권호 표지

Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)

  • 연3회간
  • /
  • 2734-1194(pISSN)
  • /
  • 2234-8417(eISSN)

과학기술표준분류

  • 수학 ＞ 응용수학

Aim & Scope

This is a broad based journal covering all branches of computational or applied mathematics with special encouragement to researchers in theoretical computer science and mathematical Informatics. Thus, the major areas, such as Numerical Analysis, Discrete Optimization, Linear and Nonlinear Programming, Theory of Computation(Computational Complexity, Automata and Formal Languages), Control Theory, Theory of Algorithms, Computational Logic, Applied Combinatorics (including graphs, codes, and designs), Coding Theory, Cryptographics, Big data, AI, Fuzzy Theory with applications, Differential Equations with applications, etc., are all included. A large variety of scientific problems also necessarily involve Algebra, Analysis, Geometry, Probability and Statistics, and so on. The journal welcomes research papers in all branches of mathematics which have some bearing on the application to scientific problems, including papers in the areas of Actuarial Science, Mathematical Biology, Mathematical Economics and Finance.

KSCI KCI SCOPUS

제29권5_6호

  1. Jiang, Li;Wang, Ting 1067
    https://doi.org/10.14317/jami.2011.29.5_6.1067 PDF KSCI
    In this paper, a preconditioned mixed-type splitting iterative method for solving the linear systems Ax = b is presented, where A is a Z-matrix. Then we also obtain some results to show that the rate of convergence of our method is faster than that of the preconditioned AOR (PAOR) iterative method and preconditioned SOR (PSOR) iterative method. Finally, we give one numerical example to illustrate our results.
  2. Madanshekaf, Ali 1075
    https://doi.org/10.14317/jami.2011.29.5_6.1075 PDF KSCI
    Among the numerous topological indices considered in chemical graph theory, only a few have been found noteworthy in practical application, Randi$\acute{c}$ index is one of them. The dendrimer nanostars is a synthesized molecule built up from branched unit called monomers. In this article, we compute the Randi$\acute{c}$ index of two types of polymer dendrimers and a fullerene dendrimer.
  3. Islam, S.;Ullah, Murad;Zaman, Gul;Idrees, M. 1081
    https://doi.org/10.14317/jami.2011.29.5_6.1081 PDF KSCI
    In this paper, a steady axisymmetric MHD flow of two dimensional incompressible fluids is studied under the influence of a uniform transverse magnetic field. The governing equations are reduced to nonlinear boundary value problem by applying the integribility conditions. Optimal Homotopy Asymptotic Method (OHAM) is applied to obtain solution of reduced fourth order nonlinear boundary value problem. For comparison, the same problem is also solved by Variational Iteration Method (VIM).
  4. Moualeu, Dany Pascal;Bowong, Samuel;Emvudu, Yves 1097
    https://doi.org/10.14317/jami.2011.29.5_6.1097 PDF KSCI
    We consider the global stability of a general tuberculosis model with two differential infectivity, n classes of latent individuals and mass action incidence. This system exhibits the traditional threshold behavior. There is always a globally asymptotically stable equilibrium state. Depending on the value of the basic reproduction ratio $\mathcal{R}_0$, this state can be either endemic ($\mathcal{R}_0$ > 1), or infection-free ($\mathcal{R}_0{\leq}1$). The global stability of this model is derived through the use of Lyapunov stability theory and LaSalle's invariant set theorem. Both the analytical results and numerical simulations suggest that patients should be strongly encouraged to complete their treatment and sputum examination.
  5. Song, Fang;Wang, Xia;Song, Xinyu 1117
    https://doi.org/10.14317/jami.2011.29.5_6.1117 PDF KSCI
    In this paper, a class of more general delayed viral infection model with lytic immune response is proposed by Song et al.[1] ([Journal of Mathematical Analysis Application 373 (2011), 345-355). We derive the basic reproduction numbers $R_0$ and $R_0^*$ 0 for the viral infection, and establish that the global dynamics are completely determined by the values of $R_0$ and $R_0^*$. If $R_0{\leq}1$, the viral-free equilibrium $E_0$ is globally asymptotically stable; if $R_0^*{\leq}1$ < $R_0$, the immune-free equilibrium $E_1$ is globally asymptotically stable; if $R_0^*$ > 1, the chronic-infection equilibrium $E_2$ is globally asymptotically stable by using the method of Lyapunov function.
  6. Yang, Yanfang;Feng, Xinlong;He, Yinnian 1129
    https://doi.org/10.14317/jami.2011.29.5_6.1129 PDF KSCI
    In this paper, a class of large time-stepping method based on the finite element discretization for the Cahn-Hilliard equation with the Neumann boundary conditions is developed. The equation is discretized by finite element method in space and semi-implicit schemes in time. For the first order fully discrete scheme, convergence property is investigated by using finite element analysis. Numerical experiment is presented, which demonstrates the effectiveness of the large time-stepping approaches.
  7. Han, Baoyan;Zhu, Bo 1143
    https://doi.org/10.14317/jami.2011.29.5_6.1143 PDF KSCI
    In this paper, we shall establish a new theorem on the existence and uniqueness of the solution to a backward doubly stochastic differential equations under a weaker condition than the Lipschitz coefficient. We also show a comparison theorem for this kind of equations.
  8. Hosseinzade, Elham;Hassanpour, Hassan 1157
    https://doi.org/10.14317/jami.2011.29.5_6.1157 PDF KSCI
    The Karush-Kuhn-Tucker (KKT) necessary optimality conditions for nonlinear differentiable programming problems are also sufficient under suitable convexity assumptions. The KKT conditions in multiobjective programming problems with interval-valued objective and constraint functions are derived in this paper. The main contribution of this paper is to obtain the Pareto optimal solutions by resorting to the sufficient optimality condition.
  9. Li, Jian-Lei;Luo, Dang;Zhang, Zhi-Jiang 1167
    https://doi.org/10.14317/jami.2011.29.5_6.1167 PDF KSCI
    In this paper, we further investigate the local Hermitian and skew-Hermitian splitting (LHSS) iteration method and the modified LHSS (MLHSS) iteration method for solving generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. When A is non-symmetric positive definite, the convergence conditions are obtained, which generalize some results of Jiang and Cao [M.-Q. Jiang and Y. Cao, On local Hermitian and Skew-Hermitian splitting iteration methods for generalized saddle point problems, J. Comput. Appl. Math., 2009(231): 973-982] for the generalized saddle point problems to generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. Numerical experiments show the effectiveness of the iterative methods.
  10. Anh, P.N.;Son, D.X. 1179
    https://doi.org/10.14317/jami.2011.29.5_6.1179 PDF KSCI
    In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed points of a finite family of strict pseudocontractions and the solution set of pseudomonotone and Lipschitz-type continuous equilibrium problems. The scheme is based on the idea of extragradient methods and fixed point iteration methods. We show that the iterative sequences generated by this algorithm converge strongly to the common element in a real Hilbert space.
  11. Kar, T.K.;Pahari, U.K. 1193
    https://doi.org/10.14317/jami.2011.29.5_6.1193 PDF KSCI
    In the present paper we consider a differential-algebraic prey-predator model with stage structure for prey and harvesting of predator species. Stability and instability of the equilibrium points are discussed and it is observed that the model exhibits a singular induced bifurcation when the economic profit is zero. It indicates that the zero economic profit brings impulse, i.e. rapid expansion of the population and the system collapses. For the purpose of stabilizing the system around the positive equilibrium, a state feedback controller is designed. Finally, numerical simulations are given to show the consistency with theoretical analysis.
  12. Zhang, Tong 1205
    https://doi.org/10.14317/jami.2011.29.5_6.1205 PDF KSCI
    In this work, a stabilized characteristic finite volume method for the time-dependent Navier-Stokes equations is investigated based on the lowest equal-order finite element pair. The temporal differentiation and advection term are dealt with by characteristic scheme. Stability of the numerical solution is derived under some regularity assumptions. Optimal error estimates of the velocity and pressure are obtained by using the relationship between the finite volume and finite element methods.
  13. Lee, H.Y.;Jung, N.S.;Ryoo, C.S. 1221
    https://doi.org/10.14317/jami.2011.29.5_6.1221 PDF KSCI
    Recently, several mathematicians have studied some interesting relations between extended q-Euler number and Bernstein polynomials(see [3, 5, 7, 8, 10]). In this paper, we give some interesting identities on the Genocchi polynomials and Bernstein polynomials.
  14. Fang, Yanqin;Zhang, Jihui 1229
    https://doi.org/10.14317/jami.2011.29.5_6.1229 PDF KSCI
    In this paper we consider a system of N-Laplacian elliptic equations with critical exponential growth. The existence and multiplicity results of solutions are obtained by a limit index method and Trudinger-Moser inequality.
  15. Liu, Wanxiang;Gao, Chengcai;Wang, Yiju 1245
    https://doi.org/10.14317/jami.2011.29.5_6.1245 PDF KSCI
    In this paper, we proposed a regularization interior point method for semidefinite programming with free variables which can be taken as an extension of the algorithm for standard semidefinite programming. Since an inexact search direction at each iteration is used, the computation of the designed algorithm is much less compared with the existing solution methods. The convergence analysis of the method is established under weak conditions.
  16. Lee, Yong-Hun;Park, Yeon-Hee 1257
    https://doi.org/10.14317/jami.2011.29.5_6.1257 PDF KSCI
    The thermal behavior of wood exposed to the outdoors is influenced by solar absorptivity and longwave emissivity. However, it is difficult to measure that properties directly. Hence we estimate the values of the parameter by using the least-square optimization technique. Finally we report the results for the computation of the values of the parameters.
  17. Bhatta, Dambaru;Riahi, Daniel N. 1269
    https://doi.org/10.14317/jami.2011.29.5_6.1269 PDF KSCI
    Here we consider magneto-convection in a mushy layer which is formed during solidification of binary alloys. The mushy layer is treated as an active porous media with variable permeability. The equations governing the layer are conservation of mass, conservation of heat, conservation of solute, magnetic induction equation, momentum equation governed by the Darcy's law and Maxwell's equations for the magnetic field. To study the second order effects on the flow without solving the second order system, we need to obtain the adjoint system for the flow. This motivates the authors we derive the adjoint system analytically for the mushy layer case. Numerical results of the adjoint system are presented for passive and active mushy layers at the onset of the motion using a set of parameters experimentalists use.
  18. Chen, Feixiang;Xiang, Ruiyin 1285
    https://doi.org/10.14317/jami.2011.29.5_6.1285 PDF KSCI
    We establishes the polynomial convergence of a new class of path-following methods for semidefinite linear complementarity problems (SDLCP) whose search directions belong to the class of directions introduced by Monteiro [9]. Namely, we show that the polynomial iteration-complexity bound of the well known algorithms for linear programming, namely the predictor-corrector algorithm of Mizuno and Ye, carry over to the context of SDLCP.
  19. Lee, Yu-Tae;Sim, Dong-Bo 1295
    https://doi.org/10.14317/jami.2011.29.5_6.1295 PDF KSCI
    We present an analytic model of an unslotted opportunistic spectrum access (OSA) network and evaluate its performance such as interruption probability, service completion time, and throughput of secondary users. Numerical examples are given to show the performance of secondary users in cognitive networks. The developed modeling and analysis method can be used to evaluate the performance of various OSA networks.
  20. Liu, Jinkui 1303
    https://doi.org/10.14317/jami.2011.29.5_6.1303 PDF KSCI
    Based on the PRP method, a new spectral PRP conjugate gradient method has been proposed to solve general unconstrained optimization problems which produce sufficient descent search direction at every iteration without any line search. Under the Wolfe line search, we prove the global convergence of the new method for general nonconvex functions. The numerical results show that the new method is efficient for the given test problems.
  21. Hu, Lin;Gan, Siqing 1311
    https://doi.org/10.14317/jami.2011.29.5_6.1311 PDF KSCI
    In this paper the Milstein method is proposed to approximate the solution of a linear stochastic differential equation with Poisson-driven jumps. The strong Milstein method and the weak Milstein method are shown to capture the mean square stability of the system. Furthermore using some technique, our result shows that these two kinds of Milstein methods can well reproduce the stochastically asymptotical stability of the system for all sufficiently small time-steps. Some numerical experiments are given to demonstrate the conclusions.
  22. Zhang, Lijuan;Yu, Lixin 1327
    https://doi.org/10.14317/jami.2011.29.5_6.1327 PDF KSCI
    This paper demonstrates that there is a unique exponentially stable equilibrium state of a class of impulsive cellular neural network with delays. The analysis exploits M-matrix theory and generalized comparison principle to derive some easily verifiable sufficient conditions for the global exponential stability of the equilibrium state. The results extend and improve earlier publications. An example with its simulation is given for illustration of theoretical results.
  23. Sen, Syamal K.;Ramakrishnan, Suja;Agarwal, Ravi P.;Shaykhian, Gholam Ali 1337
    https://doi.org/10.14317/jami.2011.29.5_6.1337 PDF KSCI
    So far as a solution of the given consistent linear system is concerned many numerical methods - both mathematically non-iterative as well as iterative - have been reported in the literature over the last couple of centuries. Most of these methods consider all the equations including linearly dependent ones in the system and obtain a solution whenever it exists. Since linearly dependent equations do not add any new information to a system concerning a solution we have proposed an algorithm that identifies them and prunes them in the process of solving the system. The pruning process does not involve row/column interchanges as in the case of Gauss reduction with partial/complete pivoting. We demonstrate here that the use of pruning as an inbuilt part of our solution process reduces computational and storage complexities and also computational error.
  24. Baek, Jong-Il;Seo, Hye-Young 1351
    https://doi.org/10.14317/jami.2011.29.5_6.1351 PDF KSCI
    We in this paper study the complete convergence and almost surely convergence for arrays of rowwise pairwise negatively dependent(ND) random variables (r.${\upsilon}$.'s) which are dominated randomly by some random variables and obtain a result dealing with complete convergence of linear processes.
  25. Sangago, Mengistu Goa 1363
    https://doi.org/10.14317/jami.2011.29.5_6.1363 PDF KSCI
    Halpern iterative algorithm is one of the most cited in the literature of approximation of fixed points of nonexpansive mappings. Different authors modified this iterative algorithm in Banach spaces to approximate fixed points of nonexpansive mappings. One of which is Hu [8] and Yao et al [21] modification of Halpern iterative algorithm for nonexpansive mappings in Banach spaces. It is the purpose of this paper to thoroughly analyze this modification and its convergence conditions. Unfortunately, Hu [8] and Yao et al [21] control conditions imposed on the modified Halpern iterative algorithm to have strong convergence are found to be not sufficient. In this paper, counterexamples are constructed to prove that the strong convergence conditions of Hu [8] and Yao et al [21] are not sufficient. It is also proved that with some additional conditions on the control parameters, strong convergence of the defined iterative algorithm is obtained in different Banach space settings.
  26. Zhang, Shuwen;Tan, Dejun 1381
    https://doi.org/10.14317/jami.2011.29.5_6.1381 PDF KSCI
    In this paper, we consider two-species periodic Gilpin-Ayala competition system with delay and impulsive effect. By using some analysis methods, sufficient conditions for the permanence of the system are derived. Further, we give the conditions of the existence and global asymptotic stable of positive periodic solution.
  27. Liu, Bingzhuang 1395
    https://doi.org/10.14317/jami.2011.29.5_6.1395 PDF KSCI
    When a Sequential Quadratic Programming (SQP) method is used to solve the nonlinear programming problems, one of the main difficulties is that the Quadratic Programming (QP) subproblem may be incompatible. In this paper, an SQP algorithm is given by modifying the traditional QP subproblem and applying a class of $l_{\infty}$ penalty function whose penalty parameters can be adjusted automatically. The new QP subproblem is compatible. Under the extended Mangasarian-Fromovitz constraint qualification condition and the boundedness of the iterates, the algorithm is showed to be globally convergent to a KKT point of the non-linear programming problem.
  28. Fazeli, S.;Shahmorad, S. 1409
    https://doi.org/10.14317/jami.2011.29.5_6.1409 PDF KSCI
    In this paper we present an operational method for solving linear Volterra-Fredholm integral equations (VFIE). The method is con- structed based on three matrices with simple structures which lead to a simple and high accurate algorithm. We also present an error estimation and demonstrate accuracy of the method by numerical examples.
  29. Janfada, Mohammad;Sadeghi, Ghadir 1421
    https://doi.org/10.14317/jami.2011.29.5_6.1421 PDF KSCI
    In this paper, using a fixed point approach, the generalized Hyeres-Ulam stability of the following quadratic functional equation $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=3(f(x)+f(y)+f(z))$ will be studied, where f is a function from abelian group G into a quasi-${\beta}$-normed space and ${\sigma}$ is an involution on the group G. Next, we consider its pexiderized equation of the form $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=g(x)+g(y)+g(z)$ and its generalized Hyeres-Ulam stability.
  30. Wang, Liang;Shi, Yimin;Chang, Ping 1435
    https://doi.org/10.14317/jami.2011.29.5_6.1435 PDF KSCI
    In this paper the estimation of the parameters as well as survival and hazard functions are presented for the two-parameter Pareto distribution by using Bayesian and non-Bayesian approaches under upper record values. Maximum likelihood estimation (MLE) and interval estimation are derived for the parameters. Bayes estimators of reliability performances are obtained under symmetric (Squared error) and asymmetric (Linex and general entropy (GE)) losses, when two parameters have discrete and continuous priors, respectively. Finally, two numerical examples with real data set and simulated data, are presented to illustrate the proposed method. An algorithm is introduced to generate records data, then a simulation study is performed and different estimates results are compared.
  31. Jeong, Jae-Ug 1453
    https://doi.org/10.14317/jami.2011.29.5_6.1453 PDF KSCI
    In this paper, we study a new class of generalized nonlinear variational-like inequalities in reflexive Banach spaces. By using the KKM technique and the concept of the Hausdorff metric, we obtain some existence results for generalized nonlinear variational-like inequalities with generalized monotone multi-valued mappings in Banach spaces. These results improve and generalize many known results in recent literature.
  32. Liang, Mao-Lin;Dai, Li-Fang;Wang, San-Fu 1463
    https://doi.org/10.14317/jami.2011.29.5_6.1463 PDF KSCI
    This paper proposes a new generalized iterative method (SSOR-like method) for solving augmented system. A functional equation relating two involved parameters is obtained, and some convergence conditions for this method are derived. This paper generalizes some foregone results. Numerical examples show that, this method is efficient by suitable choices of the involved parameters.
  33. Huang, Pengzhan;Abduwali, Abdurishit 1477
    https://doi.org/10.14317/jami.2011.29.5_6.1477 PDF KSCI
    We propose a numerical method for solving Allen-Cahn equation, in both one-dimensional and two-dimensional cases. The new scheme that is explicit, stable, and easy to compute is obtained and the proposed method provides a straightforward and effective way for nonlinear evolution equations.
  34. Ahn, Sun-Shin;Han, Gyeong-Ho 1489
    https://doi.org/10.14317/jami.2011.29.5_6.1489 PDF KSCI
    The notions of $\mathcal{N}$-subalgebra, (positive implicative) $\mathcal{N}$-ideals of d-algebras are introduced, and related properties are investigated. Characterizations of an $\mathcal{N}$-subalgebra and a (positive implicative) $\mathcal{N}$-ideals of d-algebras are given. Relations between an $\mathcal{N}$-subalgebra, an $\mathcal{N}$-ideal and a positive implicative N-ideal of d-algebras are discussed.
  35. Sun, Yu-dong;Shi, Yi-min;Gu, Xin 1501
    https://doi.org/10.14317/jami.2011.29.5_6.1501 PDF KSCI
    In this study, assume that the stock price obeys the stochastic differential equation driven by mixed fractional Brownian motion, and the short rate follows the Vasicek model. Then, the Black-Scholes partial differential equation is held by using fractional Ito formula. Finally, the pricing formulae of the barrier option are obtained by partial differential equation theory. The results of Black-Scholes model are generalized.
  36. Zheng, Xiuyun 1511
    https://doi.org/10.14317/jami.2011.29.5_6.1511 PDF KSCI
    In this paper, we consider the smoothing Newton method for the nonlinear complementarity problems with $P_0$-function. The proposed algorithm is based on a new smoothing function and it needs only to solve one linear system of equations and perform one line search per iteration. Under the condition that the solution set is nonempty and bounded, the proposed algorithm is proved to be convergent globally. Furthermore, the local superlinearly(quadratic) convergence is established under suitable conditions. Preliminary numerical results show that the proposed algorithm is very promising.
  37. Song, Seok-Zun;Kang, Mun-Hwan 1525
    https://doi.org/10.14317/jami.2011.29.5_6.1525 PDF KSCI
    The $m{\times}n$ Boolean matrix A is said to be of Boolean rank r if there exist $m{\times}r$ Boolean matrix B and $r{\times}n$ Boolean matrix C such that A = BC and r is the smallest positive integer that such a factorization exists. We consider the the sets of matrix ordered pairs which satisfy extremal properties with respect to Boolean rank inequalities of matrices over nonbinary Boolean algebra. We characterize linear operators that preserve these sets of matrix ordered pairs as the form of $T(X)=PXP^T$ with some permutation matrix P.
  38. Lv, Yibing 1533
    https://doi.org/10.14317/jami.2011.29.5_6.1533 PDF KSCI
    In this paper, a class of nonlinear bilevel programs, i.e. the lower level problem is linear programs, is considered. Aiming at this special structure, we append the duality gap of the lower level problem to the upper level objective with a penalty and obtain a penalized problem. Using the penalty method, we give an existence theorem of solution and propose an algorithm. Then, a numerical example is given to illustrate the algorithm.
  39. Zou, Yu-Mei 1541
    https://doi.org/10.14317/jami.2011.29.5_6.1541 PDF KSCI
    In this paper, using B.Ricceri's three critical points theorem, we prove the existence of at least three classical solutions for the problem $$\{u^{(4)}(t)={\lambda}f(t,\;u(t)),\;t{\in}(0,\;1),\\u(0)=u(1)=u^{\prime}(0)=u^{\prime}(1)=0,$$ under appropriate hypotheses.
  40. Kim, Young-Ho 1549
    https://doi.org/10.14317/jami.2011.29.5_6.1549 PDF KSCI
    In this paper, we give an estimate on the difference between $x^n(t)$ and x(t) and it clearly shows that one can use the Picard iteration procedure to the approximate solutions to stochastic functional differential equations with infinite delay at phase space BC(($-{\infty}$, 0] : $R^d$) which denotes the family of bounded continuous $R^d$-valued functions ${\varphi}$ defined on ($-{\infty}$, 0] with norm ${\parallel}{\varphi}{\parallel}={\sup}_{-{\infty}<{\theta}{\leq}0}{\mid}{\varphi}({\theta}){\mid}$ under non-Lipschitz condition being considered as a special case and a weakened linear growth condition.
  41. Sun, Yibing;Han, Zhenlai;Zhao, Ping;Sun, Ying 1557
    https://doi.org/10.14317/jami.2011.29.5_6.1557 PDF KSCI
    In this paper, we consider the oscillation of the following certain second order nonlinear differential equations $(r(t)(x^{\prime}(t))^{\alpha})^{\prime}+q(t)x^{\beta}(t)=0$>, where ${\alpha}$ and ${\beta}$ are ratios of positive odd integers. New oscillation theorems are established, which are based on a class of new functions ${\Phi}={\Phi}(t,s,l)$ defined in the sequel. Also, we establish some interval oscillation criteria for this equation.
  42. Kotsireas, Ilias S.;Koukouvinos, Christos;Simos, Dimitris E. 1571
    https://doi.org/10.14317/jami.2011.29.5_6.1571 PDF KSCI
    In this paper, we construct inequivalent Hadamard matrices based on several new and old full orthogonal designs, using circulant and symmetric block matrices. Not all orthogonal designs produce inequivalent Hadamard matrices, because the corresponding systems of equations do not possess solutions. The systems of equations arising when we search for inequivalent Hadamard matrices from full orthogonal designs using circulant and symmetric block matrices, can be concisely described using the periodic autocorrelation function of the generators of the block matrices. We use Maple, Magma, C and Unix tools to find many new inequivalent Hadamard matrices.
  43. Chakrabarti, A.;Martha, S.C. 1583
    https://doi.org/10.14317/jami.2011.29.5_6.1583 PDF KSCI
    A special system of partial differential equations (PDEs) occur in a natural way while studying a class of irrotational inviscid fluid flow problems involving infinite channels. Certain aspects of solutions of such PDEs are analyzed in the context of flow problems involving multiple layers of fluids of different constant densities in a channel associated with arbitrary bottom topography. The whole analysis is divided into two parts-part A and part B. In part A the linearized theory is employed along with the standard Fourier analysis to understand such flow problems and physical quantities of interest are derived analytically. In part B, the same set of problems handled in part A are examined in the light of a weakly non-linear theory involving perturbation in terms of a small parameter and it is shown that the original problems can be cast into KdV type of nonlinear PDEs involving the bottom topography occurring in one of the coefficients of these equations. Special cases of bottom topography are worked out in detail and expressions for quantities of physical importance are derived.
  44. Wanicharpichat, Wiwat 1603
    https://doi.org/10.14317/jami.2011.29.5_6.1603 PDF KSCI
    Let R be a ring with identity. If a, b, $c{\in}R$ such that a+b+c = 1, then the distributive laws from addition over multiplication hold in R, that is a+(bc) = (a+b)(a+c) when ab = ba, and (ab)+c = (a+c)(b+c) when ac = ca. An application to obtains, if A,B are idempotent matrices and AB = BA = 0 then there exists an idempotent matrix C such that A + BC = (A + B)(A + C), and also A + BC = (I - C)(I - B). Some other cases and applications are also presented.