Evaluation of decay times in coupled spaces: an efficient search algorithm within the Bayesian framework

This paper discusses an efficient method for evaluating multiple decay times within the Bayesian framework. Previous works [N. Xiang and P. M. Goggans, J. Acoust. Soc. Am. 110, 1415-1424 (2001); 113, 2685-2697 (2003); N. Xiang, P. M. Goggans, T. Jasa, and M. Kleiner, 117, 3707-3715 (2005)] have applied the Bayesian inference to cope with demanding tasks in estimating multiple decay times from Schroeder decay functions measured or calculated in acoustically coupled spaces. Since then a number of recent works call for efficient estimation methods within the Bayesian framework. An efficient analysis is of practical significance for better understanding and modeling the sound energy decay process in acoustically coupled spaces or even in single spaces for reverberation time estimation. This paper will first formulate the Bayesian posterior probability distribution function (PPDF) in a matrix form to reduce the dimensionality as applied to the decay time evaluation. Based on existence of only global extremes of PPDFs as observed from extensive experimental data, this paper describes a dedicated search algorithm for an efficient estimation of decay times.     

Four-Dimensional Geometric Quantities versus the Usual Three-Dimensional Quantities: The Resolution of Jackson’s Paradox

In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors N_s, N_t and M_s, M_t, respectively, are given. The torques N_s, N_t (the angular momentums M_s, M_t), taken together, contain the same physical information as the bivector N (the bivector M). The usual approaches that deal with the 3D quantities etc. and their transformations are objected from the viewpoint of the invariant special relativity (ISR). In the ISR, it is considered that 4D geometric quantities are well-defined both theoretically and experimentally in the 4D spacetime. This is not the case with the usual 3D quantities. It is shown that there is no apparent electrodynamic paradox with the torque, and that the principle of relativity is naturally satisfied, when the 4D geometric quantities are used instead of the 3D quantities.     

Separation and investigation of structure-mobility relationship of gonadotropin-releasing hormones by capillary zone electrophoresis in conventional and isoelectric acidic background electrolytes

Capillary zone electrophoresis (CZE) has been applied to qualitative and quantitative analysis, separation and physicochemical characterization of synthetic gonadotropin-releasing hormones (GnRHs) and their analogs and fragments. Structurally related peptides were separated in conventional and isoelectric acidic background electrolytes (BGEs), pH 2.18-2.50. Best separation was achieved in isoelectric BGE composed of 200 mM iminodiacetic acid, pH 2.32. The effective electrophoretic mobilities, m(ep), of GnRHs in five BGEs were determined and four semiempirical models correlating effective mobility with charge, q, and relative molecular mass, M(r), (m(ep) versus q/M(r)(k), where k is related to the molecular shape) were tested to describe the migration behavior of GnRHs in CZE. None of the models was found to be quite definitively applicable for the whole set of 10 GnRHs differing in size (tetrapeptide-decapeptide) and positive charge (0.91-3.00 elementary charges). Nevertheless, for the dependence of m(ep) on q/M(r)(k), the highest coefficient of correlation, R=0.995-0.999, was obtained for k close to the value 0.5 in all five acidic BGEs. This indicates that the most probable structure of GnRHs in these BGEs can be predicted as a random coil.     

Atom transfer radical addition in the presence of catalytic amounts of copper(I/II) complexes with tris(2-pyridylmethyl)amine

Highly efficient atom transfer radical addition of polyhalogenated compounds to alkenes catalyzed by copper(I/II) complexes with tris(2-pyridylmethyl)amine in the presence of a radical initiator [2,2'-azobis(2-methylpropionitrile)] was reported.     

Mechanochemical Desymmetrization of Unbiased Bis- and Tris-alkynes to Access 3,5-Isoxazoles-Alkyne Adducts and Unsymmetrical Bis-3,5-isoxazoles**

A mechanochemical desymmetrization of symmetrical bis- and tris-alkynes by a controlled 1,3-dipolar cycloaddition reaction using nitrile oxide dipoles (NOs). This operationally simple protocol allows access to 3,5-isoxazole-alkyne adducts from easily prepared or commercially available symmetrical bis- and tris-alkynes in moderate to excellent yields. In addition, we have highlighted the synthetic utility of 3,5-isoxazole-alkyne by developing a route to access, for the first time, β-ketoenamine-alkyne derivatives, and unsymmetrical bis-3,5-isoxazoles.     

Mechanochemistry for Synthesis

Mechanochemical solvent‐free reactions by milling, grinding or other types of mechanical action have emerged as a viable alternative to solution chemistry. Mechanochemistry offers not only a possibility to eliminate the need for bulk solvent use, and reduce the generation of waste, but it also unlocks the door to a different reaction environment in which synthetic strategies, reactions and molecules previously not accessible in solution, can be achieved. This Minireview examines the potential of mechanochemistry in chemical and materials synthesis, by providing a cross‐section of the recent developments in using ball milling for the formation of molecules and materials based on covalent and coordination bonds.