Enhancing signal-to-noise ratio and resolution in low-field NMR relaxation measurements using post-acquisition digital filters

The traditional way to enhance signal-to-noise ratio (SNR) of nuclear magnetic resonance (NMR) signals is to increase the number of scans. However, this procedure increases the measuring time that can be prohibitive for some applications. Therefore, we have tested the use of several post-acquisition digital filters to enhance SNR up to one order of magnitude in time domain NMR (TD-NMR) relaxation measurements. The procedures were studied using continuous wave free precession (CWFP-T₁) signals, acquired with very low flip angles that contain six times more noise than the Carr–Purcell–Meiboom–Gill (CPMG) signal of the same sample and experimental time. Linear (LI) and logarithmic (LO) data compression, low-pass infinity impulse response (LP), Savitzky–Golay (SG), and wavelet transform (WA) post-acquisition filters enhanced the SNR of the CWFP-T₁ signals by at least six times. The best filters were LO, SG, and WA that have high enhancement in SNR without significant distortions in the ILT relaxation distribution data. Therefore, it was demonstrated that these post-acquisition digital filters could be a useful way to denoise CWFP-T₁, as well as CPMG noisy signals, and consequently reducing the experimental time. It was also demonstrated that filtered CWFP-T₁ method has the potential to be a rapid and nondestructive method to measure fat content in beef and certainly in other meat samples.     

A versatile protocol for the preparation of substituted 1- and 2-naphthyl piperazines from aminonaphthols

Aminonaphthols are easily transformed into a variety of 1- and 2-naphthyl piperazines using a sequence of diazotization, iodide substitution and Pd(0) catalyzed coupling reactions.     

Zn-doping effect on the energy barrier to magnetization reversal in superparamagnetic nickel ferrite nanoparticles

Measurements of ac-susceptibility and dc-magnetization were carried out on samples of Ni_1-xZn_xFe₂O₄ nanoparticles (x=0, 0.25, 0.5, 0.75) with average diameters 〈D〉≈7 nm. Values of the superparamagnetic blocking temperature T̄_B were obtained from the characteristic temperature behavior of the imaginary susceptibility χ_imag. An Arrhenius-type law, which accurately describes the relationship between the observation time τ_obs and the blocking temperature, was used to determine the effective energy barrier to magnetization reversal U_eff. A Zn-content dependence of the energy barrier is observed, where U_eff changes little for 0≤x≤0.25, it peaks at x=0.5, and decreases back upon further Zn-doping. The large increase of U_eff at x=0.5 is attributed to an enhanced magnetic anisotropy induced by the crossover between two spatial arrangements of spins in the A and B sub-lattices of the ferrimagnetic inverse spinel. PACS 75.50.Bb; 75.50.Gg; 75.30.Et     

The six-vertex model eigenvectors as critical limit of the eight-vertex model bethe ansatz

The critical limit of the eight-vertex model eigenvectors obtained by means of the generalized Bethe Ansatz is shown to give the six-vertex eigenvectors as constructed in a previous paper by two of the authors. Furthermore, an explicit mapping is established between these eigenvectors and the usual Bethe Ansatz eigenvectors of the six-vertex model. This allows one to show that the indexv labeling the eight-vertex eigenstates becomes exactly the third component of the total spin in the critical limit.     

Complete caps in projective spaces PG (n, q)

A computer search in the finite projective spaces PG(n, q) for the spectrum of possible sizes k of complete k-caps is done. Randomized greedy algorithms are applied. New upper bounds on the smallest size of a complete cap are given for many values of n and q. Many new sizes of complete caps are obtained.     

Higher-Order Simple Lie Algebras

It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their generalised Jacobi identities turn out to be satisfied by the antisymmetric tensors (or higher-order “structure constants”) which characterise the Lie algebra cocycles. This analysis allows us to present a classification of the higher-order simple Lie algebras as well as a constructive procedure for them. Our results are synthesised by the introduction of a single, complete BRST operator associated with each simple algebra. Received: 3 June 1996 / Accepted: 8 November 1996     

Interactions of xanthines with activated carbon: II. The adsorption equilibrium

In the present work, we have studied the adsorption of xanthine derivatives by activated carbon sorbents in aqueous solutions. The study comprised both kinetic, equilibrium and thermodynamic aspects. The kinetic results were reported in a previous paper; the equilibrium-related results are discussed here. The two types of carbon used exhibit some differences but the equilibrium isotherms obtained are all of the H-3 type in the classification of Giles. This suggests a high affinity of the sorbents for the sorbates. We also found that the overall adsorption process comprises more than one individual adsorption-desorption process of which one leads to the formation of a “monolayer” and the other to the “precipitation” of the sorbate on the sorbent surface (multilayer adsorption); the amount of sorbate adsorbed in monolayer form was seemingly greater in C-A14.     

Potentiometric studies on the complexation of copper(II) by phenolic acids as discrete ligand models of humic substances

Studies on the complexation of copper(II) by phenolic acids, as ligand models of humic substances were done by potentiometry. The acids under study were: 3,4-dihydroxyhydrocinnamic acid or hydrocaffeic acid (1), 3,4-dihydroxyphenylacetic acid (2) and 3,4-dihydroxybenzoic acid or protocatechuic acid (3). Acidity constants of the ligands and the formation constants of metal-ligand complexes were evaluated by computer programs. The carboxylic group of the phenolic acids has different pK_a1 values, being the dissociation constants intrinsically related with the distance between the function and the aromatic nucleus. The results obtained allow concluding that acidity constants of the catechol moiety of the compounds are similar with pK_a2 and pK_a3 values between 9.47-9.41 and 11.55-11.70. The complexation properties of the three ligands towards copper(II) ion are quite similar, being the species found not different either in nature or stability. Although the model ligands have some structural differences no significant differences were found in their complexation properties towards copper(II). So, it can be postulated that complexation process is intrinsically related with the presence of a catechol group.