Electronegativity: Quantum observable

The question whether electronegativity may be considered as quantum observable is responded in positive by a special ionization‐affinity wave function construction within the fermionic Fock space for the valence state of a chemical system. The present approach consecrates electronegativity as the minus eigen‐energy of the unperturbed occupied valence state involved in addition and release of electrons by atoms‐in‐molecules interactions. This way, the earlier crisis raised by Bergmann and Hinze concerning the assignment of chemical potential to electronegativity quantification is here solved in the favor of Parr density functional picture. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Aspects on the Functional Optimization of an Industrial Robot Structure Implemented in Military Logistical Activities

The authors of the present paper outline aspects on the optimization of the a TR-type industrial robot structure movements in order to generate the manipulation space to a flexible manufacturing cell with a parallel organization designed for the pallet and container operation of paint-filled recipients. The paper contains the direct and inverted geometrical modelling of the robot structure using the 3*3 rotation matrix method and the algebra method. After knowing the characteristic point movement of the prehension device, graphics for the variation of the TR robot's general coordinates and for the trajectory of the prehension device's characteristic point of its work space were performed by using the Mathematica 6.0 soft. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Programming the supramolecular helical polymerization of dendritic dipeptides via the stereochemical information of the dipeptide

Many natural biomacromolecules are homochiral and are built from constituents possessing identical handedness. The construction of synthetic molecules, macromolecules, and supramolecular structures with tailored stereochemical sequences can detail the relationship between chirality and function and provide insight into the process that leads to the selection of handedness and amplification of chirality. Dendritic dipeptides, previously reported from our laboratory, self-assemble into helical porous columns and serve as fundamental mimics of natural porous helix-forming proteins and supramolecular polymers. Herein, the synthesis of all stereochemical permutations of a self-assembling dendritic dipeptide including homochiral, heterochiral, and differentially racemized variants is reported. A combination of CD/UV-vis spectroscopy in solution and in film, X-ray diffraction, and differential scanning calorimetry studies in solid state established the role of the stereochemistry of the dipeptide on the thermodynamics and mechanism of self-assembly. It was found that the highest degree of stereochemical purity, enantiopure homochiral dendritic dipeptides, exhibits the most thermodynamically favorable self-assembly process in solution corresponding to the greatest degree of helical order and intracolumnar crystallization in solid state. Reducing the stereochemical purity of the dendritic dipeptide through heterochirality or by partially or fully racemizing the dendritic dipeptide destructively interferes with the self-assembly process. All dendritic dipeptides were shown to coassemble into single columns regardless of their stereochemistry. Because these columns exhibit no deracemization, the thermodynamic advantage of enantiopurity and homochirality suggests a mechanism for stereochemical selection and chiral amplification.     

Thermal analysis of sulfonated polymers tested as polymer electrolyte membrane for PEM fuel cells

An aromatic polymer, poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) was sulfonate with different sulfonation degrees (30, 50, and 75?% theoretical degree) to obtain an electrolytic polymer suitable as proton exchange membrane for fuel cells. Thermal behaviors of sulfonated PPO were tested by differential scanning calorimetry and thermogravimetry. The sulfonation degrees were correlated with glass transitions temperatures (T _g) and the percent of weight loss. One notices a good fitting between sulfonation degree and the percent of weight loss thanks splitting of sulfonic moieties but it is not the same for glass transition temperatures that have a random variation.     

Extremal Problems for Mappings with Generalized Parametric Representation in $${{\mathbb {C}}}^{n}$$

In this paper we are concerned with the family \(\widetilde{S}^t_A(\mathbb {B}^n)\) (\(t\ge 0\)) of normalized biholomorphic mappings on the Euclidean unit ball \(\mathbb {B}^n\) in \({\mathbb {C}}^n\) that can be embedded in normal Loewner chains whose normalizations are given by time-dependent operators \(A\in \widetilde{\mathcal {A}}\), where \(\widetilde{\mathcal {A}}\) is a family of measurable mappings from \([0,\infty )\) into \(L({\mathbb {C}}^n)\) which satisfy certain natural assumptions. In particular, we consider extreme points and support points associated with the compact family \(\widetilde{S}^t_A(\mathbb {B}^n)\), where \(A\in \widetilde{\mathcal {A}}\). We prove that if \(f(z,t)=V(t)^{-1}z+\cdots \) is a normal Loewner chain such that \(V(s)f(\cdot ,s)\in \mathrm{ex}\,\widetilde{S}^s_A(\mathbb {B}^n)\) (resp. \(V(s)f(\cdot ,s)\in \mathrm{supp}\,\widetilde{S}^s_A(\mathbb {B}^n)\)), then \(V(t)f(\cdot ,t)\in \mathrm{ex}\, \widetilde{S}^t_A(\mathbb {B}^n)\), for all \(t\ge s\) (resp. \(V(t)f(\cdot ,t)\in \mathrm{supp}\,\widetilde{S}^t_A(\mathbb {B}^n)\), for all \(t\ge s\)), where V(t) is the unique solution on \([0,\infty )\) of the initial value problem: \(\frac{d V}{d t}(t)=-A(t)V(t)\), a.e. \(t\ge 0\), \(V(0)=I_n\). Also, we obtain an example of a bounded support point for the family \(\widetilde{S}_A^t(\mathbb {B}^2)\), where \(A\in \widetilde{\mathcal {A}}\) is a certain time-dependent operator. We also consider the notion of a reachable family with respect to time-dependent linear operators \(A\in \widetilde{\mathcal {A}}\), and obtain characterizations of extreme/support points associated with these families of bounded biholomorphic mappings on \(\mathbb {B}^n\). Useful examples and applications yield that the study of the family \(\widetilde{S}^t_A(\mathbb {B}^n)\) for time-dependent operators \(A\in \widetilde{\mathcal {A}}\) is basically different from that in the case of constant time-dependent linear operators.     

An Algebraic Perspective on Multivariate Tight Wavelet Frames

Recent advances in real algebraic geometry and in the theory of polynomial optimization are applied to answer some open questions in the theory of multivariate tight wavelet frames whose generators have at least one vanishing moment. Namely, several equivalent formulations of the so-called Unitary Extension Principle (UEP) are given in terms of Hermitian sums of squares of certain nonnegative Laurent polynomials and in terms of semidefinite programming. These formulations merge recent advances in real algebraic geometry and wavelet frame theory and lead to an affirmative answer to the long-standing open question of the existence of tight wavelet frames in dimension d=2. They also provide, for every d, efficient numerical methods for checking the existence of tight wavelet frames and for their construction. A class of counterexamples in dimension d=3 show that, in general, the so-called sub-QMF condition is not sufficient for the existence of tight wavelet frames. Stronger sufficient conditions for determining the existence of tight wavelet frames in dimension d≥3 are derived. The results are illustrated on several examples.     

Investigation of the ferroelectric–relaxor crossover in Ce-doped BaTiO3 ceramics by impedance spectroscopy and Raman study

BaCe _x Ti_{1? x} O₃ (x?=?0.06, 0.10, and 0.20) solid solutions were prepared via conventional the solid-state reaction and sintered at 1500°C for 4?h, resulting in dense single phase ceramics with homogeneous microstructures. The electric field dependence of permittivity of the BaCe _x Ti_{1? x} O₃ ceramics was investigated in detail, together with the ferroelectric–paraelectric phase transition features. A transformation from normal to relaxor ferroelectrics was observed by increasing the Ce concentration. For low-Ce content, a substitution of Ce on both A and B site positions was proposed from the dielectric study and confirmed by Raman analysis.     

Synthesis, structural analysis, and visualization of a library of dendronized polyphenylacetylenes

A library of eleven high cis-content cis-transoidal polyphenylacetylenes (PPAs) dendronized with self-assembling dendrons was prepared from a library of fifteen convergently synthesized macromonomers. Using [Rh(C triple bond CPh)(nbd)(PPh(3))(2)] (nbd=2,5-norbornadiene) in the presence of 10 equiv of N,N-dimethylaminopyridine, predictive control over molecular weight and narrow molecular weight distribution are obtained. The PPA backbone serves as a helical scaffold for the self-assembling dendrons. The dendron primary structure dictates the diameter of the cylindrical PPAs in bulk, both in the self-organized hexagonal columnar (Phi(h)) lattice determined by X-ray diffraction (XRD) and in monolayers on highly ordered pyrolytic graphite (HOPG) and mica visualized by atomic force microscopy (AFM). Thermal and bulk phase characteristics of the cylindrical PPAs reinforces the generality that flexible polymer backbones adopt a helical conformation within the cylindrical macromolecules generated by polymers jacketed with self-assembling dendrons.     

Exploring and expanding the structural diversity of self-assembling dendrons through combinations of AB, constitutional isomeric AB2, and AB3 biphenyl-4-methyl ether building blocks

General, efficient and inexpensive methods for the synthesis of dendritic building blocks methyl 3',4'-dihydroxybiphenyl-4-carboxylate, 3',5'-dihydroxybiphenyl-4-carboxylate, and methyl 3',4',5'-trihydroxybiphenyl-4-carboxylate were elaborated. In all syntheses the major step involved an inexpensive Ni(II)-catalyzed Suzuki cross-coupling reaction. These three building blocks were employed together with methyl 4'-hydroxybiphenyl-4-carboxylate in a convergent iterative strategy to synthesize seven libraries containing up to three generations of 3',4'-, 3',5'-, and 3',4',5'-substituted biphenyl-4-methyl ether based amphiphilic dendrons. These dendrons self-assemble into supramolecular dendrimers that self-organize into periodic assemblies. Structural and retrostructural analysis of their assemblies demonstrated that these dendrons self-assemble into hollow and non-hollow supramolecular dendrimers exhibiting dimensions of up to twice those reported for architecturally related dendrons based on benzyl ether repeat units. These new dendrons expand the structural diversity and demonstrate the generality of the concept of self-assembling dendrons based on amphiphilic arylmethyl ethers.     

Nonholonomic Black Ring and Solitonic Solutions in Finsler and Extra Dimension Gravity Theories

We study stationary configurations mimicking nonholonomic locally anisotropic black rings (for instance, with ellipsoidal polarizations and/or imbedded into solitonic backgrounds) in three/six dimensional pseudo-Finsler/Riemannian spacetimes. In the asymptotically flat limit, for holonomic configurations, a subclass of such spacetimes contains the set of five dimensional black ring solutions with regular rotating event horizon. For corresponding parameterizations, the metrics and connections define Finsler–Einstein geometries modeled on tangent bundles, or on nonholonomic (pseudo) Riemannian manifolds. In general, there are vacuum nonholonomic gravitational configurations which can not be generated in the limit of zero cosmological constant.