Decomposition and reconstruction of multidimensional signals using polyharmonic pre-wavelets

In this paper, we build a multidimensional wavelet decomposition based on polyharmonic B-splines. The pre-wavelets are polyharmonic splines and so not tensor products of univariate wavelets. Explicit construction of the filters specified by the classical dyadic scaling relations is given and the decay of the functions and the filters is shown. We then design the decomposition/recomposition algorithm by means of downsampling/upsampling and convolution products.     

UPLC Method for Determination of Moxonidine and Its Degradation Products in Active Pharmaceutical Ingredient and Pharmaceutical Dosage Form

A simple, rapid, isocratic, stability-indicating reverse phase ultra-performance liquid chromatographic (RP-UPLC) method was developed and validated for the routine analysis of moxonidine in the presence of its degradation products in active pharmaceutical ingredient and pharmaceutical dosage forms. Forced degradation studies were performed according to the guidance of International Conference for Harmonization and were used to evaluate moxonidine intrinsic stability. The drug was subjected to acid, neutral and base hydrolysis as well as to oxidative, thermal and photolytic decomposition in both solution and solid state. The drug appeared to be unstable towards acid and base hydrolysis. To achieve desirable conditions for UPLC analysis, the method development was done with the assistance of experimental design and multivariate optimization methodology by means of Derringer’s desirability function. Stress samples were analyzed according to the experimental plan for fractional factorial screening design and Box-Behnken optimization design. The chromatographic separation was achieved on a C₁₈ Hypersil Gold aq. column (100 mm × 2.1 mm, 1.9 μm) with the mobile phase consisting of methanol–ammonium acetate buffer (10 mM, pH 3.43) mixture (0.9:99.1, v/v) pumped at a flow rate of 870 μL min^?1 and detection wavelength of 255 nm. The UPLC–MS and UPLC–MS/MS analyses were further used to characterize the found degradation products. The validation of the proposed method was also performed considering selectivity, linearity, accuracy, precision, limit of detection and limit of quantification, and the results indicated that the method fulfilled all required criteria. The method was successfully applied to the analysis of commercial tablets.     

Calibration frequency for gas proportional counters

A laboratory that employs nuclear detectors should have a calibration procedure, and its practice is detailed in the bibliography, but the frequency of that calibration is not settled in any case. The aim of this work is to establish an optimum frequency for efficiency calibration in an alpha/beta gas proportional counter, related with the results' adequate routine controls. The results obtained in the application of this purpose to a real instrument (D200 Canberra) are also presented.     

Stationarity preserving and efficiency increasing probability mass transfers made possible

We develop an efficient computational algorithm that produces efficient Markov chain Monte Carlo (MCMC) transition matrices. The first level of efficiency is measured in terms of the number of operations needed to produce the resulting matrix. The second level of efficiency is evaluated in terms of the asymptotic variance of the resulting MCMC estimators. Results are first given for transition matrices in finite state spaces and then extended to transition kernels in more general settings.     

Synthesis and electronic properties of bis-styryl substituted trimeric aryleneethynylenes. Comparison of cruciforms with iso-cruciforms

Four 1,2-distyryl-4,5-bis(phenylethynyl)benzenes are described. A two step synthesis, a combination of Horner and Sonogashira methods is utilized. The targets and their para isomers were examined by UV-vis and fluorescence spectroscopies as well as by cyclic voltammetry. They show solvatochromic behavior and are easily oxidized if the styryl units carry dialkylamino substitutents. Single crystal structures of three derivatives have been obtained.     

On the measure of the absolutely continuous spectrum for Jacobi matrices

We apply the methods of classical approximation theory (extreme properties of polynomials) to study the essential support ${\Sigma }_{\mathrm{ac}}$ of the absolutely continuous spectrum of Jacobi matrices. First, we prove an upper bound on the measure of ${\Sigma }_{\mathrm{ac}}$ which takes into account the value distribution of the diagonal elements, and implies the bound due to Deift–Simon and Poltoratski–Remling.Second, we generalise the differential inequality of Deift–Simon for the integrated density of states associated with the absolutely continuous spectrum to general Jacobi matrices.     

Azathia crown ethers carrying pyrene pendant as receptor molecules for metal sensor systems

A series of crown ethers carrying a pyrene group with nitrogen–sulfur donor atoms, that differ in having three, four and five sulfur atoms in the macrocycle was designed and synthesized by the reaction of the corresponding macrocyclic compound and 1-bromomethylpyrene. The influence of metal cations such as Mn²⁺, Fe²⁺, Fe³⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺, Cd²⁺, Hg²⁺, Pb²⁺ and Al³⁺ on the spectroscopic properties of the ligands was investigated in acetonitrile–dichloromethane (1:1) by means of absorption and emission spectrometry. Absorption spectra show isosbestic points in the spectrophotometric titration of Fe²⁺, Zn²⁺, Cu²⁺, Pb²⁺ and Hg²⁺. The results of spectrophotometric titration experiments disclosed the complexation compositions and complex stability constants of the novel ligands with Fe²⁺, Zn²⁺, Cu²⁺, Pb²⁺ and Hg²⁺ cations. The monoazatetrathia crown ether showed good sensitivity for Cu²⁺ with linearity in the range 5.0×10^?7–2.5×10^?6 M and detection limit of 1.6×10^?8 M.     

Conditionally Gaussian random sequences for an integrated variance estimator with correlation between noise and returns

Correlation between microstructure noise and latent financial logarithmic returns is an empirically relevant phenomenon with sound theoretical justification. With few notable exceptions, all integrated variance estimators proposed in the financial literature are not designed to explicitly handle such a dependence, or handle it only in special settings. We provide an integrated variance estimator that is robust to correlated noise and returns. For this purpose, a generalization of the forward filtering backward sampling algorithm is proposed, to provide a sampling technique for a latent conditionally Gaussian random sequence. We apply our methodology to intraday Microsoft prices and compare it in a simulation study with established alternatives, showing an advantage in terms of root‐mean‐square error and dispersion.