Young measures generated by a class of integrands: a narrow epicontinuity and applications to Homogenization

Given a subset E of convex functions from into which satisfy growth conditions of order p>1 and an open bounded subset of , we establish the continuity of a map μΦ_μ from the set of all Young measures on equipped with the narrow topology into a set of suitable functionals defined in and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization.     

Exact Values of Widths of Classes of Analytic Functions on the Disk and Best Linear Approximation Methods

In the Hardy space H _p, (p1, 0< 1, H _p,1 H _p) we develop best linear approximation methods (previously studied by Taikov and Ainulloev) for the classes W(r,,) of analytic functions on the unit disk and calculate the exact values of linear, Gelfand, and informational n-widths of these classes.     

用迈克耳孙干涉仪测量杨氏模量

提出用迈克耳孙干涉仪测金属杨氏模量的新方法,并从实验上测定了碳钢丝的杨氏模量。     

用动力学法测杨氏模量实验及其实验装置的研制

介绍了新研制的用动力学法杨氏模量的实验装置,它具有功耗低,灵敏度高的特点;教学中测量悬线不同位置时的共振频率,用作图法拟合出其精确值,以减少由于悬线不在节点引起的系统性误差,测量精密度比传统的静态拉伸法高一个量级以上。     

Elastic constants of lead-bismuth alloys

A study of ultrasonic velocities and internal friction has been carried out in Pb-Bi alloys in the concentration range of 0 to 49.5 atomic % Bi using the composite oscillator technique. From the velocity and density data a set of elastic constants namely, Young’s modulus, rigidity modulus, bulk modulus and Poisson’s ratio are estimated. The results are interpreted in terms of the phase changes occurring in the alloy system. Internal friction is found to be more sensitive than the elastic constants to the phase changes.     

Zum Fließverhalten kurzglasfasergefüllter Thermoplastschmelzen im stationären und instationären Bereich

Zusammenfassung Durch Zugabe von Glasfasern wird das rheologische Verhalten von Kunststoffschmelzen verändert. Kurzglasfasergefüllte Styrol-Acrylnitril-Copolymere mit verschiedenen Füllgraden wurden mit dem Rotations-und dem Kapillarrheometer untersucht. Sowohl im stationären Bereich als auch im instationären Bereich (Anlauf- und Abklingverhalten) sind Unterschiede zum ungefüllten Material festzustellen: Mit Zunahme des Faseranteils steigt der Schubmodul, und das viskoelastische Überschwingen wird geringer als bei ungefüllten Systemen. Erhöhung von Temperatur, Schergeschwindigkeit und Faseranteil führen zu einer Verkürzung der Relaxationszeiten, Steigerung des hydrostatischen Druckes erwartungsgemäß zu deren Verlängerung.

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Summary The rheological behaviour of polymer melts is changed by addition of glass fibres. Experiments were conducted with styrene-acrylonitrile copolymers filled with various amounts of short fibres on a rotational and a capillary rheometer, both under steadystate and transient conditions. It is observed that by adding fibres the shear modulus increases but the stress overshoot decreases. With increase of temperature, shear rate and fibre content relaxation times become shorter whereas with higher hydrostatic pressures they grow longer, as is to be expected.

Mit 9 Abbildungen und 2 Tabellen     

On the least values of -norms for the Kontorovich–Lebedev transform and its convolution

We establish analogs of the Hausdorff–Young and Riesz–Kolmogorov inequalities and the norm estimates for the Kontorovich–Lebedev transformation and the corresponding convolution. These classical inequalities are related to the norms of the Fourier convolution and the Hilbert transform in L_p spaces, 1p∞. Boundedness properties of the Kontorovich–Lebedev transform and its convolution operator are investigated. In certain cases the least values of the norm constants are evaluated. Finally, it is conjectured that the norm of the Kontorovich–Lebedev operator is equal to . It confirms, for instance, by the known Plancherel-type theorem for this transform when p=2.     

The Effect of Temperature on Lattice Mechanical Properties of Noble and Transition Metals

A simple pseudopotential model is used for the calculation of the temperature dependence of lattice mechanical properties which also depend on the phonon density of states such as lattice heat capacity C _V , Debye temperature _D, harmonic contribution to free energy, thermal pressure, isothermal bulk modulus corrected to the fourth order, volume thermal expansion coefficient , Debye-Waller factor, mean-square displacement, Debye-Waller temperature parameter, and X-ray characteristic temperature _M of Cu, Ag, Au, Ni, Pd, Pt, Rh, and Ir. The contribution of d-like electrons is taken into account by introducing repulsive short-range Born-Mayer-like term. Very recently proposed screening function due to Sarkar et al. has been used to obtain the screened form factor. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings show the ability of our model potential to reproduce wide class of properties in noble and transition metals.