Showing papers by "University of Duisburg-Essen published in 1994"

On the Hodge structure of projective hypersurfaces in toric varieties

Abstract: This paper generalizes classical results of Griffiths, Dolgachev and Steenbrink on the cohomology of hypersurfaces in weighted projective spaces. Given a $d$-dimensional projective simplicial toric variety $P$ and an ample hypersurface $X$ defined by an polynomial $f$ in the homogeneous coordinate ring $S$ of $P$ (as defined in an earlier paper of the first author), we show that the graded pieces of the Hodge filtration on $H^d(P - X)$ are naturally isomorphic to certain graded pieces of $S/J(f)$, where $J(f)$ is the Jacobian ideal of $f$. We then discuss how this relates to the primitive cohomology of $X$. Also, if $T$ is the torus contained in $X$, then the intersection of $X$ and $T$ is an affine hypersurface in $T$, and we show how recent results of the second author can be stated using various ideals in the ring $S$. To prove our results, we must give a careful description (in terms of $S$) of $d$-forms and $(d-1)$-forms on the toric variety $P$. For completeness, we also provide a proof of the Bott-Steenbrink-Danilov vanishing theorem for simplicial toric varieties. Other topics considered in the paper include quasi-smooth hypersurfaces and $V$-submanifolds, the structure of the complement of $U$ when $P$ is represented as the quotient of an open subset $U$ of affine space, a generalization of the Euler exact sequence on projective space, and the relation between graded pieces of $R/J(f)$ and the moduli of ample hypersurfaces in $P$.

„Mathematische Weltbilder” bei Studienanfängern — eine Erhebung

Abstract: The starting-point for research on “mathematical world views” („mathematische Weltbilder”) is the thesis that these “mathematical world views” play a central and significant role in the individual learning and doing of mathematics. An investigation on first-year students (mathematics and chemistry) has been carried out in which several conceptions („Vorstellungen”) of mathematics have been identified and measured. It can be proved that these components partly constitute a “world view” and do take effect on doing mathematics. The results show that the factors of a “word view” influence others not monocausally, bu reciprocally whereby complexes of components are constituted. One complex covers the attitudes („Haltungen”) concerning the question whether and in how far mathematics is a process (of cognition, intellectual progress and building theory) or a system (e.g. a “toolbox” and a “formulary” as well as an abstract, formal theory). A second complex consists of the attitudes with respect to “pleasure in mathematics education” (connected with “don’t separate school mathematics from mathematics”), “self-assessment of the current mathematical performance” and “learning not only for the written class test; derivations and proofs are not unimportant”. Thus a “mathematical world view” turns out to be a complex structure which essentially influences the learning and doing of mathematics, and both of the mentioned complexes characterize a prototype of a “mathematical world view” which is ideal for mathematical performance. The students’ “mathematical world views” contain some attitudes which have either detrimental or more promoting attitudes concerning learning and doing of mathematics. Especially doubtful or even serious though not surprising or unexpected is the fact that the “world view” of the “chemists” (compared to that of the “mathematicians”) provides clearly worse conditions for learning and doing mathematics. The “chemists” show a more restricted “world view”, typically for users and “customers”, whereas the “mathematicians” rather turned out to be producers of mathematics.

Parameterization of linear observers and its application to observer design

Abstract: With the aid of the factorization approach linear observers and their estimation error dynamics are parameterized. This result provides a dual representation of the well-known linear controller parameterization and gives a new insight into the observer design which may be used for the observer construction and robust observer design. >

Influence of the dipole interaction on the direction of the magnetization in thin ferromagnetic films.

Abstract: In this paper we investigate the influence of a surface anisotropy and the dipole interaction on the magnetization of thin films The surface anisotropy favors a perpendicular orientation while the dipole interaction favors an in-plane magnetization It is shown that these competing interactions for certain values of the parameters may result in a temperature-driven switching transition from an out-of-plane to an in-plane ordered state

Kleine Ringe, 78. Tri‐tert‐butyl(trimethylsilyl)cyclobutadien und Tri‐tert‐butyl(trimethylsilyl)tetrahedran

Abstract: Small Rings, 78[1]. - Tri-tert-butyl(trimethylsilyl)cyclobutadiene and Tri-tert-butyl(trimethylsilyl)tetrahedrane The chemistry of diazo(1,2,3-tri-tert-butylcyclopropenyl)(trimethylsilyl)methane (6) is unexpectedly diverse. Upon irradiation it fragments exclusively into the acetylenes 7 and 8. Flash thermolysis, on the other hand, gives — aside from the two acetylenes — tri-tert-butylazete (10) and trimethylsilyl cyanide (11). Upon heating 6 presumably isomerizes via betaine 17 to Dewar-diazabenzene 13 — which is split into 10 and 11 — and diazabenzvalene 18. This reaction course is supported by the isolation of the carbonyliron complexes 15 and 16, — The CuCl-catalyzed thermal decomposition again follows a different route. Under these conditions tri-tert-butyl(trimethylsilyl)cyclobutadiene (5) is formed, probably as a weak CuCl complex. Only after addition of ethylenebis(diphenylphosphane) free cyclobutadiene 5 can be isolated. Upon irradiation of 5 a quantitative isomerization to tri-tert-butyl(trimethylsilyl)tetrahedrane (29) occurs. This second, spectroscopically unequivocally confirmed tetrahedrane melts at 179°C. In solution the isomerization to cyclobutadiene 5 starts at about 160°C. That means, it is thermally even more stable than tetra-tert-butyltetrahedrane.

A CMOS floating-point vector-arithmetic unit

Abstract: This work describes a floating-point arithmetic unit based on the CORDIC algorithm. The unit computes a full set of high level arithmetic and elementary functions: multiplication, division, (co)sine, hyperbolic (co)sine, square root, natural logarithm, inverse (hyperbolic) tangent, vector norm, and phase. The chip has been integrated in 1.6 /spl mu/m double-metal n-well CMOS technology and achieves a normalized peak performance of 220 MFLOPS. >

In vitro differentiation of E-N-CAM expressing rat neural precursor cells isolated by FACS during prenatal development

Abstract: Most fetal rat brain cells expressing the embryonal, highly sialylated form of the cell adhesion molecule N-CAM (E-N-CAM) are precursor cells, as judged from the absence of marker molecules specific for mature neural cell types. However, the detection of E-N-CAM+ cells in frozen sections does not provide information on the lineage-specific differentiation of these cells during development. To investigate their differentiation behaviour in vitro, E-N-CAM+ cells were isolated at different times of brain development by fluorescence-activated cell sorting (FACS), using a monoclonal antibody (Mab RB21-7) which specifically recognizes polysialic acid (PSA) residues on E-N-CAM. Double-immunofluorescence analyses showed that the majority of E-N-CAM+ cells isolated on prenatal days 15 to 18 differentiated into neurons while a small subset of Mab RB21-7 binding cells proved to be astrocytic precursors and/or bipotential. The proportion of E-N-CAM+ astrocytic precursors increased during later development (prenatal day 22) concomitantly with the onset of gliogenesis. While conversion of E-N-CAM to mature forms of N-CAM was never observed in neurons during cultivation, E-N-CAM+ cells of the astrocyte lineage switched to N-CAM soon after the onset of GFAP expression. A lineage-specific transition of E-N-CAM to mature N-CAM expression is, therefore, suggested for these astrocytic progenitor cells during rat brain development.

Ordnungsgrundsätze der Erwachsenenbildung in Deutschland

Abstract: Die Erwachsenenbildung/Weiterbildung ist in Deutschland – wie in den meisten anderen industrialisierten Landern auch – in einem historischen Stadium, in dem sie zwar einerseits quantitativ und qualitativ als eigenstandiger Bildungsbereich erkennbar, anderer seits aber noch nicht systematisch gestaltet oder geordnet ist. Unter Erwachsenenbil dung/Wei ter bildung wird heute gemas der Definition des Deutschen Bildungsrates (1970) die „Fortsetzung oder Wiederaufnahme organisierten Lernens nach Abschluss einer unterschiedlich ausgedehnten ersten Bildungsphase“ (ebd, S. 197) ver standen. Weiterbildung umfasst danach ganz unterschiedliche Bereiche wie etwa berufliche und betriebliche Weiterbildung, Fortbildung und Umschulung, politische Bildung, ge werk schaft li che Bildung, Allgemeinbildung und kulturelle Bildung. Erwachsenenbildung umfasst danach Angebote, die von einer einzelnen Abendveranstal tung bis zu mehrjahrigen Ausbildungs gangen gehen, Einrichtungen vollig unterschiedlicher Zielrichtung, Rechtsform, Arbeits weise sowie soziale und personelle Zusammenhange ganz unterschiedlicher Provenienz. Erwachsenenbildung ist ein ge wach sener Bereich, der historisch aus unterschiedlichen Zusammenhangen heraus entstanden, aktuell dis parat organisiert und kaum uberschaubar ist. Ordnungsgrundsatze fur die Erwachsenenbildung gelten jeweils nur fur Teilbereiche von ihnen.

A shock tube study on the thermal decomposition of CS2 based on S(3P) and S(1D) concentration measurements

Abstract: The thermal decomposition of CS2 highly diluted in Ar was studied behind reflected shock waves by monitoring time-dependent absorption profiles of S(3P) and S(1D) using atomic resonance absorption spectroscopy (ARAS). The rate coefficient of the reaction: $$\begin{gathered} CS_2 + M\mathop \to \limits^{k_1 } CS + S + M, \hfill \\ k_1 = 5.1 \times 10^{14} \exp \left( {\frac{{ - 38150K}}{T}} \right)cm^3 mol^{ - 1} s^{ - 1} \hfill \\ \end{gathered} $$ (R1) . was determined in experiments with initial concentrations of CS2 between 5 and 50 ppm at post-shock conditions of 2300 K≤T≤3360 K and total densities between 2.2×1018 cm−3 and 3.9×1018 cm−3. In experiments with higher initial concentrations of 100 ppm CS2 in Ar, the S(3P) concentrations were found to reach quasi-stationary values. From the steady state assumption a value for the rate coefficient of the most probable S consuming reaction: $$\begin{gathered} CS_2 + S\mathop \rightleftharpoons \limits^{k_2 } CS + S_2 , \hfill \\ k_2 \approx 1.2 \times 10^{13} cm^3 mol^{ - 1} s^{ - 1} \hfill \\ \end{gathered} $$ (R2) . was estimated at temperatures between 2100 K and 2340 K.

Manifolds in the Skeletons of Convex Polytopes, Tightness, and Generalized Heawood Inequalities

Abstract: If a 2-dimensional manifold in the 2-dimensional skeleton of a convex d-polytope P contains the 1-skeleton of P then d is bounded in terms of the genus of the surface: this is essentially Heawood’s inequality. In this paper we prove a higher dimensional analogue about 2k-dimensional manifolds containing the k-skeleton of a simplicial convex polytope. Related conjectures are formulated for tight polyhedral submanifolds and generalized Heawood inequalities, including an Upper Bound Conjecture for combinatorial manifolds.

Chelat-stabilisierte 1,3-bis(acyloxy)-1,3-diethyldiboroxane aus Triethylboroxin und Carbonsäureanhydriden

Abstract: Chelate-Stabilized 1,3-Bis(acyloxy)-1,3-diethyldiboroxanes from Triethylboroxin and Carboxylic Acid Anhydrides Triethylboroxin (A) reacts with carboxylic acid anhydrides (RCO)2O [R = Me: 1a; Et: 1b; tBu: 1d; Ph: 1e] with various rates to give high yields of the 3,7-dialkyl-1,5-diethyl-4,8,9-trioxa-2,6-dioxonia-1,5-diboratabicyclo[3.3.1]nona-2,6-dienes OB(Et)OC(R)OB(Et)OC(R)O (2) [R = Me: 2a (X-ray crystal structure analysis); Et: 2b; tBu: 2d; Ph: 2e], presumably via the unstable compounds OB(Et)OB(Et)OC(R)OB(Et)OC(R)O (3a,b, d, e). Compound 1c (R = CF3) reacts with A to form a mixture of 1,3-diethyl-1,3-bis(trifluoroacetoxy)diboroxane OC(CF3)OB(Et)OB(Et)O(CF3)CO (2c′) and 2c (R = CF3) at room temperature. Whereas two compounds of the type 2 do not comproportionate, 1a–e spontaneously form the mixed substituted carboxylic acid anhydrides 1ab etc. on mixing at room temperature (GC, 13C NMR). - From the 17O-enriched A* and 1a–e the 17O-enriched compounds 2a*-e* with BO*B and YYBO*OCR groups are obtained. A* exchanges O atoms up to 200°C with succinic anhydride (1f) forming 1f* or with phthalic acid anhydride (1g) forming 1g* and 3g*. - The mixed carboxylic acid anhydrides 1xy are cleaved, and the mixtures of 1 are separated with A to yield the uniform 3,7-dialkyl-substituted compounds 2.

A quantitative ring dye laser absorption diagnostic for free SiH2 (X̃1A1) radicals at high temperatures

Abstract: The silylene radical (SiH2) was detected in reacting high temperature mixtures of disilane (Si2H6) highly diluted in argon by time-resolved ring dye laser absorption measurements at λ = 579.35 nm. The measured absorption was caused by a single line transition in the A−X(0,2,0)−(0,0,0) band of SiH2 which was exclusively initiated by the narrow bandwidth laser source. The absorption profiles were measured in the reaction zone behind reflected shock waves at temperatures between 1000 and 1900 K, and at pressures 0.2 bar⩽p⩽1.3 bar. Several calibration experiments were performed at temperatures above 1500 K and low initial Si2H6 concentrations. To establish the connection between measured absorption and the SiH2 concentrations, numerical simulations on disilane pyrolysis were performed based on a reaction kinetic model. From both the measured absorption and the calculated SiH2 concentrations the silylene absorption cross section was determined to be σSiH2 = 1.3 × 10-17cm2, at the reference conditions ν0 = 17260.82 cm-1, T0 =1757 K and p0 = 0.3 bar. A spectroscopic model was introduced to describe the temperature and pressure dependence of the SiH2 absorption cross section at the given wavelength. All measured concentration time-histories of SiH2 radicals formed during the thermal decomposition of disilane in the given experimental range could be verified. The detection limit was about 1×1013cm-3 for an absorption path length of 8 cm and the laser diagnostic was proved well suited for kinetic studies of elementary reactions involving silylene.

Elimination of fluconazole during continuous veno-venous haemodialysis (CVVHD) in a single patient.

Abstract: Fluconazole is a bis-triazolyl antifungal agent for the treatment of superficial and systemic fungal infections with minimum inhibitory concentrations (MIC) of 0.13-0.8 mg• 1 -a for Candida albicans [1]. It is only 12 % protein-bound and 80 % of the parent drug is eliminated unchanged via the kidneys [3]. Its pharmacokinetics have been studied in patients undergoing intermittent haemodialysis (HD) and continuous ambulatory peritoneal dialysis (CAPD) [2-4] but not in patients undergoing continuous veno-venous haemodialysis (CVVHD). We wish to report a case in which the pharmacokinetics of fluconazole during CVVHD therapy were studied. A 61-year-old, 76-kg woman with grade IV mitral valve insufficiency after endocarditis was admitted initially for an operative mitral valve reconstruction. The patient presented with mild renal failure (serum creatinine: 1.3 mg • dl-1). At the first day after the successful implantation of a Carpentier ring, the patient again showed all signs of mitral valve insufficiency proved by echocardiography. Rethoracotomy was performed and a St. Jude Medical M 29 valve was implanted. After the second operation the patient needed high-dose catecholamine therapy. Renal and lung functions worsened. We had to continue artificial ventilation and it was necessary to start CVVHD therapy because of

Synthesen und Reaktionen acyclischer fluororganischer Thiocarbenium-Ionen†

Abstract: Syntheses and Reactions of Fluoroorganic Acyclic Thiocarbenium Ions1 Arsenic pentafluoride oxidizes (F3CS)4C (1) but not (F3CS)2C = C(SCF3)2 (2) to yield the stable salt (F3CS)3C+AsF-6 (3). It reacts with halide ions to form (F3CS)3CX (3a–c, X = F, Cl, Br). Iodide is oxidized to iodine with formation of (F3CS)3CC(SCF3)3 (4) which reacts with nitrogen dioxide to give (F3CS)3CNO2 (3e). - (F3CS)3C+AsF-6 (3) removes from (F)-SCF3 (5a) a ring-bound fluorine atom to afford (F3CS)3CF and -SCF3]+AsF−6 (5). When (F3CS)3CCl (3b) is treated with AsF5, 3 and [(F3CS)2-CCl]+AsF−6 (6) are formed in a 2:1 molar ratio. The latter reacts with F− or Cl− to give (F3CS)2CClX (6a,b; X = F, Cl). AsF5 is capable of abstracting a fluoride ion from (F3CS)3 - n Cln,CF only if n = 0 or 1. For n = 2 no similar reaction takes place, but with AlCl3 in BCl3 halogen exchange to F3CSCCl3 (7b) is observed. - Alkylation of (F3CS)2CS (8) with H3CF/AsF5 yields [(F3CS)2CSCH3]+AsF−6 (9), which adds a fluoride ion to give (F3CS)2(H3CS)CF (9a). The molecular structures of (F3CS)2C = C(SCF3)2 (2) and (F3CS)3CC(SCF3)3 (4) have been determined by X-ray diffraction methods.

Rational Points of Bounded Height on Compactifications of Anisotropic Tori

Abstract: We investigate the analytic properties of the zeta-function associated with heights on equivariant compactifications of anisotropic tori over number fields. This allows to verify conjectures about the distribution of rational points of bounded height.

From crystalline boryl‐substituted and boryl‐coupled 2,2,4,4,6,6‐hexamethyl‐cyclotrisilazanes to β‐SiC and BN

Abstract: [Me2SiNBFN(SiMe3)2]3 (1) is synthesized in the reaction of trilithiated hexamethylcyclotrisilazane with F2BN(SiMe3)2. The mono- and dilithium derivatives of the six-membered ring (Me2SiNH)2 Me2SiNSiFMe2 react with the F2B-substituted cyclotrisilazane F2B(NSiMe2)3(SiFMe2)2 in the molar ratio 1:1 or 1:2 to give the BF-coupled rings 2 and 3. The crystal structure analysis of 1 and 3 and pyrolysis of 1 and 3 with formation of silicon boron carbonitride and its crystallisation to composite powders at very high temperatures are reported.

Thermal decomposition of CH2 verified by product concentration measurements of C, H, and CH

Abstract: At temperature T>-2200 K, ketene (CH2CO) is known as a convenient, reproducible and well-defined CH2 source. In experiments performed behind reflected shock waves, the subsequent reactions of CH2 were monitored by concentration measurements of various product species, including C, H, and CH, using atomic resonance absorption and ring dye laser absorption spectroscopy. The time histories of these species were investigated in various initial ketene (5–75ppm)/argon mixtures in the temperature range 2200–3400 K at pressures 0.7≤p≤2.4 bar. From the concentration slopes at t≈0, apparent rate coefficients for C, H, and CH formation were determined, but only the C concentration profiles at early reaction times have direct kinetic significance. From these data, the rate coefficient of the thermal decomposition reaction C H 2 + M ⇋ k 2 C + H 2 + M k 2 = 1.60 × 10 14 exp ⁡ ( − 32 , 200 K / T ) c m 3 m o l − 1 s − 1 (R2)

Phosphanylsubstituierte 1,2‐Azaborole

Abstract: 1,2-Azaborolyl Complexes, XXX[1]. — Phosphanyl-Substituted 1,2-Azaboroles 1-tert-Butyl-2-methyl-1,2-azaborolyllithium (LiAb, 1) and TlCl equilibrate at -75°C in THF under action of light to TlAb (2) and LiCl. Compound 2 decomposes above -50°C with elimination of thallium and the neutral isomers 1-tert-butyl-2,5-dihydro-2-methyl-1H-1,2-azaborole and 1-tert-bu-tyl-2,3-dihydro-2-methyl-1H-1,2-azaborole. Whilst 1 reacts with Ph2PCl in only very small amounts to give the expected Ph2P-substituted azaborole ring 3, TlAb (2) forms this compound by reaction with Ph2PCl in high yields. The yellow oily 3 is characterized by 1H-; 11B-, 13C-, and 31P-NMR data. The Me3Si-substituted derivative 1-tert-butyl-3-(diphenyl-phosphanyl)-2,3-dihydro-2-methyl-3-(trimethylsilyl)-1H-1,2-azaborole (5), available via 4, the Li salt of 3, and ClSiMe3, forms yellow crystals which could be used for an X-ray structure analysis. As expected, the Ph2P and Me3Si groups substitute the boron neighboring C3 atom of the planar ring framework. The crystal structure of 5 shows the two expected enantiomers.

Concordance between parental origin of chromosome 13q loss and chromosome 6p duplication in sporadic retinoblastoma.

Abstract: Two hypotheses are capable of explaining nonrandom loss of one parent's alleles at tumor suppressor loci in sporadic cases of several pediatric cancers, including retinoblastoma--namely, preferential germ-line mutation or chromosome imprinting. We have examined 74 cases of sporadic retinoblastoma for tumors in which at least two genetic events--loss of heterozygosity for chromosome 13q markers and formation of an isochromosome 6p--have occurred. Sixteen cases were found to contain both events. In 13 of 16 such tumors, the chromosomes 13q that were lost and chromosomes 6p that were duplicated are derived from the same parent. These data may be explained within the framework of the genome imprinting model but are not predicted by preferential germ-line mutation.

Transition from Poissonian to Gaussian-orthogonal-ensemble level statistics in a modified Artin's billiard

Abstract: One wall of an Artin's billiard on the Poincar\'e half-plane is replaced by a one-parameter (${\mathit{c}}_{\mathit{p}}$) family of nongeodetic walls. A brief description of the classical phase space of this system is given. In the quantum domain, the continuous and gradual transition from the Poisson-like to Gaussian-orthogonal-ensemble (GOE) level statistics due to the small perturbations breaking the symmetry responsible for the ``arithmetic chaos'' at ${\mathit{c}}_{\mathit{p}}$=1 is studied. Another GOE\ensuremath{\rightarrow}Poisson transition due to the mixed phase space for large perturbations is also investigated. A satisfactory description of the intermediate level statistics by the Brody distribution was found in both cases. The study supports the existence of a scaling region around ${\mathit{c}}_{\mathit{p}}$=1. A finite-size scaling relation for the Brody parameter as a function of 1-${\mathit{c}}_{\mathit{p}}$ and the number of levels considered can be established.