Estimation of the offspring mean of a supercritical or near-critical size-dependent branching process

We consider a single-type supercritical or near-critical size-dependent branching process ${\left\{N_n\right\}}_n$ such that the offspring mean converges to a limit $m?1$ with a rate of convergence of order $N_n^{\alpha }$ as the population size $N_n$ grows to ∞ and the variance may change at the rate $N_n^{\beta }$, where $\alpha >0$ and $?1?\beta <1$. The offspring mean depends on an unknown parameter ${\theta }_0$ that we estimate on the non-extinction set by using the conditional least squares method. We prove the strong consistency of the estimator of ${\theta }_0$ as $n\to \infty$ under some general conditions on the asymptotic behavior of the process. We also give its asymptotic distribution for a certain class of size-dependent branching processes. To cite this article: N. Lalam, C. Jacob, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Estimation of a regression function on a poisson process

We give sufficient conditions of weak consistency for the fixed-bandwidth regressogram estimator.     

On asymptotic efficiency of tests of fit based on the Deheuvels empirical process

We consider some goodness-of-fit tests which are functionals of the modified empirical process defined in the spirit of a Deheuvels paper published in 2007. We calculate their Bahadur efficiency for simple alternatives and find conditions of local optimality for the analog of the Kolmogorov test. Bibliography: 10 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 361, 2008, pp. 66–77.     

Mathematical modelling of phononic nanoplate and its size-dependent dispersion and topological properties

A new model with analysis for the propagation of flexural waves in a phononic plate at nanoscale is developed. The Gurtin-Murdoch theory for surface elasticity is adopted to model the surface heterogeneity. The Mindlin (or first-order) plate theory is further generalized to establish the governing equations for flexural waves in a phononic plate with surface effect, for which the plane wave expansion method is applied to derive the dispersion relation. A numerical model is developed using the finite element method and very good consistency between theory and numerical solution is observed. It is found that the surface density and the surface residual stress play the main role that affects the band structures. The surface effect can be approximately regarded as the competition between frequency decrease due to surface density and frequency increase caused by surface residual stress, which effectively increases the low-frequency bands but decreases the high-frequency bands. The quantum spin Hall effect is observed in the phononic plate at nanoscale, and the surface effect is studied numerically. By applying the k.p perturbation method, a theoretical framework is established to calculate the spin Chern number, which is an important topological invariant that determines the quantum spin Hall effect. Based on the topological analysis, an efficient waveguide with a zig-zag path is designed, in which a topologically protected wave in the interface state can robustly propagate along the path against disorders. The theory and numerical study developed in this paper will help better understand the size-dependent quantum spin Hall effect in nanostructures and it may also provide guidance for the design of topological wave devices at nanoscale.     

根据子样本的过程能力指数及其置信区间的估计

自1980年以来,分析过程能力的统计方法有显著的进展,已在实践中得到大量应用.过程能力指数是衡量生产过程中的产品尺寸适合规格限和接近目标值的能力.最普遍使用的能力指数是cp和cpk,这些指数曾被广泛地应用于日本、美国和英国的各工业公司和企业.文中对这些指数提出根据子样本估计标准差、能力指数及其置信区间的简单近似方法.     

Estimation and filtering on a doubly stochastic poisson process

An explicit formula for the characteristic function of a doubly stochastic Poisson process is derived in this paper by means of the harmonic decomposition of its intensity function that we suppose to be Gaussian. The statistical moments are then obtained, as well as the sample function density of the process. These results are applied to estimate the parameters of several well-known processes. Finally, a linear filtering procedure for the intensity function is developed and the algorithm is implemented by computers.     

Mathematical modelling of the flotation deinking process

The overall flotation deinking process can be divided into four basic microprocesses:

• 1.(1) collision or capture of an (ink) particle by an air bubble
• 2.(2) adhesion of an (ink) particle to the air bubble by sliding
• 3.(3) development of a three-phase contact at the air bubble/water/particle interface, and
• 4.(4) bubble/particle stability or instability after an aggregate is formed each of these microprocesses have an associated probability that they will occur successfully in a flotation cell.

In this paper, the associated probabilities of each microprocess are employed in the development of a kinetic- or population balance-type model of the overall flotation process. The overall model contains two kinetic constants: the first, k₁ governs the overall probability of a free ink particle successfully intercepting and adhering to an air bubble; the second, k₂ is a measure of the probability that a bubble/particle aggregate pair will become unstable and split to yield a “new” free ink particle.The solution to the kinetic model is presented in terms of k₁ and k₂, which are themselves functions of system parameters such as bubble and particle physical properties (e.g., diameter, density), fluid properties (e.g., viscosity, surface tension), etc. From this solution, a definition of a theoretical flotation efficiency, as well as other system performance parameters are presented.     

HGLM modelling of dropout process using a frailty model

Summary  We introduce a shared random-effect model, derived from frailty models to account for informative dropout. We extend the iterative weighted least squares algorithm for hierarchical generalized linear models to shared random-effect models. Monte-Carlo simulations are carried out to illustrate that the proposed method works well whether the random-effect distribution is correctly specified or not. This study was supported by a grant of the Korea Health 21 R & D Project, Ministry of Health & Welfare, Republic of Korea. (01-PJ1-PG3-51200-0002).     

Feed-forward modelling and fuzzy logic based control strategy for powertrain efficiency improvement in a parallel hybrid electric vehicle

With the stricter limitations on both fuel consumption and air pollution, the advantages of a hybrid electric vehicle are becoming more evident than ever. In the present study, an energy management system for a hybrid electric vehicle is developed. Because the plant under consideration is nonlinear, multi-domain, time-varying, has multiple uncertainties and, in addition, the designed control strategy must be able to obey the driver's commands and achieve the par-internship for a new generation of vehicle regulations, the fuzzy logic approach is chosen. A feed-forward hybrid vehicle simulation model is used to demonstrate the validity and the convenience of the current approach and its results have been compared with the other parallel hybrid electric vehicle control strategies. Simulation results show considerable improvement in the efficiency of the internal combustion engine and, consequently, fuel consumption and acceleration performances.     

Estimation of the discord time for a process of the Ornstein-Uhlenbeck type

A consistent estimate is constructed for the discord time of a process of the Ornstein-Uhlenbeck type. The rate of the almost sure convergence of this estimate is investigated and the confidence interval is determined.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 9, pp. 1198–1204, September, 1993.     

Estimation of cardinal utility based on a nonlinear theory

Empirical studies have demonstrated that cardinal utility functions assessed via gamble-based methods are often incoherent because of the probability and certainty effects. These effects are caused by apparent risk attitudes different from those admissible within the linear (expected) utility theory. The incoherences can also be accentuated by the effects of chaining and serial positioning of responses. To filter out these effects and obtain an unbiased measurement of the strength of preference, and a simultaneous measurement of risk attitude, we devised the independent-gamble, nonlinear-inference (IGNI) method: the utility function of outcomes and the risk function of probabilities are estimated jointly from assessed certainty equivalents of independent gambles by using a nonlinear utility theory for inference. The method contrasts with all popular utility assessment techniques in that it estimates a cardinal function in the two-dimensional space of outcomes and probabilities. Hence, it allows us to obtain novel insights into the nature of utility functions and the probability effect. Both are illustrated by empirical results for fifty-four subjects.     

Macroscopic modelling of the selective beam melting process

The present contribution is concerned with the macroscopic modelling of the selective beam melting process by using finite elements. In this context the objective is to detail a continuum model to describe the process. Furthermore two different solution approaches are applied to the model and compared in terms of performance. An adaptive mesh refinement strategy is also demonstrated to increase the quality of the solution in the vicinity of the beam. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bending analysis of size-dependent functionally graded annular sector microplates based on the modified couple stress theory

In the present paper, a non-classical model for functionally graded annular sector microplates under distributed transverse loading is developed based on the modified couple stress theory and the first-order shear deformation plate theory. The model contains a single material length scale parameter which can capture the size effect. The material properties are graded through the thickness of plates according to a power-law distribution of the volume fraction of the constituents. The equilibrium equations and boundary conditions are simultaneously derived from the principle of minimum total potential energy. The system of equilibrium equations is then solved using the generalized differential quadrature method. The effects of length scale parameter, power-law index and geometrical parameters on the bending response of annular sector plates subjected to distributed transverse loading are investigated.     

A network modelling approach for assessing the efficiency of prevention strategies

Survey data and a simulation model based on a stochastic pair formation process are used to construct networks of sexual contacts. We model heterosexual partnerships which can be steady or casual depending on their average duration. Transmission of an infectious disease can take place in pairs of a susceptible and an infected individual. We study networks of sexual contacts accumulated during 1 year for different types of mixing patterns. The networks are constructed on the basis of data from a survey in The Netherlands. We analyze the network structure for different mixing patterns and investigate the relationship between network structure and disease spread; furthermore we study the effect of prevention measures on the structure of the network.     

Estimation of the reliability of a classification algorithm as based on a new information model

A new approach to the estimation of the reliability of classification algorithms is proposed. The approach is based on an unconventional information model of such algorithms. Examples of new estimates are given, which are compared with usual statistical estimates.     

Estimation of the attainability set for a linear system based on a linear matrix inequality

The problem under consideration is the construction of an attainability set’s internal approximation for a full controllable linear time-invariant system. This approximation is obtained as an intersection of two domains given by quadratic forms. One of these forms is based on parameters of the original system. The other form is produced by the solution to some linear matrix inequality. The method proposed here is illustrated by a numerical example.     

Judgemental modelling based on geometric least square

The Analytic Hierarchy Process developed by T.L. Saaty has received widespread attention in the literature. However this has not been without some criticisms, including the problems of meaning of consistency and large data requirements. This paper addresses the last two problems and presents a new method of calculating preference vectors. To the user the procedure is essentially the same, but the data requirements can be made less onerous and at the same time feedback is provided permitting a greater understanding of the data inputs. Preliminary results indicate the acceptability of the proposed methodology.     

Towards modelling the curing process in particle-filled electro-active polymers

A large actuation voltage is required to produce a desired mechanical deformation in dielectric elastomers. To reduce the amount of the actuation voltage, several mechanisms can be applied and the inclusion of high dielectric permittivity fillers in the matrix material in the uncured stage is one of them. Moreover, to obtain a maximum advantage from the high dielectric permittivity fillers, an electric field is applied during the curing process which helps the particles to align in a preferred direction. The stiffness gaining during curing is modelled by an appropriate constitutive relation where the temporal evolution of the material parameters is considered. In this paper we present a phenomenologically-inspired large strain framework for simulating the curing process of polymers that can work under the use of an electro-mechanically coupled load. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)