Fourier analysis of the approximation power of principal shift-invariant spaces

The approximation order provided by a directed set {S _h } _h>0 of spaces, each spanned by thehZ ^d -translates of one function, is analyzed. The nearoptimal approximants of [R2] from eachs _h to the exponential functions are used to establish upper bounds on the approximation order. These approximants are also used on the Fourier transform domain to yield approximations for other smooth functions, and thereby provide lower bounds on the approximation order. As a special case, the classical Strang-Fix conditions are extended to bounded summable generating functions.The second part of the paper consists of a detailed account of various applications of these general results to spline and radial function theory. Emphasis is given to the case when the scale {s _h } is obtained froms ₁ by means other than dilation. This includes the derivation of spectral approximation orders associated with smooth positive definite generating functions.     

Uranium association with corroding carbon steel surfaces

We investigated the association of uranium with clean and corroded surfaces of 1010 carbon steel. Studying steel contaminated by uranium species will have an important effect on the development of methods used to clean radioactively contaminated metal waste. X‐ray photoelectron spectroscopy, synchrotron infrared microspectroscopy and laboratory‐based Fourier transform infrared analysis of steel surfaces exposed to uranyl nitrate showed the presence of crystallized hydrated uranyl oxides, uranyl hydroxides, iron oxyhydroxides and iron oxides. In general, heavily corroded areas physically shield the uranium species, which tended to associate spatially with hydroxyl groups and lepidocrocite. Lightly corroded areas contained uranium species with stronger axial U–O bonding. Infrared spectroscopy, Rutherford backscattering spectroscopy and energy‐dispersive spectroscopy mapping analysis revealed that the uranium species are well distributed within the upper micron of the thick corrosion layer and associated more with areas of high hydroxide content. Parameters such as the concentration of uranyl nitrate solution used to expose the carbon steel coupons, the method of contamination (dipped or sprayed with dilute uranyl nitrate solution) and the degree of corrosion (accelerated corrosion before and/or after contamination) played significant roles in the distribution and nature of the uranyl hydroxide/iron oxyhydroxide corrosion products found on the surface of all coupons. These factors must be considered in the development and optimization of decontamination processes for metal waste. Copyright © 2003 John Wiley & Sons, Ltd.     

RP-HPLC study of redox equilibria in vanadium-PAR binary and ternary systems: Direct determination of vanadium in steel

The reversed-phase high-performance liquid Chromatographic (RP-HPLC) behaviour of the binary chelates of V(V) and V(IV) with 4-(2-pyridylazo) resorcinol (PAR) and ternary chelates of vanadium with PAR and auxiliary ligands: hydrogen peroxide, hydroxylamine, tartrate and citrate were studied using a C₁₈ column. The complex double-peak chromatograms of V(IV)/V(V)-PAR systems were studied and the origin of each peak was proved. Vanadium in ternary systems with PAR and hydrogen peroxide was found exclusively in V(V)-H₂O₂-PAR complex (single peak on the chromatogram) despite its initial oxidation state. The double role of hydroxylamine (complex agent and reductor) in vanadium systems with PAR was confirmed: in the V(V) system three species were identified (V(V)-PAR, V(V)-NH₂OH-PAR and V(IV)-PAR), but in the V(IV) system only two: V(IV)-PAR and V(V)-NH₂OH-PAR. Citrate and tartrate giving single peak were found as auxiliary ligands in ternary V(V) systems of analytical importance. Due to its masking potential towards iron (III) ions, citrate was chosen as the most suitable third component of a ternary vanadium system with PAR, to form the basis of an RP-HPLC method for direct determination of V in steel.     

混合控制下腐蚀过程的电化学动力学参数测定

通过恒电量脉冲技术测定Q235碳钢在天然海水中腐蚀过程的电化学动力学参数. 分别利用不同极化幅度的恒电量瞬态响应分析获得极化电阻和Tafel斜率, 进而计算腐蚀电流icorr. 并对比了恒电量方法和考虑扩散影响的稳态极化曲线方法的测量结果. 结果表明, 采用恒电量强极化积分算法(CPSI)获得的Tafel斜率与极化曲线方法有很好的相关性. 同时, CPSI测定的阴极Tafel斜率符合氧还原反应的理论Tafel斜率值. 因此, 采用恒电量瞬态响应测量大大减小了浓差极化的影响, 有利于快速测定电荷传递和扩散传质混合控制下腐蚀过程的电化学动力学参数.     

Matrix summability and a generalized Gibbs phenomenon

Letf be a real-valued function sequence {f _k } that converges to on a deleted neighborhoodD of . If there is a subsequence {f _k(j) } and a number sequencex such that lim _j x _j = and either lim _j f _k(j) (x _j )>lim sup _x (x) or lim _j f _k(j) (x _j ) x (x), thenf is said to display theGibbs phenomenon at . IfA is a (real) summability matrix, thenAf is a function sequence given by(Af) _n (x)= _k=0 a _n,k f _k (x). IfAf displays the Gibbs phenomenon wheneverf does, thenA is said to beGP-preserving. By replacingf _k (x) withf _k (x _j )F _k,j , the Gibbs phenomenon is viewed as a property of the matrixF, andGP-preserving matrices are determined by properties of the matrix productAF. The general results give explicit conditions on the entries {a _n,k } that are necessary and/or sufficient forA to beGP-preserving. For example: if(x)0 thenF displaysGP iff lim _k,j F _k,j 0, and ifA isGP-preserving then lim _n,k A _n,k 0. IfA is a triangular matrix that is stronger than convergence, thenA is notGP-preserving. The general results are used to study the preservation of the Gibbs phenomenon by matrix methods of Nörlund, Hausdorff, and others.     

The raised-cosine wavelets in computerized tomography

In Computerized Tomography (CT), an image must be recovered from its sampled projections in the form of values of the Radon transform. In this work a method of recovering the image is based on the properties of the raised-cosine wavelet. This wavelet has a closed form which allows for certain precomputations and avoids convolution. The rate of convergence of the resulting algorithm to the image density function is found under suitable hypotheses. This algorithm is then tested on the standard Shepp–Logan     

Synthesis of the four enantiomers of diethyl 1,2-di(N-Boc-amino)propylphosphonates

A simple and efficient synthetic strategy to all four enantiomerically pure diethyl 1,2-di(N-Boc-amino)propylphosphonates has been elaborated starting from the corresponding N-[(R)-(1-phenylethyl)]aziridine-(2S)- and N-[(S)-(1-phenylethyl)]aziridine-(2R)-carboxaldehydes, employing a one-pot three-components Kabachnik-Fields reaction followed by the hydrogenolytic removal of the chiral auxiliary and aziridine ring opening with simultaneous protection of the amino groups as the N-Boc derivatives.     

On the simplicity of some kac-moody groups

Recently, Marcuson extended the classical construction of Tits systems in Steinberg groups to include the Kac-Moody Steinberg groups associated with the infinite dimensional versions of the great Lie algebras. If these Lie algebras and their Kac-Moody groups are viewed as limits of their finite dimensional counterparts, more direct methods may be employed. In fact, the Kac-Moody Chevalley groups of these Lie algebras are seen to be simple.     

Electrochemical Characterization of Stainless Steel as a New Electrode Material in a Medical Device for the Diagnosis of Sudomotor Dysfunction

An electrochemical sensor detects the risk of diabetes and prediabetes; low potentials are applied to nickel electrodes and electrical responses are measured. Although the contact of nickel with skin is short, the risk of allergical reactions cannot be discarded. SS 304L, with lower Ni content, was tested in carbonate buffer solutions containing chloride, lactate and urea to investigate its sensitivity to different parameters in sweat and compare it to nickel. The results show that SS 304L is a suitable material for the assessment of sudomotor dysfunction due to its high capacity to detect the deviation in Cl^? concentration. Sensitivity of SS 304L to Cl^? is much higher than for nickel.     

Polymer complexes. LXXVI. Synthesis,characterization, CT‐DNA binding,molecular docking and thermal studies of sulfoxine polymer complexes

Novel polymer complexes of 8‐hydroxyquinoline‐5‐sulfonic acid hydrate ( H ₂ L ) with Cu²⁺, Co²⁺ and Ni²⁺ chloride were prepared and characterized. Microanalysis, magnetic susceptibility, IR spectra, electron spin resonance, mass spectra, X‐ray, molar conductance, thermal, and UV–Vis spectra studies have been used to confirm the structure of the prepared polymer complexes. The molecular and electronic structures of the hydrogen bond conformers for ligand ( H ₂ L ) were optimized theoretically and the quantum chemical parameters were calculated. On the basis of elemental and IR data, the chemical structure of metal chelates commensurate that the tri‐dentate (H₂L) coordinate to metal chlorides through oxygen atom of phenolic OH and oxygen atom of SO₃‐H group by replacing H atoms and nitrogen of the quinoline ring. The magnetic studies suggested the octahedral geometrical structure for all produced polymer complexes with general formula {[ML (OH₂)₃] .xH₂O}_n (M = Cu²⁺, x = 1.; Co²⁺, x = 2 and Ni²⁺, x = 2) in molar ratio (1:1). Coats–Redfern and Horowitz–Metzger methods have been used for calculating the activation thermodynamic parameters of the thermal decomposition for H ₂ L and its polymer complexes. The interaction between H ₂ L and its transition metal complexes with the calf thymus DNA (CT‐DNA) was determined by UV–Vis spectra. Binding efficiency between H ₂ L with the receptors of the prostate cancer (PDB code 2Q7L Hormone) and the breast cancer (PDB code 1JNX Gene regulation) was studied by molecular docking. The inhibition behaviour of H ₂ L against the corrosion of carbon steel / HCl (2 M) solution was studied by weight loss, Tafel polarisation, electrochemical impedance spectroscopy (EIS) and electrochemical frequency modulation (EFM) techniques. The adsorption isotherm was found to be Friendlish isotherm. The morphology of inhibited carbon steel? s surface was studied using scanning electron microscope (SEM) and energy dispersive X‐ray spectroscopy (EDS).