Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors

We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta–gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.     

Synthesis and novel reactivity of halomethyldimethylsulfonium salts

Iodomethyl-, chloromethyl-, and fluoromethyldimethylsulfonium salts, 4b-d, have been synthesized and are observed to be highly reactive molecules that exhibit extraordinary diversity with respect to the nature of their reactivity, undergoing facile direct substitution (S(N)2) reactions, but also being highly susceptible to electron-transfer reactions. Cyclic voltametry experiments indicated that the iodomethyldimethylsulfonium compound, 4b, is a potent electron acceptor, even surpassing the reactivity of perfluoro-n-alkyl iodides in that capacity. The iodo- and chloromethyldimethylsulfonium salts, 4b,c, as well as the analogous iodomethyltrimethylammonium salt, 3a, are shown to be reactive SET acceptors.     

Naphthalene amidine imide dyes by transamination of naphthalene bisimides

Derivatives of naphthalene-1,4,5,8-tetracarboxylic acid with amidine structures have been prepared. The light absorption of the bisimide derivatives in the UV region is shifted to the visible for the amidine imides, which also fluoresce with a large Stokes shift. It has been shown how the bisimide-lactam rearrangement can be extended to amidine structures.     

High-energy phosphate metabolism during incremental calf exercise in humans measured by 31 phosphorus magnetic resonance spectroscopy (31P MRS)

Several previous 31 phosphorus magnetic resonance spectroscopy ((31)P MRS) studies performing incremental or progressive muscle exercises have observed that a decrease in pH is accompanied with an acceleration in phosphocreatine (PCr) hydrolysis. The purpose of this study was to investigate the relationship between PCr breakdown and pH during isotonic, exhaustive, incremental plantar flexion exercises. We included eight healthy, male volunteers into this study. Using a 1.5 Tesla MR scanner and a self-built exercise bench, we performed serial free induction decay (FID) (31)P MRS measurements with a time resolution of 1 min at rest, isotonic calf muscle exercise, and recovery. The exercise protocol consisted of 5-min intervals with 4.5, 6, 7.5, and 9 W workload followed by 9-min recovery. Changes in PCr and inorganic phosphate (Pi) were determined as percent changes in comparison to the baseline. In addition, pH values were calculated. This study obtained significant decreases in PCr corresponding to the gradual increases in workload. In each workload level that was succeeded by all volunteers, PCr hydrolysis passed into a steady state. After an early biphasic response, we detected a significant decrease in pH from the first to the second minute of the 6-W workload level followed by a further continuous decrease in pH up to the second minute of the recovery phase. The decrease in pH was not accompanied by acceleration in PCr hydrolysis. In conclusion, this study shows that PCr hydrolysis during incremental plantar flexion exercises passes into a steady state at different workload levels. The observed decrease in pH does not result in acceleration of PCr hydrolysis.     

Cardiac phosphorus-31 two-dimensional chemical shift imaging in patients with hereditary hemochromatosis

Hemochromatosis is a hereditary iron overload syndrome characterized by increased iron storage, followed by liver cirrhosis and is often associated with restrictive cardiomyopathy. The purpose of this study was to detect alterations of cardiac high-energy phosphate metabolism in patients with hereditary hemochromatosis (HHC) prior to the development of structural heart diseases. Therefore cardiac phosphorus-31 two-dimensional chemical shift imaging ((31)P 2D CSI) was employed. Twenty-four male patients (mean age 47.2 +/- 12 years) homozygous for the C282Y mutation in the hemochromatosis associated HFE gene and twenty-four male healthy volunteers (mean age 47 +/- 11 years) as age-matched controls were included in this study. Using a 1.5-Tesla whole-body magnetic resonance scanner, electrocardiograph-triggered transversal 31P 2D CSI was performed. Left ventricle mean phosphocreatine (PCr) to beta-adenosine triphosphate (beta-ATP) ratios of patients with HHC (1.60 +/- 0.41) were significantly decreased in comparison to healthy volunteers (1.93 +/- 0.36; p = 0.004). Furthermore, we detected moderate, negative correlations between left ventricular PCr to beta-ATP ratios and transferrin saturation, cholesterol, low-density lipoprotein as well as triglyceride. This study shows that 31P 2D CSI permits the detection of alterations of cardiac high-energy phosphate metabolism in patients with HHC, but without any evidence for heart disease. The decreased PCr to beta-ATP ratios in HHC might be caused by mitochondrial impairment due to cardiac iron overload.     

2,4‐Disila‐1,3,5‐oxadiazin,Cyclodisilazan‐Carbonsäure‐silylamid und ‐silylester

The lithium salts of the Me₃Si‐ as well as Me₃Si‐ and Me₂SiF‐substituted Cyclotrisilazanes I and II react with tert‐butylacylchloride under ring contraction and formation of the cyclodisilazane‐silylester, Me₃SiN(SiMe₂–N)₂SiMe₂–O–CO–CMe₃ ( 1 ). The lithium salt of the fluorodi‐methylsilyl‐substituted cyclotrisilazan III forms with benzoylchloride primarily in the analogous reaction the carboxy‐silyl‐amide, Me₂SiF(N–SiMe₂)₂SiMe₂–NH–CO–C₆H₅⁺ ( 2 ), which can be converted with III and benzoylchloride into the cyclodisilazane‐silylester, Me₂SiF(NSiMe₂)₂SiMe₂–O–CO–C₆H₅, ( 3 ). A silylester substituted six‐membered disila‐oxadiazine ( 4 ) is the result of the reaction of the lithiated cyclotrisilazane, (Me₂SiNH)₂, (Me₂SiNLi) with tert‐butyl‐acylchloride. The reaction includes anionic ring contraction and can be rationilized by a process analogous to keto‐enol‐tautomerism. Dilithiated octamethyl‐cyclotetrasilazane, (Me₂SiNHMe₂SiNLi)₂, reacts with tert‐butyl‐acylchloride or benzoylchloride in a molar ratio 1:2 to yield symmetrically acylestersubstituted cyclodisilazanes, (RCO–O–SiMe₂–NSiMe₂)₂, R = C₆H₅ ( 5 ), CMe₃ ( 6 ). The reaction mechanisms are discussed and the crystal structures of 2 and 6 are reported.     

Modelling of Technical Systems: Application to Hydrodynamic Torque Converters and Couplings

First a short survey of modelling of technical systems is presented. The different methods of modelling are applied to hydrodynamic torque converters and couplings. The results of linear modelling around an operating point, of nonlinear modelling for larger operating areas and of hybrid modelling using simplified physical laws are illustrated. Simulations for large excitations show the validity of the models. The advantages and disadvantages of the different methods are discussed.     

Impact of aging on cardiac high-energy phosphate metabolism determined by phosphorus-31 2-dimensional chemical shift imaging (31P 2D CSI)

Previous echocardiographic and experimental animal studies have shown that cardiac function, structure, and metabolism change with age. The aim of this study was to evaluate the impact of age on left ventricular high-energy phosphate metabolism. Using a 1.5 Tesla whole-body MR scanner 31P 2D CSI (8 x 8 phase encoding steps, 320 mm field of view) was performed in 76 healthy male volunteers (41.7 +/- 13 years) without any history of coronary heart disease. Fourier interpolation, corrections for T1 saturation effects, the nucleus Overhauser effect, and the blood contamination were applied to the spectroscopic data. The volunteers were divided into two groups, younger (n = 37) and older (n = 39) than 41.7 years. In all volunteers, laboratory specimen were sampled, and transthoracal echocardiography was carried out. Significant differences in left ventricular phosphocreatine (PCr) to beta-adenosine-triphosphate (beta-ATP) ratios (2.16 vs. 1.83, p < 0.001), fasting serum glucose levels (83.3 vs. 98.7 mg/dl, p < 0.001), E/A (1.51 vs. 1.14 p < 0.001), and ejection fraction (EF, 65.3 vs. 59.9%, p = 0.005) were detected between the two groups of volunteers, younger and older than 41.7 years. Moreover, age correlated moderately to well with left ventricular PCr to beta-ATP ratios (r = -0.44), fasting serum glucose levels (r = 0.4), E/A (r = -0.7), left ventricular myocardial mass (r = -0.41), and EF (r = -0.55). In conclusion, our study shows that left ventricular PCr to beta-ATP ratios decrease moderately with age, as suggested by previous experimental animal studies. Additionally, age correlates negatively with E/A, left ventricular myocardial mass, and EF, as reported by previous echocardiography studies. The present study is the first to show the impact of age on left ventricular PCr to beta-ATP values in humans.     

Cyclosilazanes and borazines: polymer precursors to silicon‐ and boron‐containing ceramics

The chemistry of cyclosilazanes and borazines is a topic of current interest in view of preceramic polymers which yield on pyrolysis various useful ceramic materials, e.g. silicon and boron carbide, silicon and boron nitride, and ternary or quaternary mixtures of these materials. These materials are hard and have high oxidative and thermal stability. Other useful properties are resistance to corrosion, thermal shock and creep, low electrical conductivity and low coefficient of thermal expansion. One of the best application prospects is the use of the preceramic polymers as protective coating material for carbon fibres. Copyright © 2000 John Wiley & Sons, Ltd.