Banach空间中多目标规划的局部有效解的必要条件

本文对Ｂａｎａｃｈ 空间中的多目标规划的局部有效解提出Ｆｒｉｔｚ Ｊｏｈｎ 必要条件和Ｋｕｈｎ－Ｔｕｃｋｅｒ必要条件,并且证明了多目标规划的Ｌａｇｒａｎｇｅ 正则性等价于一个标量规划问题的Ｌａｇｒａｎｇｅ 正则性．     

The use of load separation criterion and normalization method in ductile fracture characterization of thermoplastic polymers

Load separation is the theoretical basis for the single-specimen J-integral experiment and the incremental calculation of J-integral crack growth resistance (J-R) curves. This criterion has been experimentally studied in nongrowing crack records in several materials, and more recently a new method to extend the applicability to growing crack experiments has been proposed in testing steel. This article examines the applicability of the load separation criterion for evaluating ductile fracture mechanics parameters in rubber-modified polystyrenes and thermally treated polypropylene in the bending configuration. This criterion allows the load to be represented as the multiplication of two independent functions: a material deformation function and a crack geometry function. Its validity is evaluated with both stationary and growing crack experiments. η-factor calculation for smooth and side-grooved specimens was also tried using the simple method of Sharobeam and Landes, in order to identify material dependency. This article also investigates the applicability of the normalization method, based on the load separation criterion for evaluating J-R curves on PP and PS. A simple approach which combines a blunt notched and a precracked specimen experiment is proposed to determine the J-R curve of the materials studied. The resulting J-R curves are compared with multiple specimen results available in the literature for these materials. A good agreement between the J-R curves obtained from this simple method and from the multiple specimen technique was found. © 1996 John Wiley & Sons, Inc.     

A Note on Weighted Korn Inequality

In this note, we show that, for domains satisfying the separation property, certain weighted Korn inequality is equivalent to the John condition. Our result generalizes previous result from Jiang–Kauranen [Calc. Var. Partial Differential Equations, 56, Art. 109,(2017)] to weighted settings.     

Artificial viscosity: back to the basics

In this paper, we take a different perspective on the derivation of artificial viscosity. Heretofore, the development of artificial viscosity has been based on the paper published in Journal of Applied Physics in 1950 authored by John von Neumann and Robert Richtmyer [1]. Earlier, in 1948, Richtmyer published a report at Los Alamos Scientific Laboratory documenting the original concept [2]. This report was the true origin of shock capturing methods and contains several key ideas that are conceptually different than the 1950 journal article. Unfortunately, this report (LA‐671) was classified until 1993. This has resulted in two issues: the misattribution of the invention of artificial viscosity as primarily being the work of von Neumann and the loss of the structurally different ideas in the original report. We seek to right the record of history here and use the ideas contained in Richtmyer's report to good effect in deriving a new shock viscosity. The focus of previous development has been the Hugoniot curve describing the locus of states connected by a single shock wave. Here we follow a path more focused upon the Rayleigh line, which is strongly guided by Richtmyer's line of development of the original artificial viscosity formulation. We provide an implementation of the method resulting from this perspective and computational results for simple shock problems. Copyright © 2014 John Wiley & Sons, Ltd.     

A novel variable‐order fractional nonlinear Klein Gordon model: A numerical approach

In this article, a novel variable order fractional nonlinear Klein Gordon model is presented where the variable‐order fractional derivative is defined in the Caputo sense. The merit of nonstandard numerical techniques is extended here and we present the weighted average nonstandard finite difference method to study numerically the proposed model. Special attention is paid to study the convergence and to the stability analysis of the numerical technique. Moreover, the truncation error is analyzed. Three test examples are provided. Comparative studies are done between the used numerical technique and the weighted average finite difference method. It is found that the stability regions are larger by using the weighted average nonstandard finite difference method.     

Quantitative Absolute Continuity of Harmonic Measure and the Dirichlet Problem: A Survey of Recent Progress

It is a well-known folklore result that quantitative, scale invariant absolute continuity (more precisely, the weak-A_∞ property) of harmonic measure with respect to surface measure, on the boundary of an open set Ω ⊂ Rⁿ⁺¹ with Ahlfors-David regular boundary, is equivalent to the solvability of the Dirichlet problem in Ω, with data in L^p(∂Ω) for some p < ∞. Drawing an analogy to the famous Wiener criterion, which characterizes the domains in which the classical Dirichlet problem, with continuous boundary data, can be solved, one may seek to characterize the open sets for which L^p solvability holds, thus allowing for singular boundary data. It has been known for some time that absolute continuity of harmonic measure is closely tied to rectifiability properties of ∂Ω, but also that rectifiability alone is not sufficient to guarantee absolute continuity. In this note, we survey recent progress in this area, culminating in a geometric characterization of the weak-A_∞ property, and hence of solvability of the L^p Dirichlet problem for some finite p. This characterization, obtained under rather optimal background hypotheses, follows from a combination of the present author's joint work with Martell, and the work of Azzam, Mourgoglou and Tolsa.     

Berkeley and Its Physics Heritage

I first sketch the settlement of Berkeley, California, the founding of the University of California at Berkeley, and the origin of its Department of Physics. I then discuss the pivotal role that Ernest O. Lawrence (1901–1958) and his invention and subsequent development of the cyclotron played in physics at Berkeley after his arrival there in 1928 through the Second World War and beyond. I close by commenting on the Lawrence Hall of Science, the educational center and science museum conceived as a living memorial to Lawrence.     

拟共形映射与John域

本证明了有界一致域必定是Hohn域和Jphn域的拟共不变性．     

Bioassay and UPLC-Q-Orbitrap-MS/MS guided isolation of polycyclic polyprenylated acylphloroglucinols from St. John's wort and their neuroprotective activity

St. John’s wort (Hypericum perforatum L.) is a popular dietary supplement ingredient used for the treatment of mild-to-moderate depression in the United States and Germany. Reported studies mainly focused on the biological evaluation and mechanism study of its crude extracts or two main components (namely, hypericin and hyperforin). However, it is unclear whether other phytochemicals including polycyclic polyprenylated acylphloroglucinols (PPAPs) contributed to the neuroprotective effects of H. perforatum. Here, bioassay and ultra performance liquid chromatography–quadrupole orbitrap mass spectrometry (UPLC-Q-Orbitrap-MS/MS) guided isolation were applied to discover bioactive PPAPs from the crude extracts of H. perforatum. A new PPAP, named hyperforen A (2), along with nine known PPAPs (1 and 3–10), were identified from an ethyl acetate extract of H. perforatum. To the best of our knowledge, compound 2 represents the first PPAP with an unprecedented bicyclo[7.3.0]dodecane core. The chemical structures of the isolates were elucidated by extensive spectroscopic analysis and electronic circular dichroism calculations. Moreover, compounds 1–3, 6, and 10 (10 μM) exhibited significant neuroprotective effects against corticosterone-induced injury in PC12 cells. Fingings from the current study suggest that bioactive PPAPs from H. perforatum are promising compouds for the management of depression.     

Why Not One More Imponderable? John William Draper's Tithonic Rays

This paper reconstructs what may have led the American professorof chemistry andnatural philosophy John William Draper to introduce a new kind ofradiation, whichhe dubbed `Tithonic rays'. After presenting his and earlierempirical findings onthe chemical action of light in Section 3, I analyze his pertinentpapers in Section 4with the aim of identifying the various types of argumentshe raised infavor of this new actinic entity (or more precisely, this newnatural kind of raybesides optical, thermal and perhaps also phosphorogenic rays).From a modernperspective, all of these obviously belong within theelectromagnetic spectrum,but not so for many thinkers of the 19th century. I close withremarks about whyDraper's interpretation was abandoned in the second half of the19th century (hehimself recanting only in 1872), and why I think such a naturalhistory ofargumentation (as one might call my approach in Section 4) may beuseful for acomparison-oriented history of science.