Dimension Functions of Orthonormal Wavelets

The article is devoted to dimension functions of orthonormal wavelets on the real line with dyadic dilations. We describe properties of dimension functions and prove several characterization theorems. In addition, we provide a method of construction of dimension functions. Various new examples of dimension functions and orthonormal wavelets are included.     

Two new zincophosphates, (H3NCH2CH2NH3)2[Zn(μ-PO4)2] and (NH4)[(H3N)Zn{(μ-PO4)Zn}3]: Crystal structures and relationships to similar open framework zinco- and aluminophospates

Two new zincophosphates, bis(ethylenediammonim) catena-bis(μ-phosphato)zincate, (H₃NCH₂CH₂NH₃)₂[Zn(μ-PO₄)₂] (1), and ammonium ammine-tris(μ-phosphato)tetrazincate, (NH₄)[(H₃N)Zn{(μ-PO₄)Zn}₃] (2), were synthesized under hydrothermal conditions and their crystal structures were determined by single-crystal X-ray diffraction analysis. The crystal structure of 1 consists of infinite macroanionic ZnP₂O₈⁴⁻ chains, running along the [0 0 1] direction, and diprotonated ethylenediammonium cations, H₂en²⁺. The crystal structure of 2 is built up from ZnO₄, Zn(NH₃)O₃ and PO₄ vertex-sharing tetrahedra connected to form an open 3D framework. The ammonium groups, NH₄⁺, are located in the channels formed by 8M-rings extending along [1 0 0]. In order to study vibrational behavior of H₂en²⁺ and NH₄⁺ cations, NH₃ molecules in 1 and 2, single-crystal Raman spectra were obtained. Structural, chemical and topological similarities to the other open framework zinco- and aluminophosphates incorporating different guest species are discussed.     

(E)‐4‐[(2‐Carbamoylhydrazinylidene)methyl]‐3‐hydroxy‐5‐hydroxymethyl‐2‐methylpyridin‐1‐ium nitrate

The title compound, C₉H₁₃N₄O₃⁺·NO₃⁻, is the first structurally characterized Schiff base derived from semicarbazide and pyridoxal. Unusually for an unsubstituted semicarbazone, the compound adopts a syn conformation, in which the carbonyl O atom is in a cis disposition relative to the azomethine N atom. This arrangement is supported by a pair of hydrogen bonds between the organic cation and the nitrate anion. The cation is essentially planar, with only a hydroxymethyl O atom deviating significantly from the mean plane of the remaining atoms (r.m.s. deviation of the remaining non‐H atoms = 0.01 Å). The molecules are linked into flat layers by N—H...O and C—H...O hydrogen bonds. O—H...O hydrogen bonds involving the hydroxymethyl group as a donor interconnect the layers into a three‐dimensional structure.     

Pulse perturbation technique for determination of piroxicam in pharmaceuticals using an oscillatory reaction system

A simple and reliable novel kinetic method for the determination of piroxicam (PX) was proposed and validated. For quantitative determination of PX, the Bray-Liebhafsky (BL) oscillatory reaction was used in a stable non-equilibrium stationary state close to the bifurcation point. Under the optimized reaction conditions (T = 55.0°C, [H₂SO₄]₀ = 7.60×10^?2 mol L^?1, [KIO₃]₀ = 5.90×10^?2 mol L^?1, [H₂O₂]₀ = 1.50×10^?1 mol L^?1 and j ₀ = 2.95×10^?2 min^?1), the linear relationship between maximal potential shift ΔE _m , and PX concentration was obtained in the concentration range 11.2–480.5 μg mL^?1 with a detection limit of 9.9 μg mL^?1. The method had a rather good sample throughput of 25 samples h^?1 with a precision RSD = 4.7% as well as recoveries RCV ≤ 104.4%. Applicability of the proposed method to the direct determination of piroxicam in different pharmaceutical formulations (tablets, ampoules and gel) was demonstrated.      

Pre-concentration of trace elements in short chain alcohols using different commercial cation exchange resins prior to inductively coupled plasma-optical emission spectrometric detection

Chelex-100, Dowex 50W-x8 and Dowex MAC-3 exchange resins were investigated for separation and pre-concentration of trace amounts of Cd, Cr, Cu, Fe, Mn, Pb, Ti and Zn in alcohols with respect to retention and desorption characteristics. Dowex 50W-x8 was found to be the best sorbent with percentages recoveries >95%. In addition, Chelex-100 appeared to be suitable for the pre-concentration of Cu, Fe and Zn, whereas Dowex MAC-3 was selective for Cu and Fe. Therefore, Dowex 50W-x8 was used for further investigations. The relative standard deviations <4% (n = 20), limits of detection and quantification were 0.1–1.2 μg L⁻¹ and 0.3–1.5 μg L⁻¹, respectively. The SPE method was validated against a certified reference material and the results were in agreement with certified values. The accuracy of the optimized method was verified by the recovery test in the spiked alcohol samples. The accuracy and spike recovery test for different metal ions were in the range 98–102% and 95–105%, respectively. The optimized method was applied to the separation and pre-concentration of metal ions in different commercial alcohol samples.     

Simultaneous determination of chromium(VI) and chromium(III) by flame atomic absorption spectrometry with a chelating ion-exchange flow injection system

Summary Simultaneous Determination of Chromium(VI) and Chromium(III) by Flame Atomic Absorption Spectrometry with a Chelating Ion-Exchange Flow Injection System A simple method is described for the simultaneous determination of chromium(VI) and chromium(III) in a flow injection system comprising chelating ion-exchange and flame atomic absorption spectrometry. Sampling rates for 2001 and 1 ml sample volumes were 120 and 60 h^–1 (240 and 120 speciations per hour), respectively. Typical relative standard deviations were 0.52% for Cr(VI) (0.50g ml^–1 and 0.67% for Cr(III) (0.10,g ml^–1) and the corresponding limits of detection were 85 ng ml^–1, and 16 ng ml^–1, respectively.On leave from University of Belgrade.     

Comparison of ethanol-soluble proteins from different rye (Secale cereale) varieties by two-dimensional electrophoresis

The major storage proteins from six rye varieties, grown under the same conditions in 1997 and 1998 in Rønhave, Denmark, were analyzed by two‐dimensional (2‐D) polyacrylamide gel electrophoresis. The proteins were extracted from ground rye kernels with 70% ethanol and separated by 2‐D electrophoresis. The gels were scanned, compared using ImageMaster® software and the data sets were analyzed by principal component analysis (PCA) using THE UNSCRAMBLER software. Afterwards MATLAB was used to make a cluster analysis of the varieties based on PCA. The analysis of the gels showed, that the protein patterns (number of different proteins and their isoelectric points and molecular weights) from the six rye varieties were different. Based on the presence of unique cultivar‐specific spots it was possible to differentiate between all six varieties if the two harvest years were investigated separately. When the results were combined from the two years five varieties could be differentiated. The results from the PCA confirmed the finding of the unique spots and cluster analysis was made in order to illustrate the results. The combination of the results from 2‐D electrophoresis and other grain characteristics showed that one protein spot was located close to the parameters bread volume and bread height.     

Graphs with maximum connectivity index

Let G be a graph and d_v the degree (=number of first neighbors) of its vertex v. The connectivity index of G is χ=∑ (d_ud_v)^−1/2, with the summation ranging over all pairs of adjacent vertices of G. In a previous paper (Comput. Chem. 23 (1999) 469), by applying a heuristic combinatorial optimization algorithm, the structure of chemical trees possessing extremal (maximum and minimum) values of χ was determined. It was demonstrated that the path P_n is the n-vertex tree with maximum χ-value. We now offer an alternative approach to finding (molecular) graphs with maximum χ, from which the extremality of P_n follows as a special case. By eliminating a flaw in the earlier proof, we demonstrate that there exist cases when χ does not provide a correct measure of branching: we find pairs of trees T, T′, such that T is more branched than T′, but χ(T)>χ(T′). The smallest such examples are trees with 36 vertices in which one vertex has degree 31.     

A stability indicating assay method for cefuroxime axetil and its application to analysis of tablets exposed to accelerated stability test conditions

Cefuroxime axetil is the esterified form of cefuroxime, injectable second generation cephalosporine antibiotic that can be given orally. Stereo and structural isomers of cefuroxime axetil (CA), anti-cefuroxime axetil (ACA) and Delta(3)-cefuroxime axetil (DCA), can be present in cefuroxime dosage forms as the process related impurities as well as possible degradation product. Sensitive and precise reversed-phase high-performance liquid chromatography (RP-HPLC) method was developed and validated for the determination of cefuroxime axetil in the presence of its degradation products in solid dosage forms. The RSD values for cefuroxime axetil, anti-cefuroxime axetil and Delta(3)-cefuroxime axetil of 1.80, 1.99 and 2.48%, respectively, indicated a good precision of the RP-HPLC method. Developed RP-HPLC method was sensitive with LOD = 0.08 microg mL(-1) and LOQ = 0.60 microg mL(-1) for anti-cefuroxime axetil and LOD = 0.06 microg mL(-1) and LOQ = 0.45 microg mL(-1) for Delta(3)-cefuroxime axetil. Holding studies were carried out on Ceroxim tablets, according to ICH regulation at 30 degrees C/60% relative humidity (RH) and 40 degrees C/75% RH for 1, 2, 3 and 6 months. The review data from the stability studies conducted, show the significant content change of Delta(3)-cefuroxime axetil.