On Preservation Theorems for Two-Variable Logic

We show that the existential preservation theorem fails for two-variable first-order logic FO². It is known that for all k ≥ 3, FO^k does not have an existential preservation theorem, so this settles the last open case, answering a question of Andreka, van Benthem, and Németi. In contrast, we prove that the homomorphism preservation theorem holds for FO².     

Solution behavior of a surfactant aldehyde–the oxidation product of an alcohol ethoxylate

It has previously been shown that alcohol ethoxylates readily undergo autoxidation and that one of the major oxidation products is the surfactant aldehyde, i.e. an ethoxylate carrying a –CH₂CHO group at the terminal end of the polyoxyethylene chain. In this work the cloud point, phase behavior and aggregation characteristics of the surfactant aldehyde produced by oxidation of C₁₂H₂₅(OCH₂CH₂)₅OH (C₁₂E₅) are determined and compared with the values obtained with the parent surfactant. It was found that the physico–chemical behavior of the two species was very similar, which indicates that a considerable portion of the aldehyde group is in hydrated state, i.e. the surfactant aldehyde consists of a mixture of aldehyde in carbonyl form and the corresponding geminal diol. The cloud point of the surfactant aldehyde decreased rapidly with time, even when it was stored at low temperature. Also the parent surfactant and its homologue C₁₂E₆ exhibited a decrease in cloud point during storage. For instance, a 1% aqueous solution of C₁₂E₆ showed a cloud point decrease from 62 to 32°C after 4 months storage at 40°C. Such a change in solution behavior can have important practical implications.     

Subadditive ergodic theorems for random sets in infinite dimensions

We prove pointwise and mean versions of the subadditive ergodic theorem for superstationary families of compact, convex random subsets of a real Banach space, extending previously known results that were obtained in finite dimensions or with additional hypotheses on the random sets. We also show how the techniques can be used to obtain the strong law of large numbers for pairwise independent random sets, as well as results in the weak topology.     

Contractibility and Connectedness of Efficient Point Sets

Using the technique of space theory and set-valued analysis, we establish contractibility results for efficient point sets in a locally convex space and a path connectedness result for a positive proper efficient point set in a reflexive space. We also prove a connectedness result for a positive proper efficient point set in a locally convex space; as an application, we give a connectedness result for an efficient solution set in a locally convex space.     

Global G-Manifold Reductions and Resolutions

The purpose of this note is to exhibit some simple and basic constructions for smooth compact transformation groups, and some of their most immediate applications to geometry.     

Plasmonic protection of the hot‐electron energy

In the Letter by K. Kempa, the definitions of two auxiliary constants in Eqs. (10) and (11) were incorrectly given by the author. He now wishes to correct these equations. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Generalization of the Hellmann-Feynman theorem

The well-known Hellmann-Feynman theorem of quantum mechanics connected with the derivative of the eigenvalues with respect to a parameter upon which the Hamiltonian depends, is generalized to include cases in which the domain of definition of the Hamiltonian of the system also depends on that parameter.     

一道积分不等式的多种证法

通过对一道积分不等式提供多种不同的证法,希望能对学生创造性思维及发散性思维的培养、开阔解题思路、提高综合应用数学知识的能力等有所帮助,并使学生对证明不等式的常用方法有所了解.     

Bell’s Theorem,Many Worlds and Backwards-Time Physics: Not Just a Matter of Interpretation

The classic “Bell’s Theorem” of Clauser, Holt, Shimony and Horne tells us that we must give up at least one of: (1) objective reality (aka “hidden variables”); (2) locality; or (3) time-forwards macroscopic statistics (aka “causality”). The orthodox Copenhagen version of physics gives up the first. The many-worlds theory of Everett and Wheeler gives up the second. The backwards-time theory of physics (BTP) gives up the third. Contrary to conventional wisdom, empirical evidence strongly favors Everett-Wheeler over orthodox Copenhagen. BTP allows two major variations—a many-worlds version and a neoclassical version based on Partial Differential Equations (PDE), in the spirit of Einstein. Section 2 of this paper discusses the origins of quantum measurement according to BTP, focusing on the issue of how we represent condensed matter objects like polarizers in a model “Bell’s Theorem” experiment. The backwards time telegraph (BTT) is not ruled out in BTP, but is highly speculative for now, as will be discussed. The views herein are not anyone’s official views, but this does constitute work produced on government time.