Multivariate technique for optimization of digestion procedure by focussed microwave system for determination of Mn, Zn and Fe in food samples using FAAS

This article describes the development by response surface methodology (RSM) of a procedure for iron, zinc and manganese determination by flame atomic absorption spectrometry (FAAS) in food samples after digestion employing a focussed microwave system. A Doehlert matrix was used to find optimal conditions for the procedure through response surface study. Three variables (irradiation power and time and composition of oxidant solution—HNO₃ + H₂O₂) were regarded as factors in the optimization study. The working conditions were established as a compromise between optimum values found for each analyte taking into consideration the robustness of the procedure. These values were 12 min, 260 W and 42% (v/v) for irradiation time, irradiation power and percent of H₂O₂ in solution, respectively. The accuracy of the optimized procedure was evaluated by analysis of certified reference materials and by comparison with a well-established closed vessel microwave dissolution methodology.     

Spectral upper bounds for the order of a k-regular induced subgraph

Let G be a simple graph with least eigenvalue λ and let S be a set of vertices in G which induce a subgraph with mean degree k. We use a quadratic programming technique in conjunction with the main angles of G to establish an upper bound of the form |S|?inf{(k+t)q_G(t):t>-λ} where q_G is a rational function determined by the spectra of G and its complement. In the case k=0 we obtain improved bounds for the independence number of various benchmark graphs.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

The role of neutral coligands on the stabilization of mono-Tp(i)Pr2 U(III) complexes

The reaction of [UI(3)(THF)(4)] with 1 equiv of KTp()i(Pr)()2 in toluene in the presence of several neutral coligands allowed the synthesis of a novel family of mono-Tp()i(Pr)()2 complexes, [UI(2)Tp()i(Pr)()2(L)(x)()] [L = OPPh(3), x = 1 (3); L = C(5)H(5)N, x = 2 (4); L = Hpz()t(Bu,Me), x = 2 (5); and L = bipy, x = 1 (6)]. The adduct with THF, [UI(2)Tp()i(Pr)()2(THF)(2)(-)(3)] (1), could also be isolated by reacting [UI(3)(THF)(4)] with 1 equiv of KTp()i(Pr)()2 in tetrahydrofuran. However, complex 1 is not a good starting material to enter into the mono-Tp()i(Pr)()2 U(III) complexes as it decomposes in solution, leading to mixtures of U(III) species coordinated with Hpz()i(Pr)()2. The solid-state structures of 3, 4, and 6 were determined by single-crystal X-ray diffraction and revealed that this family of mono-Tp()i(Pr)()2 complexes can be six- (3) or seven-coordinated (4 and 6), depending on the nature of the neutral coligand. Complex 3 displays distorted octahedral coordination geometry, while 4 and 6 display distorted pentagonal bipyramid and capped octahedral geometries, respectively. Complexes 3 and 6 are static in solution, and the patterns of the (1)H NMR spectra are consistent with the C(s)() symmetry found in the solid state. The other complexes (1, 4, and 5) are fluxional, but the dynamic processes involved can be slowed by decreasing the temperature.     

The crystal structure of triphenyltin isothiocyanate

The crystal structure of Ph₃SnNCS has been determined by single crystal X-ray diffraction. The crystals are monoclinic, P2₁, a = 19.02(3), b = 11.67(2), c = 15.49(2)Å;, β = 95.64(10)°, Z = 8. The molecules are arranged in infinite zig-zag S…SnNCS…Sn&.sbnd; chains similar to those in Me₃SnNCS, but with slightly longer SnN, shorter SnS bonds, and almost planar SnC₃ units. Principal mean bond lengths and angles are: SnN, 2.22(5); NC, 1.17(8); CS, 1.58(7); SSn, 2.92(1); SnC, 2.09(3); CC, 1.38(2)Å; SnNCm 161(4); CSSn, 97(3); SSnN, 175(3) and CSnC, 119.8(1.5)°.     

The uranium-nitrogen bond in U IV complexes supported by the hydrotris(3,5-dimethylpyrazolyl)borate ligand

Insertion of benzonitrile and acetonitrile into the U-C bond of [U(Tp(Me2))Cl(2)(CH(2)SiMe(3))](Tp(Me2)= HB(3,5-Me(2)pz)(3)) gives the ketimide complexes [U(Tp(Me2))Cl(2){NC(R)(CH(2)SiMe(3))}](R = Ph (1); Me (2)). The identity of complex was ascertained by a single-crystal X-ray diffraction study. In the solid state exhibits octahedral geometry with a short U-N bond length to the ketimide ligand. We also report herein the synthesis and the X-ray crystal structures of the uranium amide complexes [U(Tp(Me2))Cl(2)(NR(2))](R = Et (3); Ph (4)). A detailed comparison of the U-N bond lengths in these compounds with other known U-N (and Th-N) distances in amide and ketimide actinide(IV) complexes is performed, confirming the short character of the U-N bond length in 1.     

General decay rate estimates for viscoelastic dissipative systems

The linear viscoelastic equation is considered. We prove uniform decay rates of the energy by assuming a nonlinear feedback acting on the boundary, without imposing any restrictive growth assumption on the damping term and strongly weakening the usual assumptions on the relaxation function. Our estimate depends both on the behavior of the damping term near zero and on the behavior of the relaxation function at infinity.