Dediazoniations of Arenediazonium Ions. Part XXI. Dediazoniation of Arenediazonium Ions Complexed with Crown Ethers

The evaluation of the dediazoniation kinetics of various m- and p-substituted benzenediazonium tetrafluoroborates in 1,2-dichloroethane at 50° in the presence of 18-crown-6, 21-crown-7 and dicyclohexano-24-crown-8 demonstrates that the rate constant for the dediazoniation within the complex (k₂) is smallest, and the equilibrium constant for complex formation (K) is largest for the complexes with 21-crown-7 (cf. Scheme 1). The logarithms of the equilibrium constants (K) for complex formation with each of the crown ethers studied correlate well with Hammett's substituent constants, σ, to give reaction constants ρ = 1.18–1.38. A linear correlation between the logarithms of the rate constants for the dediazoniation within the complex with those of the dediazoniation rate constants of uncomplexed diazonium ions (log k₂ vs. log.k₁), found for most substituted diazonium salts, indicates that the dediazoniation mechanism of the complexed diazonium ions is not significantly different from that of the free ions. For very electrophilic diazonium ions (p-Cl, m-CN), k₂ was much larger than expected on the basis of the linear log k₂ vs. log k₁ relationship. Analysis of the dediazoniation products showed that this was due to a change in mechanism from heterolytic to homolytic dediazoniation. The complexation rate of diazonium salts by crown ethers (k_c) is practically diffusion controlled and does not change much with the size of the crown ether. The decomplexation rate (k_d), however, is significantly lower for complexes with 21-crown-7, than for those with 18-crown-6 and dicyclohexano-24-crown-8, and is therefore the reason for the variations in the equilibrium constant (K) and thus for the fact that complexes of arenediazonium salts with 21-crown-7 are the most stable. The amounts of the N_α-N_β rearrangement, as well as those of the exchange of the ¹⁵N-labelled diazonio group with external nitrogen during dediazoniation of p-toluenediazonium salt were independent of the addition of crown ethers. A dediazoniation mechanism involving a charge transfer, as well as an insertion-type diazonium ion-crown ether complex is proposed. In this mechanism, dediazoniation of the insertion complex does not take place directly, but through the charge-transfer complex.     

Comparison of Solutions of the General Nonlinear Amplitude Equation and a Modified Schrӧdinger Equation

We review the dynamics of narrow and broad-band optical pulses in nonlinear dispersive media. A major problem that arises during the development of theoretical models, which describe accurately and correctly the behavior of these pulses, is the limited application of the nonlinear Schr?dinger equation. It describes very well the evolution of nanosecond and picosecond laser pulses. However, when we investigate the propagation of femtosecond and attosecond light pulses, it is necessary to use the more general nonlinear amplitude equation. We show that in this equation two additional terms are included and they have a significant impact on the phase of the pulse. We perform numerical simulations and show the temporal shift of the position of fundamental solitons. This effect depends on the initial duration of the laser pulses. To clarify the influence of the additional terms on the parameters of the optical pulses, we consider the nonlinear amplitude equation, which is a modified nonlinear Schr?dinger equation.     

Overproduction of Laccase and Pectinase by Microbial Associations in Solid Substrate Fermentation

The growth and the enzymatic production of two microbial fungal associations were studied: Aspergillus niger and Fusarium moniliforme and Trametes versicolor and Aspergillus niger. The synergistic interrelations between the species of the first mixed culture increased the biosynthesis of α-amylase and pectinase. T. versicolor and A. niger proved to be compatible partners in the overproduction of the enzyme laccase, whose synthesis surpassed 8.4 times the enzymatic level in the monoculture, with both of the mixed microbial populations cocultivation facilitating the amplified synthesis of enzymes rather than their growth acceleration. A further proof of the presence of synergism established by the cultures was the enzyme volumetric productivities in both of the mixed microbial cultures, which increased parallel to the rise in the combined biomass synthesis. The competent selection of compatible partners can adjust the desired enzymatic levels and compositions in mixed fungal systems aimed at a number of specified designations. Thus, a very high level of laccase production (97,600 IU/g dry weight) was achieved. The chosen fungal strains produce a variety of different enzymes, but first microbial association produces mainly amylase and pectinase, necessary for their growth, and second association produces mainly laccase and pectinase.     

Impulsive control on global asymptotic stability for a class of impulsive bidirectional associative memory neural networks with distributed delays

In this paper, we study the problem of global asymptotic stability for a class of bidirectional associative memory neural networks with distributed delays and nonlinear impulsive operators. We establish stability criteria by employing Lyapunov functions and the Razumikhin technique. These results can easily be used to design and verify globally stable networks. An illustrative example is given to demonstrate the effectiveness of the obtained results.     

Column solid phase extraction and determination of ultra-trace Au,Pd and Pt in environmental and geological samples

A new sorbent based on cysteine modified silica gel (SiG-cys) was prepared and studied for preconcentration and separation of noble metals Au(III), Pd(II), Pt(II), Pt(IV). Its extraction efficiency was examined by batch and column solid phase extraction procedures. Laboratory experiments performed showed that sorbent is characterized with high selectivity, permiting quantitative sorption (93–97%) of noble metals Au, Pd and Pt from acidic media 0.1–2 mol L^? 1 HCl and unsignificant sorption (less than 2%) for common base metals like Cu, Fe, Mn and Zn. The analytes retained on the sorbent are effectively eluted with 0.1 mol L^? 1 thiourea in 0.1 mol L^? 1 HCl and measured by ETAAS or ICP OES under optimal instrumental parameters. The sorbent showed high mechanical and chemical stability and extraction efficiency was not changed after 500 cycles of sorption/desorption. The sorbent was successfully applied in analyticals procedures for preconcentration and determination of Au, Pd and Pt in geological and soil samples. Detection limits (3σ criteria) achieved, depending on the instrumental methods used are: ETAAS (0.005 μg L^? 1 for Au in river and sea water, 0.002 μg g^? 1 for Au in copper ore and copper concentrate); ICP OES (0.03 μg L^? 1 for Pd and 0.06 μg L^? 1 for Pt in river and sea water, 0.006 μg g^? 1 for Pd in copper ore and copper concentrate and 0.002 μg g^? 1 for soluble Pt in soil). The accuracy of the procedures developed was confirmed by added/found method for sea and river water; by the analysis of national certified materials (copper ore and copper concentrate for Au and Pd) and by determination of the sum of soluble Pt(II) + Pt(IV) in spiked soil samples.     

Multi‐component analysis: blind extraction of pure components mass spectra using sparse component analysis

The paper presents sparse component analysis (SCA)‐based blind decomposition of the mixtures of mass spectra into pure components, wherein the number of mixtures is less than number of pure components. Standard solutions of the related blind source separation (BSS) problem that are published in the open literature require the number of mixtures to be greater than or equal to the unknown number of pure components. Specifically, we have demonstrated experimentally the capability of the SCA to blindly extract five pure components mass spectra from two mixtures only. Two approaches to SCA are tested: the first one based on ?₁ norm minimization implemented through linear programming and the second one implemented through multilayer hierarchical alternating least square nonnegative matrix factorization with sparseness constraints imposed on pure components spectra. In contrast to many existing blind decomposition methods no a priori information about the number of pure components is required. It is estimated from the mixtures using robust data clustering algorithm together with pure components concentration matrix. Proposed methodology can be implemented as a part of software packages used for the analysis of mass spectra and identification of chemical compounds. Copyright © 2009 John Wiley & Sons, Ltd.     

Empirical kernel map approach to nonlinear underdetermined blind separation of sparse nonnegative dependent sources: pure component extraction from nonlinear mixture mass spectra

Nonlinear underdetermined blind separation of nonnegative dependent sources consists in decomposing a set of observed nonlinearly mixed signals into a greater number of original nonnegative and dependent component (source) signals. This hard problem is practically relevant for contemporary metabolic profiling of biological samples, where sources (a.k.a. pure components or analytes) are aimed to be extracted from mass spectra of nonlinear multicomponent mixtures. This paper presents a method for nonlinear underdetermined blind separation of nonnegative dependent sources that comply with a sparse probabilistic model, that is, sources are constrained to be sparse in support and amplitude. This model is validated on experimental pure component mass spectra. Under a sparse prior, a nonlinear problem is converted into an equivalent linear one comprised of original sources and their higher‐order, mostly second‐order, monomials. The influence of these monomials, which stand for error terms, is reduced by preprocessing a matrix of mixtures by means of robust principal component analysis and hard, soft and trimmed thresholding. Preprocessed data matrices are mapped in high‐dimensional reproducible kernel Hilbert space (RKHS) of functions by means of an empirical kernel map. Sparseness‐constrained nonnegative matrix factorizations in RKHS yield sets of separated components. They are assigned to pure components from the library using a maximal correlation criterion. The methodology is exemplified on demanding numerical and experimental examples related respectively to extraction of eight dependent components from three nonlinear mixtures and to extraction of 25 dependent analytes from nine nonlinear mixture mass spectra recorded in nonlinear chemical reaction of peptide synthesis. Copyright © 2014 John Wiley & Sons, Ltd.     

Nonlinear mixture‐wise expansion approach to underdetermined blind separation of nonnegative dependent sources

Underdetermined blind separation of nonnegative dependent sources consists in decomposing a set of observed mixed signals into greater number of original nonnegative and dependent component (source) signals. That is an important problem for which very few algorithms exist. It is also practically relevant for contemporary metabolic profiling of biological samples, such as biomarker identification studies, where sources (a.k.a. pure components or analytes) are aimed to be extracted from mass spectra of complex multicomponent mixtures. This paper presents a method for underdetermined blind separation of nonnegative dependent sources. The method performs nonlinear mixture‐wise mapping of observed data in high‐dimensional reproducible kernel Hilbert space (RKHS) of functions and sparseness‐constrained nonnegative matrix factorization (NMF) therein. Thus, the original problem is converted into new one with increased number of mixtures, increased number of dependent sources, and higher‐order (error) terms generated by nonlinear mapping. Provided that amplitudes of original components are sparsely distributed, which is the case for mass spectra of analytes, sparseness‐constrained NMF in RKHS yields, with significant probability, improved accuracy relative to the case when the same NMF algorithm is performed on the original problem. The method is exemplified on numerical and experimental examples related respectively to extraction of 10 dependent components from five mixtures and to extraction of 10 dependent analytes from mass spectra of two to five mixtures. Thereby, analytes mimic complexity of components expected to be found in biological samples. Copyright © 2013 John Wiley & Sons, Ltd.     

Optical solitons and bifurcation analysis in fiber Bragg gratings with Lie symmetry and Kudryashov’s approach

A combination of Lie symmetry analysis and Kudryashov’s approach secures optical soliton solutions with fiber Bragg gratings. The bifurcation analysis is carried out, and the phase portrait is presented.