A Duality Method in Prediction Theory of Multivariate Stationary Sequences

Let W be an integrable positive Hermitian q × q–matrix valued function on the dual group of a discrete abelian group G such that W^–1 is integrable. Generalizing results of T. Nakazi [N] and of A. G. Miamee and M. Pourahmadi [MiP] for q = 1 we establish a correspondence between trigonometric approximation problems in L²(W) and certain approximation problems in L²(W^–1). The result is applied to prediction problems for q–variate stationary processes over G , inparticular, to the case G = ℤ.     

Characterisation of Grinding‐Relevant Particle Properties by Inverting a Population Balance Model

An approach for the quantitative characterisation of feed materials in impact grinding is presented. With the help of dimensional reasoning and a fracture mechanic model two material parameters can be derived which describe the breakage probability quantitatively. The influence of stress intensity (impact energy), stress number, initial particle size and material are separated clearly. The two derived material parameters can be determined by single particle impact experiments with narrow size fractions of the feed material. A single mastercurve for the selection function of five different polymers, limestone and glass describes the breakage behaviour for two decades of initial particle size. The procedure using narrow feed size fractions can be simplified by using feed material with a broad particle size distribution. Then the appropriate population balance has to be inverted in order to determine the particle properties. Both, the population balance and the inversion are presented and validated with experimental results.     

High-resolution cardiac imaging using an interleaved 3D double slab technique

A three-dimensional (3D) gradient-echo sequence with interleaved double-slab excitation was developed and optimized for the requirements in pediatric cardiac imaging. For this purpose high contrast between blood and myocardium signal should be obtained without the use of contrast agents. An acceptable measuring time for a large region examined with high spatial resolution should be achieved as well, especially with regard to the small structures of the heart and vessels of infants. The presented approach works with gradient moment nulling and a short echo time of 5.5 ms resulting in generally high signal intensity and only minor signal losses due to turbulent flow. The sequence allows simultaneous ECG-gated recording of two separately excited slabs with small thickness (10 mm) and with a distance of several centimeters between them. Thus, common effects of presaturation in 3D imaging can be avoided, although a relatively short measuring time is achievable. In order to get a 3D data set with good signal homogeneity of blood and of the other structures across a large volume of interest several double-slab measurements with suitable positions must be performed. The latter aspect is especially important for postprocessing techniques as multiple planar reconstruction and maximum intensity projection. Examples of applications of the new technique and appropriately postprocessed images are presented allowing demonstration even of subtle cardiac malformations.     

Functionalization of Living Polymers via Ethoxysilane Based Compounds: Synthesis and Interaction with Silica Particles

To optimize the reaction of ω-carbanionic styrene or butadiene/styrene polymers with ethoxysilane based compounds, the influence of several experimental parameters on the orientation of the functionalization reaction and its yield was examined. The resulting end-functionalized polymers were systematically investigated by SEC, ¹H NMR and elementary analysis. The orientation of the reaction was found to be directly depending on the chemical nature of the chain end and / or on the type of additive (ethers, LiCl). Best results were obtained with tetraethoxysilane, provided the functionalization is conducted around 5°C, and the active chain end of isoprenyl type. These reactions were extended to bifunctional polymers, the reaction product of butyllithium with m-diisopropenylbenzene being used as an initiator. The efficiency of this initiator for the synthesis of well-defined bifunctionalized polydienes almost quantitatively fitted with three alkoxy functions at both chain ends was demonstrated. Some preliminary results on the mechanical properties of mixtures of functionalized polymers with silica were mentioned.     

Poly(ethylene oxide) macromonomer based hydrogels as a template for the culture of hepatocytes

Macromonomer based poly(ethylene oxide) (PEO) hydrogels were tested with respect to their ability to serve as a template for the survival and the growth of hepatocytes. Two systems were considered : either the surface of preexisting hydrogels, with controlled structural parameters, were seeded with isolated rat hepatocytes or the hepatocytes were dispersed in physiological medium containing the macromonomer/initiator and heated to 37°C. In the first case, cells were examined at given times after spreading over two days. The results were compared to those observed for the dispersion of fibroblasts onto a surface of the same type of hydrogels. The effects of the structure of the hydrogels and its chemical nature on the extent of hepatocyte attachment (or encapsulation) and the morphology were investigated.     

Über chirale Methylzinkaminoalkoxide

Chiral Methylzinc Amino Alkoxides Dimethylzinc reacts with (S)‐N‐methylpyrrolidinyl‐2‐methanol, (R/S)‐1‐phenyl‐2‐(N‐methylamino)‐ethanol, and (S)‐α,α‐diphenyl‐2‐pyrrolidinyl‐2‐methanol in molar ratio 1 : 1 with formation of the corresponding methylzinc amino alkoxides 1 – 3 . As a consequence of the Zn–N‐interaction new centres of chirality containing asymmetric surrounded N‐atoms are formed. Compounds 1 – 3 were characterized by their ¹H and ¹³C nmr spectra. The crystal structures of 1 – 3 were determined by single crystal structur analysis. 1 and 2 are trimeric in solid state, 3 is forming dimeric molecules.     

Vertex pancyclic in‐tournaments

An in‐tournament is an oriented graph such that the negative neighborhood of every vertex induces a tournament. The topic of this paper is to investigate vertex k‐pancyclicity of in‐tournaments of order n, where for some 3 ≤ k ≤ n, every vertex belongs to a cycle of length p for every k ≤ p ≤ n. We give sharp lower bounds for the minimum degree such that a strong in‐tournament is vertex k‐pancyclic for k ≤ 5 and k ≥ n − 3. In the latter case, we even show that the in‐tournaments in consideration are fully (n − 3)‐extendable which means that every vertex belongs to a cycle of length n − 3 and that the vertex set of every cycle of length at least n − 3 is contained in a cycle of length one greater. In accordance with these results, we state the conjecture that every strong in‐tournament of order n with minimum degree greater than is vertex k‐pancyclic for 5 < k < n − 3, and we present a family of examples showing that this bound would be best possible. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 84–104, 2001     

Kristallstruktur,Infrarot‐ und Ramanspektren von Kupfertrihydrogenperiodatmonohydrat,CuH3IO6 · H2O

Crystal Structure, Infrared and Raman Spectra of Copper Trihydrogenperiodate Monohydrate, CuH₃IO₆ · H₂O The hitherto unknown compound CuH₃IO₆ · H₂O was studied by X‐ray, IR‐ and Raman spectroscopic methods. The crystal structure was determined by X‐ray single‐crystal studies (space group P2₁2₁2₁, Z = 4, a = 532.60(10), b = 624.00(10), c = 1570.8(3) pm, R1 = 1.85%, 1559 unique reflections (I > 2σ(I))). Isolated, meridionally configurated H₃IO₆^2– ions are coordinated to the copper ions forming double‐ropes in [100]. These ropes are connected in [010] and [001] by hydrogen bonds. The copper ions possess a square pyramidal co‐ordination with the hydrate H₂O on top. The infrared and Raman spectra as well as group theoretical treatment are presented and discussed with respect to the strength of the hydrogen bonds and the co‐ordination of the CuO₅₍₊₁₎ polyhedra and the H₃IO₆^2– ions at the C₁ lattice sites. The hydrogen bonds of the H₂O molecules and H₃IO₆^2– ions (HO–H…O–IO₅H₃ and H₂IO₅O–H…O–IO₅H₃) greatly differ in strength, as shown from both the respective O…O distances: 282.6 and 298.6 pm (H₂O), and 258.8, 259.7, and 270.9 pm (H₃IO₆^2–) and the OD stretching modes of isotopically dilute samples: 2498 and 2564 cm^–1 (90 K) (HDO), and 1786, 2024, and 2188 cm^–1 (H₂DIO₆^2–). The IO stretching modes of the H₃IO₆^2– ions (696–788 cm^–1 and 555–658 cm^–1, 295 K) display the different strength of the respective I–O and I–O(H) bonds (r_I–O: 181.1–188.3 pm and 189.2–194.5 pm).     

Scattering properties of agarose gels

Static light scattering and small angle neutron scattering measurements are reported for agarose hydrogels prepared under various conditions of concentration and temperature. For the wide range of transfer wave vector explored, these measurements show that the gels do not display fractal behaviour. Their structure is better described by a stretched exponential form, in which the value of the exponent is n = 0.2. As found by other authors, a maximum in the scattering intensity is observed in the light scattering spectra. The position of the maximum, q_max, depends on the concentration and on the thermal history of the sample. The inverse length 1/q_max is in good agreement with published measurements of the pore size D in this system. Preliminary measurements by small angle scattering indicate that the sol-gel transition is not of spinodal type.     

Dibenzocycloheptanones construction through a removable P-centered radical: synthesis of allocolchicine analogues

Dibenzocycloheptanones containing a tricyclic 6–7–6-system are present in numerous biologically active natural molecules. However, the simple and efficient preparation of derivatives containing a dibenzocycloheptanone scaffold remains difficult to date. Herein, we report a versatile strategy for the construction of these challenging seven-membered rings using a 7-endo-trig cyclization which is initiated by a phosphorus-centered radical. This approach provides a step-economical regime for the facile assembly of a wide range of phosphorylated dibenzocycloheptanones. Remarkably, we also have devised a traceless addition/exchange strategy for the preparation of dephosphorylated products at room temperature with excellent yields. Therefore, this protocol allows for the concise synthesis of biorelevant allocochicine derivatives.

Dibenzocycloheptanones containing a tricyclic 6–7–6-system are present in numerous biologically active natural molecules.