Parametric methods for frequency-selective MR spectroscopy-a review

Accurate quantitation of the spectral components in a pre-selected frequency band for magnetic resonance spectroscopy (MRS) signals is a frequently addressed problem in the MR community. One obvious application for such a frequency-selective technique is to lower the computational burden in situations when the measured data sequence contains too many samples to be processed using a standard full-spectrum method. Among the frequency-selective methods previously proposed in the literature, only a few possess the two features of primary concern: high robustness against interferences from out-of-band components and low computational complexity. In this survey paper we consider five spectral analysis methods which can be used for MRS signal parameter estimation in a selected frequency band. We re-derive the filter diagonalization method (FDM) in a new way that allows an easy comparison to the other methods presented. Then we introduce a frequency-selective version of the method of direction estimation (MODE) which has not been applied to MR-spectroscopy before. In addition, we present a filtering and decimation technique using a maximum phase bandpass FIR-filter and relate it to a similar ARMA-modeling approach known as SB-HOYWSVD (sub-band high-order Yule-Walker singular value decomposition). Finally, we study the numerical performances of these four methods and compare them to that of the recently introduced SELF-SVD (Singular Value Decomposition-based method usable in a SELected Frequency band) in several examples using simulated MR data, and discuss the benefits and disadvantages of each technique.     

An extremal problem related to Kolmogoroff’s inequality for bounded functions

LetA andB be positive numbers andm andn positive integers,m. Then there is for complex valued functions φ onR with sufficient differentiability and boundedness properties a representation wherev ₁ andv ₂ are bounded Borel measures withv ₁ absolutely continuous, such that there exists a function φ with ∣φ⁽ⁿ⁾∣ ?A and ∣φ∣ ?A onR and satisfying $$\varphi ^{(m)} (0) = A\int_R {\left| {d\nu _1 } \right|} + B\int_R {\left| {d\nu _2 } \right|} .$$ This result is formulated and proved in a general setting also applicable to derivatives of fractional order. Necessary and sufficient conditions are given in order that the measures and the optimal functions have the same essential properties as those which occur in the particular case stated above.     

On the unicellularity ofl p (w)

A method of D. V. Yakubovich is sharpened to give extensions of results by him and M. P. Thomas on the right translation-invariant subspace structure for weightedl ^p (Z ⁺) and weightedl ^p (⁺), when the weight tends to 0 at infinity faster than exponentially.     

Study of the reaction products of flavonols with 2,2-diphenyl-1-picrylhydrazyl using liquid chromatography coupled with negative electrospray ionization tandem mass spectrometry

The products obtained after the reaction between flavonols and the stable free radical 2,2-diphenyl-1-picrylhydrazyl (DPPH(*)) in both methanol and acetonitrile were characterized using liquid chromatography coupled with negative electrospray ionization tandem mass spectrometry (LC/ESI-MS/MS) and NMR spectroscopy. The flavonols studied were quercetin, kaempferol and myricetin. In methanol, two reaction products of oxidized quercetin were identified using LC/ESI-MS/MS and NMR. Quercetin was oxidized through a transfer of two H-atoms to DPPH(*) and subsequently incorporated either two CH(3)OH molecules or one CH(3)OH- and one H(2)O molecule giving the products 2-(3,4-dihydroxyphenyl)-3,5,7-trihydroxy-2,3-dimethoxy-2,3-dihydrochromen-4-one and 2-(3,4-dihydroxyphenyl)-3,3,5,7-tetrahydroxy-2-methoxy-2,3-dihydrochromen-4-one, respectively. LC/ESI-MS/MS analysis revealed that in methanol, kaempferol and myricetin also gave rise to methoxylated oxidation products similar to that identified for quercetin. Kaempferol, in addition, also exhibited products where a kaempferol radical, obtained by a transfer of one H-atom to DPPH(*), reacted with CH(3)OH through the addition of CH(3)O(*), yielding two isomeric products. When the reaction took place in acetonitrile, LC/ESI-MS/MS analysis showed that both quercetin and myricetin formed stable isomeric quinone products obtained by a transfer of two H-atoms to DPPH(*). In contrast, kaempferol formed two isomeric products where a kaempferol radical reacted with H(2)O through the addition of OH(*), i.e. similar to the reaction of kaempferol radicals with CH(3)OH.     

Studies on the Complexation Behavior of Thorium(IV). 1. Hydrolysis Equilibria

The stability constants of thorium(IV) hydrolysis species have been measured at15, 25, and 35°C (in 1.0 mol dm^–3 NaClO₄) using both potentiometry and solventextraction. The results indicate the presence of the monomeric speciesTh(OH)³⁺, Th(OH)²⁺ ₂, Th(OH)⁺ ₃, and Th(OH)₄, in addition to the polymericspecies Th₄(OH)^{8+ 8} and Th₆(OH)⁹⁺ ₁₅. The polymeric species were found to beimportant, although the total thorium concentration was limited to 0.01–0.1mmol-dm^–3. The solvent extraction measurements required the use of acetylacetone.As such, the stability constants of thorium(IV) with acetylacetone were alsomeasured using both potentiometry and solvent extraction. All logarithms of thestability constants were found to be linear functions of the reciprocal absolutetemperature indicating that H ^o and S^o of reaction are both independent oftemperature (over the temperature range examined in the study).     

Atmospheric chemistry of CHF2CHO: study of the IR and UV-vis absorption cross sections, photolysis, and OH-, Cl-, and NO3-initiated oxidation

The infrared and ultraviolet-visible absorption cross sections, effective quantum yield of photolysis, and OH, Cl, and NO3 reaction rate coefficients of CHF2CHO are reported. Relative rate measurements at 298 +/- 2 K and 1013 +/- 10 hPa gave kOH = (1.8 +/- 0.4) x 10(-12) cm3 molecule(-1) s(-1) (propane as reference compound), kCl = (1.24 +/- 0.13) x 10(-11) cm3 molecule(-1) s(-1) (ethane as reference compound), and kNO3 = (5.9 +/- 1.7) x 10(-17) cm3 molecule(-1) s(-1) (trans-dichloroethene as reference compound). The photolysis of CHF2CHO has been investigated under pseudonatural tropospheric conditions in the European simulation chamber, Valencia, Spain (EUPHORE), and an effective quantum yield of photolysis equal to 0.30 +/- 0.05 over the wavelength range 290-500 nm has been extracted. The tropospheric lifetime of CHF2CHO is estimated to be around 1 day and is determined by photolysis. The observed photolysis rates of CH3CHO, CHF2CHO, and CF3CHO are discussed on the basis of results from quantum chemical calculations.     

AGP Propagator calculations

The use of the antisymmetrized geminal power (AGP ) consistent reference state for RPA polarization propagator calculations is explored. Illustrative applications to the three lowest electronic states (³B₁, ¹A₁, and ¹B₁) of the methylene radical are reported with comparisons to other theoretical methods and experiment.     

Efficient isolation of polyaromatic fraction from aliphatic compounds in complex extracts using dimethylformamide-pentane partitionings

A liquid-liquid partitioning method was optimized for the rapid and quantitative separation of polycyclic aromatic hydrocarbons (PAHs) and polychlorinated biphenyls (PCBs) from aliphatic hydrocarbons in complex primary extracts. This technique was based on the selective extraction of PAHs and PCBs from an aliphatic solvent into dimethylformamide (DMF). Partition experiments demonstrated that the optimal performance was achieved with a DMF (5% H2O)-n-pentane binary system. The optimized application of two consecutive DMF (5% H2O)-n-pentane treatments to extracts from two different polluted sediments facilitated the elimination of alkanes and unresolved complex mixture by more than 94% while the average recoveries of spiked deuterated-PAHs and 13C labeled PCBs ranged from 84 to 94 and 75 to 96%, respectively.