Minimax Results and Finite-Dimensional Separation

In this paper, we review and unify some classes of generalized convex functions introduced by different authors to prove minimax results in infinite-dimensional spaces and show the relations between these classes. We list also for the most general class already introduced by Jeyakumar (Ref. 1) an elementary proof of a minimax result. The proof of this result uses only a finite-dimensional separa- tion theorem; although this minimax result was already presented by Neumann (Ref. 2) and independently by Jeyakumar (Ref. 1), we believe that the present proof is shorter and more transparent.     

广义变系数模型的Bayesian B样条估计

提出了广义变系数模型函数系数的一种新的估计方法．我们用B样条函数逼近函数系数,不具体选择节点的个数,而是节点个数取均匀的无信息先验,样条函数系数取正态先验,用Bayesian模型平均的方法估计各个函数系数．这种估计方法一个主要特点是允许各个函数系数所需节点个数的后验分布不同,因此允许不同函数系数使用不同的光滑参数．另外,本文还给出了Bayesian B样条估计的计算方法,并通过模拟例子,说明广义变系数模型的函数系数可以由Bayesian B样条估计方法得到很好的估计．     

Ribaucour Transformations for Hypersurfaces in Space Forms

The theory of Ribaucour transformations for hypersurfaces in space forms is established. For any such hypersurface M, that admits orthonormal principal vector fields, it was shown the existence of a totally umbilic hypersurface locally associated to M by a Ribaucour transformation. A method of obtaining linear Weingarten surfaces in a three-dimensional space form is provided. By applying the theory, a new one-parameter family of complete constant mean curvature (cmc) surfaces in the unit sphere, locally associated to the flat torus, is obtained. The family contains a class of complete cmc cylinders in the sphere. In particular, one gets a family of complete minimal surfaces and minimal cylinders, locally associated to the Clifford torus.Mathematics Subject Classifications (2000): 53C20.     

Temperature effect on deposition rate of silicon nitride films

Temperature effects on deposition rate of silicon nitride films were characterized by building a neural network prediction model. The silicon nitride films were deposited by using a plasma enhanced chemical vapor deposition system and process parameter effects were systematically characterized by 2⁶⁻¹ fractional factorial experiment. The process parameters involved include a radio frequency power, pressure, temperature, SiH₄, N₂, and NH₃ flow rates. The prediction performance of generalized regression neural network was drastically improved by optimizing multi-valued training factors using a genetic algorithm. Several 3D plots were generated to investigate parameter effects at various temperatures. Predicted variations were experimentally validated. The temperature effect on the deposition rate was a complex function of parameters but N₂ flow rate. Larger decreases in the deposition rate with the temperature were only noticed at lower SiH₄ (or higher NH₃) flow rates. Typical effects of SiH₄ or NH₃ flow rate were only observed at higher or lower temperatures. A comparison with the refractive index model facilitated a selective choice of either SiH₄ or NH₃ for process optimization.     

Eigenvalue approach to study the effect of rotation and relaxation time in generalized magneto-thermo-viscoelastic medium in one dimension

The fundamental equations of the problems of generalized thermoelasticity with one relaxation parameter including heat sources in infinite rotating magneto-thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace transform domain for a one dimensional problem. These equations have been solved by the eigenvalue approach to determine deformations, stress, and temperature. The results have been compared to those available in the existing literature. The graphs have been drawn to show the effect of rotation in the medium.     

Estimating Sampling Errors in REA Survey: A Model Approach for the Synthetic Presentation of Results for Main Variables Involved in Economic Analysis

A new sample business survey for agriculture, the REA survey, and a project of integration with the FADN network (RICA in Italy) have significantly changed the production of statistical information nowadays available with reference to the agricultural sector. On the basis of this relevant information, new economic analyses are being developed on farms’ performance, agricultural households’ income and the Common Agricultural Policy (CAP). In this paper the authors estimate the relationship between the levels of variables of interest and their sampling errors using models in order to improve the accessibility of the information on estimates accuracy to the final users (agricultural analysts, policy makers). The paper is the result of a joint research of the three authors. Sections 1–3 and 6 by Pizzoli, Sects. 4 and 5 by Rondinelli, Sect. 7 by Filiberti, conclusions joint to the three authors.     

A quasilinearization method for a class of integro-differential equations with mixed nonlinearities

We develop an extended form of the quasilinearization method for an initial value problem involving a nonlinear integro-differential equation with mixed nonlinearities, occurring in distributed-infective and distributed-contact models. In fact, a monotone sequence of iterates converging uniformly and quadratically to a solution of the problem is obtained. Some interesting observations are presented.     

On Polynomial Functions over Finite Commutative Rings

Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.     

Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets

Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their elements converging to zero sufficiently slowly. When these sets are convex hulls of sets with power-type covering numbers, the bounds are tight. The arguments exploit properties of generalized Hadamard matrices. The results are illustrated by examples from machine learning, neurocomputing, and nonlinear approximation.     

Curvature Conditions for Immersions of Submanifolds and Applications

Some curvature conditions about the geodesics emanating from a submanifold are obtained. These conditions are used to to study the topological and geometric properties of the ambient spaces which admit some minimal submanifolds.