Generalized equivalence of pairs of matrices

Pairs (A ₁ B ₁) and (A ₂ B ₂) of matrices over a principal ideal domain R are called the generalized equivalent pairs if A ₂=UA ₁ V ₁ B ₂=UB ₁ V ₂ for some invertible matrices U V ₁ V ₂ over R. A special form is established to which a pair of matrices can be reduced by means of generalized equivalent transformations. Besides necessary and sufficient conditions are found, under which a pair of matrices is generalized equivalent to a pair of diagonal matrices. Applications are made to study the divisibility of matrices and multiplicative property of the Smith normal form.     

Synthesis of 1-(R-Phenyl)-5-(R-Methyl)-1H-1,2,3-triazole-4-carboxylic Acids by One-Pot Tandem Reaction

Substituted 1H-1,2,3-triazole-4-carboxylic acids were synthesized by a three-component reaction of arylazides, ethyl 4-chloro-3-oxobutanoate, and either O- or S-nucleophiles in the presence of a base catalyst. The reaction most probably proceeded as a [3 + 2] cyclocondensation reaction between arylazide and ethyl 4-chloro-3-oxobutanoate with the further nucleophilic substitution of chlorine in the chloromethyl group. Reaction optimization was performed to carry out the reaction with an O-nucleophile. Conditions were found under which diethyl 2,5-dihydroxyterephthalate (the product of self-condensation of two molecules of ethyl 4-chloro-3-oxobutanoate with the further oxidation by azide) was obtained.     

Reactions of trialkoxynitridomolybdenum with low-coordinate phosphorus compounds containing a P=N double bond

The reactions of N≡Mo(OR)(3) (R = (t)Bu, (i)Pr) with (Me(3)Si)(2)NPNSiMe(3) (1), (Me(3)Si)(2)NPN(t)Bu (2), (Me(3)Si)(2)NPS(N(t)Bu) (3) and (Me(3)Si)(2)NP(NSiMe(3))(2) (4) have been studied. Reported complexes were synthesized via 1,2-addition of an Mo-OR bond across the P=N bond, resulting in four-membered metallacycles of the corresponding σ(2)λ(3)-iminophosphine or σ(3)λ(5)-iminophosphorane with trialkoxynitridomolybdenum. The structure of all new compounds was elucidated by (1)H, (13)C and (31)P NMR spectroscopy. Compounds [(Me(3)Si)(2)N-P(NSiMe(3))(O-(t)Bu)]{((t)BuO)(2)Mo≡N} (5), [(Me(3)Si)(2)N-PS(N(t)Bu)(O-(t)Bu)]{((t)BuO)(2)Mo≡N} (7), [(Me(3)Si)(2)N-P(NSiMe(3))(2)(O-(t)Bu)]{((t)BuO)(2)Mo≡N} (8) and [(Me(3)Si)(2)N-P(NSiMe(3))(2)(O-(i)Pr)]{((i)PrO)(2)Mo≡N} (12) were also characterized by single X-ray analysis and shown to be metallacycles containing the Mo atom with an intact terminal nitrido ligand.     

Synthesis of calixarene-based ketocyanine fluorophores

Cup-shaped calix[4]arenes bearing one or two ketocyanine fluorophore fragments at the wide rim of the macrocycle are synthesized by condensation of formyl calix[4]arenes with arylmethylene(hetarylmethylene)cyclopentanones in the presence of the ionic liquid, dimethylammonium dimethylcarbamate (DIMCARB) and characterized using UV-vis and fluorescence spectroscopy. Strong positive solvatofluorochromism for the calixarene ketocyanines is observed.     

Monitoring the mean of multivariate financial time series

Timely detection of changes in the mean vector of multivariate financial time series is of great practical importance. In this paper, the covariance dynamics of the multivariate stochastic processes is assessed by either the RiskMetrics approach, the constant conditional correlation, or the dynamic conditional correlation models. For online monitoring of mean changes, we introduce several control schemes based on exponential smoothing and cumulative sums, which explicitly account for heteroscedasticity. The detecting ability of the introduced charts is compared for different processes in a Monte Carlo simulation study. The empirical study illustrates monitoring of changes in the mean vector of daily returns of exchange rates. Copyright © 2013 John Wiley & Sons, Ltd.     

Oxa-spirocycles: synthesis,properties and applications

A general approach to a new generation of spirocyclic molecules – oxa-spirocycles – was developed. The key synthetic step was iodocyclization. More than 150 oxa-spirocyclic compounds were prepared. Incorporation of an oxygen atom into the spirocyclic unit dramatically improved water solubility (by up to 40 times) and lowered lipophilicity. More potent oxa-spirocyclic analogues of antihypertensive drug terazosin were synthesized and studied in vivo.

A general practical approach to a new generation of spirocyclic molecules – oxa-spirocycles – is developed.     

Dual-Fluorescence Probe of Environment Basicity (Hydrogen Bond Accepting Ability) Displaying no Sensitivity to Polarity

3-Hydroxyquinolones (3HQs) are a new class of water soluble dual fluorescence probes that can monitor both polarity and basicity (H-bond accepting ability) parameters. Both parameters play an important role in proteins and lipid membranes. Nevertheless, no method exists actually to measure the basicity parameter separately from the polarity. To achieve this aim, we synthesized 2-benzofuryl-3-hydroxy-4(1H)-quinolone (3HQ-Bf) and characterized its photophysical properties by UV, steady-state and time-resolved fluorescence spectroscopy. Due to its extended conjugation and totally planar conformation, 3HQ-Bf is characterized by a high fluorescence quantum yield. In solution, this dye shows an excited state intramolecular proton transfer (ESIPT) reaction resulting in two tautomer bands in the emission spectra. The ESIPT reaction can be considered as irreversible and is governed by rate constants from 0.6 to 8 × 10⁹ s⁻¹, depending on the solvent. The analysis of the spectral properties of 3HQ-Bf in a series of organic solvents revealed a marginal sensitivity to the solvent polarity, but an exquisite sensitivity to solvent basicity, as shown by the linear dependence of the logarithm of the emission bands intensity ratio, log(I_N*/I_T*), as well as the absorption or emission maxima wavenumbers as a function of the solvent basicity parameter. This probe may find useful applications through coupling to a protein ligand, for characterizing the H-bond acceptor ability at the ligand binding site as well as for studying the basicity changes of lipid membranes during their chemo- and thermotropic conversions.     

Q-Band Loop-Gap Resonator for EPR Applications with Broadband-Shaped Pulses

Recently, Q-band-pulsed electron paramagnetic resonance spectroscopy has strongly advanced its performance by the introduction of high-power microwave amplifiers and the use of shaped pulses. For such applications, the resonator Q value has to be low enough to achieve sufficient bandwidth for short microwave pulses and to reduce the ring-down time after the pulses. However, a low Q value reduces the detection sensitivity as well as the conversion efficiency of the microwave input power to the magnetic field strength at the sample position. Therefore, the resonator Q value has to be optimized for a given microwave input power and specific application. We designed a three-loop/two-gap resonator using CST Microwave Studio for such applications, and tested its performance in comparison with a standard Bruker D2 Q-band microwave resonator by accomplishing broadband SIFTER experiments on a nitroxide model compound.     

Protolytic properties of the structurally rigid analogs of 2,6-distyrylpyridine. Widening the pH sensitivity range by the photochemical E→Z isomerisation and introduction of substituents capable to protolytic interactions

Protolytic interactions in the series of prospective fluorescent ratiometric wide-range pH indicators — structurally rigid analogs of 2,6-distyrylpyridine — (3E,5E)-3,5-dibenzylidene-8-phenyl-1,2,3,5,6,7-hexahydrodicyclopentano[b,e]pyridine — were investigated. The pyridine nitrogen atom basicity in these compounds is significantly lower in comparison with that of unsubstituted heterocycle and 2,6-distyrylpyridine. The photochemical E→Z photoisomerization and the side benzene rings substituents influence on the acid-base equilibria were studied. The complex multi-stage mechanism of the acid-base interactions of the polysubstituted compounds was elucidated. The most significant spectral effects were typical to the N,N-dialkylamino substituted compounds of the investigated series. The widest pH sensitivity interval covering nearly the full range of 0–14 units was demonstrated for compounds with both proton donor and proton acceptor substituents.      

Fluorometric Detection of Adenosine Triphosphate with 3-Hydroxy-4′-(dimethylamino)flavone in Aqueous Solutions

An effect of appearance of new band in the excitation spectra of 3-hydroxy-4′-(dimethylamino)flavone (FME probe) in presence of adenosine triphosphate (ATP) is described. Considerable shift of new band up to the red and increase of fluorescence intensity points to the formation of FME-ATP associate, in which FME molecule undergoes to a strong electrostatic stabilization by tetra-charged ATP anion. It is shown the FME anion formation is possible under influence of ATP in the studied conditions. The dynamics of the observed effect is studied in mitochondria. The registered phenomenon allows the quantitative evaluation of ATP concentration in the range of 10⁻³–10⁻⁵ M. In contrast to ATP, other nucleoside phosphates do not give a new band in the excitation spectra of FME probe. This implies the possibility of the in vivo determination of the ATP concentration.