A Closer Look at the Uncertainty Relation of Position and Momentum

We consider particles prepared by a single slit diffraction experiment. For those particles the standard deviation σ _p of the momentum is discussed. We find out that σ _p =∞ is not an exception but a rather typical case. A necessary and sufficient condition for σ _p <∞ is given. Finally, the inequality σ _p Δx≥π ℏ is derived and it is shown that this bound cannot be improved.     

A priori estimates for a singular limit approximation of the constitutive laws for chiral media in the time domain

The equations for the evolution of electromagnetic fields in chiral media, in the time domain, are nonlocal in time. In this work we study the validity of a singular limit (local in time) approximation for these nonlocal in time equations, by estimating the size of the difference of the fields as predicted by both models. In particular, we establish an a priori estimate for this difference, depending on the time horizon, properties of the domain, spatial properties of the initial data and the source terms and the chirality measure β of the approximating model.     

Generalized variational-like inequalities for pseudo-monotone type III operators

Our aim in this paper is mainly to prove some existence results for solutions of generalized variational-like inequalities with (η,h)-pseudo-monotone type III operators defined on non-compact sets in topological vector spaces.     

The Intrinsic Shape of the cubic cP124 Clathrate Structure

It is shown how the Periodic Nodal Surface PNS D*&Y** separates perfectly the two partial structures of the cubic cP124 type. Condensed metal‐centered [M@E20] pentagonal dodecahedra of covalently bonded E atoms form a 3‐connected net. This partial structure is embedded in a zeolite‐type labyrinth containing chains of the remaining metal atoms. The shape of this ensemble represents the principle of the intrinsic curvature of solids. The relations of the structure to the β‐manganese structure are discussed in detail. Furthermore, some details concerning the electron balance in the covalent E₁₀₀ net are reported.     

一类不能作为自同构群的有限群

本文证明了阶小于ｐ９的有限交换ｐ－群不能作为有限群的自同构群，从而推进了ＭａｃＨａｌｅ的结果．     

Invariant Measures for Set-Valued Dynamical Systems

A continuous map on a compact metric space, regarded as a dynamical system by iteration, admits invariant measures. For a closed relation on such a space, or, equivalently, an upper semicontinuous set-valued map, there are several concepts which extend this idea of invariance for a measure. We prove that four such are equivalent. In particular, such relation invariant measures arise as projections from shift invariant measures on the space of sample paths. There is a similarly close relationship between the ideas of chain recurrence for the set-valued system and for the shift on the sample path space.

     

LSC(X,R*)上Way-Below关系的一个注

本文指出文献［１］中关于下半连续函数格ＬＳＣ（Ｘ,Ｒ^*）上Ｗａｙ－ｂｅｌｏｗ关系的一个结论是错误的,并且给出一个修正的命题及其证明．     

Green Fluorescent Protein (GFP) as a Marker for Cell Viability After UV Irradiation

Generation of Chinese Hamster Ovary (CHO) cell lines stably expressing green fluorescent protein (GFP) was achieved using a plasmid vector that encoded the red-shifted pCX-xGFP under the control of a strong hybrid promoter composed of a CMV enhancer and a -actin/-globin gene promoter. Cotransfection of the promoter-less pSV2-Neo helper plasmid transmitting neomycin resistance was followed by selection with the antibiotic G418. Constitutive GFP expression could be visualized in living and fixed cells using fluorescence spectroscopy, fluorescence microscopy, and flow cytometry. DNA repair-proficient (AA8) and deficient (UV5) CHO strains were used for survival tests after UVC irradiation. Cells carrying the GFP construct (AA8-pGFP, UV5-pGFP) show the same response to UV irradiation (colony forming ability) as their nontransformed parental cell lines (AA8, UV5). Using GFP as a marker for cell viability, cells were harvested after certain postirradiation growth periods and the numbers of GFP expressing cells and fluorescence intensities were determined by FACS analysis. Generally, GFP fluorescence in irradiated cells is not seen when cell membranes are damaged (leak-out of the soluble GFP). Irradiated cells without membrane damage express GFP continuously (leading to a dose-dependent increase in GFP contents).     

On Colimits in Categories of Relations

We study (finite) coproducts and colimits of -chains in Rel(C), the 2-category of relations over a given category C. The former exist and are the same as in C provided that C is extensive. The latter do not exist for example in Rel(Set). However, the canonical construction of those colimits in the category of sets can be generalized to Rel(Set). The canonical cocone is shown to satisfy a 2-categorical universal property, namely that of an lax adjoint cooplimit. Sufficient conditions for any base category C to admit the construction are given.A necessary and sufficient condition for the construction to yield colimits of -chains in the category of maps of Rel(C) is also given.     

On Isomorphisms of Relations Embedded into Each Other

In this paper, we consider analogs of the Cantor--Bernstein theorem for sets with binary relations. In Sec. 1, we prove an analog of this theorem for arbitrary binary relations; in Sec. 2, we consider an application; in Sec. 3, we study a class of relations with the Cantor-- Bernstein property and a class of exact relations, and prove that these classes are closed under certain operations.