Inequalities for some blocks of finite groups

We analyze some inequalities for numbers of characters in p-blocks of finite groups and prove them in the case of blocks with a normal defect group, as well as in the case of certain blocks in non-abelian simple groups. Received: 27 October 2005     

Conformational Relaxation of p‐Phenylenevinylene Trimers in Solution Studied by Picosecond Time‐Resolved Fluorescence

Two p‐phenylenevinylene (PV) trimers, containing 3′‐methylbutyloxyl (in MBOPV3) and 2′‐ethylhexyloxyl (in EHOPV3) side chains, are used as model compounds of PV‐based conjugated polymers (PPV) with the purpose of clarifying the origin of fast (picosecond time) components observed in the fluorescence decays of poly[2‐methoxy‐5‐(2′‐ethylhexyloxy)‐p‐phenylenevinylene] (MEH‐PPV). The fluorescence decays of MBOPV3 and EHOPV3 reveal the presence of similar fast components, which are assigned to excited‐state conformational relaxation of the initial population of non‐planar trimer conformers to lower‐energy, more planar conformers. The rate constant of conformational relaxation k_CR is dependent on solvent viscosity and temperature, according to the empirical relationship k_CR=aη_o^?α?exp(?αE_η/RT), where aη_o^?α is the frequency factor, η_o is the pre‐exponential coefficient of viscosity, E_η is the activation energy of viscous flow. The empirical parameter α, relating the solvent microscopic friction involved in the conformational change to the macroscopic solvent friction (α=1), depends on the side chain. The fast component in the fluorescence decays of MEH‐PPV polymers (PPVs), is assigned to resonance energy transfer from short to longer polymer segments. The present results call for revising this assignment/interpretation to account for the occurrence of conformational relaxation, concurrently with energy transfer, in PPVs.     

Existence of nash equilibria for constrained stochastic games

In this paper, we consider constrained noncooperative N-person stochastic games with discounted cost criteria. The state space is assumed to be countable and the action sets are compact metric spaces. We present three main results. The first concerns the sensitivity or approximation of constrained games. The second shows the existence of Nash equilibria for constrained games with a finite state space (and compact actions space), and, finally, in the third one we extend that existence result to a class of constrained games which can be “approximated” by constrained games with finitely many states and compact action spaces. Our results are illustrated with two examples on queueing systems, which clearly show some important differences between constrained and unconstrained games.Mathematics Subject Classification (2000): Primary: 91A15. 91A10; Secondary: 90C40     

Modification of propylene-α-olefin copolymers by maleic anhydride grafting and blending

Five commercial random propylene-α-olefin copolymers were functionalized with maleic anhydride by reactive mixing. Materials and blends of the original polymers with the grafted ones were characterized by IR, SEC, rheology, XRD, and DSC. The effects of ethylene content and average molecular weights on the effectiveness of scission and grafting reactions were investigated. Functionalization gives place to thermo-rheologically simple materials whose dynamic properties are in agreement with the measured molecular weights. The blends, which stand as miscible ones, display terminal dynamic moduli and crystallization and melting temperatures that show slight positive deviation with respect to linear mixing rules.     

Initial Carbon−Carbon Bond Formation during the Early Stages of Methane Dehydroaromatization

Methane dehydroaromatization (MDA) is among the most challenging processes in catalysis science owing to the inherent harsh reaction conditions and fast catalyst deactivation. To improve this process, understanding the mechanism of the initial C?C bond formation is essential. However, consensus about the actual reaction mechanism is still to be achieved. In this work, using advanced magic‐angle spinning (MAS) solid‐state NMR spectroscopy, we study in detail the early stages of the reaction over a well‐dispersed Mo/H‐ZSM‐5 catalyst. Simultaneous detection of acetylene (i.e., presumably the direct C?C bond‐forming product from methane), methylidene, allenes, acetal, and surface‐formate species, along with the typical olefinic/aromatic species, allow us to conclude the existence of at least two independent C?H activation pathways. Moreover, this study emphasizes the significance of mobility‐dependent host–guest chemistry between an inorganic zeolite and its trapped organic species during heterogeneous catalysis.     

Arched beams of Bresse type: observability and application in thermoelasticity

Nonlinear Dynamics - This is the first paper of a trilogy intended by the authors in what concerns a unified approach to the stability of thermoelastic arched beams of Bresse type under...     

Semigroups of partial transformations with kernel and image restricted by an equivalence

Semigroup Forum - For an arbitrary set X and an equivalence relation $$\mu$$ on X, denote by $$P_\mu (X)$$ the semigroup of partial transformations $$\alpha$$ on X such that $$x\mu \subseteq x(\ker...     

Dendritic-Like Molecules Built on a Pillar[5]arene Core as Hole Transporting Materials for Perovskite Solar Cells

Multi-branched molecules have recently demonstrated interesting behaviour as charge-transporting materials within the fields of perovskite solar cells (PSCs). For this reason, extended triarylamine dendrons have been grafted onto a pillar[5]arene core to generate dendrimer-like compounds, which have been used as hole-transporting materials (HTMs) for PSCs. The performances of the solar cells containing these novel compounds have been extensively investigated. Interestingly, a positive dendritic effect has been evidenced as the hole transporting properties are improved when going from the first to the second-generation compound. The stability of the devices based on the best performing pillar[5]arene material has been also evaluated in a high-throughput ageing setup for 500 h at high temperature. When compared to reference devices prepared from spiro-OMeTAD, the behaviour is similar. An analysis of the economic advantages arising from the use of the pillar[5]arene-based material revealed however that our pillar[5]arene-based material is cheaper than the reference.     

Quantitative proton magnetic resonance determination of N,N‐dimethylformamide in one intermediate of the Quimi‐Hib vaccine

Quimi‐Hib is a conjugate vaccine against Haemophilus influenza type b (Hib) where the Hib antigen is the only one produced by chemical synthesis. NMR has become the alternative of choice for the identity of intermediates during the chemical synthesis of Hib antigen. We explore a rapid quantitative proton magnetic resonance (qHNMR) assay for the determination of N,N‐dimethylformamide (DMF) as a residual in one of the critical intermediates. The proposed assay has been shown to be accurate, precise for intermediate precision conditions (relative standard deviation <3% for spectrometer‐to‐spectrometer variations), specific (no detected interferences), and rugged (percentage difference <3% for day‐to‐day and spectrometer‐to‐spectrometer variations). The quantitative NMR assay can replace the common chromatographic methods for monitoring the DMF contents in one crucial step of the synthetic scheme. Copyright © 2012 John Wiley & Sons, Ltd.