Effect of varying two key parameters in simulating evacuation for a dormitory in China

Student dormitories are both living and resting areas for students in their spare time. There are many small rooms in the dormitories. And the students are distributed densely in the dormitories. High occupant density is the main characteristic of student dormitories. Once there is an accident, such as fire or earthquake, the losses will be cruel. Computer evacuation models developed overseas are commonly applied in working out safety management schemes. The average minimum widths of corridor and exit are the two key parameters affecting the evacuation for the dormitory. The effect of varying these two parameters will be studied in this paper by taking a dormitory in our university as an example. Evacuation performance is predicted with the software FDS + Evac. The default values in the software are used and adjusted through a field survey. The effect of varying either of the two parameters is discussed. It is found that the simulated results agree well with the experimental results. From our study it seems that the evacuation time is not in proportion to the evacuation distance. And we also named a phenomenon of “the closer is not the faster”. For the building researched in this article, a corridor width of 3 m is the most appropriate. And the suitable exit width of the dormitory for evacuation is about 2.5 to 3 m. The number of people has great influence on the walking speed of people. The purpose of this study is to optimize the building, and to make the building in favor of personnel evacuation. Then the damage could be minimized.     

Global analysis of multiple routes of disease transmission on heterogeneous networks

In this paper, we propose and study an SIS epidemic model with multiple transmission routes on heterogeneous networks. We focus on the dynamical evolution of the prevalence. Through mathematical analysis, we obtain the basic reproduction number _R0$R_0$ by investigating the local stability of the disease-free equilibrium and also investigate the effects of various immunization schemes on disease spread. We further obtain that the disease will die out independent of the initial infections if the basic reproduction number is less than one, otherwise if the basic reproduction number is larger than one, the system converges to a unique endemic equilibrium, which is globally stable and thus the disease persists in the population. Our theoretical results are conformed by a series of numerical simulations and suggest a promising way for the control of infectious diseases with multiple routes.     

On number system constructions

We investigate various number system constructions. After summarizing earlier results we prove that for a given lattice Λ and expansive matrix M: Λ → Λ if ρ(M ⁻¹) < 1/2 then there always exists a suitable digit set D for which (Λ, M, D) is a number system. Here ρ means the spectral radius of M ⁻¹. We shall prove further that if the polynomial f(x) = c ₀ + c ₁ x + ··· + c _k x ^k ∈ Z[x], c _k = 1 satisfies the condition |c ₀| > 2 Σ _i=1 ^k |c _i | then there is a suitable digit set D for which (Z ^k , M, D) is a number system, where M is the companion matrix of f(x). The research was supported by OTKA-T043657 and Bolyai Fellowship Committee.     

Anelastic Approximation as a Singular Limit of the Compressible Navier–Stokes System

Considering compressible Navier–Stokes system in a slab geometry in the regime when both Mach and Froude numbers vanish at the same rate, we study the behavior of corresponding weak solutions, that are known to exist globally-in-time (for large data). We establish their convergence to a solution of the so-called anelastic approximation when the limit flow is stratified, i.e., the limit density depends effectively on the vertical coordinate.     

Analysis of a conducting fluid in a thin annulus with rotating insulated walls under radial magnetic effect

This work considers an electrically conducting fluid filled between two concentric cylindrical walls relatively close to each other. A theoretical solution for the steady Taylor–Couette flow between these two electrically insulated rotating cylinders under the influence of a radial magnetic field is provided in this work. By solving the appropriate set of governing equations simultaneously, the profiles of fluid tangential velocity component and induced magnetic field were obtained as complicated functions involving the modified Bessel functions of the first and second kinds of the first-order in terms of radial coordinates and Hartmann number. A computational study was also performed to validate the present theoretical solution. The analytical and computational results are identical when Ha = 1 while these results only slightly deviate from each other as Ha increases. Current results show that, the presence of the external magnetic field causes the flow close to the slower cylinder to accelerate while that close to the faster cylinder to decelerate. This has clearly implied the fact that an external magnetic field tends to make the velocity distribution across the inner and outer cylinders more uniform.     

A grey relational projection method for multi-attribute decision making based on intuitionistic trapezoidal fuzzy number

With respect to multiple attribute decision making (MADM) problems in which the attribute value takes the form of intuitionistic trapezoidal fuzzy number, and the attribute weight is unknown, a new decision making analysis methods are developed. Firstly, some operational laws and expected values of intuitionistic trapezoidal fuzzy numbers, and distance between two intuitionistic trapezoidal fuzzy numbers, are introduced. Then information entropy method is used to determine the attribute weight, and the grey relational projection method combined grey relational analysis method and projection method is proposed, and to rank the alternatives are done by the relative closeness to PIS which combines grey relational projection values from the positive ideal solution and negative ideal solution to each alternative. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Small perturbations and pairs of matrices that have the same immanent

We study the behaviour of the covering number of an element of a family of vectors under small perturbations. We apply this study to obtain results on the pairs of matrices that have the same immanent.