The first general method for alpha-trifluoromethylation of carboxylic acids using BrF3

2-Carbomethoxy-1,1-bis(methylsulfide)-1-alkenes, easily made from carboxylic acids, CS(2) and MeI, were treated with BrF(3) producing eventually the desired alpha-trifluoromethyl carboxylate derivatives--RCH(CF(3))COOR'--in good yields.     

From alkyl halides to alkyltrifluoromethyls using bromine trifluoride

Under the right conditions, bromine trifluoride can be a useful tool for generating new types of reactions and compounds. Thus, tris(methylthio)alkyl derivatives, easily prepared from the corresponding alkyl bromides, were converted to the corresponding RCHBrCF2SMe or RCHBrCF3 compounds. The bromine atom, however, could be easily reduced forming eventually R'CF2SMe or R'CF3. If desired, the bromine atom can serve as an entry for constructing terminal difluoroolefins.     

Saint-Venant's principle in linear two-dimensional elasticity for non-striplike domains

Let be a simply connected domain in the x ₁-x ₂ plane which lies within the strip 0<x ₂, is a simple closed piecewise smooth curve. Let l= [(x ₁, x ₂): (x ₁, x ₂) and x ₁>0], _l = [(x ₁ x ₂): (x ₁ ,x ₂) and x ₁>1>0].Suppose that a two-dimensional homogeneous isotropic elastic body occupies , that a self-equilibrated stress loading is applied to - l, and that l is stress-free. Knowles [2] and Flavin [6] showed that the elastic energy in _l decays exponentially with respect to l with an exponential decay constant of the form k/b, where k is a universal constant. It is shown here that a decay constant of the form c/ may be obtained where c is a universal constant and is a characteristic dimension of , which is more appropriate than b for general non-striplike domains. In addition, an appropriate decay theorem is obtained for coil-like domains.     

Possible origin of efficient navigation in small worlds

The small-world phenomenon is one of the most important properties found in social networks. It includes both short path lengths and efficient navigation between two individuals. It is found by Kleinberg that navigation is efficient only if the probability density distribution of an individual to have a friend at distance r scales as P(r) ～ r(-1). Although this spatial scaling is found in many empirical studies, the origin of how this scaling emerges is still missing. In this Letter, we propose the origin of this scaling law using the concept of entropy from statistical physics and show that this scaling is the result of optimization of collecting information in social networks.     

Oxygen and hydrogen profiles and electrical properties of unintentionally doped gallium nitride grown by hydride vapor phase epitaxy

Commercially available hydride vapor phase epitaxy gallium nitride (GaN) is characterized with the aim to correlate the oxygen and hydrogen secondary ion mass spectrometry profiles of a GaN wafer with the electrical properties of the sample. A GaN layer model, including doping profile and mobility, is derived, utilizing electrical (capacitance–voltage, Hall), structural (high resolution X‐ray diffraction) and optical (polarized infrared spectroscopy) methods. Oxygen and hydrogen are easily incorporated during hydride vapor phase epitaxy growth of GaN. Oxygen is an n‐type dopant in GaN, whereas hydrogen may passivate some of the donors. Electrical and optical properties correlate with a low defect concentration top GaN layer and a high defect concentration GaN interlayer.     

Evaluation of choice set generation algorithms for route choice models

This paper discusses choice set generation and route choice model estimation for large-scale urban networks. Evaluating the effectiveness of Advanced Traveler Information Systems (ATIS) requires accurate models of how drivers choose routes based on their awareness of the roadway network and their perceptions of travel time. Many of the route choice models presented in the literature pay little attention to empirical estimation and validation procedures. In this paper, a route choice data set collected in Boston is described and the ability of several different route generation algorithms to produce paths similar to those observed in the survey is analyzed. The paper also presents estimation results of some route choice models recently developed using the data set collected.     

Uniform CLT for Markov chains and its invariance principle: A martingale approach

The convergence of stochastic processes indexed by parameters which are elements of a metric space is investigated in the context of an invariance principle of the uniform central limit theorem (UCLT) for stationary Markov chains. We assume the integrability condition on metric entropy with bracketing. An eventual uniform equicontinuity result is developed which essentially gives the invariance principle of the UCLT. We translate the problem into that of a martingale difference sequence as in Gordin and Lifsic.⁽⁷⁾ Then we use the chaining argument with stratification adapted from that of Ossiander.⁽¹¹⁾ The results of this paper generalize those of Levental⁽¹⁰⁾ and Ossiander.⁽¹¹⁾