A Suprasystem of Probability Distributions

A set of differential equations is described whose solutions represent a general system of probability distribution functions. Previously reported systems of such distribution functions are special cases of this general system. The differential equations can be used to represent distribution functions and generate their related statistics in cases for which no simple formula for the distribution is known. The generality of this suprasystem of distribution functions and its potential utility are discussed.     

A Spatially Continuous Model of Carbohydrate Digestion and Transport Processes in the Colon

A spatially continuous mathematical model of transport processes, anaerobic digestion and microbial complexity as would be expected in the human colon is presented. The model is a system of first-order partial differential equations with context determined number of dependent variables, and stiff, non-linear source terms. Numerical simulation of the model is used to elucidate information about the colon-microbiota complex. It is found that the composition of materials on outflow of the model does not well-describe the composition of material in other model locations, and inferences using outflow data varies according to model reactor representation. Additionally, increased microbial complexity allows the total microbial community to withstand major system perturbations in diet and community structure. However, distribution of strains and functional groups within the microbial community can be modified depending on perturbation length and microbial kinetic parameters. Preliminary model extensions and potential investigative opportunities using the computational model are discussed.     

A Likelihood Ratio Test of the Equality of Paired Survival Data with Censoring

A test is developed to determine whether the mean survival times are equal when dealing with paired survival data. We assume the data follow a bivariate exponential distribution for which the variables are conditionally independent. The unconditional distribution is derived in which the distribution of the nuissance variable is general. A method based on the likelihood ratio is derived to obtain the test. The data are allowed to have both left and right censoring.     

A Fortran Program for Evaluation of the Effectiveness Factor of Biocatalysts in the Presence of External and Internal Diffusional Limitations

A Fortran program called SPEFF for evaluation of the effectiveness factor of immobilized enzyme preparations of spherical form in the presence of external and internal mass transfer resistances is described, and a listing of the program is given. Enzyme distribution in the bioparticle may be uniform or nonuniform. In the latter case the enzyme distribution is approximated by fifth-order polynomial. In the program differential equations are replaced by the system of non-linear algebraic equations, and the latter are solved by Newton iteration technique. The program is developed for Michaelis-Menten kinetics with allowance for competitive product inhibition and substrate inhibition. After slight modifications the program can be used for computation of the effectiveness factor of a membrane with an immobilized enzyme, or in the case when the enzyme kinetics are more complex. A typical run on a PDP-11/45 computer took 10-20 seconds. A typical computation time in the case of IBM-compatible TURBO PC was 15-30 seconds.     

Immunohistochemical demonstration of the distribution of serotonin neurons in the brainstem of the rat and cat

The morphological characteristics and distribution of the somata of serotonin-containing neurons in the brainstem of rats and cats were studied by use of the peroxidase-anti peroxidase (PAP) immunohistochemical method employing highly specific antibodies to serotonin. Antibodies were raised in rabbits against an antigen prepared by coupling serotonin to bovine thyroglobulin and using formaldehyde as the coupling reagent. The distribution pattern of serotonin neurons observed in the present material is essentially in agreement with that described by other investigators who used the Falck-Hillarp method. In addition, this immunohistochemical technique revealed serotonin-containing perikarya in the following regions: 1) the periaqueductal gray, especially lateral to the nucleus raphe dorsalis, 2) the nucleus interpeduncularis, 3) the nucleus parabrachialis ventralis and dorsalis, 4) the field of the lemniscus lateralis, and 5) the reticular formation of the pons and medulla oblongata. The described immunohistochemical procedure makes it possible to study central serotonin neurons in detail without pharmacological pretreatment. The wide distribution of serotonin neurons demonstrated in this study should be considered when interpreting experiments dealing with the serotonin system.     

Some notes on the trichoptera of standing waters in Africa,mainly south of the Zambezi

Summary In this paper records of Trichoptera in literature dealing with the standing waters of Africa south of the Zambezi, and from the relevant collections of material, are brought together and compared with those from elsewhere in the Ethiopian Region. The Trichopterous fauna of different types of standing waters in Southern Africa is described, and reasons for the lack of variety in the fauna are suggested. One of the main restrictive factors in their distribution appears to be the hydrogen ion concentration in the water, or some other factor controlled by it.National Institute for Water ResearchRead at the Annual Congress of the Limnological Society of Southern Africa.     

Time-accurate,parallel, multi-zone,multi-block solver to study the human cardio-vascular system

A parallel, time-accurate flow solver is devised to study the human cardio-vascular system. The solver is capable of dealing with moving boundaries and moving grids. It is designed to handle complex, three-dimensional vascular systems. The computational domain is divided into multiple block subdomains. At each cross section the plane is divided into twelve sub-zones to allow flexibility for handling complex geometries and, if needed, appropriate parallel data partitioning. The unsteady, three-dimensional, incompressible Navier-Stokes equations are solved numerically. A second-order in time and third-order upwind finite volume method for solving time-accurate incompressible flows based on pseudo-compressibility and dual time-stepping technique is used. For parallel execution, the flow domain is partitioned. Communication between the subdomains of the flow on Riken's VPP/700E supercomputer is implemented using MPI message-passing library. A series of numerical simulations of biologically relevant flows is used to validate this code.     

Effects of elastic property of the wall on flow characteristics through arterial stenoses

Hemodynamic characteristics of blood flow through arterial stenoses are numerically investigated in this work. The blood is assumed as a Newtonian fluid and the pulsatile nature of flow is modeled by using measured values of the flowrate and pressure for the canine femoral artery. An isotropic elastic and incompressible material is assumed for the wall at each axial section, but a non-uniform distribution of the shear modulus in axial direction is used to model the high stiffness of the wall at the stenosis location. Full Navier equations for a thick wall are used as the governing equations for the wall displacements. A continuous grid extending over the flow field and the wall is considered and governing equations are transformed for use in the computational domain. Discretized forms of the transformed wall and flow equations, which are coupled through the boundary conditions at their interface, are obtained by control volume method and simultaneously solved using the well-known SIMPLER algorithm. To study the effects of wall deformability, solutions are obtained for both rigid and elastic walls. The results indicate that deformability of the wall causes an increase in the time average of pressure drop, but a decrease in the maximum wall shear stress. Displacement and stress distributions in the wall are presented.     

Modelling of pattern formation and oscillations in pH and transmembrane potential near the cell membrane of Chara corallina

A mathematical model of potencial-dependent proton transfer across the membrane of Chara corallina cells is considered. To construct the model, partial differential equations describing the system dynamics in time and in space were used. The variables of the model are the proton concentration and membrane potential. The model describes the experimentally observed inhomogeneous distribution of transmembrane potential and pH along the membrane and oscillations of the potential and pH in time. A mechanism of the distribution of pH and membrane potential along the Chara corallina cell is suggested.     

Nonuniformity of the chemical composition of a capillary discharge plasma

A steady-state distribution of the concentration of two ion species in a capillary discharge plasma is studied using MHD equations for a plasma with a spatially nonuniform, time-dependent chemical composition. In our case, the set of equations is significantly simplified because of the steady-state character and symmetry of the problem. Even with such simplification, however, some results could be obtained only by numerical integration. The factors affecting the distribution of heavy ions are studied. It is shown that the distribution of the heavy impurity over the discharge cross section can be much more nonuniform than the distribution of the main component (hydrogen). A simple criterion for such a nonuniformity is obtained.     

A critical review of mathematical models and data used in diabetology

The literature dealing with mathematical modelling for diabetes is abundant. During the last decades, a variety of models have been devoted to different aspects of diabetes, including glucose and insulin dynamics, management and complications prevention, cost and cost-effectiveness of strategies and epidemiology of diabetes in general. Several reviews are published regularly on mathematical models used for specific aspects of diabetes. In the present paper we propose a global overview of mathematical models dealing with many aspects of diabetes and using various tools. The review includes, side by side, models which are simple and/or comprehensive; deterministic and/or stochastic; continuous and/or discrete; using ordinary differential equations, partial differential equations, optimal control theory, integral equations, matrix analysis and computer algorithms.     

A simple method for the determination of DNA molecular weight distribution

A method is described for the molecular weight distribution of DNA which is determined from sedimentation-velocity analysis. Knowing the distribution of sedimentation coefficients for a single DNA concentration it is possible to extrapolate such a distribution to infinite dilution of the solute in a simple way. Two versions (using two or three terms of a series) of extrapolating equations are considered and discussed in detail. The sedimentation coefficients distribution calculated from these equations differs only insignificantly with that obtained in a conventional way.     

A functional model of the rat kidney

Summary A mathematical model of the nephron was developed by writing a set of material balance equations for the flow of urea, salt and water along the length of the nephron. The geometric proportions have been elaborated in a foregoing study and are taken here as a basis, in particular the model configuration of the collecting duct system. The medullary interstitial solute concentration profiles are taken to increase linearly in outer and inner zone. The several transepithelial fluxes are driven by diffusion, osmosis, solvent drag and active transport. The development of osmotic gradient in the inner medulla is taken here to be caused by active secretion of salt into the descending limb of Henle's loop. The parameters in the flux equations for all parts of the nephron and the concentration values at the end of each tubular section are determined by collecting and averaging the values given in literature and by extrapolating the measurement data.The simulation of the model equations with these averaged parameters resulted in concentration profiles which at the ends of the several tubular sections were consistent with the values observed in experimental investigations.This work was supported by the Deutsche Forschungsgemeinschaft.     

A reappraisal of the Palaeopantopoda with description of a species from the Jurassic

The Devonian fossil Palaeoisopus appears, in the light of recent evidence from newly found specimens, to be much nearer extant pycnogonids than previously surmised. The fossil record of the Pycnogonida is extended to the Jurassic on the basis of a long overlooked Solenhofen example. Most of the specimens ascribed to the common Solenhofen Phalangites cannot be pycnogonids, but it is possible that we are dealing with a complex of superficially similar fossils. A revision of the classification of the fossil pycnogonids (Order Palaeopantopoda) is suggested in the light of this new material.     

木虱次目化石研究进展

截止目前,全世界古昆虫学者共发表30余篇关于世界木虱次目Psyllidomorpha昆虫化石的文章。共记载12科、64属、123种,分布于14个国家。本文统计了世界已记载的木虱次目的化石名录、地理分布及地质年代,初步总结世界木虱次目昆虫化石的组成特征,提出木虱次目化石研究中存在的问题,及对未来研究的展望。     

A Simple Phenomenological Theory of Tissue Growth

A simple phenomenological framework for modeling growth of living tissues is proposed. Growth is defined as a change of mass and configuration of the tissue. Tissue is considered as an open system where mass conservation is violated and the full-scale mass balance is applied. A possible structure of constitutive equations is discussed with reference tosimple growing materials. 'Thermoelastic' formulation of the simple growing material is specified. Within this framework traction free growth of cylindrical and spherical bodies is examined. It is shown that the theory accommodates the case where stresses are not generated in uniform volumetric growth. It is also found that surface growth corresponds to aboundary layersolution of the governing equations. This finding proves the ability of continuum mechanics to describe surface growth. The latter is contrary to the usual use of purely kinematical theories, which do not involve balance and constitutive equations, for treating surface growth.     

The flux-force relations across complex membranes with active transport

Equations are derived for the total material flux, and the total electric current flux, across a complex membrane system with active transport. The equations describe the fluxes as linear functions of forces across the system, and specifically of electrical potential, hydrostatic pressure, chemical potentials, and active transport rates. The equations can be simplified for experimental studies by making one or more of the forces equal to zero. The osmotic pressure difference across a membrane system is shown to be a function of the electrical potential and chemical potential differences and of the active transport rates. The transmembrane potential is shown to be the sum of a diffusion potential and an active transport potential. A simple equation is derived describing the current across a membrane as a linear function of the electrical potential and the active transport rate. Specific examples of the application of the equations to nerve membrane potentials are considered.     

Bibliography on the genus Marenzelleria and its geographical distribution, principal topics and nomenclature

A bibliography is given for the genus Marenzelleria. All together, 236 publications were found dealing with M. viridis, M. wireni and M. jonesi and their synonyms. The contents of the publications are briefly reviewed in tabular form identifying the nomenclature used, the geographical distribution and the topic of the paper in each case.     

Nonlocal equation for the symmetric part of the electron distribution function in an inhomogeneous plasma

A nonlocal kinetic equation is derived for the symmetric part of the distribution function of suprathermal electrons. It is shown that Albritton equations are merely local approximations to the total kinetic equation. Even in the simplest situation, the local approximations of the nonlocal effects are impossible to construct because of the interdependence of the variables. A self-similar solution to the equations under study is proposed.