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41.
A q × n array with entries from 0, 1,…,q − 1 is said to form a difference matrix if the vector difference (modulo q) of each pair of columns consists of a permutation of [0, 1,… q − 1]; this definition is inverted from the more standard one to be found, e.g., in Colbourn and de Launey (1996). The following idea generalizes this notion: Given an appropriate δ (-[−1, 1]t, a λq × n array will be said to form a (t, q, λ, Δ) sign-balanced matrix if for each choice C1, C2,…, Ct of t columns and for each choice = (1,…,t) Δ of signs, the linear combination ∑j=1t jCj contains (mod q) each entry of [0, 1,…, q − 1] exactly λ times. We consider the following extremal problem in this paper: How large does the number k = k(n, t, q, λ, δ) of rows have to be so that for each choice of t columns and for each choice (1, …, t) of signs in δ, the linear combination ∑j=1t jCj contains each entry of [0, 1,…, q t- 1] at least λ times? We use probabilistic methods, in particular the Lovász local lemma and the Stein-Chen method of Poisson approximation to obtain general (logarithmic) upper bounds on the numbers k(n, t, q, λ, δ), and to provide Poisson approximations for the probability distribution of the number W of deficient sets of t columns, given a random array. It is proved, in addition, that arithmetic modulo q yields the smallest array - in a sense to be described. 相似文献
42.
《Journal of Functional Analysis》2007,247(1):138-168
We investigate some basic questions concerning the relationship between the restricted Grassmannian and the theory of Banach Lie-Poisson spaces. By using universal central extensions of Lie algebras, we find that the restricted Grassmannian is symplectomorphic to symplectic leaves in certain Banach Lie-Poisson spaces, and the underlying Banach space can be chosen to be even a Hilbert space. Smoothness of numerous adjoint and coadjoint orbits of the restricted unitary group is also established. Several pathological properties of the restricted algebra are pointed out. 相似文献
43.
Iddo Eliazar 《Queueing Systems》2007,55(1):71-82
We explore M/G/∞ systems ‘fed’ by Poissonian inflows with infinite arrival rates. Three processes – corresponding to the system's state, workload, and queue-size – are studied and analyzed. Closed form formulae characterizing the system's stationary structure and correlation structure are derived. And, the issues of queue finiteness, workload summability, and Long Range Dependence are investigated.
We then turn to devise a ‘reverse engineering’ scheme for the design of the system's correlation structure. Namely: how to construct an M/G/∞ system with a pre-desired ‘target’ workload/queue auto-covariance function. The ‘reverse engineering’ scheme is applied
to various examples, including ones with infinite queues and non-summable workloads.
AMS Subject Classifications Primary: 60K25; Secondary: 60G55, 60G10 相似文献
44.
Peter A. Markowich Gerhard Rein Gershon Wolansky 《Journal of statistical physics》2002,106(5-6):1221-1239
We consider the Schrödinger–Poisson system in the repulsive (plasma physics) Coulomb case. Given a stationary state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov function. To obtain such states we start with a given Casimir functional and construct a new functional which is in some sense dual to the corresponding energy-Casimir functional. This dual functional has a unique maximizer which is a stationary state of the Schrödinger–Poisson system and lies in the stability class. The stationary states are parameterized by the equation of state, giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels. 相似文献
45.
We have carried out some photon interaction measurements using 59.54 keV γ-rays from a 241Am source. These include γ attenuation studies as well as photoelectric absorption studies in various samples. The attenuation
studies have been made using leaf and wood samples, samples like sand, sugar etc., which contain particles of varying sizes
as well as pellets and aqueous solutions of rare earth compounds. In the case of the leaf and wood samples, we have used the
γ-ray attenuation technique for the determination of the water content in fresh and dried samples. The variation of the attenuation
coefficient with particle size has been investigated for sand and sugar samples. The attenuation studies as well as the photoelectric
studies in the case of rare earth elements have been carried out on samples containing such elements whose K-absorption edge
energies lie below and close to the γ-energy used. Suitable compounds of the rare earth elements have been chosen as mixture
absorbers in these investigations. A narrow beam good geometry set-up was used for the attenuation measurements. A well-shielded
scattering geometry was used for the photoelectric measurements. The mixture rule was invoked to extract the values of the
mass attenuation coefficients for the elements from those of the corresponding compounds. The results are consistent with
theoretical values derived from the XCOM package. 相似文献
46.
Wolfgang Stadje 《Journal of Theoretical Probability》1998,11(1):197-208
For increasing sequences of real numbers we consider two types of asymptotic behavior that remind of the defining property of a (homogeneous) Poisson process according to which the numbers of points in disjoint intervals are independent and follow Poisson distributions with specified parameters. We prove that almost all paths of a Poisson process show this asymptotic behavior, and characterize the Poisson process by these properties. Further we discuss the connection to equidistribution notions. 相似文献
47.
Consider discrete storage processes that are modulated by environmental processes. Environmental processes cause interruptions in the input and/or output processes of the discrete storage processes. Due to the difficulties encountered in the exact analysis of such discrete storage systems, often Poisson flow and/or fluid flow models with the same modulating environmental processes are proposed as approximations for these systems. The analysis of Poisson flow and fluid flow models is much easier than that of the discrete storage processes. In this paper we give sufficient conditions under which the content of the discrete storage processes can be bounded by the Poisson flow and the fluid flow models. For example, we show that Poisson flow models and the fluid flow models developed by Kosten (and by Anick, Mitra and Sondhi) can be used to bound the performance of infinite (finite) source packetized voice/data communication systems. We also show that a Poisson flow model and the fluid flow model developed by Mitra can be used to bound the buffer content of a two stage automatic transfer line. The potential use of the bounding techniques presented in this paper, of course, transcends well beyond these examples.Supported in part by NSF grant DMS-9308149. 相似文献
48.
The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed.
After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations
of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion
of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations
of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total
trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding
Heisenberg equations.
Project supported by Prof. T.D. Lee’s NNSC Grant, the National Natural Science Foundation of China, the Foundation of Ph.
D. Directing Programme of Chinese University, and the Chinese Academy of Sciences. 相似文献
49.
Richard F. Serfozo 《Queueing Systems》1989,5(1-3):5-36
A Markovian network process describes the movement of discrete units among a set of nodes that process the units. There is considerable knowledge of such networks, often called queueing networks, in which the nodes operate independently and the routes of the units are independent. The focus of this study, in contrast, is on networks with dependent nodes and routings. Examples of dependencies are parallel processing across several nodes, blocking of transitions because of capacity constraints on nodes, alternate routing of units to avoid congestion, and accelerating or decelerating the processing rate at a node depending on downstream congestion. We introduce a general network process representing the numbers of units at the nodes and derive its equilibrium distribution. This distribution takes the form of a product of functions of vectors in which the arguments of the functions satisfy an interchangeability property. This new type of distribution may apply to other multi-variate processes as well. A basic idea in our approach is a linking of certain micro-level balance properties of the network routing to the processing rates at the nodes. The link is via routing-balance partitions of nodes that are inherent in any network. A byproduct of this approach is a general characterization of blocking of transitions without the restriction that the process is reversible, which had been a standard assumption. We also give necessary and sufficient conditions under which a unit moving in the network sees a time average for the unmoved units (called the MUSTA property). Finally, we discuss when certain flows between nodes in an open network are Poisson processes.This research was sponsored in part by Air Force Office of Scientific Research contract 84-0367. 相似文献
50.
A. Pellegrinotti 《Journal of statistical physics》1988,53(5-6):1327-1336
A transformation on the two-dimensional torus which is related to the problem of limit distribution for the distance between the levels in the kicked-rotator model is considered. The first four moments of the r.w. which describe the numbers of visits of a point in a rectangle of measure are calculated. It is shown that when 0 they converge to the first four moments of a Poisson r.w. 相似文献