Stochastic comparability and dual q-functions

In this paper we discuss the relationship and characterization of stochastic comparability, duality, and Feller–Reuter–Riley transition functions which are closely linked with each other for continuous time Markov chains. A necessary and sufficient condition for two Feller minimal transition functions to be stochastically comparable is given in terms of their density q-matrices only. Moreover, a necessary and sufficient condition under which a transition function is a dual for some stochastically monotone q-function is given in terms of, again, its density q-matrix. Finally, for a class of q-matrices, the necessary and sufficient condition for a transition function to be a Feller–Reuter–Riley transition function is also given.

Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.

Applications of Feller-Reuter-Riley transition functions

A Feller–Reuter–Riley function is a Markov transition function whose corresponding semigroup maps the set of the real-valued continuous functions vanishing at infinity into itself. The aim of this paper is to investigate applications of such functions in the dual problem, Markov branching processes, and the Williams-matrix. The remarkable property of a Feller–Reuter–Riley function is that it is a Feller minimal transition function with a stable q-matrix. By using this property we are able to prove that, in the theory of branching processes, the branching property is equivalent to the requirement that the corresponding transition function satisfies the Kolmogorov forward equations associated with a stable q-matrix. It follows that the probabilistic definition and the analytic definition for Markov branching processes are actually equivalent. Also, by using this property, together with the Resolvent Decomposition Theorem, a simple analytical proof of the Williams' existence theorem with respect to the Williams-matrix is obtained. The close link between the dual problem and the Feller–Reuter–Riley transition functions is revealed. It enables us to prove that a dual transition function must satisfy the Kolmogorov forward equations. A necessary and sufficient condition for a dual transition function satisfying the Kolmogorov backward equations is also provided.

Strong ergodicity of monotone transition functions

By revealing close links among strong ergodicity, monotone, and the Feller–Reuter–Riley (FRR) transition functions, we prove that a monotone ergodic transition function is strongly ergodic if and only if it is not FRR. An easy to check criterion for a Feller minimal monotone chain to be strongly ergodic is then obtained. We further prove that a non-minimal ergodic monotone chain is always strongly ergodic. The applications of our results are illustrated using birth-and-death processes and branching processes.

Feller transition functions, Resolvent Decomposition Theorems, and their application in unstable denumerable Markov processes

This paper surveys the recent progresses made in the field of unstable denumerable Markov processes. Emphases are laid upon methodology and applications. The important tools of Feller transition functions and Resolvent Decomposition Theorems are highlighted. Their applications particularly in unstable denumerable Markov processes with a single instantaneous state and Markov branching processes are illustrated.

Prospect for EPM application to environmental technology

EPM seems to have good prospects for the future not only in the materials processing but also in environmental technologies by the help of superior features like contactless processing, clean heating and melting, and good controllability. In the present paper, the authors commentate on the possibility of EPM to avoid environmental issues of energy, resources and hazardous wastes by the use of the functions of Lorentz force and Joule heating. Firstly, the present situation and future trend of electric power generation is outlined, and then some examples of the application of EPM to environmental technologies are introduced, which have been performed by the author’s group. Examples are as follows: production of spherical solar cell from a liquid jet by using intermittent electromagnetic force; fabrication of semi-solid Al-Si slurry for die-casting of vehicle-parts to reduce the weight of vehicle; electromagnetic separation of nonmetallic inclusions from liquid Al scrap and its application to the fabrication of partially particle-reinforced aluminum alloy; electromagnetic melting of hazardous wastes from power plants to stabilize wastes in glass state.

Central nervous system drugs: Low temperature X-ray structures of (I) the base 5-(2,3-dichlorophenyl)-2,4-diamino-6-fluoromethyl-pyrimidine (4030W92) and (II) 5-(2,6-dichlorophenyl)-1-H-2,4-diamino-6-methyl-pyrimidine methanesulphonic acid salt (227C89)

The X-ray crystal structures of (I), the base 4030W92, 5-(2,3-dichlorophenyl)-2,4-diamino-6-fluoromethyl-pyrimidine, C11H9Cl2FN4, and (II) 227C89, the methanesulphonic acid salt of 5-(2,6-dichlorophenyl)-1-H-2,4-diamino-6-methyl-pyrimidine, C11H11Cl2N4 center dot CH3O3S, have been carried out at low temperature. A detailed comparison of the two structures is given. Structure (I) is non-centrosymmetric, crystallizing in space group P2(1) with unit cell a = 10.821(3), b = 8.290(3), c = 13.819(4) angstrom, beta = 105.980(6)degrees, V = 1191.8(6) angstrom(3), Z = 4 (two molecules per asymmetric unit) and density (calculated) = 1.600 mg/m(3). Structure (II) crystallizes in the triclinic space group P (1) over bar with unit cell a = 7.686(2), b = 8.233(2), c = 12.234(2) angstrom, alpha = 78.379(4), beta = 87.195(4), gamma = 86.811(4)degrees, V = 756.6(2) angstrom(3), Z = 2, density (calculated) = 1.603 mg/m(3). Final R indices [I > 2sigma(I)] are R1 = 0.0572, wR2 = 0.1003 for (I) and R1 = 0.0558, wR2 = 0.0982 for (II). R indices (all data) are R1 = 0.0983, wR2 = 0.1116 for (I) and R1 = 0.1009, wR2 = 0.1117 for (II). 5- Phenyl-2,4 diaminopyrimidine and 6-phenyl-1,2,4 triazine derivatives, which include lamotrigine (3,5-diamino-6-(2,3-dichlorophenyl)-1,2,4-triazine), have been investigated for some time for their effects on the central nervous system. The three dimensional structures reported here form part of a newly developed data base for the detailed investigation of members of this structural series and their biological activities.

Understanding changes in cardiovascular pathophysiology

Cardiovascular pathophysiological changes, such as hypertension and enlarged ventricles, reflect the altered functions of the heart and its circulation during ill-health. This article examines the normal and altered anatomy of the cardiac valves, the contractile elements and enzymes of the myocardium, the significance of the different factors associated with cardiac output, and the role of the autonomic nervous system in the heart beat. It also explores how certain diseases alter these functions and result in cardiac symptoms. Nurses can benefit from knowledge of these specific changes, for example, by being able to ask relevant questions in order to ascertain the nature of a patients condition, by being able to take an effective patient history and by being able to read diagnostic results, such as electrocardiograms and cardiac enzyme results. All this will help nurses to promote sound cardiac care based on a physiological rationale.