Generalized Topological Representation for Complete Join-Semilattices

This paper describes a generalization of the Papert–Papert–Isbell adjunction between topological spaces and frames to a generalized one between the category of generalized topological spaces and the category of complete join-semilattices. Within these categories we aim to study certain separation axioms in a categorical point of view.     

Time-dependent behaviors of a FGPM hollow sphere under the coupling of multi-fields

This paper presents an analytical solution for time-dependent behaviors of a hollow sphere made of functionally graded piezoelectric material (FGPM) under the coupling of multi-fields. Material properties, electric parameters, permeability, thermal conductivity and creep parameters vary smoothly through the radial direction of the FGPM spherical structure according to a simple power-law. Using equations of equilibrium, stress–strain and strain-displacement in a differential equation, containing creep strains, for displacement are obtained. Firstly, ignoring creep strains in the differential equation, a closed form solution for the initial electromagnetothermoelastic stresses at zero time is presented, and considering Von Mises stress balance equation, the effective electromagnetothermoelastic stresses are also presented. Secondly, considering only creep strains, creep stress rates are obtained by using the Prandtl–Reuss equations and Norton’s law. Finally, time-dependent creep stress redistributions at any time t_i are obtained iteratively. The aim of this research is to understand the effects of the graded index on creep behavior of hollow spherical structures and design optimum FGPM hollow spherical structures.     

Effect of magneto-thermo-viscoelasticity in an unbounded body with a spherical cavity subjected to a harmonically varying temperature without energy dissipation

The present work is devoted to study effects of the thermally induced vibration, magnetic field and viscoelasticity in an isotropic homogeneous unbounded body with a spherical cavity. The GN model of thermoelasticity without energy dissipation is applied. The closed form solutions for distributions of displacement, temperature and radial and hoop stresses are illustrated. The boundary conditions for the temperature and mechanical and Maxwell’s stresses are employed. The solutions valid in the case of small frequency are deduced and the results are compared with the corresponding results obtained in other generalized thermoelasticity theories. The results obtained are calculated for a copper material and presented graphically. It’s deduced that the magnetic field, viscosity and thermally induced vibration are very pronounced on displacement, temperature and stresses.     

22号初等元胞自动机的极限语言复杂性

§1Introduction Thetaskofthispaperistosolvetheproblemproposedin[1],i.e.,toexplorethe complexityoflimitset,orequivalently,limitlanguageoftheelementarycellularautomaton ofrule22bythetoolsofformallanguagetheory.Cellularautomata(abbreviatedasCA),asmathematicalmodelsforcomplexnatural systemscontaininglargenumbersofsimpleidenticalcomponentswithlocalinteractions,havebeenwidelyusedinphysical,biological,chemicalandcomputationalsystems[2].Despitetheirsimpleconstruction,someCAcandisplayveryrichandcompl…     

The Positive Lightness of Digraphs,Embeddable in a Surface,without 4-Cycles

The positive lightness of a digraph is the minimum arc value, where the value of an arc is the maximum of the in-degrees of its terminal vertices. We determine upper bounds for the positive lightness of digraphs with nonzero minimum in-degree and a given girth $k⩾5$ which can be embedded in a surface S. These bounds are tight for surfaces of nonnegative Euler characteristics. We further obtain bounds for classes of graphs where 3-cycles are permitted.     

Analytical method based on Walsh function combined with orthogonal polynomial for fractional transport equation

In this paper a novel method based on Walsh function combined with a Chebyshev polynomials of the first kind was applied for the resolution of fractional transport equation in three-dimensions. A specific application of the method is discussed.     

Dynamic changes of nucleolar DNA configuration and distribution during the cell cycle in Allium sativum cells

To investigate the correlation between subnucleolar structure and function, the precise distribution and configuration of nucleolar DNA during the cell cycle of Allium sativum were determined using the NAMA-Ur DNA-specific staining technique. We showed that nucleolar DNA is present in two forms: compacted chromatin clumps and a decondensed DNA cloud. The form of the DNA within the nucleolus varied greatly as the cell cycle progressed. During telophase, chromosomes extended into the prenucleolar body. In early G1 phase, DNA was only located in the fibrillar centers in the form of the condensed chromatin clump, while in mid-G1, S and G2 phases, the two forms of DNA were distributed in the fibrillar centers (FC) and dense fibrillar component (DFC). In prophase of mitosis, nucleolar DNA, along with FC and DFC, was linked into a network structure and condensed into a large chromatin clump. The area of the DNA cloud in the dense fibrillar component changed during different phases of the cell cycle. Our results demonstrated that the configuration of nucleolar DNA undergoes a series of decondensations and condensations during the cell cycle to fulfill the function of the nucleoli during the different phases.     

Hopf bifurcation analysis in a synaptically coupled FHN neuron model with delays

This paper presents an investigation of stability and Hopf bifurcation of the synaptically coupled nonidentical FHN model with two time delays. We first consider the existence of local Hopf bifurcations, by regarding the sum of the two delays as a parameter, then derive explicit formulas for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions, using the normal form method and center manifold theory. Finally, numerical simulations are carried out for supporting the theoretical analysis.     

Introducing Weingarten cyclic surfaces in R3

In this paper, Cyclic surfaces are introduced using the foliation of circles of curvature of a space curve. The conditions on a space curve such that these cyclic surfaces are of type Weingarten surfaces or HK-quadric surfaces are obtained. Finally, some examples are given and plotted.