Separating the solution sets of analytical and polynomial systems

A linear inequality system with infinitely many constraints is polynomial (analytical) if its index set is a compact interval of the real line and all its coefficients are polynomial (analytical, respectively) functions of the index on this interval. This paper provides an example of analytical system whose solution set cannot be the solution set of any polynomial system. Research supported by DGES of Spain and FEDER of UE, Grant BFM2002-04114-C02-01. Research supported by CONACyT of Mexico, Grant 130036. Research partially supported by CONACyT of Mexico, Grant 44003.     

Smoothing minimally supported frequency wavelets: Part II

The main purpose of this paper is to give a procedure to “mollify” the low-pass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA. Hence, we are able to approximate (in the L ² -norm) MSF wavelets by wavelets with any desired degree of smoothness on the Fourier transform side. Although the MSF wavelets we consider are bandlimited, this may not be true for their smooth approximations. This phenomena is related to the invariant cycles under the transformation x ↦2x (mod2π). We also give a characterization of all low-pass filters for MSF wavelets. Throughout the paper new and interesting examples of wavelets are described.     

Density estimation and adaptive control of markov processes: Average and discounted criteria

We consider a class of discrete-time Markov control processes with Borel state and action spaces, and ^d i.i.d. disturbances with unknown distribution . Under mild semi-continuity and compactness conditions, and assuming that is absolutely continuous with respect to Lebesgue measure, we establish the existence of adaptive control policies which are (1) optimal for the average-reward criterion, and (2) asymptotically optimal in the discounted case. Our results are obtained by taking advantage of some well-known facts in the theory of density estimation. This approach allows us to avoid restrictive conditions on the state space and/or on the system's transition law imposed in recent works, and on the other hand, it clearly shows the way to other applications of nonparametric (density) estimation to adaptive control.Research partially supported by The Third World Academy of Sciences under Research Grant No. MP 898-152.     

Defect concentration in Ti-substituted YIG from TG curves

The article discusses theory and experiment about the measurement of defect concentration in Ti-substituted yttrium iron garnet by means of thermogravimetry techniques. The two possible cases arising from oxygen interchange with atmosphere, oxygen vacancies and interstitial cations, may be analyzed quantitatively from the derived expressions. The possibility of another type of defects being present in the samples, not associated to oxygen evolution, is not excluded. Measurements were carried out in air and CO₂ for different Ti contents. The substitution tends to increase slightly the defect parameter θ in YIG, while a CO₂ reducing atmosphere is much more effective than the Ti substitution for increasing θ. Calculations for a given single-phased sample sintered in air show two possibilities: a deficit of one oxygen atom for every 2.5 unit cells of 96 atoms, or one excess cation for every 3.5 cells. Other samples show very similar results. The accuracy involved in the measurements is about 2–3%.     

Proton nuclear magnetic resonance characterisation of glycosaminoglycans using chemometric techniques

Various types of glycosaminoglycans (GAGs) including heparins, chondroitin sulfates, dermatan sulfate and hyaluronic acid were studied from their proton nuclear magnetic resonance (1H NMR) spectra using chemometric techniques. Despite the complexity of the 1H NMR signals, data analysis using principal component analysis enabled the different GAG classes to be distinguished and permitted their classification according to their chemical structure. The analysis of the composition of the major disaccharide unit and other relevant chemical structures in the heparin samples was performed using partial least squares regression.     

Structure of hydroxycinnamic acid derivatives established by high-perfomance liquid chromatography with photodiode-array detection

Summary The present paper describes the development of a method for the differentiation of hydroxycinnamic acid derivatives by HPLC with photodiode-array detection. Furthermore spectral data of the compounds under investigation are given. Whereas p-coumaric acid derivatives are distinguishable from caffeic and ferulic acid derivatives by the positions of their spectrum maxima and their convexity interval value, it is not possible to distinguish between caffeic and ferulic acid derivatives because of overlapping spectrum maxima and convexity interval values.     

Reactivity of 2-deoxy-2-iodoglycosyl isothiocyanates with O-, S-, and N-nucleophiles. Synthesis of glycopyranoso-fused thiazoles

The reactivity of 2-deoxy-2-iodoglycosyl isothiocyanates toward O- and S-nucleophiles gives an easy access to 2-deoxy-2-iodoglycopyranosyl thiocarbamates and dithiocarbamates. Internal nucleophilic displacement of the iodine by the sulfur atom in these compounds allows the preparation of glycopyranoso[1,2-d]-1,3-thiazoles and glycopyranoso[1,2-d]-1,3-thiazolidin-2-one or -2-thione. Reaction with amines or polyamines as N-nucleophiles led directly to 2-aminoglycopyranoso[1,2-d]-1,3-thiazoles without isolation of the intermediate thioureas. Methyl 2-deoxy-2-iodoglycopyranosyl thiocarbamates also allow the synthesis of 2-deoxyglycopyranosyl thiocarbamates or 2-deoxy-2-iodoglycopyranosyl carbamates.     

Determination of manganese in brain samples by slurry sampling graphite furnace atomic absorption spectrometry

A simple procedure for the determination of manganese in different sections of human brain samples by graphite furnace atomic absorption spectrometry has been developed. Brain sections included cerebellum, hypothalamus, frontal cortex, vermix and encephalic trunk. Two sample preparation procedures were evaluated, namely, slurry sampling and microwave-assisted acid digestion. Brain slurries (2% w/v) could be prepared in distilled, de-ionized water, with good stability for up to 30 min. Brain samples were also digested in a domestic microwave oven using 5 ml of concentrated HNO₃. A mixed palladium+magnesium nitrate chemical modifier was used for thermal stabilization of the analyte in the electrothermal atomizer up to pyrolysis temperatures of 1300 °C, irrespective of the matrix. Quantitation of manganese was conducted in both cases by means of aqueous standards calibration. The detection limits were 0.3 and 0.4 ng ml⁻¹ for the slurry and the digested samples, respectively. The accuracy of the procedure was checked by comparing the results obtained in the analysis of slurries and digested brain samples, and by analysis of the NIST Bovine Liver standard reference material (SRM 1577a). The ease of slurry preparation, together with the conventional set of analytical and instrumental conditions selected for the determination of manganese make such methodology suitable for routine clinical applications.