Asymptotic analysis of elastic curved rods

We consider a sequence of curved rods which consist of isotropic material and which are clamped on the lower base or on both bases. We study the asymptotic behaviour of the stress tensor and displacement under the assumptions of linearized elasticity when the cross‐sectional diameter of the rods tends to zero and the body force is given in the particular form. The analysis covers the case of a non‐smooth limit line of centroids. We show how the body force and the choice of the approximating curved rods can affect the strong convergence and the limit form of the stress tensor for the curved rods clamped on both bases. Copyright © 2006 John Wiley & Sons, Ltd.     

绝对连续测度的Loeb代数

It is proved that if μ and v be finite measures on a measurable space (X,S) and v is absolutely continuous with respect to v, then it is holds that L(^*S,^*v) C L(^*S,^*v), while L(^*S,^*v) and L(^*S,^*v) are the Loeb algebras with respect to measure spaces (X,S,μ) and(X,S,μ).     

Coercive boundary value problems for regular degenerate differential-operator equations

This study focuses on nonlocal boundary value problems (BVP) for degenerate elliptic differential-operator equations (DOE), that are defined in Banach-valued function spaces, where boundary conditions contain a degenerate function and a principal part of the equation possess varying coefficients. Several conditions obtained, that guarantee the maximal L_p regularity and Fredholmness. These results are also applied to nonlocal BVP for regular degenerate partial differential equations on cylindrical domain to obtain the algebraic conditions that ensure the same properties.     

<Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> linear interpolator for missing values in time series

We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL ₁ approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed. This research was supported by a CityU Research Grant and Natural Science Foundation of China.     

Elliptic systems with nonlinearity q greater or equal than two with controlled growth. Global Hölder continuity of solutions to the Dirichlet problem

Hölder regularity up to the boundary of the solutions to the Dirichlet problem for second order elliptic systems with nonlinearity q>2 and with controlled growth is proved when n?q+2.     

Synthesis and absolute configuration of cordiaquinone K, antifungal and larvicidal meroterpenoid isolated from the Panamanian plant, Cordia curassavica

Total synthesis of cordiaquinone K, a new antifungal and larvicidal meroterpenoid, is reported. The absolute configuration of cordiaquinone K was confirmed by the synthesis.     

Continuous Selectors of Fixed Point Sets of Multifunctions with Decomposable Values

Existence theorems of continuous selectors whose values are fixed points of multivalued contractions are proved. As an application, the existence of continuous selectors to generalized solution sets of partial differential inclusions, depending on a parameter, is obtained.     

Second Order Representations of the Least Absolute Deviation Regression Estimator

We consider exact weak and strong Bahadur-Kiefer representations of the least absolute deviation estimator for the linear regression model. The precise behavior of these representations is obtained under minimal conditions.     

Degeneracy in NLP and the development of results motivated by its presence

We study notions of nondegeneracy and several levels of increasing degeneracy from the perspective of the local behavior of a local solution of a nonlinear program when problem parameters are slightly perturbed. Ideal nondegeneracy at a local minimizer is taken to mean satisfaction of second order sufficient conditions, linear independence and strict complimentary slackness. Following a brief exploration of the relationship of these conditions with the classical definition of nondegeneracy in linear programming, we recall a number of optimality and regularity conditions used to attempt to resolve degeneracy and survey results of Fiacco, McCormick, Robinson, Kojima, Gauvin and Janin, Shapiro, Kyparisis and Liu. This overview may be viewed as a structured survey of sensitivity and stability results: the focus is on progressive levels of degeneracy. We note connections of nondegeneracy with the convergence of algorithms and observe the striking parallel between the effects of nondegeneracy and degeneracy on optimality conditions, stability analysis and algorithmic convergence behavior. Although our orientation here is primarily interpretive and noncritical, we conclude that more effort is needed to unify optimality, stability and convergence theory and more results are needed in all three areas for radically degenerate problems.Research supported by National Science Foundation Grant ECS 90-00560 and Grant N00014-89-J-1537 Office of Naval Research     

Reply to “nonequivalence of ether theories and special relativity. comment on recent interpretation of Lorentz' Ether theory”

The role played by coordinates in the formulation of an absolute spacetime theory is assessed. It is shown that recent criticism on previous work of ours is wrong.