Eugen Grycko

Classification with Set-Valued Decision Functions

An important variant of the classification problem can be formulated as follows: given a learning sample (supervised learning) a classifier shall be determined, whose probability of correct classification is a good approximation of the maximal (Bayesian) correct classification probability. If there is no parametric familiy available which encloses the class-specific distributions of the observable, then the statistician is forced to apply non-parametric procedures (e.g. density estimators).

On Voltage and Power Indicators for Thermal Noise in Metals

Recently a formula for the variance of the thermal voltage between the ends of a conductor has been proposed. We discuss this formula and present numerical values of theoretic voltage and power indicators for a selection of metals. The values obtained for copper are compared with some empirical data. AMS Subject Classification: 83B30, 83B31

Selected Phenomena of Spontaneous Electric Noise

Recently a modified Drude model of the valence electron gas in metals was investigated mathematically. The implications of this model suggest that the thermal noise voltage increases for example with the length of the metallic conductor. This observation prompted us to carry out some innovative experiments whose outcomes confirmed qualitatively the Drude model. We discuss some implications of this model in the light of the performed measurements.

On a Statistical Interrelation Between Boiling Point and Debye Temperature

Debye temperature Θ D of a substance plays a role in Solid State Theory; its experimental determination however requires a sophisticated device such that the value of Θ D is not available for many substances. A statistical possibility of approximation of Θ D is presented for substances whose boiling point and molecular mass are known. This approximation is based on the notion of zero entropy temperature, which serves as a regressor; statistical considerations reveal a strong correlation between the regressor and Debye temperature. This result can be interpreted as a bridge between Fluid and Solid State Theories.