Optimal control of a stochastic hybrid system with discounted cost

We address the optimal control problem of a very general stochastic hybrid system with both autonomous and impulsive jumps. The planning horizon is infinite and we use the discounted-cost criterion for performance evaluation. Under certain assumptions, we show the existence of an optimal control. We then derive the quasivariational inequalities satisfied by the value function and establish well-posedness. Finally, we prove the usual verification theorem of dynamic programming.

The complexity of certain incremental code generation problems

This paper looks at the complexity of four different incremental problems. The following are the problems considered: (1) Interval partitioning of a flow graph (2) Breadth first search (BFS) of a directed graph (3) Lexicographic depth first search (DFS) of a directed graph (4) Constructing the postorder listing of the nodes of a binary tree. The last problem arises out of the need for incrementally computing the Sethi-Ullman (SU) ordering [1] of the subtrees of a tree after it has undergone changes of a given type. These problems are among those that claimed our attention in the process of our designing algorithmic techniques for incremental code generation. BFS and DFS have certainly numerous other applications, but as far as our work is concerned, incremental code generation is the common thread linking these problems. The study of the complexity of these problems is done from two different perspectives. In [2] is given the theory of incremental relative lower bounds (IRLB). We use this theory to derive the IRLBs of the first three problems. Then we use the notion of a bounded incremental algorithm [4] to prove the unboundedness of the fourth problem with respect to the locally persistent model of computation. Possibly, the lower bound result for lexicographic DFS is the most interesting. In [5] the author considers lexicographic DFS to be a problem for which the incremental version may require the recomputation of the entire solution from scratch. In that sense, our IRLB result provides further evidence for this possibility with the proviso that the incremental DFS algorithms considered be ones that do not require too much of preprocessing.

Microwave heating in multiphase systems: evaluation of series solutions

The 1D electric field and heat-conduction equations are solved for a slab where the dielectric properties vary spatially in the sample. Series solutions to the electric field are obtained for systems where the spatial variation in the dielectric properties can be expressed as polynomials. The series solution is used to obtain electric-field distributions for a binary oil-water system where the dielectric properties are assumed to vary linearly within the sample. Using the finite-element method temperature distributions are computed in a three-phase oil, water and rock system where the dielectric properties vary due to the changing oil saturation in the rock. Temperature distributions predicted using a linear variation in the dielectric properties are compared with those obtained using the exact nonlinear variation.

Computer-Aided Reliability Analysis of Complicated Networks

A computer-aided procedure is described for analyzing the reliability of complicated networks. This procedure breaks down a network into small subnetworks whose reliability can be more readily calculated. The subnetworks which are searched for are those with only two nodes; this allows the original network to be considerably simplified.

Computer-Aided Reliability Analysis of Complicated Networks

A computer-aided procedure is described for analyzing the reliability of complicated networks. This procedure breaks down a network into small subnetworks whose reliability can be more readily calculated. The subnetworks which are searched for are those with only two nodes; this allows the original network to be considerably simplified.

The pursuit-evasion problem of two aircraft in a horizontal plane

The pursuit-evasion problem of two aircraft in a horizontal plane is modelled as a zerosum differential game with capture time as payoff. The aircraft are modelled as point masses with thrust and bank angle controls. The games of kind and degree for this differential game are solved.

A numerical study of variable coefficient elliptic Cauchy problem via projection method

In this paper, we investigate a numerical method for the solution of an inverse problem of recovering lacking data on some part of the boundary of a domain from the Cauchy data on other part for a variable coefficient elliptic Cauchy problem. In the process, the Cauchy problem is transformed into the problem of solving a compact linear operator equation. As a remedy to the ill-posedness of the problem, we use a projection method which allows regularization solely by discretization. The discretization level plays the role of regularization parameter in the case of projection method. The balancing principle is used for the choice of an appropriate discretization level. Several numerical examples show that the method produces a stable good approximate solution.

Wet and dry spell characteristics of global tropical rainfall

In this study, we analyze satellite-based daily rainfall observations to compare and contrast the wet and dry spell characteristics of tropical rainfall. Defining a wet (dry) spell as the number of consecutive rainy (nonrainy) days, we find that the distributions of wet spells appear to exhibit universality in the following sense. While both ocean and land regions with high seasonal rainfall accumulation (humid regions; e. g., India, Amazon, Pacific Ocean) show a predominance of 2-4 day wet spells, those regions with low seasonal rainfall accumulation (arid regions; e. g., South Atlantic, South Australia) exhibit a wet spell duration distribution that is essentially exponential in nature, with a peak at 1 day. The behavior that we observed for wet spells is reversed for the dry spell characteristics. In other words, the main contribution to the dry part of the season, in terms of the number of nonrainy days, appears to come from 3-4 day dry spells in the arid regions, as opposed to 1 day dry spells in the humid regions. The total rainfall accumulated in each wet spell has also been analyzed, and we find that the major contribution to seasonal rainfall for arid regions comes from 1-5 day wet spells; however, for humid regions, this contribution comes from wet spells of duration as long as 30 days. We also explore the role of chance as well as the influence of organized convection in determining some of the observed features.

Modeling the vulnerability of an urban groundwater system due to the combined impacts of climate change and management scenarios

Climate change impact on a groundwater-dependent small urban town has been investigated in the semiarid hard rock aquifer in southern India. A distributed groundwater model was used to simulate the groundwater levels in the study region for the projected future rainfall (2012-32) obtained from a general circulation model (GCM) to estimate the impacts of climate change and management practices on groundwater system. Management practices were based on the human-induced changes on the urban infrastructure such as reduced recharge from the lakes, reduced recharge from water and wastewater utility due to an operational and functioning underground drainage system, and additional water extracted by the water utility for domestic purposes. An assessment of impacts on the groundwater levels was carried out by calibrating a groundwater model using comprehensive data gathered during the period 2008-11 and then simulating the future groundwater level changes using rainfall from six GCMs Institute of Numerical Mathematics Coupled Model, version 3.0 (INM-CM. 3.0); L'Institut Pierre-Simon Laplace Coupled Model, version 4 (IPSL-CM4); Model for Interdisciplinary Research on Climate, version 3.2 (MIROC3.2); ECHAM and the global Hamburg Ocean Primitive Equation (ECHO-G); Hadley Centre Coupled Model, version 3 (HadCM3); and Hadley Centre Global Environment Model, version 1 (HadGEM1)] that were found to show good correlation to the historical rainfall in the study area. The model results for the present condition indicate that the annual average discharge (sum of pumping and natural groundwater outflow) was marginally or moderately higher at various locations than the recharge and further the recharge is aided from the recharge from the lakes. Model simulations showed that groundwater levels were vulnerable to the GCM rainfall and a scenario of moderate reduction in recharge from lakes. Hence, it is important to sustain the induced recharge from lakes by ensuring that sufficient runoff water flows to these lakes.

On Additive Combinatorics of Permutations of Z(n)

Let Z(n) denote the ring of integers modulo n. A permutation of Z(n) is a sequence of n distinct elements of Z(n). Addition and subtraction of two permutations is defined element-wise. In this paper we consider two extremal problems on permutations of Z(n), namely, the maximum size of a collection of permutations such that the sum of any two distinct permutations in the collection is again a permutation, and the maximum size of a collection of permutations such that no sum of two distinct permutations in the collection is a permutation. Let the sizes be denoted by s (n) and t (n) respectively. The case when n is even is trivial in both the cases, with s (n) = 1 and t (n) = n!. For n odd, we prove (n phi(n))/2(k) <= s(n) <= n!.2(-)(n-1)/2/((n-1)/2)! and 2 (n-1)/2 . (n-1/2)! <= t (n) <= 2(k) . (n-1)!/phi(n), where k is the number of distinct prime divisors of n and phi is the Euler's totient function.

Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self-Mappings

p(>= 2)-cyclic and contractive self-mappings on a set of subsets of a metric space which are simultaneously accretive on the whole metric space are investigated. The joint fulfilment of the p-cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self-mappings in order to be Kannan self-mappings. The existence and uniqueness of best proximity points and fixed points is also investigated as well as some related properties of composed self-mappings from the union of any two adjacent subsets, belonging to the initial set of subsets, to themselves.

Stability and Limit Oscillations of a Control Event-Based Sampling Criterion

This paper investigates the presence of limit oscillations in an adaptive sampling system. The basic sampling criterion operates in the sense that each next sampling occurs when the absolute difference of the signal amplitude with respect to its currently sampled signal equalizes a prescribed threshold amplitude. The sampling criterion is extended involving a prescribed set of amplitudes. The limit oscillations might be interpreted through the equivalence of the adaptive sampling and hold device with a nonlinear one consisting of a relay with multiple hysteresis whose parameterization is, in general, dependent on the initial conditions of the dynamic system. The performed study is performed on the time domain.

Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

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