Semiempirical fine-tuning for Hartree–Fock ionization potentials of atomic ions with non-integral atomic number

Amovilli and March (2006) [8] used diffusion quantum Monte Carlo techniques to calculate the non-relativistic ionization potential I(Z)$I(Z)$ in He-like atomic ions for the range of (fractional) nuclear charges Z   lying between the known critical value _Zc=0.911$Z_{\mathrm{c}}=0.911$ at which I(Z)$I(Z)$ tends to zero and Z=2$Z=2$. They showed that it is possible to fit I(Z)$I(Z)$ to a simple quadratic expression. Following that idea, we present here a semiempirical fine-tuning of Hartree–Fock ionization potentials for the isoelectronic series of He, Be, Ne, Mg and Ar-like atomic ions that leads to excellent estimations of _Zc$Z_{\mathrm{c}}$ for these series. The empirical information involved is experimental ionization and electron affinity data. It is clearly demonstrated that Hartree–Fock theory provides an excellent starting point for determining I(Z)$I(Z)$ for these series.     

Stochastic electromagnetic plane-wave pulse with non-uniform correlation distribution

Stochastic electromagnetic plane-wave (SEPW) pulse with non-uniform correlation distribution is introduced. The realizability condition for such pulse is derived. It is found that the evolution properties of the intensity and the degree of polarization of an SEPW pulse with non-uniform correlation distribution in dispersive media are much different from those of an SEPW pulse with uniform correlation distribution.     

Structural Assignment of Stilbenethiols and Chalconethiols and Differentiation of Their Isomeric Derivatives by Means of 1H‐ and 13C‐NMR Spectroscopy

Abstract

The ¹H‐ and ¹³C‐NMR spectra of some substituted stilbenes and chalcones were assigned unambiguously on the basis of a combination of homo‐ (COSY) and heteronuclear (HETCOR) two‐dimensional methods, the chemical shifts, as well as spin‐coupling constants. The A_ik empirical parameters of the –O–C(S)–N(CH₃)₂, –S–C(O)–N(CH₃)₂, and –SH group were calculated to help predict the chemical shifts of substituted stilbenes, 4′‐nitrostilbenes, and chalcones. The ¹H‐ and ¹³C‐NMR spectra have been shown to be able to differentiate between the isomers of O‐stilbenyl (4, 5) and S‐stilbenyl N,N‐dimethylthiocarbamates (7, 8) as well as O‐chalconyl (6) and S‐chalconyl N,N‐dimethylthiocarbamates (9).     

On the transposition anti-involution in real Clifford algebras I: the transposition map

A particular orthogonal map on a finite-dimensional real quadratic vector space (V,?Q) with a non-degenerate quadratic form Q of any signature (p,?q) is considered. It can be viewed as a correlation of the vector space that leads to a dual Clifford algebra C?(V*,?Q) of linear functionals (multiforms) acting on the universal Clifford algebra C?(V,?Q). The map results in a unique involutive automorphism and a unique involutive anti-automorphism of C?(V,?Q). The anti-involution reduces to reversion (resp. conjugation) for any Euclidean (resp. anti-Euclidean) signature. When applied to a general element of the algebra, it results in transposition of the element matrix in the left regular representation of C?(V,?Q). We also give an example for real spinor spaces. The general setting for spinor representations will be treated in part II of this work [R. Ab?amowicz and B. Fauser, On the transposition anti-involution in real Clifford algebras II: Stabilizer groups of primitive idempotents, Linear Multilinear Algebra, to appear].     

On dominance core and stable sets for cooperative ellipsoidal games

Abstract

The allocation problem of rewards or costs is a central question for individuals and organizations contemplating cooperation under uncertainty. The involvement of uncertainty in cooperative games is motivated by the real world where noise in observation and experimental design, incomplete information and further vagueness in preference structures and decision-making play an important role. The theory of cooperative ellipsoidal games provides a new game theoretical angle and suitable tools for answering this question. In this paper, some solution concepts using ellipsoids, namely the ellipsoidal imputation set, the ellipsoidal dominance core and the ellipsoidal stable sets for cooperative ellipsoidal games, are introduced and studied. The main results contained in the paper are the relations between the ellipsoidal core, the ellipsoidal dominance core and the ellipsoidal stable sets of such a game.     

Well-Posedness in Critical Spaces for the Full Compressible Mhd Equations

In this paper we prove local well-posedness in critical Besov spaces for the full compressible MHD equations in ?N, N≥ 2${?}^N,\hspace{0.17em}N\ge \hspace{0.17em}2$ under the assumptions that the initial density is bounded away from zero. The proof relies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.     

数字散斑相关技术进展及应用

数字散斑相关技术是廿世纪末发展的一项光力学测量技术,历经20年各国学者的研究改进积累,目前已成为一种成熟的测量方法,并已成功地应用于力学测量中。本文回顾和叙述了这些进展,并列举在各方面的应用实例以进一步扩展其应用领域。数字散斑相关技术的八个关键问题即1.相关公式,2.搜索技术,3.亚像素搜索,4.散斑图,5.减噪,6.补偿技术,7.位移场至应变场转换,8.三维位移场测量。最后将叙述数字相关技术在材料测试、结构模型及实物监测、岩石力学、复合材料性能研究、生物力学等方面的广泛应用情况。     

Diffusion of Myelin Oligodendrocyte Glycoprotein in Living OLN-93 Cells Investigated by Raster-Scanning Image Correlation Spectroscopy (RICS)

Many membrane proteins and lipids are partially confined in substructures ranging from tens of nanometers to micrometers in size. Evidence for heterogeneities in the membrane of oligodendrocytes, i.e. the myelin-producing cells of the central nervous system, is almost exclusively based on detergent methods. However, as application of detergents can alter the membrane phase behaviour, it is important to investigate membrane heterogeneities in living cells. Here, we report on the first investigations of the diffusion behavior of the myelin-specific protein MOG (myelin oligodendrocyte glycoprotein) in OLN-93 as studied by the recently developed RICS (raster-scanning image correlation spectroscopy) technique. We implemented RICS on a standard confocal laser-scanning microscope with one-photon excitation and analog detection. Measurements on FITC-dextran were used to evaluate the performance of the system and the data analysis procedure. Ellen Gielen and Nick Smisdom contributed equally to this work.