Polygonal heat conductors with a stationary hot spot

We consider a convex polygonal heat conductor whose inscribed circle touches every side of the conductor. Initially, the conductor has constant temperature and, at every time, the temperature of its boundary is kept at zero. The hot spot is the point at which temperature attains its maximum at each given time. It is proved that, if the hot spot is stationary, then the conductor must satisfy two geometric conditions. In particular, we prove that these geometric conditions yield some symmetries provided the conductor is either pentagonal or hexagonal. This research was partially supported by Grants-in-Aid for Scientific Research (B) (# 12440042) and (B) (# 15340047) of Japan Society for the Promotion of Science, and by a Grant of the Italian MURST.     

Displacement measurements in structural elements by optical techniques

Speckle metrology and holographic interferometry (HI) have been used in several civil engineering applications. We present the results obtained by applying speckle photography (SP) to the study of two quadratic shearwalls with different boundary conditions, and the potential of the technique in the study of this kind of structures is described. The analysis of Young's fringes obtained with this technique at certain points on each shearwall provides the whole field of displacement measurements. HI has been used to measure the three components of absolute displacement, verifying that the bulging phenomenon does not affect the in-plane components when the applied load remains on the same plane as the shearwall. A qualitative analysis is carried out following an electronic speckle pattern interferometry (ESPI) technique. The results obtained by optical techniques are compared to the numerical results obtained by the finite element method (FEM), finding good correlation between them in all the cases.     

Polymerization kinetics and microstructure of waterborne acrylic/alkyd nanocomposites synthesized by miniemulsion

Waterborne acrylic‐alkyd nanocomposites are expected to combine the positive properties of alkyd resins and acrylic polymers. In this work, the kinetics of the miniemulsion polymerization used to synthesize these nanocomposites and the effect of the process variables on the polymer architecture and particle morphology was investigated. It was found that resin hydrophobicity and the type of initiator strongly affected the microstructure of these materials. The mechanisms responsible for these effects were discussed. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4871–4885, 2009     

Photophysics and Photochemistry of z‐Chlorprothixene in Acetonitrile†

Chlorprothixene (CPTX, Taractan^®) is a low potency antipsychotic mainly used for the treatment of psychotic disorders (e.g. schizophrenia) and acute mania occurring as part of bipolar disorders. As in the case of other numerous drugs used in the treatment of psychiatric disorders, CPTX presents geometric isomerism. Therefore, in vitro irradiation induces a rapid Z/E isomerization, which can affect its pharmacokinetic properties. This photoisomerization is not dependent on the oxygen concentration. The Z/E quantum yields determined for zCPTX in acetonitrile are 0.22 and 0.21 in anaerobic and aerobic environments, respectively. In the presence of water, both isomers decompose to produce 2‐chlorothioxanthone (CTX) after prolonged irradiation. This process strongly depends on the water concentration and the irradiation time, i.e. it is autocatalyzed by the CTX through a triplet‐energy transfer mechanism. The protonation state of the terminal amino group, on the other hand, has no effect on the isomerization process, but inhibits the formation of CTX. These results indicate that the phototoxicity of zCPTX is somehow affected by the formation of CTX.     

A Counterexample on Sample-Path Optimality in Stable Markov Decision Chains with the Average Reward Criterion

This note deals with Markov decision chains evolving on a denumerable state space. Under standard continuity-compactness requirements, an explicit example is provided to show that, with respect to a strong sample-path average reward criterion, the Lyapunov function condition does not ensure the existence of an optimal stationary policy.     

The Heck-Matsuda arylation of 2-hetero-substituted acrylates

The Heck-Matsuda arylation of 2-aza and 2-oxo-substituted acrylates is described. Several reaction conditions were evaluated including the influence of solvents, temperature, catalysts, and stoichiometry. While the oxygenated system was successfully arylated in benzonitrile with Pd₂(dba)₃ as catalyst, the aza-acrylate furnished methoxylated products. The methoxylated products were subjected to an elimination/reduction protocol to obtain the corresponding N,O-protected phenylalanine derivatives. A one-pot procedure for the preparation of phenylalanine derivatives from 2-aza-substituted acrylates is presented.     

Denumerable controlled Markov chains with average reward criterion: Sample path optimality

We consider discrete-time nonlinear controlled stochastic systems, modeled by controlled Makov chains with denumerable state space and compact action space. The corresponding stochastic control problem of maximizing average rewards in the long-run is studied. Departing from the most common position which usesexpected values of rewards, we focus on a sample path analysis of the stream of states/rewards. Under a Lyapunov function condition, we show that stationary policies obtained from the average reward optimality equation are not only average reward optimal, but indeed sample path average reward optimal, for almost all sample paths.Research supported by a U.S.-México Collaborative Research Program funded by the National Science Foundation under grant NSF-INT 9201430, and by CONACyT-MEXICO.Partially supported by the MAXTOR Foundation for applied Probability and Statistics, under grant No. 01-01-56/04-93.Research partially supported by the Engineering Foundation under grant RI-A-93-10, and by a grant from the AT&T Foundation.     

Proximal methods in reflexive Banach spaces without monotonicity

We introduce the concept of hypomonotone point-to-set operators in Banach spaces, with respect to a regularizing function. This notion coincides with the one given by Rockafellar and Wets in Hilbertian spaces, when the regularizing function is the square of the norm. We study the associated proximal mapping, which leads to a hybrid proximal-extragradient and proximal-projection methods for nonmonotone operators in reflexive Banach spaces. These methods allow for inexact solution of the proximal subproblems with relative error criteria. We then consider the notion of local hypomonotonicity and propose localized versions of the algorithms, which are locally convergent.     

Effective Descent Morphisms in Some Quasivarieties of Algebraic, Relational, and More General Structures

We show that the class of effective descent morphisms coincides with the class of regular epimorphisms in suitable categories of internal structures in an exact category. In particular this applies to quasivarieties of (ordinary) first-order structures closed under strong homomorphic images.     

Quaternary Stereogenic Centers through Enantioselective Heck Arylation of Acyclic Olefins with Aryldiazonium Salts: Application in a Concise Synthesis of (R)‐Verapamil

We describe herein a highly regio‐ and enantioselective Pd‐catalyzed Heck arylation of unactivated trisubstituted acyclic olefins to provide all‐carbon quaternary stereogenic centers. Chiral N,N ligands of the pyrimidine‐ and pyrazino‐oxazoline class were developed for that purpose, providing the desired products in good to high yields with enantiomeric ratios up to >99:1. Both linear and branched substituents on the olefins were well‐tolerated. The potential of this new method is demonstrated by the straightforward synthesis of several O‐methyl lactols and lactones containing quaternary stereocenters, together with a concise enantioselective total synthesis of the calcium channel blocker verapamil.