An energy-transport model for semiconductors derived from the Boltzmann equation

An energy-transport model is rigorously derived from the Boltzmann transport equation of semiconductors under the hypothesis that the energy gain or loss of the electrons by the phonon collisions is weak. Retaining at leading order electron-electron collisions and elastic collisions (i.e., impurity scattering and the elastic part of phonon collisions), a rigorous diffusion limit of the Boltzmann equation can be carried over, which leads to a set of diffusion equations for the electron density and temperature. The derivation is given in both the degenerate and nondegenerate cases.     

Characterizations based on conditional expectations of the doubled truncated distribution

The expression of the continuous distribution function F(x) is obtained whenever % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaerbhv2BYDwAHbacfiGaa8xBaiaabIcacaWG4bGaaiilaiaadMha% caqGPaGaa8hiaiaab2dacaWFGaGaa8xraiaa-HcacaWFybGaa8hiai% aa-XhacaWFGaGaa8hEaiaa-bcacqGHKjYOcaWFGaGaa8hwaiaa-bca% cqGHKjYOcaWFGaGaa8xEaiaa-Lcaaaa!53EE!\[m{\rm{(}}x,y{\rm{)}} {\rm{ = }} E(X | x \le X \le y)\]is known. Moreover, we obtain the necessary and sufficient conditions so that any function m: ² is the conditional expectation % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadweacaGGOaGaamiwaerbhv2BYDwAHbacfiGaa8hiaiaacYha% caWFGaGaa8hEaiaa-bcacqGHKjYOcaWFGaGaa8hwaiaa-bcacqGHKj% YOcaWFGaGaa8xEaiaacMcaaaa!4D0D!\[E(X | x \le X \le y)\]of a random variable X with continuous distribution function. Furthermore, we relate m(x,y) to order statistics.     

Series representation for semistable laws and their domains of semistable attraction

If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk _n wherek _n+1 ck _n then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG).     

Conformational statistics of polymer chain terminally attached to wall (Ⅲ)——NRW model loop chain

When the two end groups of a linear polymer chain are absorbed on a solid surface,the polymer chain forms the "loop" conformation.Investigation has been made on the conformational statistics of a model loop chain by the normal landom walk (NRW) on a lattice confined in the half-infinite space.Based on the conformational distribution function of the NRW model tail chain,it is easy to deduce an analytical formula expressing the conforma-tional number of the model loop chain.It was found that the ratio of the conformational number of the model loop chain to that of the free chain varies with the power function N-2/3 when the chain length N→∞ The same result was obtained by means of the recursion equation.The ratio of the mean square end-to-end distance h2 for the model loop chain to its mean square bond length I2 is 2N/3 Compared with the free chain with the same length N,the mean square end-to-end distance of the model loop chain contracts to a certain extent.The basic relationships deduced were support     

Asymptotic expansions of the distributions of some test statistics

Summary A modified Wald statistic for testing simple hypothesis against fixed as well as local alternatives is proposed. The asymptotic expansions of the distributions of the proposed statistic as well as the Wald and Rao statistics under both the null and alternative hypotheses are obtained. The powers of these statistics are compared and its is shown that for special structures of parameters some statistics have same power in the sence of order . The results obtained are applied for testing the hypothesis about the covariance matrix of the multivariate normal distribution and it is shown that none of the tests based on the above statistics is uniformly superior. Research supported by the National Science Foundation Grant MCS 830149.     

Synthesis of benzopyran derivatives,XV Preparation of arylsulfonyloxy-2,2-dimethyl-2H-chromenes

Summary Arylsulfonyloxy-2,2-dimethyl-2H-chromenes (26–35) have been synthesized by reduction of arylsulfonyloxy-2,2-dimethyl-4-chromanones (6–15) followed by dehydration.

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Synthese von Benzopyranderviaten. 15. Mitt.: Darstellung von Arylsulfonyloxy-2,2-dimethyl-2H-chromenen

Zusammenfassung Reduktion von Arylsulfonyloxy-2,2-dimethyl-4-chromanonen (6–15) und anschließende Dehydratisierung liefert Arylsulfonyloxy-2,2-dimethyl-2H-chromene (26–35).

     

Equilibrium conformations of polymer chains Part II. Conformons in networks

With regard to the ideal network it is shown that the concept ofN non-interacting polymer chains can be transformed in a problem of non interacting excitations (called conformons) for rubber elasticity. Modelling the interaction on permanent crosslinks as a scattering problem and taking the finite chain length into account, an interpretation of the second Mooney coefficient can be given. There is some evidence that the junctions move by constrained self diffusion.Dedicated to Prof. Dr. W. Ruland on the occasion of his 60th birthday.     

Synthesis and conformational analysis of naphth[1′,2′:5,6][1,3]oxazino[3,2-c][1,3]benzoxazine and naphth[1′,2′:5,6][1,3]oxazino[3,4-c][1,3]benzoxazine derivatives

A new functional group, the hydroxy group, was inserted into a Betti base by reaction with salicylaldehyde, and the naphthoxazine derivatives thus obtained were converted by ring-closure reactions with formaldehyde, acetaldehyde, propionaldehyde or phosgene to the corresponding naphth[1′2′:5,6][1,3]oxazino[3,2-c][1,3]benzoxazine derivatives. Further, the conformational analysis of these polycyclic compounds by NMR spectroscopy and an accompanying molecular modelling are reported; especially, both quantitative anisotropic ring current effects of the aromatic moieties in these compounds and steric substituent effects were employed to determine the stereochemistry of the naphthoxazinobenzoxazine derivatives.     

Automated molecular design: A new fragment-joining algorithm

Summary A popular first step in the problem of structure-based, de novo molecule design is to identify regions where specific functional groups or chemical entities would be expected to interact strongly. When the three-dimensional structure of the receptor is not available, it may be possible to derive a pharmacophore giving the three-dimensional relationships between such chemical groups. The task then is to design synthetically feasible molecules which not only contain the required groups, but which can also position them in the desired relative orientation. One way to do this is to first link the groups using an acyclic chain. We have investigated the application of the tweak algorithm [Shenkin, P.S. et al., Biopolymers, 26 (1987) 2053] for generating families of acyclic linkers. These linking structures can subsequently be braced using a ring-joining algorithm [Leach, A.R. and Lewis, R.A., J. Comput. Chem., 15 (1994) 233], giving rise to an even wider variety of molecular skeletons for further studies.     

Synthesis,Conformation, and Metabolism of a Selenium Bilirubin

Summary. A symmetrical C(10)-selena-bilirubin analog, 8,12-bis(2-carboxyethyl)-7,13-dimethyl-2,3,17,18-tetraethyl-10-selenabiladiene-ac-1,19(21H,24H)-dione was synthesized from 8-(2-carboxyethyl)-2,3-diethyl-7-methyl-(10H)-dipyrrin-1-one in one step by reaction with diselenyl dichloride. The selena-rubin exhibited UV-vis and NMR spectroscopic properties similar to those of the parent mesobilirubin, and like bilirubin and mesobilirubin, it adopts an intramolecularly hydrogen-bonded conformation, shaped like a ridge-tile but with a steeper pitch. The longer C–Se bond lengths (2.2Å) and smaller bond angles at C–Se–C (88°), as compared to C–CH₂–C (1.5Å, 106°), lead to an interplanar angle between the two dipyrrinones of only 72°, which is considerably less than that of bilirubin (100°) and close to that (74°) of its 10-thia-rubin analog. Despite the conformational distortion, the sensitivity of Se toward oxidation and the typically weak C–Se bond, the selena-rubin is metabolized in normal rats, like bilirubin, to acyl glucuronides, which are secreted into bile. In mutant (Gunn) rats lacking bilirubin glucuronosyl transferase (UGT1A1), glucuronide or other metabolites of the selena-rubin were not detected in bile, demonstrating the importance of hepatic glucuronidation for its biliary excretion.