Sequential Power-Dependence Theory

Existing methods for predicting resource divisions in laboratory exchange networks do not take into account the sequential nature of the experimental setting. We extend network exchange theory by considering sequential exchange. We prove that Sequential Power-Dependence Theory—unlike Power-Dependence Theory and most other exchange theories—has a unique point prediction for resource divisions in every network, and we show that these point predictions fare well in comparison to those from established theories.     

Confinement, average forces, and the Ehrenfest theorem for a one-dimensional particle

The topics of confinement, average forces, and the Ehrenfest theorem are examined for a particle in one spatial dimension. Two specific cases are considered: (i) A free particle moving on the entire real line, which is then permanently confined to a line segment or ‘a box’ (this situation is achieved by taking the limit V ₀?→?∞ in a finite well potential). This case is called ‘a particle-in-an-infinite-square-well-potential’. (ii) A free particle that has always been moving inside a box (in this case, an external potential is not necessary to confine the particle, only boundary conditions). This case is called ‘a particle-in-a-box’. After developing some basic results for the problem of a particle in a finite square well potential, the limiting procedure that allows us to obtain the average force of the infinite square well potential from the finite well potential problem is re-examined in detail. A general expression is derived for the mean value of the external classical force operator for a particle-in-an-infinite-square-well-potential, $\hat{F}$ . After calculating similar general expressions for the mean value of the position ( $\hat{X}$ ) and momentum ( $\hat{P}$ ) operators, the Ehrenfest theorem for a particle-in-an-infinite-square-well-potential (i.e., $\mathrm{d}\langle\hat{X}\rangle/\mathrm{d}t=\langle\hat{P}\rangle/M$ and $\mathrm{d}\langle\hat{P}\rangle/\mathrm{d}t=\langle\hat{F}\rangle$ ) is proven. The formal time derivatives of the mean value of the position ( $\hat{x}$ ) and momentum ( $\hat{p}$ ) operators for a particle-in-a-box are re-introduced. It is verified that these derivatives present terms that are evaluated at the ends of the box. Specifically, for the wave functions satisfying the Dirichlet boundary condition, the results, $\mathrm{d}\langle\hat{x}\rangle/\mathrm{d}t=\langle\hat{p}\rangle/M$ and $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t=\mathrm{b.t.}+\langle\hat{f}\rangle$ , are obtained where b.t. denotes a boundary term and $\hat{f}$ is the external classical force operator for the particle-in-a-box. Thus, it appears that the expected Ehrenfest theorem is not entirely verified. However, by considering a normalized complex general state that is a combination of energy eigenstates to the Hamiltonian describing a particle-in-a-box with v(x)?=?0 ( $\Rightarrow\hat{f}=0$ ), the result that the b.t. is equal to the mean value of the external classical force operator for the particle-in-an-infinite-square-well-potential is obtained, i.e., $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t$ is equal to $\langle\hat{F}\rangle$ . Moreover, the b.t. is written as the mean value of a quantity that is called boundary quantum force, f _B. Thus, the Ehrenfest theorem for a particle-in-a-box can be completed with the formula $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t=\langle{{f_\mathrm{B}}}\rangle$ .     

Thermodynamic and transport properties of nitrogen and butane mixtures

A force field has been developed to describe the phase behaviour, interfacial, and transport properties of nitrogen and hydrocarbon mixtures under conditions relevant to those found in the high pressure extraction of oil from underground reservoirs. A Gibbs ensemble Monte Carlo method is used to parametrize intermolecular potentials for the pure components by matching experimental and simulated liquid and vapour coexisting densities. Also the surface tension, diffusion coefficient and shear viscosity of nitrogen and its mixtures with butane have been determined. The latter properties were obtained by canonical molecular dynamics simulations. The diffusion coefficient and shear viscosity were calculated by a Green-Kubo method. Results for pure nitrogen are given for temperatures ranging from 70 K to 110K. For mixtures of nitrogen with butane, results are presented at 339.4 K and 380.2 K. Good agreement is found between the results of simulations and available experimental data.     

Modular synthesis of diphospholipid oligosaccharide fragments of the bacterial cell wall and their use to study the mechanism of moenomycin and other antibiotics

We present a flexible, modular route to GlcNAc-MurNAc-oligosaccharides that can be readily converted into peptidoglycan (PG) fragments to serve as reagents for the study of bacterial enzymes that are targets for antibiotics. Demonstrating the utility of these synthetic PG substrates, we show that the tetrasaccharide substrate lipid IV (3), but not the disaccharide substrate lipid II (2), significantly increases the concentration of moenomycin A required to inhibit a prototypical PG-glycosyltransferase (PGT). These results imply that lipid IV and moenomycin A bind to the same site on the enzyme. We also show the moenomycin A inhibits the formation of elongated polysaccharide product but does not affect length distribution. We conclude that moenomycin A blocks PG-strand initiation rather than elongation or chain termination. Synthetic access to diphospholipid oligosaccharides will enable further studies of bacterial cell wall synthesis with the long-term goal of identifying novel antibiotics.     

Nine enzymes are required for assembly of the pacidamycin group of peptidyl nucleoside antibiotics

Pacidamycins are a family of uridyl peptide antibiotics that inhibit the translocase MraY, an essential enzyme in bacterial cell wall biosynthesis that to date has not been clinically targeted. The pacidamycin structural skeleton contains a doubly inverted peptidyl chain with a β-peptide and a ureido linkage as well as a 3'-deoxyuridine nucleoside attached to DABA(3) of the peptidyl chain via an enamide linkage. Although the biosynthetic gene cluster for pacidamycins was identified recently, the assembly line of this group of peptidyl nucleoside antibiotics remained poorly understood because of the highly dissociated nature of the encoded nonribosomal peptide synthetase (NRPS) domains and modules. This work has identified a minimum set of enzymes needed for generation of the pacidamycin scaffold from amino acid and nucleoside monomers, highlighting a freestanding thiolation (T) domain (PacH) as a key carrier component in the peptidyl chain assembly as well as a freestanding condensation (C) domain (PacI) catalyzing the release of the assembled peptide by a nucleoside moiety. On the basis of the substrate promiscuity of this enzymatic assembly line, several pacidamycin analogues were produced using in vitro total biosynthesis.     

Thermal conductivity of open‐cell polyolefin foams

The thermal conductivity and the cellular structure of novel open‐cell polyolefin foams produced by compression molding and based on blends of an ethylene‐vinyl acetate copolymer (EVA) and a low‐density polyethylene (LDPE) have been studied in the temperature range between 24 and 50 °C. The experimental results have shown that the cellular structure of the analyzed materials has interconnected cells because of the presence of large and small holes in the cell walls, this structure being clearly different to the typical structure of open‐cell polyurethane foams. It has been found that at low temperatures the materials have a slightly higher thermal conductivity than closed‐cell polyolefin foams of similar densities. The different mechanisms of heat flow, conduction, convection, and radiation have been analyzed by using experimental measurements and a theoretical model. It has been proved that, in spite of having an open‐cell structure, the convention mechanism is negligible, being the radiation mechanism the one which made different the conductivity of materials with varying cellular structures. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 212–221, 2008     

β-Na（Y_（1.5-x-y）Na_（0.5））F_6：Yb_xTm_y纳米颗粒的合成及其上转换发光性质

本文采用水热合成法制备了β-Na（Y1.5-x-yNa0.5）F6：YbxTmy（x=0.2~1.0,y=0.001~0.008）纳米颗粒,并利用X射线粉末衍射仪、透射电子显微镜和F-4600荧光分光光度计表征了其样品的物相、形貌和发光性质.结果表明样品物相为六角相,颗粒平均直径约22nm,并探讨了Yb3＋和Tm3＋掺杂浓度对样品的上转换发光性质的影响,结果表明敏化剂Yb3＋的最佳掺杂浓度为60%,而激活剂Tm3＋的最佳掺杂浓度为0.6%.     

Absolutely isolated singularities of a differential equation

In this paper we solve the problemof desingularization of an absolutely isolatedsingularity of a differential equation, including thedicritical case. As an application, we prove thefiniteness of the number of dicritical points in theblowing up tree of an absolutely isolated singularity.     

Decarboxylative Cyclization of Allylic Cyclic Carbamates: Mechanism Studies and Applications to the Synthesis of Natural Products

The mechanism of decarboxylative cyclization of allylic cyclic carbamates 1 leading to 2-substituted △~3-piperidines and-pyrrolidines, as well as its applications to the total synthesis of (--)codonopsine, are described.