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A geometric formulation of singular partial differential equations (PDEs) is considered. Surgery techniques and integral bordism groups are utilized, following previous works by Prástaro on PDEs, in order to build global solutions crossing also singular points and to study their stability properties. 相似文献
33.
This study focuses on nonlocal boundary value problems (BVPs) for linear and nonlinear elliptic differential-operator equations (DOEs) that are defined in Banach-valued function spaces. The considered domain is a region with varying bound and depends on a certain parameter. Some conditions that guarantee the maximal Lp -regularity and Fredholmness of linear BVPs, uniformly with respect to this parameter, are presented. This fact implies that the appropriate differential operator is a generator of an analytic semigroup. Then, by using these results, the existence, uniqueness and maximal smoothness of solutions of nonlocal BVPs for nonlinear DOEs are shown. These results are applied to nonlocal BVPs for regular elliptic partial differential equations, finite and infinite systems of differential equations on cylindrical domains, in order to obtain the algebraic conditions that guarantee the same properties. 相似文献
34.
Marco Carvalho Alexey Sorokin Vladimir Boginski Balabhaskar Balasundaram 《Optimization Letters》2013,7(4):695-707
One way to achieve reliability with low-latency is through multi-path routing and transport protocols that build redundant delivery channels (or data paths) to reduce end-to-end packet losses and retransmissions. However, the applicability and effectiveness of such protocols are limited by the topological constraints of the underlying communication infrastructure. Multiple data delivery paths can only be constructed over networks that are capable of supporting multiple paths. In mission-critical wireless networks, the underlying network topology is directly affected by the terrain, location and environmental interferences, however the settings of the wireless radios at each node can be properly configured to compensate for these effects for multi-path support. In this work we investigate optimization models for topology designs that enable end-to-end dual-path support on a distributed wireless sensor network. We consider the case of a fixed sensor network with isotropic antennas, where the control variable for topology management is the transmission power on network nodes. For optimization modeling, the network metrics of relevance are coverage, robustness and power utilization. The optimization models proposed in this work eliminate some of the typical assumptions made in the pertinent network design literature that are too strong in this application context. 相似文献
35.
Wassim M. Haddad Emmanuel G. Collins Jr. Raymond Moser 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(4):299-318
Models of systems are always inexact. Hence, to better predict the performance of a system it is necessary to take into account uncertainty in a nominal model of a system. The structured singular value was developed to nonconservatively analyze robust stability and performance for systems with multiple-block uncertainty. In practice, optimization techniques are used to compute an upper bound on the structured singular value. For dynamic uncertainty with bounded magnitude and arbitrary phase (i.e., "complex uncertainty"), the standard approach to computing an upper bound involves finding diagonal scaling matrices D(jω) that minimize σmax (D(jω)G(jω)D-1(jω)) over a (theoretically) infinite number of frequencies. The order of the corresponding stable, minimum phase, rational function D(s) (if it exists) is hence arbitrary, which can lead to very high order controllers when D(s) is used for controller synthesis. This paper develops a fixed-structure approach to computing an upper bound for the complex structured singular value. In particular, by relying on results from mixed-norm H2/H∞ analysisD(s) is a priori constrained to be a rational matrix function of a chosen order and a new approach to computing an upper bound on the structured singular value is developed. The results are illustrated using two examples which clearly demonstrate the suboptimality of standard curve fitting. The proposed approach can be extended to mixed uncertainty and structured singular value controller synthesis without D — K type iteration. 相似文献
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Suppose that for i = 1,2, a Bernoulli random variable with success probability θi is observable from population i. The problem is to estimate θ = θ1θ2 using a Bayesian approach with squared error estimation loss in θ. For estimating θ, the best nonrandom sampling scheme, the two-stage sampling scheme, and the optimal sampling scheme are discussed. It is shown that the two-stage sampling scheme is typically asymptotically optimal, and can improve the Bayes risk (over the best nonrandom allocation) up to fifty percent 相似文献
38.
Let ∏1,…,∏k denote k independent populations, where a random observation from population ∏ i has a uniform distribution over the interval (0,θ i ) and θ i is a realization of a random variable having an unknown prior distribution G i . Population ∏ i is said to be a good population if θ i ≥θ0, where θ0 is a given, positive number. This paper provides a sequence of empirical Bayes procedures for selecting the good populationsamong ∏1,…,∏ k . It is shown that these procedures are asymptotically optimal and that the order of associated convergence rates is O(n-r/4) for some r, 0<r<2, where n is the number of accumulated past observations at hand 相似文献
39.
《Physics letters. [Part B]》2002,524(1-2):55-64
Bose–Einstein correlations of both neutral and like-sign charged pion pairs are measured in a sample of 2 million hadronic Z decays collected with the L3 detector at LEP. The analysis is performed in the four-momentum difference range 300 MeV<Q<2 GeV. The radius of the neutral pion source is found to be smaller than that of charged pions. This result is in qualitative agreement with the string fragmentation model. 相似文献
40.