Morphological study of the organization behavior of rod-coil copolymers and their blends in thin solid films

A detailed study of the self-assembly ability of triblock coil-rod-coil copolymers containing a rigid di(styryl)-anthracene segment covalently linked to oxadiazole-based blocks and their binary blends with oxadiazole-based homopolymers is presented here. The self-organized microdomains seem to pack into a fascinating ordered hexagonal structure obtained at a critical concentration without any significant influence of the sample preparation method, based on evidence obtained by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and fluorescence microscopy studies. The compatibilization efficiency of these coil-rod-coil copolymers in polymer blends composed of an electron-accepting polyoxadiazole and a luminescent polyanthracene-based pair was studied by atomic force microscopy (AFM). The common feature of all observed morphologies is the compatibilizing function of the rod-coil molecule, which intercalates between the incompatible domains to prevent the formation of well-defined phase separated nanostructured surfaces.     

Synthesis of N-acyl-2-pyrrolidinones from the corresponding N-acyl-GABA derivatives

In this work, the synthesis of 1-(pyridine-3-carbonyl)pyrrolidin-2-one ( 1a ) and 1-(2-propyl-1-pentanoyl)pyrrolidin-2-one ( 1b ) by cyclization of the corresponding GABA derivatives, is reported. Two different methods are developed. For the synthesis of 1a , the parent molecule 4-[(pyridine-3-carbonyl)-amino]butanoic acid ( 2a ) is treated first with thionyl chloride and then with triethylamine. The second derivative, 1b , is produced by an intramolecular dehydration of 4-(2-propylpentanoylamino)butanoic acid ( 2b ) using an acid catalyst.     

Complexes derived from the general copper(II)/maleamic acid/N,N′,N′′-chelate reaction systems: Synthetic,reactivity, structural and spectroscopic studies

The synthetic investigation of the Cu^II/maleamate(−1) ion (HL⁻)/N,N′,N′′-chelate general reaction system has allowed access to compounds [Cu₂(HL)₂(bppy)₂](ClO₄)₂·H₂O (1·H₂O), [Cu(HL)(bppy)(ClO₄)] (2) and [Cu(HL)(terpy)(H₂O)](ClO₄) (4) (bppy = 2,6-bis(pyrazol-1-yl)pyridine, terpy = 2,2′;6′,2′′-terpyridine). In the absence of externally added hydroxides, compound [Cu₂(L′)₂(bppy)₂](ClO₄)₂ (3) was obtained from MeOH solutions; L′⁻ is the monomethyl maleate(−1) ligand which is formed in situ via the Cu^II-assisted HL⁻ → L′⁻ transformation. In the case of tptz-containing (tptz = 2,4,6-tris(2-pyridyl)-1,3,5-triazine) reaction systems, the Cu^II-assisted hydrolysis of tptz to pyridine-2-carboxamide (L1) afforded complex [Cu(L1)₂(NO₃)₂] (5). The crystal structures of 1–5 are stabilized by intermolecular hydrogen bonding and π–π stacking interactions. Characteristic IR bands of the complexes are discussed in terms of the known structures and the coordination modes of the ligands.     

A descent hybrid conjugate gradient method based on the memoryless BFGS update

In this work, we present a new hybrid conjugate gradient method based on the approach of the convex hybridization of the conjugate gradient update parameters of DY and HS+, adapting a quasi-Newton philosophy. The computation of the hybrization parameter is obtained by minimizing the distance between the hybrid conjugate gradient direction and the self-scaling memoryless BFGS direction. Furthermore, a significant property of our proposed method is that it ensures sufficient descent independent of the accuracy of the line search. The global convergence of the proposed method is established provided that the line search satisfies the Wolfe conditions. Our numerical experiments on a set of unconstrained optimization test problems from the CUTEr collection indicate that our proposed method is preferable and in general superior to classic conjugate gradient methods in terms of efficiency and robustness.     

A proof of W. T. Gowers' theorem

W. T. Gowers' theorem asserts that for every Lipschitz function and 0$">, there exists an infinite-dimensional subspace of such that the oscillation of on is at most . The proof of this theorem has been reduced by W. T. Gowers to the proof of a new Ramsey type theorem. Our aim is to present a proof of the last result.

     

Derivation and evaluation of the fourth moment of NMR lineshape in zero-field

An expression for the fourth moment in zero-field NMR has been analytically derived and numerically evaluated for a rigid cubic lattice. Model simulations have been performed to calculate the second moment, the fourth moment, the ratio of the fourth moment to the square of the second moment, and the width of the resonance line for a crystal and a polycrystalline material in high-field as well as in zero-field NMR. The simulation results allow us to draw two conclusions: (1) zero-field NMR gives sharper and better defined spectra than the high-field NMR and (2) the ratio of the high- to zero-field resonance line-widths is 4 for a crystal, whereas it is 11 for a polycrystalline material.     

On the Asphericity of Length Five Relative Group Presentations

We investigate asphericity of the relative group presentation G,t |atbtctdtet=1 and prove it aspherical provided thesubgroupof G generated by ab^–1, bc^–1, cd^–1, de^–1is neither finite cyclic nor a finite triangle group. We alsoprove a similar result for the closely related relative grouppresentation G,s,t | sßst=1=tts^–1. 2000 MathematicsSubject Classification: 20F05, 57M05.     

Sensitivity analysis and decomposition of unreliable production lines with blocking

The analysis of finitebuffered, unreliable production lines is often based on the method of decomposition, where the original system is decomposed into a series of twostage subsystems that can be modeled as quasi birthdeath processes. In this paper, we present methods for computing the gradients of the equilibrium distribution vector for such processes. Then we consider a specific production line with finite buffers and machine breakdowns and develop an algorithm that incorporates gradient estimation into the framework of Gershwin's approximate decomposition. The algorithm is applied to the problem of workforce allocation to the machines of a production line to maximize throughput. It is shown that this problem is equivalent to a convex mathematical programming problem and, therefore, a globally optimal solution can be obtained.     

Measurable events indexed by products of trees

A tree T is said to be homogeneous if it is uniquely rooted and there exists an integer b ≥ 2, called the branching number of T, such that every t ∈ T has exactly b immediate successors. A vector homogeneous tree T is a finite sequence (T ₁,...,T _d ) of homogeneous trees and its level product ?T is the subset of the Cartesian product T ₁×...×T _d consisting of all finite sequences (t ₁,...,t _d ) of nodes having common length. We study the behavior of measurable events in probability spaces indexed by the level product ?T of a vector homogeneous tree T. We show that, by refining the index set to the level product ?S of a vector strong subtree S of T, such families of events become highly correlated. An analogue of Lebesgue’s density Theorem is also established which can be considered as the “probabilistic” version of the density Halpern-Läuchli Theorem.