Heat conduction in a rock mass with an annular hot water store

Vast subterranean caverns may be used for hot water storage in distinct heating schemes; such caverns can be annular, with a central pillar. This paper considers the quasi-steady solution of the heat conduction equation for this geometry with periodic temperature variations     

Interface interactions in modulated phases,and upsilon points

Certain features in Frenkel-Kontorova and other models of phases with a one-dimensional modulation can be analyzed by assuming parallel interfaces separating sets of lattice planes belonging to two different phases, and treating the free energy to create interfaces, as well as the interaction of two, three, or more interfaces, as phenomenological parameters. A strategy employed by Fisher and Szpilka for interacting defects can be extended to the case of interfaces, allowing a systematic study of the phase diagram by ignoring all interface interactions, and then successively taking into account pair, triple, and higher-order terms. The possible phase diagrams which can occur near the point where =0 include: various sorts of endpoints analogous to critical endpoints, an accumulation point of first-order transitions and triple points, and a self-similar structure which we call an upsilon point, which turns out to be an accumulation point of an infinite number of segments of first-order transition lines, each of which terminates in two upsilon points.     

A decomposition result for a class of polling models

Boxma and Groenendijk have shown that the workload in polling models decomposes into two independent variables. This paper demonstrates a different type of decomposition that has an explicit multi-dimensional form. This decomposition does not apply to all polling models, but does, for example, apply to models with constant switch-over times and either exhaustive or gated service disciplines. For such models, we show that the population of customers present in the system (represented by a vector indicating the number of customers at each queue) at key time points breaks into two independent subpopulations: (1) the population of customers present in the related model with zero switch-over times; (2) another population, which is particularly easy to analyze. This result has a number of theoretical and applied implications.     

Optimal estimation in random coefficient regression models

In linear regression models with random coefficients, the score function usually involves unknown nuisance parameters in the form of weights. Conditioning with respect to the sufficient statistics for the nuisance parameter, when the parameter of interest is held fixed, eliminates the nuisance parameters and is expected to give reasonably good estimating functions. The present paper adopts this approach to the problem of estimation of average slope in random coefficient regression models. Four sampling situations are discussed. Some asymptotic results are also obtained for a model where neither the regressors nor the random regression coefficients replicate. Simulation studies for normal as well as non-normal models show that the performance of the suggested estimating functions is quite satisfactory.     

A constrained min‐max algorithm for rival models of the same economic system

There are well established rival theories about the economy. These have, in turn, led to the development of rival models purporting to represent the economic system. The models are large systems of discrete-time nonlinear dynamic equations. Observed data of the real system does not, in general, provide sufficient information for statistical methods to invalidate all but one of the rival models. In such a circumstance, there is uncertainty about which model to use in the formulation of policy. Prudent policy design would suggest that a model-based policy should take into account all the rival models. This is achieved as a pooling of the models. The pooling that yields the policy which is robust to model choice is formulated as a constrained min-max problem. The minimization is over the decision variables and the maximization is over the rival models. Only equality constraints are considered.A successive quadratic programming algorithm is discussed for the solution of the min-max problem. The algorithm uses a stepsize strategy based on a differentiable penalty function for the constraints. Two alternative quadratic subproblems can be used. One is a quadratic min-max and the other a quadratic programming problem. The objective function of either subproblem includes a linear term which is dependent on the penalty function. The penalty parameter is determined at every iteration, using a strategy that ensures a descent property as well as the boundedness of the penalty term. The boundedness follows since the strategy is always satisfied for finite values of the parameter which needs to be increased a finite number of times.The global and local convergence of the algorithm is established. The conditions, involving projected Hessian approximations, are discussed under which the algorithm achieves unit stepsizes and subsequently Q-superlinear convergence.     

Multicolor particle systems with large threshold and range

In this paper we consider the Greenberg-Hastings and cyclic color models. These models exhibit (at least) three different types of behavior. Depending on the number of colors and the size of two parameters called the threshold and range, the Greenberg-Hastings model either dies out, or has equilibria that consist of debris or fire fronts. The phase diagram for the cyclic color models is more complicated. The main result of this paper, Theorem 1, proves that the debris phase exists for both systems.     

A review of statistical models for global optimization

A review of statistical models for global optimization is presented. Rationality of the search for a global minimum is formulated axiomatically and the features of the corresponding algorithm are derived from the axioms. Furthermore the results of some applications of the proposed algorithm are presented and the perspectives of the approach are discussed.     

M/G/1/N vacation model with varying E-limited service discipline

We define and analyze anM/G/1/N vacation model that uses a service discipline that we call theE-limited with limit variation discipline. According to this discipline, the server provides service until either the system is emptied (i.e. exhausted) or a randomly chosen limit ofl customers has been served. The server then goes on a vacation before returning to service the queue again. The queue length distribution and the Laplace-Stieltjes transforms of the waiting time, busy period and cycle time distributions are found. Further, an expression for the mean waiting time is developed. Several previously analyzed service disciplines, including Bernoulli scheduling, nonexhaustive service and limited service, are special cases of the general varying limit discipline that is analyzed in this paper.     

广义线性模型(六)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 :建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的 :《MultivariateStatisticalModel ingBasedonGeneralizedLinearModles》。     

Analytic models for commuting operator tuples on bounded symmetric domains

For a domain in and a Hilbert space of analytic functions on which satisfies certain conditions, we characterize the commuting -tuples of operators on a separable Hilbert space  such that is unitarily equivalent to the restriction of to an invariant subspace, where is the operator -tuple on the Hilbert space tensor product  . For the unit disc and the Hardy space , this reduces to a well-known theorem of Sz.-Nagy and Foias; for a reproducing kernel Hilbert space on such that the reciprocal of its reproducing kernel is a polynomial in and  , this is a recent result of Ambrozie, Müller and the second author. In this paper, we extend the latter result by treating spaces for which ceases to be a polynomial, or even has a pole: namely, the standard weighted Bergman spaces (or, rather, their analytic continuation) on a Cartan domain corresponding to the parameter in the continuous Wallach set, and reproducing kernel Hilbert spaces for which is a rational function. Further, we treat also the more general problem when the operator is replaced by ,  being a certain generalization of a unitary operator tuple. For the case of the spaces on Cartan domains, our results are based on an analysis of the homogeneous multiplication operators on , which seems to be of an independent interest.