Mathematical Aspects of the Heap Paradox and the Hidden Parameter

Mathematical Notes -     

On the spectra of finite-dimensional quadratic Bose operators

A complete study of the spectrum of a finite-dimensional Bose operator is carried out in the paper. The cases in which the spectrum is discrete or continuous are studied. Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 835–854, June, 1997. Translated by A. M. Chebotarev     

Changes in the Laser-Induced Fluorescence Spectrum of Myocardium Tissue with Decrease in Its Viability

We investigated the laser-induced fluorescence spectra (LIF) of porcine cardiac tissues with different degrees of viability. The data obtained are compared with the results of routine histological investigations and also with the experiments performed with the use of fluorescent probes. It has been found with a high degree of reliability that the loss of the viability of the myocardium tissue leads to the alteration of its LIF spectra. This can be used for low-invasive rapid control of transplant viability in the process of its preparation and during surgery.     

Zeroth-order phase transitions and Zipf law quantization

From the standpoint of thermodynamic averaging of fission microprocesses, we investigate the origin of radioactive release in an NPP after an accident or after resource depletion. The genesis of the NPP release is interpreted as a new thermodynamic phenomenon, a zeroth-order phase transition. This problem setting results in a problem in probabilistic number theory. We prove the corresponding theorem leading to quantization of the Zipf law for the frequency of a zeroth-order phase transition with different values of the jump of the Gibbs thermodynamic potential. We introduce the notion of hole dimension. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 118–142, January, 2007.     

Observation of a “giant” step of the field electron emission current from a high-temperature superconductor

An abrupt rise of the field electron emission (FEE) current from a high-temperature superconductor (HTSC) being in the normal state has been detected. The current amplification with a factor reaching ∼10⁶ occurs as an HTSC emitter is heated in the temperature range 110–170 K. The features of the temperature dependence of FEE are discussed. Measured parameters of the effect observed are presented. Possible mechanisms of the process under consideration are discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 13–16, May, 2007.