弱闭T(N)-模的预零化子的等距映射

本文刻划了弱闭T(N)-模的预零化子间的等距映射.设u,W分别为由左连续序同态N→~N和N→~N所确定的弱闭T(N)-模, u(?),W(?)分别为u,W的预零化子,Φ为由u(?)到W(?)上的线性等距映射.若(0)*=(0)#=(0),dim(0)+≠1且min{dim(H(?)~H),dim(He(?)^H)}≥2,则存在酉算子Ui,Vi(i=1,2),使得Φ(A)=U1AV*1或Φ(A)=U2A*V2*.     

The catalyzed hydrosilation reaction: substituent effects

Ab initio electronic structure calculations using MP2 wavefunctions have been used to investigate a reaction path for the hydrosilation reaction catalyzed by divalent titanium [modeled by TiH₂, TiCl₂, and Ti(C₅H₅)₂]. Optimized structures and energies are presented. All model reactions predict a barrierless reaction path compared to a barrier of 78 kcal/mol for the uncatalyzed reaction. Received: 11 August 1998 / Accepted: 3 September 1998 / Published online: 23 February 1999     

Analyzing completeness of axiomatic functional systems for temporal × modal logics

In previous works, we presented a modification of the usual possible world semantics by introducing an independent temporal structure in each world and using accessibility functions to represent the relation among them. Different properties ofthe accessibility functions (being injective, surjective, increasing, etc.) have been considered and axiomatic systems (called functional) which define these properties have been given. Only a few ofthese systems have been proved tobe complete. The aim ofthis paper is to make a progress in the study ofcompleteness for functional systems. For this end, we use indexes as names for temporal flows and give new proofs of completeness. Specifically, we focus our attention on the system which defines injectivity, because the system which defines this property without using indexes was proved to be incomplete in previous works. The only system considered which remains incomplete is the one which defines surjectivity, even ifwe consider a sequence ofnatural extensions ofthe previous one (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The weak conjecture on spherical classes

Let be the mod 2 Steenrod algebra. We construct a chain-level representation of the dual of Singer's algebraic transfer, which maps Singer's invariant-theoretic model of the dual of the Lambda algebra, , to and is the inclusion of the Dickson algebra, , into . This chain-level representation allows us to confirm the weak conjecture on spherical classes (see [9]), assuming the truth of (1) either the conjecture that the Dickson invariants of at least k = 3 variables are homologically zero in }, (2) or a conjecture on ${\mathcal{A}}$ -decomposability of the Dickson algebra in $\Gamma_k^{\wedge}$. We prove the conjecture in item (1) for k = 3 and also show a weak form of the conjecture in item (2). Received November 27, 1996; in final form March 6, 1998     

Efficient method to prepare diethylphosphonacetamides

An efficient and versatile synthetic method is described to synthesize diethylphosphonacetamides in a single step.     

Learning rates of gradient descent algorithm for classification

In this paper, a stochastic gradient descent algorithm is proposed for the binary classification problems based on general convex loss functions. It has computational superiority over the existing algorithms when the sample size is large. Under some reasonable assumptions on the hypothesis space and the underlying distribution, the learning rate of the algorithm has been established, which is faster than that of closely related algorithms.     

A comparison of magnetic resonance imaging methods for fluid content imaging in porous media

Quantitative measurements are important for imaging fluid content in porous media. Conventional MRI methods suffer from contrast because of relaxation times in porous media, resulting in measurements of apparent fluid content, not the true fluid content. We compare four magnetic resonance imaging methods for fluid content imaging in several water‐saturated reservoir core plugs: frequency‐encoded spin echo, single point ramped imaging with T₁ enhancement, hybrid spin echo single point imaging (SE‐SPI), and T₂ mapping SE‐SPI. 1‐D profiles obtained with each method were compared in terms of image quality, image sensitivity, and quantification of water content. The image quality of short T₂ lifetime samples suffered from blurring in hybrid SE‐SPI images. Image sensitivity was the highest in the profiles obtained with frequency‐encoded spin echo. The quantification of frequency‐encoded spin echo, T₂ mapping SE‐SPI, and hybrid SE‐SPI suffered in core plugs with a significant population of short T₂ components because of T₂ attenuation. Overall, single point ramped imaging with T₁ enhancement was found to be the most general method for fluid content imaging. Copyright © 2013 John Wiley & Sons, Ltd.     

Supramolecular nanostructures from self‐assembly of T‐shaped rod building block oligomers

T‐shaped coil–rod–coil oligomers, consisting of a dibenzo[a,c]phenazine unit and phenyl groups linked together with acetylenyl bonds at the 2,7‐position of dibenzo[a,c]phenazine as a rigid segment have been synthesized. The coil segments of these new molecules composed of poly(ethylene oxide) (PEO)–poly(propylene oxide) (PPO) incorporating lateral methyl groups between the rod and coil segment and two flexible alkyl groups connecting with the rigid segment at the 4,6‐position of dibenzo[a,c]phenazine, respectively. The experimental results reveal that the length of the flexible PEO coil chain influence construction of various supra‐nanostructures from lamellar structure to rectangular columnar structure. It is also shown that introduction of different length of alkyl side chain groups in the backbone of the T‐shaped molecules affect the self‐organization behavior to form hexagonal perforate layer or oblique columnar structures. In addition, lateral methyl groups attached to the surface of rod and coil segments, dramatically influence the self‐assembling behavior in the crystalline phase. T‐shaped molecules containing a lateral methyl group at the surface of rod and PEO coil segments, self‐assemble into 3D body‐centered tetragonal structures in the crystalline phase, while molecules without a lateral methyl group based on PEO coil chain self‐organize into 2D oblique columnar crystalline structures. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 5021–5028     

Copper‐Catalyzed Ritter‐Type Reaction of Unactivated Alkenes with Dichloramine‐T

It was shown that dichloramine‐T ( 1 ) reacted with cyclohexene in acetonitrile to give N¹‐(2‐chlorocyclohexyl) amidine 2a and N‐(2‐chlorocyclohexyl)acetamide ( 3 ) via the competitive addition of acetonitrile and N‐chloro‐N‐tosylamino anion to cyclohexenechloronium ion. This reaction can be catalyzed by Cu(OAc)₂, primarily affording 2a . Furthermore, the resulting 2a can be cyclized to benzimidazol 14a in good yield by treating with KOH in dioxane.     

Improved Self‐Energy Calculations for Pressure Broadening of Spectral Lines in Dense Plasmas

Pressure broadening of Lyman‐lines of hydrogen‐like lithium (Li²⁺) has been studied using a quantum statistical approach to the line shape in dense plasmas, for details see [1]. In this communication, we concentrate on the electronic self‐energy, which is a basic input to the theory of spectral line profiles. We discuss the effect of strong, i.e. close, collisions which have been neglected so far for Li²⁺ plasmas, but play generally an important role in dense plasmas, as has been shown in [2]. We present a method to calculate an improved electronic self‐energy including strong collisions based on a two‐body T‐matrix and an effective optical potential. The method is tested for level broadening of the ground state of hydrogen (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)