Lamé hypersurfaces and Lagrange multipliers

Starting with a standard calculus problem of finding the rectangle of maximum area, which can be inscribed in an ellipse, we generalizethe result to Lamé curves and hypersurfaces, before investigating the volume enclosed by a generalized Lamé hypersurface. Suggestions of classroom use and a selection of possible classroom exercises are also given.     

国内外股市波动溢出效应——基于多元GARCH模型的实证研究

通过对多个股票市场间波动溢出效应的研究,可以了解波动风险在市场间的传导路径和方向,以及在股市因外部冲击动荡前做出短期预测。本文以美国、日本、香港和我国沪市作为研究对象,采用多元GARCH模型对国内外股市波动溢出关系进行了研究。结果表明:只有香港股市对沪市具有显著的波动溢出,美、日股市对沪市的波动溢出则不显著,但由于美、日股市波动均对香港股市具有传染效应,它们可以借助对香港股市波动的影响间接地引起我国沪市的波动。所以,对我国沪市外部波动风险的把握在短期上应主要关注香港股市波动,其次还必须关注日本和美国股市的波动,尤其是美国股市的波动。     

A single dual-mode gas sensor for early safety warning of Li-ion batteries: Micro-scale Li dendrite and electrolyte leakage

Li dendrites and electrolyte leakage are common causes of Li-ion battery failure. H₂, generated by Li dendrites, and electrolyte vapors have been regarded as gas markers of the early safety warning of Li-ion batteries. SnO₂-based gas sensors, widely used for a variety of applications, are promising for the early safety detection of Li-ion batteries, which are necessary and urgently required for the development of Li-ion battery systems. However, the traditional SnO₂ sensor, with a single signal, cannot demonstrate intelligent multi-gas recognition. Here, a single dual-mode (direct and alternating current modes) SnO₂ sensor demonstrates clear discrimination of electrolyte vapors and H₂, released in different states of Li-ion batteries, together with principal component analysis (PCA) analysis. This work provides insight into the intelligent technology of single gas sensors.     

Analysis of bending, vibration and stability for thin plate on elastic foundation by the multivariable spline element method

I.IntroductionTheplatestructuresonelasticfoundationareofpracticalimportanceinwide-spreadapplicationsinengineering.Basedonrapidprogressofscienceandtechnologyaswellasengineeringconstructions,differentmodelsofeIasticfoundationaredeve1oped,sucha,Winkler,Vlazo…     

Singular perturbation of first boundary value problem for higher order elliptic equations (II)

In this paper we discuss singular perturbations of first boundary value problem for higher order elliptic equations of two parameter and obtain the asymptotic expression for the formal solution containing two-parameter as well as the estimation of its remainder term. These results are the extensions of (2) and (3).     

An extension of the method of least squares

The standard method of least squares assumes that there is a linear relationship relating two variables, only one of which has an error in it. A discussion of the validity of this assumption leads to the desirability of a technique which applies to the more general situation where both variables are subject to error. This includes relating the relevant statistical distance to be minimized to the Euclidean distance. The corresponding statistical formulae are derived, and simple comparisons are then made for various ranges of the statistical parameters.     

On a multivariable extension for the extended Jacobi polynomials

The main object of this paper is to construct a systematic investigation of a multivariable extension of the extended Jacobi polynomials and give some relations for these polynomials. We derive various families of multilinear and multilateral generating functions. We also obtain relations between the polynomials extended Jacobi polynomials and some other well-known polynomials. Other miscellaneous properties of these general families of multivariable polynomials are also discussed. Furthermore, some special cases of the results are presented in this study.     

Radix representations, self-affine tiles, and multivariable wavelets

We investigate the connection between radix representations for and self-affine tilings of . We apply our results to show that Haar-like multivariable wavelets exist for all dilation matrices that are sufficiently large.

     

Fixed-order robust compensators via min-max principle

An important (some say, the major) reason for using feedback control is the presence of uncertain parameters which are a natural part of any real dynamical model. In this paper, we consider uncertain constant parameters in a time-invariant linear plant and announce some new results concerning robust compensator synthesis. Using the min-max principle, we derive necessary conditions for fixed-order linear robust controllers assuring asymptotic stability or relative stability. These necessary conditions are an extension of the Lagrange multiplier method. This is achieved using a cost function based on the inverse of the so-called critical constraint. We present both matrix and polynomial versions; the latter allows controllers of fixed structure. We suggest a probability-one homotopy algorithm and solve some examples from the literature.The authors wish to thank Professor R. Bental, Faculty of Industrial Engineering at the Technion, for his suggestion to replace the cost function based on the inverse critical polynomial by a logarithmic function.