Cis‐trans Isomerism in Copper(II) Complexes with N‐acyl Thiourea Ligands

The N‐acyl thiourea complexes bis[N,N‐diethyl‐N′‐(p‐nitrobenzoyl)‐thioureato]copper(II) ( 1a,1b ) and bis(N,N‐diphenyl‐N′‐benzoylthioureato)copper(II) ( 2a,2b ) crystallize in each case in two modifications. X‐ray structural analysis shows that 1a and 1b are cis‐trans isomers. This is very unusual for N‐acyl thioureato complexes because with exception of one platinum(II) complex up to now only cis complexes have been found. In contrast X‐ray structural analysis of both forms 2a and 2b of the other complex shows no cis‐trans pair. Both modifications are cis complexes. In solution both isomers of the copper(II) complexes are observable by EPR spectroscopy.     

Energy transfer in the nanostar: the role of coulombic coupling and dynamics

We present a theoretical investigation of energy transfer in the phenylene ethynelene dendrimer known as the nanostar. Data from extensive molecular dynamics simulations are used to model the dynamical effects caused by torsional motion of the phenyl groups. We compare rate constants for energy transfer between the two-ring chromophore and the three-ring chromophore obtained via the F?rster model, the ideal dipole approximation (IDA), and the transition density cube (TDC) method, which has as its limit an exact representation of the Coulombic coupling. We find that the rate constants obtained with the TDC are extremely sensitive to the phenyl group rotation, whereas the constants computed with the F?rster model and the IDA are not. The implications of these results for the interpretation of recent pump-probe experiments on the nanostar are discussed in detail. Finally, we predict the temperature dependence of the rate constant for energy transfer.     

An MD simulation of the decoy action of Epstein�CBarr virus LMP1 protein mimicking the CD40 interaction with TRAF3

The Epstein?CBarr virus (EBV) is associated with a variety of malignancies and chronic active EBV infection is a severe systemic disease associated with high rates of mortality and morbidity. In this paper, the dynamics of the interaction of EBV-expressed latent membrane protein 1 (LMP1) with cellular signaling intermediate tumor necrosis factor receptor (TNFR)-associated factor 3 (TRAF3) is simulated using standard classical molecular dynamics (MD) protocols. For comparison, the dynamics of the interaction of TRAF3 with CD40, a TNFR mimicked by LMP1 to effect EBV infection is also calculated under similar conditions. Essential dynamics (ED) analysis is carried out to identify important degrees of vibrational freedom that relate to protein function and virus infection. Both the MD simulation and ED analysis reveal novel interactions that help explain the structural decoy action of LMP1 over CD40. These interactions involve the consensus sequence PXQXTXX shared by CD40 and LMP1. In LMP1, we have found novel interaction of Asp 209 with TRAF3 and the interaction is crucial although the adjacent Asp 210 was suggested to be essential by the X-ray analysis. In CD40, it is found that the hairpin formation is not indispensable for the interaction with TRAF3.     

Representation of Continuous Functions and Its Applications

In this work, we introduce a Representation of continuous real-valued functions defined over a real Hilbert space. As a consequence, we can introduce a Sandwich Theorem for semi-continuous functions, a Separation Theorem for closed sets and a representation Theorem of lower semi-continuous functions.     

Statistical analysis of autoregressive fractionally integrated moving average models in R

The autoregressive fractionally integrated moving average (ARFIMA) processes are one of the best-known classes of long-memory models. In the package afmtools for R, we have implemented a number of statistical tools for analyzing ARFIMA models. In particular, this package contains functions for parameter estimation, exact autocovariance calculation, predictive ability testing and impulse response function computation, among others. Furthermore, the implemented methods are illustrated with applications to real-life time series.     

On certain conditions for the existence of solutions of equilibrium problems

The main purpose of this paper is the study of sufficient and/or necessary conditions for existence of solutions of equilibrium problems. We discuss some of the assumptions of the problem, under which the introduced conditions are sufficient and/or necessary, and also analyze the effect of these assumptions on the connection between the solution sets of the equilibrium problem and of a related convex feasibility problem.     

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (Optimization 52:301?C316, 2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.     

On the Theta Semigroup

In this paper we consider a semigroup on trigonometric expansions ${\{{\mathcal T}_t: t \geq 0\}}$ that will be called the Theta semigroup since its kernel is a multiple of ?? ₃(x, q), the third Jacobi theta function. We study properties of this semigroup and prove that it is a positive diffusion semigroup. We also obtain that its subordinated semigroup is the classical Poisson semigroup. The extensions to higher dimensions and to periodic ultra distributions are also considered.     

A New Approach to a Multicriteria Optimization Problem

We present a new approach to a multicriteria optimization problem, where the objective and the constraints are linear functions. From an equivalent equilibrium problem, first suggested in [5,6,8], we show new characterizations of weakly efficient points based on the partial order induced by a nonempty closed convex cone in a finite-dimensional linear space, as in [7]. Thus, we are able to apply the analytic center cutting plane algorithm that finds equilibrium points approximately, by Raupp and Sosa [10], in order to find approximate weakly efficient solutions of MOP.     

Platinum(II) Mixed Ligand Complexes with Thiourea Derivatives,Dimethyl Sulphoxide and Chloride: Syntheses,Molecular Structures,and ESCA Data

The platinum(II) mixed ligand complexes [PtCl(L^1‐6)(dmso)] with six differently substituted thiourea derivatives HL, R₂NC(S)NHC(O)R′ (R = Et, R′ = p‐O₂N‐Ph: HL¹; R = Ph, R′ = p‐O₂N‐Ph: HL²; R = R′ = Ph: HL³; R = Et, R′ = o‐Cl‐Ph: HL⁴; R₂N = EtOC(O)N(CH₂CH₂)₂N, R′ = Ph: HL⁵) and Et₂NC(S)N=CNH‐1‐Naph (HL⁶), as well as the bis(benzoylthioureato‐κO, κS)‐platinum(II) complexes [Pt(L^{1, 2})₂] have been synthesized and characterized by elemental analysis, IR, FAB(+)‐MS, ¹H‐NMR, ¹³C‐NMR, as well as X‐ray structure analysis ([PtCl(L¹)(dmso)] and [PtCl(L^{3, 4})(dmso)]) and ESCA ([PtCl(L^{1, 2})(dmso)] and [Pt(L^{1, 2})₂]). The mixed ligand complexes [PtCl(L)(dmso)] have a nearly square‐planar coordination at the platinum atoms. After deprotonation, the thiourea derivatives coordinate bidentately via O and S, DMSO bonds monodentately to the Pt^II atom via S atom in a cis arrangement with respect to the thiocarbonyl sulphur atom. The Pt—S‐bonds to the DMSO are significant shorter than those to the thiocarbonyl‐S atom. In comparison with the unsubstituted case, electron withdrawing substituents at the phenyl group of the benzoyl moiety of the thioureate (p‐NO₂, o‐Cl) cause a significant elongation of the Pt—S(dmso)‐bond trans arranged to the benzoyl‐O—Pt‐bond. The ESCA data confirm the found coordination and bonding conditions. The Pt 4f_7/2 electron binding energies of the complexes [PtCl(L^{1, 2})(dmso)] are higher than those of the bis(benzoylthioureato)‐complexes [Pt(L^{1, 2})₂]. This may indicate a withdrawal of electron density from platinum(II) caused by the DMSO ligands.