Polyhedral billiards, eigenfunction concentration and almost periodic control

We study dynamical properties of the billiard flow on convex polyhedra away from a neighbourhood of the non-smooth part of the boundary, called ``pockets''. We prove there are only finitely many immersed periodic tubes missing the pockets and moreover establish a new quantitative estimate for the lengths of such tubes. This extends well-known results in dimension $2$. We then apply these dynamical results to prove a quantitative Laplace eigenfunction mass concentration near the pockets of convex polyhedral billiards. As a technical tool for proving our concentration results on irrational polyhedra, we establish a control-theoretic estimate on a product space with an almost-periodic boundary condition. This extends previously known control estimates for periodic boundary conditions, and seems to be of independent interest.Comment: 32 pages, a few sections reorganised and a few results adde

Cybernetic Education - a New Developmental Weapon in the 21st Century

A univalent, not multivalent, approach to the “concept” of strategic and geopolitical creation and management experiences a civilization twilight, i.e., a transitional discrepancy in the comprehension of cohabitation of education, development, and cohabitational dignity from an industrial to an informatical-technological 21stcentury civilization, as a struggle of unnatural and natural transition generators, i.e., as a clash of the rich and the poor in the realization of the truth pertinent to a democratic, global, and market-oriented society. The identification of a method and system for the registration of civilizational transitional ups and downs, as a new iconography of an ethical, evolutional, and ecumenical equilibrium of the essence of life in the 21st-century informatical-technological civilization, becomes the topic of the work of the 2nd Pan-European forum, the Croatia 2007 Symposium, titled Cybernetic Education — A New Developmental Weapon in the 21st Century, i.e., in a struggle against the incubation and explosion of the proper, foreign, and natant parasitism viri. The symposial Conclusion integrally promotes the role and importance of the “startup” strategy and geopolitics, as a new cybernetic-holistic etiquette and culture in an approach to the creation and management of a creative process in the 21stcentury transition.education, development, cybernetics, ecumenism, holism

Elementary Andreev Processes in a Driven Superconductor-Normal Metal Contact

We investigate the full counting statistics of a voltage-driven normal metal(N)-superconductor(S) contact. In the low-bias regime below the superconducting gap, the NS contact can be mapped onto a purely normal contact, albeit with doubled voltage and counting fields. Hence in this regime the transport characteristics can be obtained by the corresponding substitution of the normal metal results. The elementary processes are single Andreev transfers and electron- and hole-like Andreev transfers. Considering Lorentzian voltage pulses we find an optimal quantization for half-integer Levitons.Comment: 8 pages, 6 figures, contribution to the special issue in memory of Markus B\"uttiker, accepted at Physica

THE GROWING IMPORTANCE OF ACTIVITIES DIVERSIFICATION FOR ENHANCING FAMILY FARMS COMPETITIVENESS

Family farms are the most significant development entities of rural areas. The welfare of the rural population depends on the success of their business operations and ability to survive in the market. Bearing this in mind, it is necessary to find ways and create the adequate conditions to activate development potentials. The objective of this study is therefore to systematize potential sources of farm households’ income, with special emphasis on how and why they diversify their income and activities. Results of the research unambiguously show that diversification of income and activities are now integral part of business activities of numerous farms. No doubt, importance of diversification will increase in future period, considering that more dynamic development of farms is not possible without engagement of all potentials at their disposal.Diversification, Competitiveness, Family farms, Agribusiness, Farm Management, Labor and Human Capital,

Control of electron-hole pair generation by biharmonic voltage drive of a quantum point contact

A time-dependent electromagnetic field creates electron-hole excitations in a Fermi sea at low temperature. We show that the electron-hole pairs can be generated in a controlled way using harmonic and biharmonic time-dependent voltages applied to a quantum contact and obtain the probabilities of the pair creations. For a biharmonic voltage drive, we find that the probability of a pair creation decreases in the presence of an in-phase second harmonic. This accounts for the suppression of the excess noise observed experimentally [Gabelli and Reulet, arXiv:1205.3638] proving that dynamic control and detection of elementary excitations in quantum conductors are within the reach of the present technology.Comment: 4+ pages, 4 figures; to appear in PRB Rapid Communication

SUR L’INSCRIPTION DE MIHAJLO A STON

A côté de plusieurs lectures déjà publiées de l’ inscription latine de Ston, dans laquelle il est question d’ un certain MIHAELUS, l’ auteur propose la lecture suivante: (PRINCEPS) MIHAELVS FORTITER SVPER8AVIT) G(R)ECO PACIFICO CV(M) OM(NINE)S ROMANO(S) et traduit: »Le Duc Mihajlo a héroïquement triomphé du Grec Pacifico et des Romains (ou des soldats romains).« L’auteur pense que par une inscription en latin vulgaire on glorifie le Duc Mihajlo Višević, qui avait résidé à Ston et gouvernait le Zahumlje dans la première moitié du Xème siècle. Il lutta avec succès contre les Byzantins, et Pacificus a pu être le chef des Byzantins dont Mihajlo a triomphé. Ici GRAECI sont synonymes, car l’ Empire romain d’ Orient était Grec. Certains mots de l’ inscription auraient pu aussi se lire autrement (FORTITER – FORTI TER, SVPERAVIT- SUPER, GRECO- CECO, OMINES- OMNES, ROMANOS- ROMANO) mais, si MIHAELVS est le Duc Mihajlo Višević, et PACIFICO le nom d’ un officier byzantin, toutes ces variantes donneront toujours obligatoirement le même contenu historique