Boundary Conditions for the Dynamical Equations of Quantum Mechanics

We discuss the problem whether the time evolution in quantum physics should be represented by the time-symmetric unitary-group evolution, i.e., whether time t extends over???∞?<?t?<?+∞ or it is more realistic to describe quantum systems by a mathematical theory, for which time t starts from a finite value t ₀: t ₀?≤?t?<?+∞, for which the mathematicians would choose t ₀?=?0,¹ but which could be any finite value. If the quantum system in the lab should be described by some kind of quantum theory, one should also admit the possibility that the solution of the dynamical equations needs to be found under boundary conditions that admit a semigroup evolution. It is remarkable that results in lab experiments indicate the existence of an ensemble of finite beginnings of time $ t_0^{(i) } $ for an ensemble of individual quanta.     

Design of an ultrahigh‐energy‐resolution and wide‐energy‐range soft X‐ray beamline

A new ultrahigh‐energy‐resolution and wide‐energy‐range soft X‐ray beamline has been designed and is under construction at the Shanghai Synchrotron Radiation Facility. The beamline has two branches: one dedicated to angle‐resolved photoemission spectroscopy (ARPES) and the other to photoelectron emission microscopy (PEEM). The two branches share the same plane‐grating monochromator, which is equipped with four variable‐line‐spacing gratings and covers the 20–2000 eV energy range. Two elliptically polarized undulators are employed to provide photons with variable polarization, linear in every inclination and circular. The expected energy resolution is approximately 10 meV at 1000 eV with a flux of more than 3 × 10¹⁰ photons s^?1 at the ARPES sample positions. The refocusing of both branches is based on Kirkpatrick–Baez pairs. The expected spot sizes when using a 10 µm exit slit are 15 µm × 5 µm (horizontal × vertical FWHM) at the ARPES station and 10 µm × 5 µm (horizontal × vertical FWHM) at the PEEM station. The use of plane optical elements upstream of the exit slit, a variable‐line‐spacing grating and a pre‐mirror in the monochromator that allows the influence of the thermal deformation to be eliminated are essential for achieving the ultrahigh‐energy resolution.     

Low-Dimensional Representations of Special Linear Groups in Cross Characteristics

The low-dimensional projective irreducible representations incross characteristics of the projective special linear groupPSL_n(q) are investigated. If n 3 and (n, q) (3,2), (3,4), (4,2), (4,3), all such representationsof the first degree (which is (qⁿ – q)/(q – 1) – with = 0 or 1) and the second degree (which is (qⁿ –1)/(q – 1) come from Weil representations. We show thatthe gap between the second and the third degree is roughly q^2n-4.1991 Mathematics Subject Classification: 20C20, 20C33.     

Augmented Lagrangian Methods for $p$-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing

In this paper, we propose a generalized penalization technique and a convex constraint minimization approach for the $p$-harmonic flow problem following the ideas in [Kang & March, IEEE T. Image Process., 16 (2007), 2251-2261]. We use fast algorithms to solve the subproblems, such as the dual projection methods, primal-dual methods and augmented Lagrangian methods. With a special penalization term, some special algorithms are presented. Numerical experiments are given to demonstrate the performance of the proposed methods. We successfully show that our algorithms are effective and efficient due to two reasons: the solver for subproblem is fast in essence and there is no need to solve the subproblem accurately (even 2 inner iterations of the subproblem are enough). It is also observed that better PSNR values are produced using the new algorithms.     

Remarks on Centers of Rings

It is proved that for matrices A,B in the n by n upper triangular matrix ring Tn(R) over a domain R,if AB is nonzero and central in Tn(R) then AB =BA.The n by n full matrix rings over right Noetherian domains are also shown to have this property.In this article we treat a ring property that is a generalization of this result,and a ring with such a property is said to be weakly reversible-over-center.The class of weakly reversible-over-center rings contains both full matrix rings over right Noetherian domains and upper triangular matrix rings over domains.The structure of various sorts of weakly reversible-over-center rings is studied in relation to the questions raised in the process naturally.We also consider the connection between the property of being weakly reversible-over-center and the related ring properties.     

De novo design of N-(pyridin-4-ylmethyl)aniline derivatives as KDR inhibitors: 3D-QSAR, molecular fragment replacement, protein-ligand interaction fingerprint, and ADMET prediction

Vascular endothelial growth factor (VEGF) and its receptor tyrosine kinase VEGFR-2 or kinase insert domain receptor (KDR) have been identified as promising targets for novel anticancer agents. To achieve new potent inhibitors of KDR, we conducted molecular fragment replacement (MFR) studies for the understanding of 3D-QSAR modeling and the docking investigation of arylphthalazines and 2-((1H-Azol-1-yl)methyl)-N-arylbenzamides-based KDR inhibitors. Two favorable 3D-QSAR models (CoMFA with q ², 0.671; r ², 0.969; CoMSIA with q ², 0.608; r ², 0.936) have been developed to predict the biological activity of new compounds. The new molecular database generated by MFR was virtually screened using Glide (docking) and further evaluated with CoMFA prediction, protein?Cligand interaction fingerprint (PLIF) and ADMET analysis. 44 N-(pyridin-4-ylmethyl)aniline derivatives as novel potential KDR inhibitors were finally obtained. In this paper, the work flow developed could be applied to de novo drug design and virtual screening potential KDR inhibitors, and use hit compounds to further optimize and design new potential KDR inhibitors.     

On contraction of nonlinear difference equations with time‐varying delays

General nonlinear difference equations with time‐varying delays are considered. Explicit criteria for contraction of such equations are presented. Then some simple sufficient conditions for global exponential stability of equilibria and for stability of invariant sets are derived. Furthermore, explicit criteria for existence, uniqueness and global exponential stability of periodic solutions are derived. Finally, the obtained results are applied to time‐varying discrete‐time neural networks with delay.     

Emission characteristics of SPAN-80 activated ZnS nanocolloids

Quantum surface effects (new emission bands, blueshifts, intensity enhancement) were observed in SPAN-80 activated ZnS nanocolloids and explained in terms of time-dependent density functional theory. The experimental evidences were demonstrated for both undoped and Cu, Mn-doped colloidal phases. The photoluminescence spectra of these materials showed a new green band at 520 nm (ZnS:Cu) and a yellow-orange band at 576 nm (ZnS:Mn) besides a blue band at 465 nm. All bands lie in the visible region and are blueshifted, show sharp emissions with narrow widths and have approximately 20-times stronger intensities in comparison with those of the bulk samples. The time-resolved luminescence spectra showed that the life-times of free electrons were 0.12 μs and 1.9 ms in ZnS:Cu and ZnS:Mn correspondingly.     

两类正规化双全纯映照子族齐次展开式的精细估计

本文考虑C~n中单位多圆柱上和一般复Banach空间中单位球上的正规化双全纯α(0■α＜1)次的殆β(-π/2＜β＜π/2)型螺形映照以及α(0＜α＜1)次的β(-π/2＜β＜π/2)型螺形映照f(其中x=0是f(x)-x的k+1阶零点),研究了它们的构造,并得到其齐次展开式的精细估计．所得的结果推广了以前相应的结论．