Remarks on the <Emphasis Type="Italic">k</Emphasis>-error linear complexity of <Emphasis Type="Italic">p</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>-periodic sequences

Recently the first author presented exact formulas for the number of 2 ⁿ -periodic binary sequences with given 1-error linear complexity, and an exact formula for the expected 1-error linear complexity and upper and lower bounds for the expected k-error linear complexity, k ≥ 2, of a random 2 ⁿ -periodic binary sequence. A crucial role for the analysis played the Chan–Games algorithm. We use a more sophisticated generalization of the Chan–Games algorithm by Ding et al. to obtain exact formulas for the counting function and the expected value for the 1-error linear complexity for p ⁿ -periodic sequences over prime. Additionally we discuss the calculation of lower and upper bounds on the k-error linear complexity of p ⁿ -periodic sequences over .      

High temperature liquid chromatography hyphenated with ESI-MS and ICP-MS detection for the structural characterization and quantification of halogen containing drug metabolites

In this paper we describe the hyphenation of high temperature liquid chromatography with ICP-MS and ESI-MS for the characterization of halogen containing drug metabolites. The use of temperature gradients up to 200°C enabled the separation of metabolites with low organic modifier content. This specific property allowed the use of detection methods that suffer from (significant) changes in analyte response factors as a function of the organic modifier content such as ICP-MS. Metabolites of two kinase inhibitors (SB-203580-Iodo and MAPK inhibitor VIII) produced by bacterial cytochrome P450 BM3 mutants and human liver microsomes were identified based on high resolution MS(n) data. Quantification was done using their normalized and elemental specific response in the ICP-MS. The importance of these kinds of quantification strategies is stressed by the observation that the difference of the position of one oxygen atom in a structure can greatly affect its response in ESI-MS and UV detection.     

Physical Properties of Superbulky Lanthanide Metallocenes: Synthesis and Extraordinary Luminescence of [EuII(CpBIG)2] (CpBIG=(4‐nBu‐C6H4)5‐Cyclopentadienyl)

The superbulky deca‐aryleuropocene [Eu(Cp^BIG)₂], Cp^BIG=(4‐nBu‐C₆H₄)₅‐cyclopentadienyl, was prepared by reaction of [Eu(dmat)₂(thf)₂], DMAT=2‐Me₂N‐α‐Me₃Si‐benzyl, with two equivalents of Cp^BIGH. Recrystallizyation from cold hexane gave the product with a surprisingly bright and efficient orange emission (45 % quantum yield). The crystal structure is isomorphic to those of [M(Cp^BIG)₂] (M=Sm, Yb, Ca, Ba) and shows the typical distortions that arise from Cp^BIG???Cp^BIG attraction as well as excessively large displacement parameter for the heavy Eu atom (U_eq=0.075). In order to gain information on the true oxidation state of the central metal in superbulky metallocenes [M(Cp^BIG)₂] (M=Sm, Eu, Yb), several physical analyses have been applied. Temperature‐dependent magnetic susceptibility data of [Yb(Cp^BIG)₂] show diamagnetism, indicating stable divalent ytterbium. Temperature‐dependent ¹⁵¹Eu Mössbauer effect spectroscopic examination of [Eu(Cp^BIG)₂] was examined over the temperature range 93–215 K and the hyperfine and dynamical properties of the Eu^II species are discussed in detail. The mean square amplitude of vibration of the Eu atom as a function of temperature was determined and compared to the value extracted from the single‐crystal X‐ray data at 203 K. The large difference in these two values was ascribed to the presence of static disorder and/or the presence of low‐frequency torsional and librational modes in [Eu(Cp^BIG)₂]. X‐ray absorbance near edge spectroscopy (XANES) showed that all three [Ln(Cp^BIG)₂] (Ln=Sm, Eu, Yb) compounds are divalent. The XANES white‐line spectra are at 8.3, 7.3, and 7.8 eV, for Sm, Eu, and Yb, respectively, lower than the Ln₂O₃ standards. No XANES temperature dependence was found from room temperature to 100 K. XANES also showed that the [Ln(Cp^BIG)₂] complexes had less trivalent impurity than a [EuI₂(thf)_x] standard. The complex [Eu(Cp^BIG)₂] shows already at room temperature strong orange photoluminescence (quantum yield: 45 %): excitation at 412 nm (24270 cm^?1) gives a symmetrical single band in the emission spectrum at 606 nm (ν_max=16495 cm^?1, FWHM: 2090 cm^?1, Stokes‐shift: 2140 cm^?1), which is assigned to a 4f⁶5d¹→4f⁷ transition of Eu^II. These remarkable values compare well to those for Eu^II‐doped ionic host lattices and are likely caused by the rigidity of the [Eu(Cp^BIG)₂] complex. Sharp emission signals, typical for Eu^III, are not visible.     

Hypersingularities in three-dimensional crack configurations in composite laminates

Three-dimensional crack configurations in composite laminates are studied by means of the Scaled Boundary Finite Element Method (SBFEM) particularly regarding stress singularities and their associated deformation modes. The SBFEM is an efficient semi-analytical method that permits solving linear elastic mechanical problems. Only the boundary needs to be discretized while the problem is considered analytically in the direction of the dimensionless radial coordinate pointing from the scaling center to the boundary . An important advantage is that it requires no additional effort for the characterization of existing stress singularities. The situation of two meeting inter-fiber cracks is investigated in detail, considering different materials and fiber / crack orientations. It is shown that in three-dimensional crack configurations in composite laminates so-called hypersingularities can occur, i.e. stress singularities which are even stronger than the classical crack singularity. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

SBFEM elements for thin-walled composite beams with arbitrary layup

The scaled boundary finite element method (SBFEM) is a semi-analytical method in which only the boundary is discretized. The results on the boundary are scaled into the domain with respect to a scaling center which must be “visible” from the whole boundary. For beam-like problems the scaling center can be selected at infinity and only the cross-section is discretized. Two new elements for thin-walled beams have been developed on the basis of the first order shear deformation theory. The beam sections are considered to be multilayered laminate plates with arbitrary layup. The arbitrary cross-section is discretized with beam elements of Timoshenko type. Using the virtual work principle gives the SBFEM equation, which is a system of differential equations of a gyroscopic type. The solution is calculated using the matrix exponential function. The elements have been tested and compared with a finite element model and they give good results. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of a Second Cation (M = Ca2+, Mg2+) on the Phase Evolution of (BaxM1–x)F2 Starting from Amorphous Deposits

A second type of cation (Mg²⁺, Ca²⁺) was introduced into BaF₂ by low‐temperature atomic beam deposition. The structure evolution from low‐temperature (–150 °C) amorphous deposits to high‐temperature (< 1000 °C) annealed crystalline phases was studied by in‐situ transmission electron microscopy and X‐ray diffraction. Amorphous (Ba_0.5, Ca_0.5)F₂ crystallizes in a first step to metastable solid solution phase (fluorite‐type), which then decomposes into the pure phases of CaF₂ and BaF₂ at higher temperature. The crystallization behavior of amorphous (Ba_xMg_1–x)F₂ is completely different. When the Mg/Ba atomic ratio is around 1:1, the mixture transforms to the ternary compound BaMgF₄ at annealing, and no decomposition occurs by further heating up to 1000 °C. When the Ba concentration is below 15 % in atomic ratio (x < 0.15), the mixture forms a solid solution phase (rutile type) with the lattice expanded by +1 % compared to rutile type MgF₂. The difference between the phase evolutions of the two mixture systems is discussed.     

Enantiomerically Pure [M6L12] or [M12L24] Polyhedra from Flexible Bis(Pyridine) Ligands

Coordination‐driven self‐assembly is one of the most powerful strategies to prepare nanometer‐sized discrete (supra)molecular assemblies. Herein, we report on the use of two constitutionally isomeric BINOL‐based bis(pyridine) ligands for this purpose. Upon coordination to Pd^II ions these self‐assemble into enantiomerically pure endo‐ and exo‐functionalized hexa‐ and dodecanuclear metallosupramolecular spheres with a chiral skeleton depending on the substitution pattern of the BINOL core. These aggregates were characterized by NMR, MS, DLS, TEM, and EELS as well as ECD. Furthermore, experimental ECD data could be compared to those obtained from theoretical simulations using a simplified Tamm–Dancoff approximation to time‐dependent DFT to rationalize the extraordinary high molar circular dichroisms. Despite the rotational freedom around the central aryl–aryl bond of these ligands, the self‐assembly process happens completely selective in a “narcissistic” self‐recognition manner.     

Structure and properties of Ce<Subscript>3</Subscript>Pd<Subscript>3</Subscript>Bi<Subscript>4</Subscript>, CePdBi,and CePd<Subscript>2</Subscript>Zn<Subscript>3</Subscript>

The intermetallic cerium compounds Ce₃-Pd₃Bi₄, CePdBi, and CePd₂Zn₃ were synthesized from the elements in sealed tantalum ampoules in an induction furnace. The compounds were characterized by X-ray powder and single crystal diffraction: CeCo₃B₂ type (ordered version of CaCu₅), P6/mmm, a = 538.4(4), c = 427.7(4) pm, wR2 = 0.0540, 115 F ² values, 9 variables for CePd₂Zn₃ and Y₃Au₃Sb₄ type, I \({\bar 4}\)3d, a = 1005.2(2) pm, w R2 = 0.0402, 264 F ² values, 9 variables for Ce₃Pd₃Bi₄, and MgAgAs type, a = 681.8(1) pm for CePdBi. The bismuthide structures are build up from three-dimensional networks of corner-sharing PdBi₄ tetrahedra with Pd–Bi distances of 281 (Ce₃Pd₃Bi₄) and 296?pm (CePdBi), respectively. The cerium atoms are located in larger voids of coordination number 12 (Ce₃Pd₃Bi₄) and 10 (CePdBi). In CePd₂Zn₃ the cerium atoms fill larger channels within the three-dimensional [Pd₂Zn₃] network with 18 (6 Pd + 12 Zn) nearest neighbors. The three compounds contain stable trivalent cerium with experimental magnetic moments of μ_eff = 2.70(2), 2.48(1), and 2.49(1) μ_B/Ce atom for CePd₂Zn₃, Ce₃Pd₃Bi₄, and CePdBi, respectively. Susceptibility and specific heat data gave no hint for magnetic ordering down to 2.1?K.