Counting finite index subgroups and the P. Hall enumeration principle

We apply the P. Hall enumeration principle to count the number of subgroups of a given index in the free pro-p group and the free abelian group. We shall present an infinite family of non-isomorphic pro-p groups with the same zeta function.     

三种电阻技术在电阻功率系数方面的比较

电阻精度的问题看起来比想象的要复杂些。电阻有三种基本类型:BulkMetal箔、薄膜及厚膜,这三种电阻表面上看起来很相似,并且可能具有类似的采购规格。但实际上,这三种电阻的制造方式均不同。本身固有的设计与处理将极大影响电气性能,因此在安装后,这三种电阻的行为均不相同。当     

The design of a Tort law to control accidents

In this paper we analyse a two-stage game involving the government and n agents who engage in a single activity (driving). The government establishes the legal policy setting and the agents proceed to play a non-cooperative game of incomplete information with a risk of accident in which their behavioral strategy is their level of care. We examine the Nash-equilibrium conditions for single-activity accidents between heterogeneous agents, ‘good’ drivers or ‘bad’ drivers allowing a variable damage function and a liability rule defined on the cube. The relative desirability for society of alternative equilibria and the conditions under which they can obtain are discussed. The constraints which circumscribe the ability of the government to induce an equilibrium involving careful driving are demonstrated. It transpires that when the proportion of good drivers increases, it becomes more difficult to sustain a careful equilibrium whereas an equilibrium of reckless behavior becomes easier to sustain. Various extensions of the models are also presented.     

Suppression of flavor symmetry breaking in B decay sum rules

While flavor symmetries are useful for studying hadronic B   decays, symmetry relations for amplitudes and decay rates are usually violated by first order symmetry breaking corrections. We point out two cases in which first order symmetry breaking is suppressed by a small ratio of amplitudes: (1) An isospin sum rule for four B→Kπ$B\to K\pi$ decays, where isospin breaking is shown to be negligible. (2) An SU(3)$\mathrm{SU}(3)$ sum rule for pairs of B→Kπ$B\to K\pi$ and B→Kη₈$B\to K{\eta }_8$, generalized to pairs of B→Kπ$B\to K\pi$, B→Kη$B\to K\eta$ and B→Kη^′$B\to K{\eta }^{\prime }$.     

Statistics on wreath products and generalized binomial-stirling numbers

Various statistics on wreath products are defined via canonical words, “colored” right to left minima and “colored” descents. It is shown that refined counts with respect to these statistics have nice recurrence formulas of binomial-Stirling type. These extended Stirling numbers determine (via matrix inversion) dual systems, which are also shown to have combinatorial realizations within the wreath product. The above setting also gives rise to a MacMahon-type equi-distribution theorem over subsets with prescribed statistics. Partially supported by Minerva Grant No. 8441 and by EC's IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant HPRN-CT-2001-00272. Partially supported by EC's IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant HPRN-CT-2001-00272.     

The dielectric response of interfacial water—from the ordered structures to the single hydrated shell

Water is the universal solvent in nature. Does this imply, however, that its interaction with its environment is also a universal feature? While this question maybe too fundamental to be answered by one method only, we present evidence that the broadening of the dielectric spectra of water presents universal features of dipolar interactions with different types of matrixes. If in aqueous solutions the starting point of water’s state can be considered as bulk, with only partial interactions with the solute, then the state of water adsorbed in heterogeneous materials is determined by various hydration centers of the inhomogeneous material (the matrix) and it is significantly different from the bulk. In both cases, the dielectric spectrum of water is symmetrical and can be described by the Cole–Cole (CC) function. The phenomenological model that describes a physical mechanism of the dipole–matrix interaction in complex systems underlying the CC behavior has been applied to water adsorbed in porous glasses. It was then extended to analyses of the dynamic and structural behavior of water in nonionic and ionic aqueous solutions. The same model is then used to analyze the CC relaxation processes observed in clays, aqueous solutions of nucleotides, and amino acids.     

Nonproteolytic cleavage of aspartyl proline bonds in the cellulosomal scaffoldin subunit from Clostridium thermocellum

Previous work from our group [Morag (Morgenstern), E., Bayer, E. A., and Lamed, R. (1991), Appl. Biochem. Biotechnol. 30, 129–136] has demonstrated an anomalous electrophoretic mobility pattern for scaffoldin, the 210-kDa cellulosome-integrating subunit of Clostridium thermocellum. Subsequent evidence [Morag, E., Bayer, E. A., and Lamed, R. (1992), Appl. Biochem. Biotechnol. 33, 205–217] indicated that the effect could be attributed to a nonproteolytic fragmentation of the subunit into a defined series of lowermolecular-weight bands. In the present work, a recombinant segment of the scaffoldin subunit was employed to determine the site(s) of bond breakage. An Asp-Pro sequence within the cohesin domain was identified to be the sensitive peptide bond. This sequence appears quite frequently in the large cellulosomal proteins, and the labile bond may be related to an as yet undescribed physiological role in the hydrolysis of cellulose by cellulosomes.     

Practical anodes for Li-ion batteries comprising metallurgical silicon particles and multiwall carbon nanotubes

Journal of Solid State Electrochemistry - Silicon is considered to be a very attractive anode material for next-generation lithium-ion batteries due to its high theoretical capacity...     

A Macrocyclic Furan with Accessible Oxidation States: Switching Between Aromatic and Antiaromatic Global Ring Currents

Macrocyclic furans are predicted to switch between global aromaticity and antiaromaticity, depending on their oxidation states. However, the macrocyclic furans reported to date are stabilized by electron withdrawing groups, which result in inaccessible oxidation states. To circumvent this problem, a post-macrocyclization approach was applied to introduce methylene-substituted macrocyclic furans, which display an extremely low oxidation potential of −0.23 vs. Fc/Fc⁺, and are partially oxidized in ambient conditions. Additional oxidation to the dication results in aromaticity switching to a global 30πe⁻ aromatic state, as indicated by the formation of a strong diatropic current observed in the ¹H NMR spectrum. NICS and ACID calculations support this trend and provide evidence for a different pathway for the global current in the neutral and dicationic states. According to these findings, macrocyclic furans can be rendered as promising p-type materials with stable oxidation states.     

New Coins From Old: Computing With Unknown Bias

Suppose that we are given a function f : (0, 1)→(0,1) and, for some unknown p∈(0, 1), a sequence of independent tosses of a p-coin (i.e., a coin with probability p of “heads”). For which functions f is it possible to simulate an f(p)-coin? This question was raised by S. Asmussen and J. Propp. A simple simulation scheme for the constant function f(p)≡1/2 was described by von Neumann (1951); this scheme can be easily implemented using a finite automaton. We prove that in general, an f(p)-coin can be simulated by a finite automaton for all p ∈ (0, 1), if and only if f is a rational function over ℚ. We also show that if an f(p)-coin can be simulated by a pushdown automaton, then f is an algebraic function over ℚ; however, pushdown automata can simulate f(p)-coins for certain nonrational functions such as . These results complement the work of Keane and O’Brien (1994), who determined the functions f for which an f(p)-coin can be simulated when there are no computational restrictions on the simulation scheme. * Supported by a Miller Fellowship. † Supported in part by NSF Grant DMS-0104073 and by a Miller Professorship. ‡ This work is supported under a National Science Foundation Graduate Research Fellowship.