Parabolic Singular Integrals in Probability Theory

The final aim of this work is to prove the Central Limit Theorem described in the motivations given below. The key for that is a Resolvant estimate, of the type of Theorem 1.1 in [21], adapted for the Parabolic Green function G(X, Y) which is the heat diffusion kernel in some domain Ω in time-space: i.e. we must estimate ${\int_{\Omega}\nabla_{Y}G(X, Y)\nabla_{Y}^{2}G(Y,Z)\;dY}The final aim of this work is to prove the Central Limit Theorem described in the motivations given below. The key for that is a Resolvant estimate, of the type of Theorem 1.1 in [21], adapted for the Parabolic Green function G(X, Y) which is the heat diffusion kernel in some domain Ω in time-space: i.e. we must estimate ò_W?_YG(X, Y)?_Y²G(Y,Z)  dY{\int_{\Omega}\nabla_{Y}G(X, Y)\nabla_{Y}^{2}G(Y,Z)\;dY}. Exactly as the estimate in [21] is based on [10] our estimate here is based on the main Theorem of this paper. This main theorem refers to rough singular integrals on the Gaussian potential on ∂Ω.     

Grundlagen der Mehrstoffanalyse mit Elektronen- und ß-Strahlung,II. Experimentelle Untersuchungen zur effektiven Kernladungszahl für den Rückstreuprozeß

Messungen un Bleiverbindungen und wassersloffhaltigen stoffen mit β-Strahlung im Energiebereich von 0,2 bis 3 MeV zeigen, daβ die in Teil I abgeleitete Formel für die Ermittlung der Effektiven Kernladungszahl selbst bei Medien extremer Zusammensetzung anwendbar ist. Die in der Literatur häufig erwāhnten Abweichungen der errechneten Kernladungszahlen von den experimentell ermittelten Ergebnissen sind hauptsächlich auf unterschiedliche Probendichte und auf die Korngröβe der Proben zurückzuführen. In der vorliegenden Arbeit sind derartige Störungen durch entsprechende Auswahl der Meβbedingungen vermieden oder durch empirische korrekturen eliminiert worden.     

15Nmethacetin test to control liver function of infants with formerly very low birth weight

Abstract

Hepatic detoxification capacities of three groups of infants aged about two were estimated using the [¹⁵N]methacetin elimination test, as well as standard serum parameters:

1. Formerly hypotrophically born infants still too small for their age (n = 23)

2. Patients suffering from severe liver diseases (n = 15)

3. Patients without liver diseases (n = 14).

17 of the infants of group 1 showed ¹⁵N elimination rates as low as the rates of the liver-diseased patients of group 2. Compared to the infants of group 3, who had normal values, the findings reflect diminished hepatic monooxygenases activities in groups 1 and 2. On the other hand, the serum parameters of the infants of group 1 did not deviate from normal values estimated in group 3. Here only group 2 showed pathological values. Consequently, the [¹⁵N]methacetin test seems to be more sensitive in controlling hepatic parameters of growth retardations than the usual serum parameters used here. Further investigations have to answer the question to which proportion intrauterine malnutrition and postnatal effects, such as environmental living conditions, contribute to the retardation of liver function development in combination with growth retardation.     

7 T versus 3 T contrast-enhanced breast Magnetic Resonance Imaging of invasive ductulolobular carcinoma: First clinical experience

Purpose

Here we describe our first experience with contrast-enhanced (CE) MRI of breast cancer at 7 tesla (T), compared to 3 T and histopathology.

Materials and Methods

A 52 year old female patient with a mammographically suspicious breast mass (BI-RADS V) underwent 7 T CE-MRI. Results were described according to the BI-RADS-MRI criteria and compared to 3 T and histopathology.

Results

After contrast administration, a homogeneously enhancing, irregular spiculated mass was depicted at both 3 T and 7 T; sizes were identical. The most malignant kinetic curve was characterized by a rapid initial rise followed by a wash-out pattern in the delayed phase, i.e. a type 3 curve, at both field strengths. Even though T1-effects of contrast agents are suggested to be reduced at higher fields, quantification of contrast enhancement-to-noise ratio showed a ratio of 4.6 at 7 T and 2.8 at 3 T when comparing contrast-to-noise of the mass before and after contrast administration. Both examinations, using a single dose of gadolinium-based contrast agent, achieved good image quality. Final histopathological evaluation showed an invasive ductulolobular carcinoma with an intraductal component.

Conclusion

This initial experience suggests that clinical contrast-enhanced 7 T MRI of the breast is technically feasible and may allow BI-RADS-conform analysis.     

Study of semiconductor lasers under simultaneous uniaxial stress and hydrostatic pressure

Abstract

We present the design of a device for the simultaneous application of uniaxial stress and hydrostatic pressure. This new apparatus will for the first time allow measurements at constant strain. Results of the simultaneous application of uniaxial stress and hydrostatic pressure to a semiconductor laser are presented and discussed.     

Optical,magneto-optical and structural properties of F centres in BaFBr

Abstract

In BaFBr, a material which can be used as a storage phosphor for X-rays, two types of F centres can be created by additive coloration or by X-irradiation. The properties of both F centres which play an important role in the storage phosphor mechanism were investigated with optical and magneto-optical methods. The absorption bands, the emission bands, production, and stability of the F centres are discussed.     

Implicit multifunction theorems in complete metric spaces

In this paper, we establish some new characterizations of metric regularity of implicit multifunctions in complete metric spaces by using lower semicontinuous envelopes of the distance functions to set-valued mappings. Through these new characterizations it is possible to investigate implicit multifunction theorems based on coderivatives and on contingent derivatives as well as the perturbation stability of implicit multifunctions.     

Lagrange and hermite interpolation by bivariate splines

We develop methods for constructing sets of points which admit Lagrange and Hermite type interpolation by spaces of bivariate splines on rectangular and triangular partitions which are uniform, in general. These sets are generated by building up a net of lines and by placing points on these lines which satisfy interlacing properties for univariate spline spaces.     

Shell models of magnetohydrodynamic turbulence

Shell models of hydrodynamic turbulence originated in the seventies. Their main aim was to describe the statistics of homogeneous and isotropic turbulence in spectral space, using a simple set of ordinary differential equations. In the eighties, shell models of magnetohydrodynamic (MHD) turbulence emerged based on the same principles as their hydrodynamic counter-part but also incorporating interactions between magnetic and velocity fields. In recent years, significant improvements have been made such as the inclusion of non-local interactions and appropriate definitions for helicities. Though shell models cannot account for the spatial complexity of MHD turbulence, their dynamics are not over simplified and do reflect those of real MHD turbulence including intermittency or chaotic reversals of large-scale modes. Furthermore, these models use realistic values for dimensionless parameters (high kinetic and magnetic Reynolds numbers, low or high magnetic Prandtl number) allowing extended inertial range and accurate dissipation rate. Using modern computers it is difficult to attain an inertial range of three decades with direct numerical simulations, whereas eight are possible using shell models.