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A NEW APPROACH FOR ASYMPTOTIC STABILITY A SYSTEM OF THE NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS
Effati, Sohrab,Nazemi, Ali Reza 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1
In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE's). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.
SOME WAITING TIME AND BOTTLENECK ANALYSIS
임종설 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.1
In this paper, some vacation policies are considered, which can be related to the past behavior of the system. The server, after serving all customers, stays idle or to wait for some time before a vacation is taken. General formulas for the waiting time and the amount of work in the system are derived for a vacation policy. Using the analysis on the vacation system, we derived the waiting time in the sequential bottleneck station.
Temporal and spatio-temporal dynamics of a mathematical model of harmful algal interaction
B. Mukhopadhyay,R. Bhattacharyya 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1
The adverse effect of harmful plankton on the marine ecosystem is a topic of deep concern. To investigate the role of such phytoplankton, a mathematical model containing distinct dynamical equations for toxic and non-toxic phytoplankton is analyzed. Stability analysis of the resulting three equation model is carried out. A continuous time variation in toxin liberation process is incorporated into the model and a stability analysis of the resulting delay model is performed. The distributed delay model is then extended to include the spatial distribution of plankton and the delay-diffusion model is analyzed with spatial and spatiotemporal kernels. Conditions for diffusion-driven instability in both the cases are derived and compared to explore the significance of these kernels. Numerical studies are performed to justify analytical findings The adverse effect of harmful plankton on the marine ecosystem is a topic of deep concern. To investigate the role of such phytoplankton, a mathematical model containing distinct dynamical equations for toxic and non-toxic phytoplankton is analyzed. Stability analysis of the resulting three equation model is carried out. A continuous time variation in toxin liberation process is incorporated into the model and a stability analysis of the resulting delay model is performed. The distributed delay model is then extended to include the spatial distribution of plankton and the delay-diffusion model is analyzed with spatial and spatiotemporal kernels. Conditions for diffusion-driven instability in both the cases are derived and compared to explore the significance of these kernels. Numerical studies are performed to justify analytical findings
Characterizations of the power function distribution by the independence of the lower record values
장세경 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.25 No.1
This paper presents characterizations of the power distribution with the parameter β = 1 by the independence of the lower record values. We prove that X ∈ POW(α,1) for α>0, if and only if XL(n) XL(m) and XL(m) for 1 ≤ m<n are independent. And we prove that X ∈ POW(α,1) for α>0, if and only if XL(m) − XL(m+1) XL(m) and XL(m) for m ≥ 1 are independent or XL(m) − XL(m+1) XL(m+1) and XL(m) for m ≥ 1 are independent.
Second order duality in vector optimization over cones
S.K. Suneja,Sunila Sharma,Vani 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.1
In this paper second order cone convex, second order cone pseudoconvex, second order strongly cone pseudoconvex and second order cone quasiconvex functions are introduced and their interrelations are dis-cussed. Further a MondWeir Type second order dual is associated with the Vector Minimization Problem and the weak and strong duality theorems are established under these new generalized convexity assumptions. In this paper second order cone convex, second order cone pseudoconvex, second order strongly cone pseudoconvex and second order cone quasiconvex functions are introduced and their interrelations are dis-cussed. Further a MondWeir Type second order dual is associated with the Vector Minimization Problem and the weak and strong duality theorems are established under these new generalized convexity assumptions.
The application of stochastic analysis to population genetics model
최원 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
In allelic model X = (x1, x2, · · · , xd), Mf (t) = f(p(t)) − Z t 0 Lf(p(t))ds is a P-martingale for diffusion operator L under the certain conditions. In this note, we try to apply diffusion processes for countable-allelic model in population genetic model and we can define a new diffusion operator L. Since the martingale problem for this operator L is related to diffusion processes, we can define a integral which is combined with operator L and a bilinar form h·, ·i. We can find properties for this integral using maximum principle.
신현경 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1
Microscopic imaging system often requires the algorithm to adjust location of camera lenses automatically in machine level. An effort to detect the best focal point is naturally interpreted as a mathematical inverse problem [1]. Following Wiener’'s point of view [2], we interpret the focus level of images as the quantified factor appeared in image degradation model: g = f*H + η, a standard mathematical model for understanding signal or image degradation process [3]. In this paper we propose a simple, very fast and robustmethod to compare the degradation parameters among the multiple images given by introducing outlier analysis of histogram.
Mark sequences in tripartite multidigraphs
S. Pirzada,U. Samee 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
A tripartite r-digraph is an orientation of a tripartite multigraph that is without loops and contains atmost r edges between any pair of vertices from distinct parts. In this paper, we obtain necessary and sufficient conditions for sequences of non-negative integers in non-decreasing order to be the sequences of numbers, called marks (or r-scores), attached to the vertices of a tripartite r-digraph. A tripartite r-digraph is an orientation of a tripartite multigraph that is without loops and contains atmost r edges between any pair of vertices from distinct parts. In this paper, we obtain necessary and sufficient conditions for sequences of non-negative integers in non-decreasing order to be the sequences of numbers, called marks (or r-scores), attached to the vertices of a tripartite r-digraph.