Infinite horizon stopping problems with (nearly) total reward criteria

We study an infinite horizon optimal stopping Markov problem which is either undiscounted (total reward) or with a general Markovian discount rate. Using ergodic properties of the underlying Markov process, we establish the feasibility of the stopping problem and prove the existence of optimal and ε$\epsilon$-optimal stopping times. We show the continuity of the value function and its variational characterisation (in the viscosity sense) under different sets of assumptions satisfied by large classes of diffusion and jump–diffusion processes. In the case of a general discounted problem we relax a classical assumption that the discount rate is uniformly separated from zero.     

On the equivalence of the BLUEs under a general linear model and its restricted and stochastically restricted models

Necessary and sufficient conditions are derived for the equalities of the best linear unbiased estimators (BLUEs) of parametric functions under a general linear model and its restricted and stochastically restricted models to hold.     

Comment on “A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family”, P. Yu,X.X. Liao,S.L. Xie,Y.L. Fu [Commun Nonlinear Sci Numer Simulat 14 (2009) 2886–2896]

In the commented paper the authors study some aspects of boundedness in the general Lorenz family, $\dot{x}=\sigma (y-x)\text{,}\dot{y}=\rho x-\gamma y-\mathit{xz}\text{,}\dot{z}=-\beta z+\mathit{xy}$, considering that it contains four independent parameters. However, as we show here by means of a linear scaling in time and coordinates, they are dealing with a system homothetically equivalent to the Lorenz system. Consequently, the novel and interesting results they provide for the general Lorenz family can be obtained working directly with the Lorenz equations, that is, dealing only with three independent parameters.     

GENERAL EQUILIBRIUM ECOSYSTEM MODELING WITH ALTERNATIVE PREFERENCE SPECIFICATIONS

This paper reconciles two sets of literature with regard to the interactive ecological and economic impacts of invasive grass species and cattle stocking. We model cattle as optimal foragers, satiation foragers, and proportional foragers in order to understand the impact that each assumption imposes on predicted economic and ecological outcomes. Through this model sensitivity (as opposed to parameter sensitivity) analysis, we are able to identify three main drivers of plant invasions: exogenous forces such as climate change or nitrogen deposition, poor land management decisions, and a misalignment of incentives between cattle and ranchers even when ranchers behave optimally.     

GENERAL MINIMAX ESTIMATORS ON THE LOCATION MATRIX OF A MIXTURE OF NORMALS

This paper considers the estimate problem on the mean matrix of mixtureof normals. In order to evaluate estimators of the mean matrix, a fundamental frameof Ф-(general) decision problem is established. Under the frame, a class of Ф-minimax estimators are constructed.     

Schur‐convexity and quadrature formulae

This paper aims to contribute to the exploration of quadrature formulae by proving that the error of a quadrature formula has the Schur‐convexity property. The emphasis is on the quadrature formulae with the maximum degree of precision. The Schur‐convexity of the error has an interesting implication – the monotonicity of the error. Namely, it turns out that the absolute value of the error is always smaller on a smaller interval (of the two which share the same midpoint).     

Accuracies and conservation errors of various ghost fluid methods for multi-medium Riemann problem

Since the (original) ghost fluid method (OGFM) was proposed by Fedkiw et al. in 1999 [5], a series of other GFM-based methods such as the gas–water version GFM (GWGFM), the modified GFM (MGFM) and the real GFM (RGFM) have been developed subsequently. Systematic analysis, however, has yet to be carried out for the various GFMs on their accuracies and conservation errors. In this paper, we develop a technique to rigorously analyze the accuracies and conservation errors of these different GFMs when applied to the multi-medium Riemann problem with a general equation of state (EOS). By analyzing and comparing the interfacial state provided by each GFM to the exact one of the original multi-medium Riemann problem, we show that the accuracy of interfacial treatment can achieve “third-order accuracy” in the sense of comparing to the exact solution of the original mutli-medium Riemann problem for the MGFM and the RGFM, while it is of at most “first-order accuracy” for the OGFM and the GWGFM when the interface approach is actually near in balance. Similar conclusions are also obtained in association with the local conservation errors. A special test method is exploited to validate these theoretical conclusions from the numerical viewpoint.     

Persistent currents in mesoscopic rings and conformal invariance

The effect of point defects on persistent currents in mesoscopic rings is studied in a simple tight-binding model. Using an analogy with the treatment of the critical quantum Ising chain with defects, conformal invariance techniques are employed to relate the persistent current amplitude to the Hamiltonian spectrum just above the Fermi energy. From this, the dependence of the current on the magnetic flux is found exactly for a ring with one or two point defects. The effect of an aperiodic modulation of the ring, generated through a binary substitution sequence, on the persistent current is also studied. The flux-dependence of the current is found to vary remarkably between the Fibonacci and the Thue-Morse sequences. Received: 4 March 1998 / Revised: 20 April 1998 / Accepted: 30 April 1998     

Regularized collocation method for Fredholm integral equations of the first kind

In this paper we consider a collocation method for solving Fredholm integral equations of the first kind, which is known to be an ill-posed problem. An “unregularized” use of this method can give reliable results in the case when the rate at which smallest singular values of the collocation matrices decrease is known a priori. In this case the number of collocation points plays the role of a regularization parameter. If the a priori information mentioned above is not available, then a combination of collocation with Tikhonov regularization can be the method of choice. We analyze such regularized collocation in a rather general setting, when a solution smoothness is given as a source condition with an operator monotone index function. This setting covers all types of smoothness studied so far in the theory of Tikhonov regularization. One more issue discussed in this paper is an a posteriori choice of the regularization parameter, which allows us to reach an optimal order of accuracy for deterministic noise model without any knowledge of solution smoothness.