Showing papers in "Journal of Applied Mathematics and Computing in 2006"
TL;DR: In this paper, the authors considered a time fractional diffusion equation on a finite domain and proposed a computationally effective implicit difference approximation (IDA) method to solve the problem, and proved that the IDA is unconditionally stable and convergent with O(tau+h^2) time and space steps.
Abstract: In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.
236 citations
TL;DR: The definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces are formulated and Pant’s theorem is proved.
Abstract: The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck’s common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant’s theorem ([21]).
94 citations
TL;DR: In this article, the notion of intuitionistic fuzzy finite switchboard state machines and (strong) homomorphisms of fuzzy finite state machines are introduced and related properties are investigated, and a congruence relation on the set of all words of all elements of X of finite length is given.
Abstract: The notion of intuitionistic fuzzy finite switchboard state machines and (strong) homomorphisms of intuitionistic fuzzy finite state machines are introduced, and related properties are investigated After we give a congruence relation on the set of all words of elements ofX of finite length, the quotient structure is discussed We show that the family of equivalence classes is a finite semigroup with identity
48 citations
TL;DR: In this paper, the authors considered two infinite classes of special finite groups and gave explicit formulas for the Fibonacci lenghts of these classes which involve the well-known Wall numbers k(n).
Abstract: Two infinite classes of special finite groups considered (The group G is special, if G 0 and Z(G) coincide). Using certain sequences of numbers we give explicit formulas for the Fibonacci lenghts of these classes which involve the well-known Wall numbers k(n).
41 citations
TL;DR: In this article, a robust numerical method for a singularly perturbed secondorder ordinary differential equation having two parameters with a discontinuous source term is presented, and theoretical bounds are derived for the derivatives of the solution and its smooth and singular components.
Abstract: A robust numerical method for a singularly perturbed secondorder ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations.
37 citations
TL;DR: The concept of an interval-valued fuzzy left (right, two-sided, interior, bi-) ideal generated by an intervalvalued fuzzy subset in semigroups is introduced.
Abstract: In this paper, we introduce the concept of an interval-valued fuzzy left (right, two-sided, interior, bi-) ideal generated by an intervalvalued fuzzy subset in semigroups. Some characterizations of such generated interval-valued fuzzy ideals are also discussed.
31 citations
TL;DR: In this paper, a mathematical study of the size of a population of diabetes mellitus patients is carried out, and the study also monitors the number of patients with complications, which may be classified as linear or non-linear.
Abstract: A mathematical study of the size of a population ofdiabetes mellitus patients is carried out in this paper. The study also monitors the number of patients with complications. By appropriate definition of a parameter, the mathematical model may be classified as linear or non-linear. The non-linear case is discussed and the critical values of the population are analysed for stability. Numerical methods are developed for solving the model equations and the results of numerical simulations are reported.
29 citations
TL;DR: In this article, it was shown that the existence of a pair of biorthogonal multiple vector-valued scaling functions guarantees the presence of pair of BVM wavelet functions.
Abstract: In this paper, we introduce biorthogonal multiple vector-valued wavelets which are wavelets for vector fields. We proved that, like in the scalar and multiwavelet case, the existence of a pair of biorthogonal multiple vector-valued scaling functions guarantees the existence of a pair of biorthogonal multiple vector-valued wavelet functions. Finally, we investigate the construction of a class of compactly supported biorthogonal multiple vector-valued wavelets.
28 citations
TL;DR: By means of the use of a triangular normT, the notion of T-fuzzy hyperideals in hypernear-rings is stated, and basic properties are investigated.
Abstract: By means of the use of a triangular normT, the notion ofT-fuzzy hyperideals in hypernear-rings is stated, and basic properties are investigated. Moreover, the notion of Noetherian hypernear-rings is introduced, and its characterization is given. At last, the properties of quotient hypernear-rings andT-fuzzy characteristic hyperideals are discussed.
23 citations
TL;DR: In this paper, a single machine SLK due date assignment scheduling problem is considered, where job processing times are controllable variables with linear costs, and the objective is to determine the optimal sequence, the optimal common flow allowance and the optimal processing time compressions to minimize a total penalty function.
Abstract: In this paper, we consider single machine SLK due date assignment scheduling problem in which job processing times are controllable variables with linear costs. The objective is to determine the optimal sequence, the optimal common flow allowance and the optimal processing time compressions to minimize a total penalty function based on earliness, tardiness, common flow allowance and compressions. We solve the problem by formulating it as an assignment problem which is polynomially solvable. For some special cases, we present an O(n logn) algorithm to obtain the optimal solution respectively.
22 citations
TL;DR: In this article, by using the Riccati transformation technique, the authors established new oscillation criteria for second-order nonlinear perturbed dynamic equation on time scales, and an example illustrating their main results is also given.
Abstract: In this paper, by using the Riccati transformation technique we establish some new oscillation criteria for second-order nonlinear perturbed dynamic equation on time scales. An example illustrating our main results is also given.
TL;DR: In this article, a smoothing method for symmetric conic linear programming (SCLP) is proposed, based on the Chen-Harker-Kanzow-Smale smoothing function.
Abstract: This paper proposes a smoothing method for symmetric conic linear programming (SCLP). We first characterize the central path conditions for SCLP problems with the help of Chen-Harker-Kanzow-Smale smoothing function. A smoothing-type algorithm is constructed based on this characterization and the global convergence and locally quadratic convergence for the proposed algorithm are demonstrated.
TL;DR: In this article, the Sterile Insect Release Method (SIRM) is used for pest control and the effect of uncertain environmental fluctuations on both fertile and sterile insects is investigated.
Abstract: Recently non-conventional approaches of pest control are getting much more importance in different parts of the world. The main reason behind this is the long list of side effects of conventional approaches (use of pesticides etc.). The present paper focuses on one such extremely useful method of insect pest control, namely the Sterile Insect Release Method (SIRM), by using a mathematical model. A blend of dynamical behaviours of the model is studied critically, which, in turn, indicates the relevance of the method. The effect of uncertain environmental fluctuations on both fertile and sterile insects is also investigated. Our analytical findings are verified through computer simulation. Some important restrictions on the parameters of the system are mentioned, which may be implemented for a better performance of SIRM.
TL;DR: In this paper, it was shown that a graph G is complete if and only if the degree of the vertices adjacent to a vertex is a function of the average of the degrees of vertices of the vertex adjacent to the vertex.
Abstract: LetG = (V, E) be a simple graph withn vertices and e edges. Letdi be the degree of the ith vertex vi
∈ V andm
i
the average of the degrees of the vertices adjacent to vertexv
i
∈ V. It is known by Caen [1] and Das [2] that
$$\frac{{4e^2 }}{n} \leqslant d_1^2 + ... + d_n^2 \leqslant e max \{ d_j + m_j |v_j \in V\} \leqslant e\left( {\frac{{2e}}{{n - 1}} + n - 2} \right)$$
. In general, the equalities do not hold in above inequality. It is shown that a graphG is regular if and only if
$$\frac{{4e^2 }}{n} = d_1^2 + ... + d_n^2 $$
. In fact, it is shown a little bit more strong result that a graphG is regular if and only if
$$\frac{{4e^2 }}{n} = d_1^2 + ... + d_n^2 = e max \{ d_j + m_j |v_j \in V\} $$
. For a graphG withn < 2 vertices, it is shown that G is a complete graphK
n
if and only if
$$\frac{{4e^2 }}{n} = d_1^2 + ... + d_n^2 = e max \{ d_j + m_j |v_j \in V\} = e\left( {\frac{{2e}}{{n - 1}} + n - 2} \right)$$
.
TL;DR: In this article, the authors investigated the scattering of waves obliquely incident on small cylindrical undulations at the bottom of a two-layer fluid wherein the upper layer has a free surface and the lower layer has an undulating bottom, assuming linear theory.
Abstract: Scattering of waves obliquely incident on small cylindrical undulations at the bottom of a two-layer fluid wherein the upper layer has a free surface and the lower layer has an undulating bottom, is investigated here assuming linear theory. There exists two modes of time-harmonic waves propagating at each of the free surface and the interface. Due to an obliquely incident wave of a particular mode, reflected and transmitted waves of both the modes are created in general by the bottom undulations. For small undulations, a simplified perturbation analysis is used to obtain first-order reflection and transmission coefficients of both the modes due to oblique incidence of waves of again both modes, in terms of integrals involving the shape function describing the bottom. For sinusoidal undulations, these coefficients are plotted graphically to illustrate the energy transfer between the waves of different modes induced by the bottom undulations.
TL;DR: For a finite group G, #Cent(G) denotes the number of centralizers of its elements, and a group G is called n-centralizer if #CentG =n, and primitive n-centerizer if G = n.
Abstract: For a finite groupG, #Cent(G) denotes the number of centralizers of its elements. A groupG is calledn-centralizer if #Cent(G) =n, and primitive n-centralizer if\(\# Cent(G) = \# Cent\left( {\frac{G}{{Z(G)}}} \right) = n\).
TL;DR: In this paper, an explicit conservative difference approximation (ECDA) for time fractional diffusion equation (TFDE) is proposed, which is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α∃ (0,1).
Abstract: Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α∃ (0,1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.
TL;DR: In this paper, an efficient numerical algorithm for approximate solutions of fourth-order boundary values problems with two-point boundary conditions is presented, where the Adomian decomposition method and a modified form of this method are applied to construct the numerical solution.
Abstract: In this paper, we present an efficient numerical algorithm for approximate solutions of fourth-order boundary values problems with twopoint boundary conditions The Adomian decomposition method and a modified form of this method are applied to construct the numerical solution The scheme is tested on one linear problem and two nonlinear problems The obtained results demonstrate the applicability and efficiency of the proposed scheme
TL;DR: In this article, the existence of steady states and their stability are studied using eigenvalue analysis and the boundedness of the exploited system is examined, and conditions for persistence and global stability of the system are derived.
Abstract: This paper deals with the problem of a ratio-dependent prey-predator model with combined harvesting The existence of steady states and their stability are studied using eigenvalue analysis Boundedness of the exploited system is examined We derive conditions for persistence and global stability of the system The possibility of existence of bionomic equilibria has been considered The problem of optimal harvest policy is then solved by using Pontryagin’s maximal principle
TL;DR: The expressions of 32 fuzzy coimplication operators (FCO) and 32 intuitionistic fuzzy implication operators (IFIO) are given and the properties which the FCOs and IFIOs should satisfy are presented.
Abstract: The expressions of 32 fuzzy coimplication operators(FCO) and 32 intuitionistic fuzzy implication operators(IFIO) are given in this paper. The Co-D-P properties which the FCOs should satisfy are presented. The FCOs and IFIOs’situation of satisfying the properties which they should satisfy, respectively, are discussed in details.
TL;DR: A canonical symmetrical trapezoidal representation for the solution of fuzzy linear system and the optimal solution of FLPFV, and a model for fuzzy linear programming problem with fuzzy variables (FLPFV), in which the right hand side of constraints are arbitrary numbers, and coefficients of the objective function and constraint matrix are regarded as crisp numbers.
Abstract: In this paper first, we find a canonical symmetrical trapezoidal(triangular) for the solution of the fuzzy linear systemA~x = ~b, where the elements inA and ~b are crisp and arbitrary fuzzy numbers, respectively. Then, a model for fuzzy linear programming problem with fuzzy variables (FLPFV), in which, the right hand side of constraints are arbitrary numbers, and coefficients of the objective function and constraint matrix are regarded as crisp numbers, is discussed. A numerical procedure for calculating a canonical symmetrical trapezoidal representation for the solution of fuzzy linear system and the optimal solution of FLPFV, (if there exist) is proposed. Several examples illustrate these ideas.
TL;DR: Property concerning approximation of fuzzy-number-valued functions by fuzzy B-spline series by means of modulus of continuity are studied and error bounds are obtained for fuzzy splines of Schoenberg type.
Abstract: We study properties concerning approximation of fuzzy-num- ber-valued functions by fuzzy B-spline series. Error bounds in approxi- mation by fuzzy B-spine series are obtained in terms of the modulus of continuity. Particularly simple error bounds are obtained for fuzzy splines of Schoenberg type. We compare fuzzy B-spline series with existing fuzzy concepts of splines.
TL;DR: In this article, an alternative representation of the generalized inverse of a matrixA is given, which drops the restriction on the nonnegativity of the spectrum ofGA for parameter matrixG satisfying R(G) =T and N(G)) =S. The corresponding error bounds are also estimated.
Abstract: In this paper an alternative representation of the generalized inverseA
T,S
(2)
of a matrixA is given out, which drops the restriction on the nonnegativity of the spectrum ofGA for parameter matrixG satisfyingR(G) =T andN(G) =S. Based on this new representation and two special Hermitian interpolation polynomials we present two iterative schemes for computing the generalized inverseA
T,S
(2)
. The corresponding error bounds are also estimated. Finally, an example is shown to illustrate our theory.
TL;DR: A fourth-order compact finite difference scheme is derived for a two-dimensional elliptic problem with a mixed derivative and constant coefficients and the computed accuracy achieved by each scheme is studied.
Abstract: We derive a fourth-order compact finite difference scheme for a two-dimensional elliptic problem with a mixed derivative and constant coefficients. We conduct experimental study on numerical solution of the problem discretized by the present compact scheme and the traditional second-order central difference scheme. We study the computed accuracy achieved by each scheme and the performance of the Gauss-Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from the difference schemes.
TL;DR: In this paper, an optimization model is introduced and existence of optimal solution is proved by infinite-dimensional op- timal theory, the optimal condition of model is given and the equivalence between optimal condition and the zero of optimality function is proved.
Abstract: The process of producing 1,3-preprandiol by microorganism continuous cultivation would attain its equilibrium state. How to get the highest concentration of 1,3-propanediol at that time is the aim for pro- ducers. Based on this fact, an optimization model is introduced in this paper, existence of optimal solution is proved. By infinite-dimensional op- timal theory, the optimal condition of model is given and the equivalence between optimal condition and the zero of optimality function is proved.
TL;DR: In this article, the authors proved Grabiec's fuzzy Banach contraction theorem and Vasuki's theorem for a complete fuzzy metric space, in the sense of Song and Veeramani.
Abstract: Fixed point theory is one of famous theories from theoretical and numerical point of views. Banach fixed point theorem plays a main role in this theory. In this article, Grabiec’s fuzzy Banach contraction theorem [3] and Vasuki’s theorem [12] for a complete fuzzy metric space, in the sense of Song [11] (or George and Veeramani), is proved by an extra condition.
TL;DR: Inverse coefficient identification problems associated with the fourth-order Sturm-Liouville operator in the steady state Euler-Bernoulli beam equation are investigated in this paper.
Abstract: Inverse coefficient identification problems associated with the fourth-order Sturm-Liouville operator in the steady state Euler-Bernoulli beam equation are investigated. Unlike previous studies in which spectral data are used as additional information, in this paper only boundary information is used, hence non-destructive tests can be employed in practical applications.
TL;DR: This paper extends the nonlinear Uzawa algorithm for solving symmetric saddle point problems iteratively to the nonsymmetric case and shows that its convergence result is deduced and its method is more efficient than other non linear Uzawa methods in some cases.
Abstract: In [A new nonlinear Uzawa algorithm for generalized saddle point problems, Appl. Math. Comput., 175(2006), 1432–1454], a nonlinear Uzawa algorithm for solving symmetric saddle point problems iteratively, which was defined by two nonlinear approximate inverses, was considered. In this paper, we extend it to the nonsymmetric case. For the nonsymmetric case, its convergence result is deduced. Moreover, we compare the convergence rates of three nonlinear Uzawa methods and show that our method is more efficient than other nonlinear Uzawa methods in some cases. The results of numerical experiments are presented when we apply them to Navier-Stokes equations discretized by mixed finite elements.
TL;DR: A negative answer to the open problem of Jun, Shim and Lele on fuzzy filters of BCI-algebras is given, a necessary and sufficient condition, under which theopen problem has a positive answer, is provided.
Abstract: In this note, a negative answer to the open problem of Jun, Shim and Lele on fuzzy filters of BCI-algebras is given, a necessary and sucient condition, under which the open problem has a positive answer, is provided. Furthermore, we give two properties of fuzzy filters of BCI- algebras which generalize some results of Jun, Shim and Lele.
TL;DR: In this article, a multi-item inventory model of breakable items is developed, where items are either complementary or substitute, and a Contractive Mapping Genetic Algo-rithm (CMGA) has been developed and implemented to find the values of dierent decision variables.
Abstract: A general methodology is suggested to solve shelf-space allo- cation problem of retailers. A multi-item inventory model of breakable items is developed, where items are either complementary or substitute. Demands of the items depend on the amount of stock on the showroom and unit price of the respective items. Also demand of one item decreases (increases) due to the presence of others in case of substitute (complemen- tary) product. For such a model, a Contractive Mapping Genetic Algo- rithm (CMGA) has been developed and implemented to find the values of dierent decision variables. These are evaluated to have maximum pos- sible profit out of the proposed system. The system has been illustrated numerically and results for some particular cases are derived. The results are compared with some other heuristic approaches- Simulated Annealing (SA), simple Genetic Algorithm (GA) and Greedy Search Approach (GSA) developed for the present model.