper was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.     

A remark on the definitions of viscosity solutions for the integro-differential equations with Lévy operators

We prove the equivalence of the three different definitions of the viscosity solution for the integro-differential equation with the Lévy operator. The two of the definitions are known in the preceding works of the author and the others, and the last one is new. A construction of a sequence of the approximating test functions to the subsolution (or the supersolution) is indispensable for the proof, and it is done explicitly in the paper.     

Existence, upper and lower solutions and quasilinearization for singular differential equations

In this paper, we discuss existence theorems in the presenceof upper and lower solutions as well as the method of quasilinearization(QSL) for general non-linear second-order singular ordinarydifferential equations. We show the existence of solutions underthe assumption of weak continuity of the non-linear part. Ifthe non-linear part is monotone decreasing, a solution may beobtained by the QSL method as the strong limit of a quadraticallyconvergent sequence of approximate solutions. Under strongerassumptions on the linear and the non-linear parts, a solutionis quadratically bracketed between two monotone sequences ofapproximate solutions of certain related linear equations.     

Powder preparation and UV absorption properties of selected compositions in the CeO2-Y2O3 system

Several approaches have been investigated to prepare fluorite-type compositions within the (1−x) CeO₂-xYO_1.5 system. The optical properties of the resulting modified-ceria materials have been characterized in order to evaluate their potential abilities as inorganic UV absorbers. Diffuse reflectance analyses reveal a strong optical absorption between 390 and 400 nm for all substituted compositions and the spectral selectivities are estimated suitable for the targeted application. Additionally, time resolved microwave conductivity (TRMC) and phenol photodegradation analyses do not indicate any photocalatytic activity for these compositions. Aqueous colloidal suspensions of the Ce_0.7Y_0.3O_1.85 UV absorber have been carried out.     

Abstract Volterra operators

We propose a new general definition of Volterra operators. Several types of evolutionary operators, including Volterra ones in the sense of A.N. Tikhonov, satisfy this definition. For equations with generalized Volterra operators we introduce the notions of local, global, and maximally extended solutions. For solutions to nonlinear equations we formulate the existence, uniqueness, and extendability conditions. The theorems proved in this paper imply both known and new results on the solvability of concrete equations. We adduce an example of the application of obtained results to the study of the Cauchy problem for functional differential equations.     

Density, ultrasonic velocity, surface tension, excess volume and viscosity of quaternary fluid solutions

Density, ultrasonic velocity, surface tension, excess volume and viscosity of quaternary non-electrolyte solution n-pentane+tolune+n-heptane+cyclohexane has been experimentally determined at 25 °C over a wide range of composition. Assuming a quaternary fluid solution to be made of six binaries, a statistical approach of Prigogine–Flory–Patterson (PFP) theory has been extended to develop the expressions for dynamic viscosity, surface tension excess volume and ultrasonic velocity of quaternary fluid system. A reasonable agreement has been achieved between theory and experiment. An attempt has also bee made to explain the nature of molecular interactions involved in the light of excess thermodynamic functions whose sign and magnitude depend upon the chain length and size of the component fluids and also studied the role of order breakers (toluene and cyclohexane) on these properties.     

具有Radon测度初值的热敏电阻问题

本文证明具有有界非负Ｒａｌｏｎ测度初值的热敏电阻问题弱解整体存在。