Searching for a counterfeit coin with b-balance

We consider the classical problem of searching for a heavier coin in a set of n coins, n-1 of which have the same weight. The weighing device is b-balance which is the generalization of two-arms balance. The minimum numbers of weighings are determined exactly for worst-case sequential algorithm, average-case sequential algorithm, worst-case predetermined algorithm, average-case predetermined algorithm.We also investigate the above search model with additional constraint: each weighing is only allowed to use the coins that are still in doubt. We present a worst-case optimal sequential algorithm and an average-case optimal sequential algorithm requiring the minimum numbers of weighings.     

Synthesis and Properties of a Heteronuclear Ag（Ⅰ）/Ni（Ⅱ） Complex

Introduction Itiswell knownthatcyanogroupsincyanometa latessuchas[Ag(CN)2]-unitscanbeusedasbridg ingligandsandapolymericstructurecanbeformed throughsilver silver(argentophilic)interactions.This propertyhasbeenexploredintheconstructionofmany oligomericandp…     

Tip-induced local anodic oxidation on p-GaAs surface with non-contact atomic force microscopy

Nano-sized oxide structures resulted from localized electrochemical oxidation induced by a negatively biased atomic force microscopy (AFM) tip operated with the non-contact mode were fabricated on p-GaAs(1 0 0) surface. The geometrical characteristics of the oxide patterns and their dependences on various fabrication parameters, e.g., the anodization time, the biased voltages, the tip scanning rates, as well as the formation mechanism and relevant growth kinetics are investigated. Results indicate that the height of the protruded oxide dots grow exponentially as a function of time in the initial stage of oxidation and soon reaches a maximum height depending linearly with the anodized voltages, in according with the behaviors predicted by space charge limited local oxidation mechanism. In addition, selective micro-Auger analysis of the anodized region reveals the formation of Ga(As)O_x, indicating the prominent role played by the field-induced nanometer-size water meniscus in producing the nanometer-scale oxide dots and bumps on p-GaAs(1 0 0) surface.     

Preparation,thermal properties,and flame retardance of epoxy–silica hybrid resins

A novel epoxy system was developed through the in situ curing of bisphenol A type epoxy and 4,4′‐diaminodiphenylmethane with the sol–gel reaction of a phosphorus‐containing trimethoxysilane (DOPO–GPTMS), which was prepared from the reaction of 9,10‐dihydro‐9‐oxa‐10‐phosphaphenanthrene‐10‐oxide (DOPO) with 3‐glycidoxypropyltrimethoxysilane (GPTMS). The preparation of DOPO–GPTMS was confirmed with Fourier transform infrared, ¹H and ³¹P NMR, and elemental analysis. The resulting organic–inorganic hybrid epoxy resins exhibited a high glass‐transition temperature (167 °C), good thermal stability over 320 °C, and a high limited oxygen index of 28.5. The synergism of phosphorus and silicon on flame retardance was observed. Moreover, the kinetics of the thermal oxidative degradation of the hybrid epoxy resins were studied. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2354–2367, 2003     

Synthesis and characterization of wholly aromatic poly(azomethine)s containing donor–acceptor triphenylamine moieties

N‐(4‐nitrophenyl)‐4′,4″‐bisformyl‐diphenylamine was synthesized from N‐(4‐nitrophenyl)‐diphenylamine by the Vilsmeier‐Haack reaction. Soluble aromatic poly(azomethine)s (PAMs) were prepared by the solution polycondensation of N‐(4‐nitrophenyl)‐4′,4″‐bisformyl‐diphenylamine and aromatic diamine in N‐methyl‐2‐pyrrolidone (NMP) at room temperature under reduced pressure. All the PAMs are highly soluble in various organic solvents, such as N,N‐dimethylacetamide (DMAc), chloroform (CHCl₃), and tetrahydrofuran (THF). Differential scanning calorimetry (DSC) indicated that these PAMs had glass‐transition temperatures (T_gs) in the range of 170–230 °C, and a 10% weight‐loss temperatures in excess of 490 °C with char yield at 800 °C in nitrogen higher than 60%. These PAMs in NMP solution showed UV‐Vis charge‐transfer (CT) absorption at 405–421 nm and photoluminescence peaks around 462–466 nm with fluorescence quantum efficiency (Φ_F) 0.10–0.99%. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels of these PAMs can be determined from cyclic voltammograms as 4.86–5.43 and 3.31–3.34 eV, respectively. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4921–4932, 2007     

用不变速度推导卢瑟福散射公式

通过横向速度变换得到两种不变速度，由此推出卢瑟福散射公式。