A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed.
In this paper, we present properties of greatest strongly connected subspaces in the case of a network (which is defined as a family of pretopologies). The network can be analyse by the union or by the intersection or by the composition of the different pretopologies.
For many years, Liapunov's direct method has been the primary technique for studying various stability also known as 'Liapunov stability' of functional differential equations.Recently, it has been noticed that some difficulties can arise when Liapunov's method is applied to certain equations, and that a suitable fixed point theorem can overcome some of these difficulties.In this paper we study a particular stability which differs from the Liapunov stability.In particular, we study the existence of asymptotically stable solutions of a system of nonlinear Volterra integral equations.We employ a fixed point theorem due to Krasnosel'skii in the analysis.
We consider a family of random maps where each of the component maps is from a family of piecewise, linear and Markov maps on a class of infinite partitions of the state space.We investigate the existence of infinite absolutely continuous invariant measures of the random maps.In a more general setting, our study establishes a positive answer to the question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically?This question is analogous to Parrondo's paradox [5] which states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game.
A high level of service for medical supplies and effective inventory policies are essential objectives for all health care industries. Medicine shortages and improper use of pharmaceuticals can not only lead to financial losses but also have a significant impact on patients. Many health systems and hospitals experience difficulties in achieving these goals as they have not addressed how medicines are managed, supplied, and used to save lives and improve health. Studies are essential to understand operations in health care industries and to offer decision support tools that improve health policy, public health, patient safety, and strategic decision-making in the pharmaceutical inventory model. We present a deterministic inventory model for pharmaceutical items having time dependent quadratic demand under the effect of deterioration. We develop a procedure for determining optimal solutions for inventory and the number of deliveries to achieve hospital (Customer Service Level) CSL targets with a minimum total cost of the system. The necessary and sufficient conditions for the existence and uniqueness of the optimal solution which could minimize the average total cost per unit time has been discussed. A numerical example illustrates the model application and behavior using MATLAB. 512 R. UTHAYAKUMAR AND S. THARANI AMS Subject Classification: 97M60
We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades [24, 5, 12, 28, 16]. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates and estimators for the measure estimation problem with specific application to random PDEs.
In this paper, we use Leggett-Williams multiple fixed point theorems to obtain sufficient conditions for the existence of at least one or two positive radial solutions of the equationx ∈ R N , N ≥ 2 subject to a linear mixed boundary condition at R 1 and R 2 .
The mean first exit time is studied for the one-dimensional problem with one-sided exit and purely time-dependent drift and diffusion.Exact mean exit times are derived when the drift coefficient is constant and the diffusion coefficient is bounded.When the drift and diffusion coefficients both vary with time, bounds on mean first exit time are derived.Examples are described that illustrate the usefulness of the results.
We consider a classical problem of stabilization of a priori unknown unstable periodic orbits in nonlinear autonomous discrete dynamical systems.A new approach was suggested in [11], where a nonlinear delay feedback control (DFC) scheme with apparently optimal gain was introduced.The optimality criteria in [11] were stated in terms of the size of the convergence region for the system multipliers.In numerical simulations it turns out that the optimal coefficients (in the above sense) produce slowly convergent recurrences.In this paper we suggest a generalization of the formulas from [11] to improve the rate of convergence while preserving stability.The subtlety of the problem is illustrated in numerous numerical simulations examples.
This article studies propagating wave of a reaction-diffusion system modeling auto-catalytic chemical reaction A+nB → (n+1)B involving two chemical species, a reactant A and an auto-catalyst B, whose diffusion coefficients, D A and D B , are unequal due to different molecular weights and/or sizes.We are investigating the extreme cases of D ≡ D B /D A ≪ 1 or D ≫ 1.We reformulate the traveling wave problem of general case to derive explicit bounds of speed for existence and non-existence.
In this work, we will present a mathematical model that describes a coupled fluid-structure interaction between the arterial wall, the blood flow inside the wall and the cerebral spinal fluid outside the wall with applications to intracranial saccular aneurysms.The governing system of differential equations includes a nonlinear power-law fluid equation coupled with a nonlinear elasticity equation describing the wall in conjunction with blood pressure that is modeled via a Fourier series.The thrust of this work involves the analysis and simulation of the associated mathematical model using classical differential equation techniques.Besides proving existence and uniqueness of the solution to the related system, analytical expressions for the associated traveling wave solutions for the governing nonlinear differential equation is also derived for a special class of problems that is biologically tractable.
The authors present an optimal control model to allocated equipment capacity between production that generates immediate revenue and engineering process improvement activity that results in increased future output. The benefit of engineering activity is modeled as a concave function of the total number of engineering lots processed to date, while the production facility is represented by a nonlinear clearing function capturing the nonlinear relationship between resource utilization and cycle time. We analyze the model to develop structural results and illustrates its behavior with numerical experiments.
In this paper we consider the application of a a new class of cumulative distribution function proposed by Ramos, Dey, Louzada and Lachos in [9] to the debugging theory.We study the Hausdorff approximation of the shifted Heaviside step function by this family.Numerical examples, illustrating our results are presented using programming environment Mathematica.We give also real examples with data provided in [30] using the new software reliability model.Dataset included [31] Year 2000 compatibility modifications, operating system upgrade, and signaling message processing.
In this work, we study the oscillatory behavior of solutions of a class of first order impulsive neutral delay differential equations of the formfor all p(t) with |p(t)| < ∞.
