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.     

Possible numbers of ones in the squares of 0–1 matrices with a given rank

For a symmetric 0–1 matrix A, we give the number of ones in A ² when rank(A) = 1, 2, and give the maximal number of ones in A ² when rank(A) = k (3 ≤ k ≤ n). The sufficient and necessary condition under which the maximal number is achieved is also obtained. For generic 0–1 matrices, we only study the cases of rank 1 and rank 2.     

MATHEMATICAL ANALYSIS OF WEST NILE VIRUS MODEL WITH DISCRETE DELAYS

The paper presents the basic model for the transmission dynamics of West Nile virus (WNV). The model, which consists of seven mutually-exclusive compartments representing the birds and vector dynamics,...     

Mathematical Analysis of West Nile Virus Model with Discrete Delays

The paper presents the basic model for the transmission dynamics of West Nile virus (WNV). The model, which consists of seven mutually-exclusive compartments representing the birds and vector dynamics, has a locally-asymptotically stable disease-free equilibrium whenever the associated reproduction number (?₀) is less than unity. As reveal in [3, 20], the analyses of the model show the existence of the phenomenon of backward bifurcation (where the stable disease-free equilibrium of the model co-exists with a stable endemic equilibrium when the reproduction number of the disease is less than unity). It is shown, that the backward bifurcation phenomenon can be removed by substituting the associated standard incidence function with a mass action incidence. Analysis of the reproduction number of the model shows that, the disease will persist, whenever ?₀ > 1, and increase in the length of incubation period can help reduce WNV burden in the community if a certain threshold quantities, denoted by Δ_b and Δ_v are negative. On the other hand, increasing the length of the incubation period increases disease burden if Δ_b > 0 and Δ_v > 0. Furthermore, it is shown that adding time delay to the corresponding autonomous model with standard incidence (considered in [2]) does not alter the qualitative dynamics of the autonomous system (with respect to the elimination or persistence of the disease).     

Estimation of Genus for Certain Arithmetic Groups

Abstract

We find the genera of arithmetic groups ?Γ₁(N), Φ? for N ≥ 1 and Φ the Fricke involution, from which we derive that the genus g(?Γ₁(N), Φ?) is zero if and only if 1 ≤ N ≤ 12 and N = 14, 15.     

Uniformly Conditioned Bases of Spectral Subspaces

A condition number of an ordered basis of a finite-dimensional normed space is defined in an intrinsic manner. This concept is extended to a sequence of bases of finite-dimensional normed spaces, and is used to determine uniform conditioning of such a sequence. We address the problem of finding a sequence of uniformly conditioned bases of spectral subspaces of operators of the form T _n  = S _n  + U _n , where S _n is a finite-rank operator on a Banach space and U _n is an operator which satisfies an invariance condition with respect to S _n . This problem is reduced to constructing a sequence of uniformly conditioned bases of spectral subspaces of operators on ? ^n×1. The applicability of these considerations in practical as well as theoretical aspects of spectral approximation is pointed out.     

The Inclusion Ideal Graph of Rings

Let R be a ring with unity. The inclusion ideal graph of a ring R, denoted by In(R), is a graph whose vertices are all nontrivial left ideals of R and two distinct left ideals I and J are adjacent if and only if I ? J or J ? I. In this paper, we show that In(R) is not connected if and only if R ? M ₂(D) or D ₁ × D ₂, for some division rings, D, D ₁ and D ₂. Moreover, we prove that if In(R) is connected, then diam(In(R)) ≤3. It is shown that if In(R) is a tree, then In(R) is a caterpillar with diam(In(R)) ≤3. Also, we prove that the girth of In(R) belongs to the set {3, 6, ∞}. Finally, we determine the clique number and the chromatic number of the inclusion ideal graph for some classes of rings.