HANDS ON WITH OPENMP4.5 and UNIFIED MEMORY: DEVELOPING APPLICATIONS FOR IBM'S HYBRID CPU+GPU SYSTEMS (PART II)
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97 MATHEMATICS AND COMPUTING↗
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Results for “Mathematical Computing”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Local Risk-Minimization for Defaultable Claims with Recovery Process
We study the local risk-minimization approach for defaultable claims with random recovery at default time, seen as payment streams on the random interval [0,{tau} Logical-And T], where T denotes the fixed time-horizon. We find the pseudo-locally risk-minimizing strategy in the case when the agent information takes into account the possibility of a default event (local risk-minimization with G-strategies) and we provide an application in the case of a corporate bond. We also discuss the problem of finding a pseudo-locally risk-minimizing strategy if we suppose the agent obtains her information only by observing the non-defaultable assets.
97 MATHEMATICS AND COMPUTING↗
A Probabilistic-Numerical Approximation for an Obstacle Problem Arising in Game Theory
We investigate a two-player zero-sum stochastic differential game in which one of the players has more information on the game than his opponent. We show how to construct numerical schemes for the value function of this game, which is given by the solution of a quasilinear partial differential equation with obstacle.
97 MATHEMATICS AND COMPUTING↗
Global Existence and Uniqueness of Weak and Regular Solutions of Shallow Shells with Thermal Effects
We study a dynamical thin shallow shell whose elastic deformations are described by a nonlinear system of Marguerre–Vlasov’s type under the presence of thermal effects. Our main result is the proof of a global existence and uniqueness of a weak solution in the case of clamped boundary conditions. Standard techniques for uniqueness do not work directly in this case. We overcame this difficulty using recent work due to Lasiecka (Appl Anal 4:1376–1422, 1998).
97 MATHEMATICS AND COMPUTING↗
Optimal Control of the Rigid Inclusion Size in the Problem of Equilibrium of Inhomogeneous Timoshenko Type Plates Containing Cracks
We consider the equilibrium problem for plates with cracks located along rigid inclusions and analyze the dependence of the solution and the derivative of the energy functional on variations of the inclusion size. We establish the solvability of the optimal control problem, where the quality functional is given by the derivative of the energy functional, whereas the control parameter correspond to the inclusion size. A similar analysis is performed for the equilibrium problems for inhomogeneous plates with rigid delaminated inclusions.
97 MATHEMATICS AND COMPUTING↗
D-Guaranteed Discrimination of Statistical Hypotheses: a Review of Results and Unsolved Problems
We compare two sequential d-guaranteed tests and an optimal d-guaranteed test based on a fixed number of observations with respect to the average number of observations within the most accepted practical applications of Bayesian probabilistic models. We consider the sequential “first skipping” test, the sequential locally efficient test based on the score statistic, and the test based on a fixed number of observations that minimizes the necessary sample size. We study various characteristics of these tests connected with the number of observations within three probabilistic models, namely, the normal (ϑ, σ{sup 2}) distribution of the observed random variable and the normal a priori distribution of ϑ with fixed σ{sup 2}; the exponential distribution with the intensity parameter ϑ and the a priori gamma distribution of ϑ; and the Bernoulli sampling with the success probability ϑ and the a priori beta distribution of ϑ. We discuss the connection of the d-posterior approach with the compound decision problem as applied to the analysis of data provided by microchips (when the false discovery rate, or FDR, for short, is treated as the d-risk of the first kind). We present the vast data on characteristics of the mentioned tests obtained by the method of mathematical modeling in several tables. We discuss unsolved problems of the d-guaranteed discrimination of hypotheses with the minimal number of observations and approaches to their solution.
97 MATHEMATICS AND COMPUTING↗
Filtration of stationary Gaussian statistical experiments
The filtration of stationary Gaussian statistical experiments is determined by a solution of the equation of optimum filtration, which is characterized by the two-dimensional matrix of covariances. The parameters of a filtered signal are set by empiric covariances.
97 MATHEMATICS AND COMPUTING↗
On Bounded Solutions of a Difference Equation with Jumps of the Operator Coefficient
We study the problem of existence of unique bounded solution of a difference equation with variable operator coefficient in the finite-dimensional Banach space.
97 MATHEMATICS AND COMPUTING↗
Estimates in the Problem of Ideals in the Algebra H{sup ∞}
By using the fixed-point approach due to D. Rutsky, the problem of ideals in H{sup ∞} is solved for “data sequences” in H{sup ∞}(l{sup 1}) (instead of H{sup ∞}(l{sup 2}) in the traditional setting). Bibliography: 7 titles.
97 MATHEMATICS AND COMPUTING↗
A{sub 1}-Regularity and Boundedness of Riesz Transforms in Banach Lattices of Measurable Functions
Let X be a Banach lattice of measurable functions on ℝ{sup n} × Ω having the Fatou property. We show that the boundedness of all Riesz transforms R{sub j} in X is equivalent to the boundedness of the Hardy–Littlewood maximal operator M in both X and X′, and thus to the boundedness of all Calderón–Zygmund operators in X. We also prove a result for the case of operators between lattices: If Y ⊃ X is a Banach lattice with the Fatou property such that the maximal operator is bounded in Y ′, then the boundedness of all Riesz transforms from X to Y is equivalent to the boundedness of the maximal operator from X to Y , and thus to the boundedness of all Calderón–Zygmund operators from X to Y .
97 MATHEMATICS AND COMPUTING↗
Sufficient Condition for Consistency of Infinite Systems
Based on the theory of double series, we obtain a sufficient condition for the existence of strictly partial solutions to infinite systems of linear algebraic equations. We prove series expansion theorems for infinite determinants of Gaussian infinite matrices. Examples of application of the proposed condition are given.
97 MATHEMATICS AND COMPUTING↗
Groups with Almost Regular and Almost Perfect Involutions
We establish the solubility of a group with Sylow 2-subgroup of the least order in the centralizer of an almost regular involution. We also study the structure of a group G with an almost perfect and almost regular involution a.
97 MATHEMATICS AND COMPUTING↗
Prym Differentials on Variable Tori
We consider multiplicative functions and Prym differentials on variable tori. We prove counterparts of the theorem on the total sum of residues for Prym differentials of any integer order on tori. As a consequence, reciprocity laws are proved. We construct elementary Prym differentials of all kinds with any integer order which holomorphically depend on the moduli of tori and characters. We derive an analogue of the Appell decomposition formula for functions with characters. We also study vector bundles of Prym differentials of any integer order over the product of Teichmueller spaces for a torus and a group of characters.
97 MATHEMATICS AND COMPUTING↗
Exact Conditions of Oscillation of Solutions to Differential Equations with Several Delays
We obtain new nonimprovable conditions of oscillation of all solutions to a linear differential equation with several variable delays and positive coefficients. These conditions have the form of the upper and lower limits of the sum of integrals of the coefficients over the sets that are determined only by the delay corresponding to this coefficient. These results differ from the well-known results in which a coarsening of the integration set is assumed.
97 MATHEMATICS AND COMPUTING↗
Neumann problem in a disk for fourth-order improperly elliptic equations
We have established and investigated the sufficient conditions of solvability of the Neumann problem for all classes of fourth-order improperly elliptic equations in a unit disk K in the space C{sup 4}(K) ∩C{sup 3,α}(K).
97 MATHEMATICS AND COMPUTING↗
A Cliffed Cape Does Not Trap Water Waves in the Sea of Constant Depth
The water wave problem is considered for a class of semi-infinite domains each having its shore shaped as a cliffed cape. In particular, the free surface of a water domain is supposed to be an infinite sector whose vertex angle is greater than π, whereas the water layer lying under the free surface is of constant depth. Under these assumptions it is shown that there are no trapped mode solutions of the problem for all values of a non-dimensional spectral parameter; in other words, no point eigenvalues are embedded in the continuous spectrum of the problem.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Integral Problem for a Partial Differential Equation of High Order in an Infinite Strip
We establish conditions for the existence, in the scale of Sobolev spaces, of a unique solution to the problem for partial differential equations of high order with integral conditions in the form of moments. The solution of this problem is constructed with the help of Fourier transforms.
97 MATHEMATICS AND COMPUTING↗
On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components
A graph is called cyclically 4-edge-connected if removing any three edges from it results in a graph in which at most one connected component contains a cycle. A 3-connected graph is 4-edge-connected if and only if removing any three edges from it results in either a connected graph or a graph with exactly two connected components one of which is a single-vertex one. We show how to associate with any 3-connected graph a tree of components such that every component is a 3-connected and cyclically 4-edge-connected graph.
97 MATHEMATICS AND COMPUTING↗