Brauer characters with cyclotomic field of values

It has been shown in an earlier paper [G. Navarro, Pham Huu Tiep, Rational Brauer characters, Math. Ann. 335 (2006) 675-686] that, for any odd prime p, every finite group of even order has a non-trivial rational-valued irreducible p-Brauer character. For p=2 this statement is no longer true. In this paper we determine the possible non-abelian composition factors of finite groups without non-trivial rational-valued irreducible 2-Brauer characters. We also prove that, if p≠q are primes, then any finite group of order divisible by q has a non-trivial irreducible p-Brauer character with values in the cyclotomic field Q(exp(2πi/q)).     

Block separation in solvable groups

If π is a set of primes, a finite group G is block π-separated if for every two distinct irreducible complex characters α, β ∈ Irr(G) there exists a prime p ∈ π such that α and β lie in different Brauer p-blocks. A group G is block separated if it is separated by the set of prime divisors of |G|. Given a set π with n different primes, we construct an example of a solvable π-group G which is block separated but it is not separated by every proper subset of π. Received: 22 December 2004     

Efficient construction of high‐resolution TVD conservative schemes for equations with source terms: application to shallow water flows

High‐resolution total variation diminishing (TVD) schemes are widely used for the numerical approximation of hyperbolic conservation laws. Their extension to equations with source terms involving spatial derivatives is not obvious. In this work, efficient ways of constructing conservative schemes from the conservative, non‐conservative or characteristic form of the equations are described in detail. An upwind, as opposed to a pointwise, treatment of the source terms is adopted here, and a new technique is proposed in which source terms are included in the flux limiter functions to get a complete second‐order compact scheme. A new correction to fix the entropy problem is also presented and a robust treatment of the boundary conditions according to the discretization used is stated. Copyright © 2001 John Wiley & Sons, Ltd.     

A Markov model for analyzing the evolution of bladder carcinoma

A Markovian approach to analyze different states of the superficial vesical carcinoma is considered, taking into account up to two recurrences and the possibility of progression. So, three transient states are considered: free of disease, first, and second recurrence; and an absorbent state, the progression. A methodology based in phase-type distributions is also used, that allows the usual quantities of interest in survival studies to be expressed in a well-structured form. This type of distribution has shown its utility in queue theory, and has the advantage that mathematical expressions can be presented in a closed form that allows algebraic treatment.     

High temperature giant dipole and isoscalar resonances

We present a systematic study of the Giant Dipole Resonance (GDR) at high temperatures (T≧4 MeV) in the framework of a semiclassical approximation that uses them ₁ andm ₃ RPA sum rules to estimate the GDR mean energy. We focus on the evolution withT of the collective nature of the GDR and of theL=0, 2, 3 and 4 isoscalar resonances. We find that the GDR remains particularly collective at highT, suggesting that it might be possible to observe it experimentally even at temperatures close to the maximum one a nucleus can sustain.     

Quadratic characters in groups of odd order

We prove that in a finite group of odd order, the number of irreducible quadratic characters is the number of quadratic conjugacy classes.     

A Flexible Pro‐porous Coordination Polymer: Non‐conventional Synthesis and Separation Properties Towards CO2/CH4 Mixtures

The novel coordination polymers [Cu(Hoxonic)(H₂O)]_n ( 1 ) and [Cu(Hoxonic)(bpy)_0.5]_n ? 1.5 n H₂O ( 2?H₂O ) (H₃oxonic: 4,6‐dihydroxy‐1,3,5‐triazine‐2‐carboxylic acid; bpy: 4,4′‐bipyridine) have been isolated and structurally characterised by ab initio X‐ray powder diffraction. The dense phase 1 contains 1D zig‐zag chains in which Hoxonic dianions bridge square‐pyramidal copper(II) ions, apically coordinated by water molecules. On the contrary, 2?H₂O , prepared by solution and solventless methods, is based on 2D layers of octahedral copper(II) ions bridged by Hoxonic ligands, further pillared by bpy spacers. The resulting pro‐porous 3D network possesses small hydrated cavities. The reactivity, thermal, magnetic and adsorptive properties of these materials have been investigated. Notably, the adsorption studies on 2 show that this material possesses unusual adsorption behaviour. Indeed, guest uptake is facilitated by increasing the thermal energy of both the guest and the framework. Thus, neither N₂ at 77 K nor CO₂ at 195 K are incorporated, and CH₄ is only minimally adsorbed at 273 K and high pressures (0.5 mmol g^?1 at 2500 kPa). By contrast, CO₂ is readily incorporated at 273 K (up to 2.5 mmol g^?1 at 2500 kPa). The selectivity of 2 towards CO₂ over CH₄ has been investigated by means of variable‐temperature zero coverage adsorption experiments and measurement of breakthrough curves of CO₂/CH₄ mixtures. The results show the highly selective incorporation of CO₂ in 2 , which can be rationalised on the basis of the framework flexibility and polar nature of its voids.     

Phosphine and Thiophene Cyclopalladated Complexes: Hydrolysis Reactions in Strong Acidic Media

The mechanisms for the hydrolysis of organopalladium complexes [Pd(CNN)R]BF₄ (R=P(OPh)₃, PPh₃, and SC₄H₈) were investigated at 25 °C by using UV/Vis absorbance measurements in 10 % v/v ethanol/water mixtures containing different sulphuric acid concentrations in the 1.3–11.7 M range. In all cases, a biphasic behavior was observed with rate constants k_1obs, which corresponds to the initial step of the hydrolysis reaction, and k_2obs, where k_1obs>k_2obs. The plots of k_1obs and k_2obs versus sulfuric acid concentration suggest a change in the reaction mechanism. The change with respect to the k_1obs value corresponds to 35 %, 2 %, and 99 % of the protonated complexes for R=PPh₃, P(OPh)₃, and SC₄H₈, respectively. Regarding k_2obs, the change occurred in all cases at about 6.5 M H₂SO₄ and matched up with the results reported for the hydrolysis of the 2‐acetylpyridinephenylhydrazone (CNN) ligand. By using the excess acidity method, the mechanisms were elucidated by carefully looking at the variation of k_i,_obs (i=1,2) versus ${c_{{\rm{H}}^ + } }$ . The rate‐determining constants, k_0,A‐1, k_0,A‐2, and k_0,A‐SE2 were evaluated in all cases. The R=P(OPh)₃ complex was most reactive due to its π‐acid character, which favors the rupture of the trans nitrogen–palladium bond in the A‐2 mechanism and also that of the pyridine nitrogen–palladium bond in the A‐1 mechanism. The organometallic bond exerts no effect on the relative basicity of the complexes, which are strongly reliant on the substituent.     

Wavefront sensing with critical sampling

Different types of nonredundant sampling patterns are shown to guarantee completeness of the basis formed by the sampled partial derivatives of Zernike polynomials, commonly used to reconstruct the wavefront from its slopes (wavefront sensing). In the ideal noise-free case, this enables one to recover double the number of modes J than sampling points I (critical sampling J=2I). With real data, noise amplification makes the optimal number of modes lower I相似文献   

Facile and versatile synthesis of rod‐coil poly(3‐hexylthiophene)‐based block copolymers by nitroxide‐mediated radical polymerization

A well‐defined and monofunctional poly(3‐hexylthiophene)‐based (P3HT) macroinitiator has been obtained through a clean, simple, and an efficient multistep synthesis process. The macroinitiator is obtained via intermolecular radical 1,2‐addition onto an ω‐acrylate‐terminated P3HT macromonomer. In a second step, well‐defined rod‐coil block copolymers were obtained by nitroxide‐mediated radical polymerization (NMRP) using the so‐called Blocbuilder^®. The polymerization was found to be controlled with various monomers such as styrene, isoprene, 4‐vinylpyridine, or methyl acrylate. This process constitutes a very promising way to obtain versatile and clean materials for organic electronics. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012