Synthesis and Reactivity of Structurally Analogous Phenylimido and Oxo Complexes of Rhenium(V) with N,N‐Dialkyl‐N′‐benzoylthioureas

[ReOCl₃(PPh₃)₂] and [Re(NPh)Br₃(PPh₃)₂] react at room temperature with equivalent amounts of N,N‐dialkyl‐N′‐benzoylthioureas (HR¹R²btu) in CH₂Cl₂ under formation of the rhenium(V) complexes [ReOCl₂(R¹R¹btu)(PPh₃)] and [Re(NPh)Br₂(R¹R²btu)(PPh₃)], respectively. The products are structurally analogous with the oxygen atoms of the benzoylthioureas binding in trans positions to the oxo or phenylimido ligands. Prolonged reaction times result in the reduction of the oxo compound by the released PPh₃ and the formation of rhenium(III) complexes of the composition [ReCl₂(PPh₃)₂(R¹R²btu)], while such a second reaction path is excluded for the phenylimido compound. Phenylimido species with more than one N,N‐dialkyl‐N′‐benzoylthioureato ligand could not be isolated, even when a large excess of HR¹R²btu was used during the reaction.     

On the regularity condition for the extremal problem under locally Lipschitz inclusion constraints

This paper deals with a regularity assumption for the existence of Lagrange Multipliers for an optimization problem in Hilbert spaces. First some results of [6] are extended; then a class of discrete systems in a Hilbert Space is considered where the regularity assumption automatically holds and the Discrete Maximum Principle is obtained.This research was partly supported by the Computer and Automation Institute of the Hungarian Academy of Sciences.     

Generalized deformed para-Bose oscillator and its coherent states

Generalized deformed commutation relations for a single-mode para-Bose oscillator are constructed. The connection of generalized deformed para-Bose oscillators with para-Bose oscillators is determined. From these, the energy spectrum of generalized deformed para-Bose oscillators and the coherent states of the annihilation operators are discussed. On leave from Department of Physics, Hanoi National University, 90 Nguyen Trai, Hanoi, Vietnam.     

Temperature‐dependent Raman scattering study of multiferroic MnWO4

We have measured polarized Raman spectra of MnWO₄ single crystals at low temperatures, and studied the temperature dependence of the various phonon modes. From our Raman studies of the MnWO₄, a new transition temperature, ∼180 K, was found. We have completely assigned the symmetries of the 18 observed Raman modes of the MnWO₄, as expected from a group theoretical analysis. These Raman modes have been classified into three groups according to weak, intermediate and strong temperature dependence of the modes in each group. Six internal modes have been identified by their weak temperature dependence of the Raman wavenumbers. The temperature dependence of the wavenumbers of the B_g modes in Mg O bonds, modes of intermediate temperature dependence group, shows an anomalous behavior under 50 K. The phonon modes of strong temperature dependence show an anomalous change at ∼180 K in the linewidths. This is believed to be a new transition temperature which involves the changes in the inter‐WO₆ octahedra structure. Copyright © 2009 John Wiley & Sons, Ltd.     

Squark Pair Production at Muon Colliders in the MSSM with CP Violation

We study the pair production of scalar quark in a muon collider within the MSSM with CP violation. We show that including the CP phases can strongly affect the cross section of the process: \(\mu^{+}\mu^{-}\rightarrow \tilde{q}_{i}\bar{\tilde{q}}_{j}\). This could have an important impact on the search for squarks and the determination of the MSSM parameters at future colliders.     

On a backward problem for fractional diffusion equation with Riemann-Liouville derivative

In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L² and H^τ norms is considered and illustrated by numerical example.     

Arbitrage and utility maximization in market models with an insider

We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses an additional information in the form of an \(\mathscr {F}_T\)-measurable discrete random variable G, we give criteria for the no unbounded profits with bounded risk property to hold, characterize optimal arbitrage strategies, and prove duality results for the utility maximization problem faced by the insider. Examples of markets satisfying NUPBR yet admitting arbitrage opportunities are provided. For the case when G is a continuous random variable, we consider the notion of no asymptotic arbitrage of the first kind (NAA1) and give an explicit construction for unbounded profits if NAA1 fails.     

Self-condensation of a thiazole-peptide bearing a 21-membered loop into a library of giant macrocycles with multiple orthogonal loops

[reaction: see text] Tetrapeptide analogue H-[Glu-Ser-Lys(Thz)]-OH, containing a turn-inducing thiazole constraint, was used as a template to produce a 21-membered structurally characterized loop by linking Glu and Lys side chains with a Val-Ile dipeptide. This template was oligomerized in one pot to a library (cyclo-[1](n)(), n = 2-10) of giant symmetrical macrocycles (up to 120-membered rings), fused to 2-10 appended loops that were carried intact through multiple oligomerization (chain extension) and cyclization (chain terminating) reactions of the template. A three-dimensional solution structure for cyclo-[1](3) shows all three appended loops projecting from the same face of the macrocycle. This is a promising approach to separating peptide motifs over large distances.