Density of rational points on Enriques surfaces

Let $X$ be an Enriques surface defined over a number field $K$. Then there exists a finite extension $K'/K$ such that the set of $K'$-rational points of $X$ is Zariski dense.Comment: 8 pages, LaTe

Luttinger-liquid-like transport in long InSb nanowires

Long nanowires of degenerate semiconductor InSb in asbestos matrix (wire diameter is around 50 \AA, length 0.1 - 1 mm) were prepared. Electrical conduction of these nanowires is studied over a temperature range 1.5 - 350 K. It is found that a zero-field electrical conduction is a power function of the temperature $G\propto T^\alpha$ with the typical exponent $\alpha \approx 4$. Current-voltage characteristics of such nanowires are found to be nonlinear and at sufficiently low temperatures follows the power law $I\propto V^\beta$. It is shown that the electrical conduction of these nanowires cannot be accounted for in terms of ordinary single-electron theories and exhibits features expected for impure Luttinger liquid. For a simple approximation of impure LL as a pure one broken into drops by weak links, the estimated weak-link density is around $10^3-10^4$ per cm.Comment: 5 pages, 2 figure

Late Jurassic of the Russian platform: Ammonite evolution and paleoenvironments

Κατά το τέλος το Αν. Ιουρασικού, στην Κεντρική Ρωσική λεκάνη έχει καταγραφεί μια σημαντική μείωση στην ποικιλότητα των αμμωνιτοειδών και έντονες μεταβολές στους μορφότυπους των οστράκων των αμμωνιτών. Κατά το τέλος του Βολγίου, οι αμμωνίτες αντιπροσωπεύονται από δύο μόνο γένη, που ανήκουν σε μία οικογένεια και τα οποία παρουσιάζουν μεγάλες μορφολογικές διαφορές στα όστρακα τους. Η μείωση της βιοποικιλότητας των αμμωνιτοειδών που παρατηρείται στο τέλος του Ιουρασικού, ξεκίνησε στο μέσο Βόλγιο και συσχετίζεται κυρίως με πτώση της θαλάσσιας στάθμηςDuring the terminal age of Late Jurassic a considerable decrease in ammonoid taxonomic diversity and distinct changes of ammonite shell morphotypes are recorded in the Central Russian Basin. By the end-Volgian, ammonites are represented by only two genera belonging to a single family, which differ markedly in their shell form. The end-Jurassic decrease in ammonoid biodiversity started in the mid-Volgian and is correlated first of all with shallowing of the se

Optical properties of small polarons from dynamical mean-field theory

The optical properties of polarons are studied in the framework of the Holstein model by applying the dynamical mean-field theory. This approach allows to enlighten important quantitative and qualitative deviations from the limiting treatments of small polaron theory, that should be considered when interpreting experimental data. In the antiadiabatic regime, accounting on the same footing for a finite phonon frequency and a finite electron bandwidth allows to address the evolution of the optical absorption away from the well-understood molecular limit. It is shown that the width of the multiphonon peaks in the optical spectra depends on the temperature and on the frequency in a way that contradicts the commonly accepted results, most notably in the strong coupling case. In the adiabatic regime, on the other hand, the present method allows to identify a wide range of parameters of experimental interest, where the electron bandwidth is comparable or larger than the broadening of the Franck-Condon line, leading to a strong modification of both the position and the shape of the polaronic absorption. An analytical expression is derived in the limit of vanishing broadening, which improves over the existing formulas and whose validity extends to any finite-dimensional lattice. In the same adiabatic regime, at intermediate values of the interaction strength, the optical absorption exhibits a characteristic reentrant behavior, with the emergence of sharp features upon increasing the temperature -- polaron interband transitions -- which are peculiar of the polaron crossover, and for which analytical expressions are provided.Comment: 16 pages, 6 figure

Remarks on endomorphisms and rational points

Let X be a variety over a number field and let f: X --> X be an "interesting" rational self-map with a fixed point q. We make some general remarks concerning the possibility of using the behaviour of f near q to produce many rational points on X. As an application, we give a simplified proof of the potential density of rational points on the variety of lines of a cubic fourfold (originally obtained by Claire Voisin and the first author in 2007).Comment: LaTeX, 22 pages. v2: some minor observations added, misprints corrected, appendix modified

Endomorphisms of abelian varieties, cyclotomic extensions and Lie algebras

We prove an analogue of the Tate conjecture on homomorphisms of abelian varieties over infinite cyclotomic extensions of finitely generated fields of characteristic zero.Comment: 9 page

Modeling of high energy impact on ice in taking into account the temperature

In this paper, the problems deep penetration of compact impactors into the ice, taking into account different temperatures were solved. The behavior of ice is described by the basic system equations of continuum mechanics, i.e., the equations of continuity, momentum and energy in the lagrangian approach. Medium are compressible, isotropic, no mass forces, internal sources of heat and thermal conductivity. Medium also includethe shockwave phenomena, as well as formation “spall” and “shear” damage. The stress tensor is divided into deviatoric and spherical components. Equation of statewas chosen in the form of Walsh. The components of the stress tensor deviator located on the elasticplastic flow model based on the equations of Prandtl-Reis associated with von Mises yield criterion. Initial impactor velosity was varied atfrom 50 to 325 m/s. Numerical simulation results showed the influence of temperature of the ice to the depth of penetration of the impactors

Safety verification of nonlinear hybrid systems based on invariant clusters

In this paper, we propose an approach to automatically compute invariant clusters for nonlinear semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u→, x→) = 0, parametric in u→, which can yield an infinite number of concrete invariants by assigning different values to u→ so that every trajectory of the system can be overapproximated precisely by the intersection of a group of concrete invariants. For semialgebraic systems, which involve ODEs with multivariate polynomial right-hand sides, given a template multivariate polynomial g(u→, x→), an invariant cluster can be obtained by first computing the remainder of the Lie derivative of g(u→, x→) divided by g(u→, x→) and then solving the system of polynomial equations obtained from the coefficients of the remainder. Based on invariant clusters and sum-of-squares (SOS) programming, we present a new method for the safety verification of hybrid systems. Experiments on nonlinear benchmark systems from biology and control theory show that our approach is efficient

Устойчивость одной модели нейрона на основе уравнения с запаздыванием

We analyze the periodical solution of a differential equation with delay describing the neuron-autogenerator dynamics. The stability of the periodical solution of the equation with certain param¬eters is investigated.Проводится анализ решения дифференциального уравнения с запаздыванием, описывающего динамику нейрона-автогенератора. Рассмотрен вопрос устойчивости периодического решения уравнения при определенных значениях параметров