A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems

In this paper, we outline the foundations of a general global optimisation strategy for the solution of multilevel hierarchical and general decentralised multilevel problems, based on our recent developments on multi-parametric programming and control theory. The core idea is to recast each optimisation subproblem, present in the hierarchy, as a multi-parametric programming problem, with parameters being the optimisation variables belonging to the remaining subproblems. This then transforms the multilevel problem into single-level linear/convex optimisation problems. For decentralised systems, where more than one optimisation problem is present at each level of the hierarchy, Nash equilibrium is considered. A three person dynamic optimisation problem is presented to illustrate the mathematical developments.     

On almost sure max-limit theorems of complete and incomplete samples from stationary sequences

Let M _n denote the partial maximum of a strictly stationary sequence (X _n ). Suppose that some of the random variables of (X _n ) can be observed and let [(M)\tilde]_n\tilde M_n stand for the maximum of observed random variables from the set {X ₁, ..., X _n }. In this paper, the almost sure limit theorems related to random vector ([(M)\tilde]_n\tilde M_n , M _n ) are considered in terms of i.i.d. case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions.     

Initial operation at liquid-helium temperature of the M =2270 kg Al 5056 gravitational-wave antenna of the Rome group

Summary We report on the cooling at liquid-helium temperature of our 2270 kg 5056 Al bar at CERN. The liquid-helium container had been filled up to 1500 liters ensuring to keep the antenna cold for more than one month. The antenna is equipped with a resonant capacitive transducer operating at constant electrical charge with a FET low-noise amplifier. The transducer is tuned to the antenna within less than I Hz and the two normal-mode frequencies are ν₋=908.160 Hz and ν₊=924.234 Hz with an applied electrical field in the transducer of 10⁶ V/m. The corresponding overall merit factors areQ ₋=5.20·10⁶ andQ ₊=7.25·10⁶. The transducer has been tested up to an electrical field of 6·10⁶ V/m: in this condition we have βQ≈10⁴. The antenna has been in operation for several weeks giving, for the Brownian noise, values in agreement with the calculated values. We report also on the results of tests performed on a DC SQUID, whose input was connected to a commercial capacitor via a transformer with turn ratio of 1000. Supported in part by Japan Society for the Promotion of Science.     

On the relative efficiency of alternative modes of producing a public sector output: The case of the developmentally disabled

This paper examines the relative efficiency of alternative methods of producing care for the developmentally disabled. A linear programming framework is used to construct a production frontier which allows measurement of relative efficiency among institutions in the sample. Tests are performed to detect influential observations in the data which might result from measurement error which could distort the efficiency measures. Different types of institutions are compared in terms of average efficiency. Policy implications of the analysis are discussed in the concluding section.     

Experimental and theoretical analyses on the microwave backscattering ability and differential radar reflectivity of non-spherical hydrometeors

This paper experimentally and theoretically examines the scattering properties of simulated non-spherical hydrometeors including water oblates, ice oblates and ice sphere-cone-oblates, in terms of the backscattering cross-section and the differential reflectivity. The experimental measurements of the backscattering cross-sections of non-spherical hydrometeor samples were performed in the Electromagnetic Scattering Laboratory of China National Space Industrial Corporation. Meanwhile, the backscattering cross-sections have been computed with the transition (T) matrix method. The theoretical results are compared with the experimental data, showing that the calculations are consistent with the observations in general. Experimental and theoretical analyses indicate that the backscattering cross-section of non-spherical particles increases as the particle size parameter increases, and fluctuates when the sizes are larger under the effect of resonance scattering. Differential reflectivity Z_DR of water oblates in natural rainfall is always greater than 0 dB whereas Z_DR of hailstones may be negative. There is a good linear relationship between differential reflectivity and aspect ratio of a particle. These derivations agree with the literature and can be used to identify the presence of hail particles and distinguish between plate-type and columnar-type hydrometeors. In this study, the measuring experiment and the T-matrix method calculations for the scattering of simulated raindrop and ice particles are also briefly described.     

Robust H ∞ Filtering for a Class of Nonlinear Discrete-Time Markovian Jump Systems

This paper considers the problem of the robust H filtering for a class of nonlinear discrete-time Markovian jump systems with real time-varying norm-bounded parameter uncertainty. For each mode, the nonlinearity is assumed to satisfy the global Lipschitz conditions and appears in both the state and measured output equations. The problem that we address is the design of a nonlinear filter which ensures robust stochastic stability and a prescribed H performance level of the filtering error system for all admissible uncertainties. A sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities; an explicit expression of a desired nonlinear H filter is also given. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.     

Asymptotic properties of Rao's test for testing hypotheses in discrete parameter stochastic processes

Summary In this note some asymptotically optimum tests for testing hypotheses concerning parameters when the observations are dependent are obtained. Test statistics based on the score functions, similar to the one proposed by Rao in the case when the observations are i.i.d. are proposed. Asymptotically UMP tests for one sided hypotheses against one sided alternatives and asymptotically UMP unbiased test for a simple hypothesis against two sided alternatives are derived. In the multiparameter case tests for simple hypotheses that have asymptotically best constant power on some family of surfaces in the parameter space are derived.     

最优多期比例再保险策略的必要条件

研究最小化保险公司破产概率的最优多期比例再保险策略,给出了保险公司最小破产概率的一个递归表达式,证明了可用动态规划方法求解此类问题.在此基础上,我们推导出最优多期比例再保险策略的几个必要条件.     

Application to other fields of techniques used for gravity wave detection

Summary The experimental techniques developed to build a sensitive gravitational wave antenna can find application in many different fields of research. In the present paper we discuss briefly two experiments that we are developing in the Istituto Fisica Spazio Interplanetario of C.N.R. More precisely, a noncryogenic gravity gradiometer to be flown on the subsatellite of the TSS and a cryogenic force sensor which will be used to verify some recent results on the interaction of neutrino with matter are described. To speed up publication the proofs were not sent to the authors and were superivised by the Scientific Committee.