Highly fluorinated aryl-substituted tris(indazolyl)borate thallium complexes: diverse regiochemistry at the B-N bond

The synthesis and characterization (mainly by (19)F NMR and X-ray diffraction) of highly fluorinated aryl-4,5,6,7-tetrafluoroindazoles and their corresponding thallium hydrotris(indazolyl)borate complexes are reported [aryl = phenyl, pentafluorophenyl, 3,5-dimethylphenyl, 3,5-bis(trifluoromethyl)phenyl]. Thanks to N-H···N hydrogen bonds, the indazoles crystallize as dimers that pack differently depending on the nature of the aryl group. The thallium hydrotris(indazolyl)borate complexes Tl[Fn-Tp(4Bo,3aryl)] resulting from the reaction of aryl-4,5,6,7-tetrafluoroindazoles [aryl = phenyl, 3,5-dimethylphenyl, 3,5-bis(trifluoromethyl)phenyl] with thallium borohydride adopt overall C(3v) symmetry with the indazolyl groups bound to boron via their N-1 nitrogen in a conventional manner. When the perfluorinated pentaphenyl-4,5,6,7-tetrafluoroindazole is reacted with thallium borohydride, a single regioisomer of C(s) symmetry having one indazolyl ring bound to boron via its N-2 nitrogen, TlHB(3-pentafluorophenyl-4,5,6,7-tetrafluoroindazol-1-yl)(2)(3-pentafluorophenyl-4,5,6,7-tetrafluoroindazol-2-yl) Tl[F27-Tp((4Bo,3C6F5)*)], is obtained for the first time. Surprisingly, the perfluorinated dihydrobis(indazolyl)borate complex Tl[F(18)-Bp(3Bo,3C6F5)], an intermediate on the way to the hydrotris(indazolyl)borate complex, has C(s) symmetry with two indazolyl rings bound to boron via N-2. The distortion of the coordination sphere around Tl and the arrangement of the complexes in the crystal are discussed.     

Neutron Transverse-Momentum Distributions and Polarized 3He within Light-Front Hamiltonian Dynamics

The possibility to extract the quark transverse-momentum distributions in the neutron from semi-inclusive deep inelastic electron scattering off polarized ³He is illustrated through an impulse approximation analysis in the Bjorken limit. The generalization of the analysis at finite momentum transfers in a Poincaré covariant framework is outlined. The definition of the light-front spin-dependent spectral function of a J = 1/2 system allows us to show that within the light-front dynamics only three of the six leading twist T-even transverse-momentum distributions are independent.     

Accuracy analysis of simplified and rigorous numerical methods applied to binary nanopatterning gratings in non-paraxial domain

A set of simplified and rigorous electromagnetic vector theories is used for analyzing the transmittance characteristics of diffraction phase gratings. The scalar diffraction theory and the effective medium theory are validated with the exact results obtained via the rigorous coupled-wave theory and the finite-difference time-domain method. The effects of surface profile parameters and also the angle of incidence is demonstrated to be a limiting factor in the accuracy of these theories. Therefore, the error of both simplified theories is also analyzed in non-paraxial domain with the intention of establishing a specific range of validity for both simplified theories.     

BPS Quivers and Spectra of Complete {\mathcal{N} = 2} Quantum Field Theories

We study the BPS spectra of ${\mathcal{N}=2}$ N = 2 complete quantum field theories in four dimensions. For examples that can be described by a pair of M5 branes on a punctured Riemann surface we explain how triangulations of the surface fix a BPS quiver and superpotential for the theory. The BPS spectrum can then be determined by solving the quantum mechanics problem encoded by the quiver. By analyzing the structure of this quantum mechanics we show that all asymptotically free examples, Argyres-Douglas models, and theories defined by punctured spheres and tori have a chamber with finitely many BPS states. In all such cases we determine the spectrum.     

Application of Multivariate Techniques in Optimization of Spectroanalytical Methods

Abstract

The present article describes fundamentals and applications of multivariate techniques used for the optimization of analytical procedures and systems involving spectroanalytical methods such as flame atomic absorption spectrometry (FAAS), electrothermal atomic absorption spectrometry (ETAAS), inductively coupled plasma optical emission spectrometry (ICP OES), and inductively coupled plasma mass spectrometry (ICP‐MS), considering the main steps of a chemical analysis. This way, applications of experimental designs in optimization of sampling systems, digestion procedures, preconcentration procedures, instrumental parameters of quantification steps of analytical methods, and robustness tests have been summarized in this work.     

Analytic Propagation for Nonlinear Weakly Hyperbolic Systems

The propagation of analyticity for sufficiently smooth solutions to either strictly hyperbolic, or smoothly symmetrizable nonlinear systems, dates back to Lax [14 Lax , P.D. ( 1953 ). Nonlinear hyperbolic equations . Comm. Pure Appl. Math. 6 : 231 – 258 . [Google Scholar]] and Alinhac and Métivier [2 Alinhac , S. , Métivier G. ( 1984 ). Propagation de l'analyticité des solutions de systèmes hyperboliques nonlinéaires [Propagation of analyticity for solutions of nonlinear hyperbolic systems]. Invent. Math. 75, 189–204 . [Google Scholar]]. Here we consider the general case of a system with real, possibly multiple, characteristics, and we ask which regularity should be a priori required of a given solution in order that it enjoys the propagation of analyticity. By using the technique of the quasi-symmetrizer of a hyperbolic matrix, we prove, in the one-dimensional case, the propagation of analyticity for those solutions which are Gevrey functions of order s for some s < m/(m ? 1), m being the maximum multiplicity of the characteristics.     

Optimization methodology assessment for the inlet velocity profile of a hydraulic turbine draft tube: part I—computer optimization techniques

In recent years, numerical and experimental investigations on the draft tube performance have confirmed the importance of the inlet swirling flow created by the runner vanes. The results indicate that it is still a challenge to get the optimal flow distribution at the draft tube inlet which gives the best machine performance over a range of operation points. Consequently, there is a need to adjust the runner-draft tube coupling to minimize the losses arising from the inlet flow distribution. This paper focus on establishing an optimization methodology for maximizing the draft tube performance as a function of the inlet velocity profile. The overall work is divides into two parts: The part one establish the inlet velocity parametrization, the numerical optimization set-up and the objective function definition. The part two validate the numerical CFD draft tube model. These steps are represented by the coupling of the commercial softwares MATLAB, FLUENT and iSIGHT. It is considered that this proved methodology will help to find a inlet velocity profile shape which will be able to suppress or mitigate the undesirable draft tube flow characteristics.     

Binary Image Compression via Monochromatic Pattern Substitution: Sequential and Parallel Implementations

We present a method for compressing binary images via monochromatic pattern substitution. Such method has no relevant loss of compression effectiveness if the image is partitioned into up to a thousand blocks, approximately, and each block is compressed independently. Therefore, it can be implemented on a distributed system with no interprocessor communication. In the theoretical context of unbounded parallelism, interprocessor communication is needed. Compression effectiveness has a bell-shaped behaviour which is again competitive with the sequential performance when the highest degree of parallelism is reached. Finally, the method has a speed-up if applied sequentially to an image partitioned into up to 256 blocks. It follows that such speed-up can be applied to a parallel implementation on a small scale system.     

A probabilistic model associated with the pressureless gas dynamics

Using a method of stochastic perturbation of a Langevin system associated with the non-viscous Burgers equation we introduce a system of PDE that can be considered as a regularization of the pressureless gas dynamics describing sticky particles. By means of this regularization we describe how starting from smooth data a δ-singularity arises in the component of density. Namely, we find the asymptotics of solution at the point of the singularity formation as the parameter of stochastic perturbation tends to zero. Then we introduce a generalized solution in the sense of free particles (FP-solution) as a special limit of the solution to the regularized system. This solution corresponds to a medium consisting of non-interacting particles. The FP-solution is a bridging step to constructing solutions to the Riemann problem for the pressureless gas dynamics describing sticky particles. We analyze the difference in the behavior of discontinuous solutions for these two models and the relations between them. In our framework we obtain a unique entropy solution to the Riemann problem in 1D case.     

Classroom note: A simple proof of an interesting Fibonacci generalization

It is reasonably well known that the ratios of consecutive terms of a Fibonacci series converge to the golden ratio. This note presents a simple, complete proof of an interesting generalization of this result to a whole family of ‘precious metal ratios’.