Randomized consistent statistical inference for random processes and fields

Statistical Inference for Stochastic Processes - We propose a randomized approach to the consistent statistical analysis of random processes and fields on $${\mathbb {R}}^m$$ and $${\mathbb {Z}}^m,...     

Spectral expansions of some representations of Lie groups

We investigate representations of classical noncompact Lie groups induced by representations of the maximal parabolic subgroup. Formulas are obtained for 5O₀(2p, 2q)/U(p, q) and U(2p, 2q) Sp(p, q).Translated from Ukrainskii Mathematicheskii Zhurnal, Vol. 42, No. 1, pp. 128–131, January, 1990.     

Direct quantitative analysis of peptides using matrix assisted laser desorption ionization

The protocol and various matrices were examined for quantification of biomolecules in both the low ca. 1200 amu and mid mass 6000-12000 amu ranges using an internal standard. Comparative studies of different matrices of MALDI quantitative analysis showed that the best accuracy and standard curve linearity were obtained for two matrices: (a) 2,5-dihydroxybenzoic acid (DHB) combined with a comatrix of fucose and 5-methoxysalicylic acid (MSA) and (b) ferulic acid/fucose. In the low mass range, the quantitative limit was in the 30 fmol range and in the mid mass range the quantitative limit was in the 250 fmol range. Linear response was observed over 2-3 decades of analyte concentration. The relative error of the standard curve slope was 1.3-1.8% with correlation coefficients of 0.996-0.998.The main problem for quantitative measurement was suppression of the signal of the less concentrated component (analyte or internal standard) by the more concentrated component. The effect was identified with saturation of the matrix by the analyte. The threshold of matrix saturation was found to be in the range of 1/(3000-5000) analyte/matrix molar ratio. To avoid matrix saturation the (analyte+internal standard) to matrix molar ratio should be below this threshold. Thus the internal standard concentration should be as low as possible.DHB/MSA/fucose and ferulic acid/fucose matrices demonstrated good accuracy and linearity for standard curves even when the internal standard had chemical properties different from the analyte. However, use of an internal standard with different chemical properties requires highly stable instrumental parameters as well as constant (analyte+internal standard)/matrix molar ratio for all samples.     

Synthesis and characterization of heavier dioxouranium(VI) dihalides

The synthesis and characterization of the dioxouranium(VI) dibromide and iodide hydrates, UO(2)Br(2)x3H(2)O (1), [UO(2)Br(2)(OH(2))(2)](2) (2), and UO(2)I(2)x2H(2)Ox4Et(2)O (3), are reported. Moreover, adducts of UO(2)I(2) and UO(2)Br(2) with large, bulky OP(NMe(2))(3) and OPPh(3) ligands such as UO(2)I(2)(OP(NMe(2))(3))(2) (4), UO(2)Br(2)(OP(NMe(2))(3))(2) (5), and UO(2)I(2)(OPPh(3))(2)(6) are discussed. The structures of the following compounds were determined using single-crystal X-ray diffraction techniques: (1) monoclinic, P2(1)/c, a = 9.7376(8) A, b = 6.5471(5) A, c = 12.817(1) A, beta = 94.104(1) degrees , V = 815.0(1) A(3), Z = 4; (2) monoclinic, P2(1)/c, a = 6.0568(7) A, b = 10.5117(9) A, c = 10.362(1) A, beta = 99.62(1) degrees , V = 650.5(1) A(3), Z = 2; (4) tetragonal, P4(1)2(1)2, a = 10.6519(3) A, b = 10.6519(3) A, c = 24.0758(6) A, V = 2731.7(1) A(3), Z = 4; (5) tetragonal, P4(1)2(1)2, a = 10.4645(1) A, b = 10.4645(1) A, c = 23.7805(3) A, V = 2604.10(5) A(3), Z = 4, and (6) monoclinic, P2(1)/c, a = 9.6543(1) A, b = 18.8968(3) A, c = 10.9042(2) A, beta =115.2134(5) degrees , V = 1783.01(5) A(3), Z = 2. Whereas 1 and 2 are the first UO(2)Br(2) hydrates and the last missing members of the UO(2)X(2) hydrate (X = Cl --> I) series to be structurally characterized, 4 and 6 contain room-temperature stable U(VI)-I bonds with 4 being the first structurally characterized room temperature stable U(VI)-I compound which can be conveniently prepared on a gram scale in quantitative yield. The synthesis and characterization of 5 using an analogous halogen exchange reaction to that used for the preparation of 4 is also reported.     

Local Lyapunov exponents for spatiotemporal chaos

Local Lyapunov exponents are proposed for characterization of perturbations in distributed dynamical systems with chaotic behavior. Their relation to usual and velocity-dependent exponents is discussed. Local Lyapunov exponents are analytically calculated for coupled map lattices using random field approximation. Boundary Lyapunov exponents describing reflection of perturbations at boundaries are also introduced and calculated.