Realization of optical limiting with a magnetic fluid film

In this paper, optical limiting property in a magnetic fluid film is studied. The relationship between the emergent power and the incident power is investigated experimentally and theoretically. It is found that the limiting threshold is linear with the diaphragm aperture which accord with the theoretical prediction. The external magnetic field will affect the limiting property, and increase the limiting threshold.     

Development of a universal constant rate thermal analysis system for being used with any thermoanalytical instrument

The SCTA method implies to control the temperature in such a way that the reaction rate changes with the time according to a function previously defined by the user. Constant Rate Thermal Analysis (CRTA) is one of the most commonly used SCTA methods and implies achieving a temperature profile at which the reaction rate remains constant all over the process at a value previously selected by the user. This method permits to minimize the influence of heat and mass transfer phenomena on the forward reaction. The scope of this work is to develop a universal CRTA temperature controller that could be adapted to any thermoanalytical device. The thermoanalytical signal is programmed to follow a preset linear trend by means of a conventional controller that at the time controls a second conventional temperature programmer that forces the temperature to change for achieving the trend programmed for the thermoanalytical signal. Examples of the performance of this control system with a Thermobalance and a Thermomechanical Analyser (TMA) are given.     

Level shift operators for open quantum systems

Level shift operators describe the second-order displacement of eigenvalues under perturbation. They play a central role in resonance theory and ergodic theory of open quantum systems at positive temperatures. We exhibit intrinsic properties of level shift operators, properties which stem from the structure of open quantum systems at positive temperatures and which are common to all such systems. They determine the geometry of resonances bifurcating from eigenvalues of positive temperature Hamiltonians and they relate the Gibbs state, the kernel of level shift operators, and zero energy resonances. We show that degeneracy of energy levels of the small part of the open quantum system causes the Fermi Golden Rule Condition to be violated and we analyze ergodic properties of such systems.     

Local algebras in the representation of MV-algebras

In this paper we present several results about local MV-algebras, extending existing results given for MV-chains. The role of local MV-algebras in sheaf representation and weak boolean product is stressed and the relationship of local MV-algebras with varieties of MV-algebras is analyzed. Presented by S. Pulmannova. Received November 11, 2005; accepted in final form December 20, 2005.     

带有奇异项的临界增长p-Laplace方程的非平凡解

本文研究了一种带有奇异项的临界增长p-Laplace方程在N维空间中的有界集上非平凡解的问题,利用山路引理和集中紧性原理,得出方程在非线性项满足一定条件下有非平凡解的结果.     

Dynamic Nonlinear Modelization of Operational Supply Chain Systems

Supply Chain Management (SCM) is an important activity in all producing facilities and in many organizations to enable vendors, manufacturers and suppliers to interact gainfully and plan optimally their flow of goods and services. To realize this, a dynamic modelling approach for characterizing supply chain activities is opportune, so as to plan efficiently the set of activities over a distributed network in a formal and scientific way. The dynamical system will result so complex that it is not generally possible to specify the functional forms and the parameters of interest, relating outputs to inputs, states and stochastic terms by experiential specification methods. Thus the algorithm that will presented is Data Driven, determining simultaneously the functional forms, the parameters and the optimal control policy from the data available for the supply chain. The aim of this paper is to present this methodology, by considering dynamical aspects of the system, the presence of nonlinear relationships and unbiased estimation procedures to quantify these relations, leading to a nonlinear and stochastic dynamical system representation of the SCM problem. Moreover, the convergence of the algorithm will be proved and the satisfaction of the required statistical conditions demonstrated. Thus SCM problems may be formulated as formal scientific procedures, with well defined algorithms and a precise calculation sequence to determine the best alternative to enact. A “Certainty equivalent principle” will be indicated to ensure that the effects of the inevitable uncertainties will not lead to indeterminate results, allowing the formulation of demonstrably asymptotically optimal management plans.     

“A priori” estimates, uniqueness and existence of positive solutions of Yamabe type equations on complete manifolds

We study the asymptotic behaviour of non-negative solutions of Yamabe type equations on a complete Riemannian manifold. Then we provide a comparison result, based on a form of the weak maximum principle at infinity, which together with the “a priori” estimates previously obtained, yields uniqueness under very general Ricci assumptions. The paper ends with an existence result and an application to the non-compact Yamabe problem.     

Engineering massive quantum memories by topologically time-modulated spin rings

We introduce a general scheme to realize perfect storage of quantum information in systems of interacting qubits. This novel approach is based on global external controls of the Hamiltonian that yield time-periodic inversions in the dynamical evolution allowing a perfect periodic quantum state reconstruction. We illustrate the method in the particularly interesting and simple case of spin systems affected by XY residual interactions with or without static imperfections. The global control is achieved by step time inversions of an overall topological phase of the Aharonov-Bohm type. Such a scheme holds both at finite size and in the thermodynamic limit, thus enabling the massive storage of arbitrarily large numbers of local states, and is stable against several realistic sources of noise and imperfections.     

Complete systems, elementary submodels and the tightness of upper hyperspaces

We introduce and study some completeness properties for systems of open coverings of a given topological space. A Hausdorff space admitting a system of cardinality κ satisfying one of these properties is of type Gκ. Hence, we define several new variants of the ?ech number and use elementary submodels to determine further results. We introduce M-hulls and M-networks, for M elementary submodel. As an application, we give estimates for both the tightness and the Lindelöf number of a generic upper hyperspace. Two recent results of Costantini, Holá and Vitolo on the tightness of co-compact hyperspaces follow from ours as corollaries.     

Probing microscopic chaotic dynamics by observing macroscopic transport processes

We derive the Kramers equation, namely, the Fokker-Planck equation for an oscillator, from a completely deterministic picture. The oscillator is coupled to a “booster”, i.e., a deterministic system in a fully chaotic state, wherein diffusion is derived from the sensitive dependence of chaos on initial conditions and friction is a consequence of the linear response of the booster to the action exerted on it by the oscillator. To deal with the Hamiltonian nature of the system of interest and of its coupling to the booster, we extend the earlier theoretical derivation of macroscopic transport coefficients from deterministic dynamics. We show that the frequency of the oscillator can be tuned to the microscopic frequencies of the booster without affecting the canonical nature of the “macroscopic” statistics. The theoretical predictions are supported by numerical simulations.