Kahler-Einstein metrics on log del Pezzo surfaces in weighted projective 3-spaces

We determine the complete list of anticanonically embedded quasi smooth log del Pezzo surfaces in weighted projective 3-spaces. We prove that many of these admit a K\"ahler-Einstein metric and most of them do not have tigers.Comment: 10 pages, LaTe

Measurement of Light Intensity Based on a Flip-flop Sensor

This paper deals with a new type of system for measuring light intensity with the use of a flip-flop sensor controlled by a so-called slow-rise voltage control pulse. A photodiode was used for quantification of the measured light intensity in the structure of the flip-flop. The theoretical considerations are compared with experimental results, and good agreement is reported

Directional correlations in quantum walks with two particles

Quantum walks on a line with a single particle possess a classical analogue. Involving more walkers opens up the possibility of studying collective quantum effects, such as many-particle correlations. In this context, entangled initial states and the indistinguishability of the particles play a role. We consider the directional correlations between two particles performing a quantum walk on a line. For non-interacting particles, we find analytic asymptotic expressions and give the limits of directional correlations. We show that by introducing delta-interaction between the particles, one can exceed the limits for non-interacting particles

Numerical modelling of electric conductance of a thin sheet

In this paper the numeric modelling of total resistance of a thin sheet, with local conductivity in randomly distributed grains higher then is that of the basic matrix, is presented. The 2D model is formed by a structure of longitudinal and transversal conductors interconnected in nodes of a square net. In all nodes, using iteration procedure, the potential is determined from which the conductance of sheet is computed between two touching electrodes. The described model can be used to imitate the behaviour of heterogeneous thin conducting sheets prepared by different techniques. The model was verified in some cases where the net resistance is well known from the theory

Full-revivals in 2-D Quantum Walks

Recurrence of a random walk is described by the Polya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full-revival of its quantum state. Localization for two dimensional quantum walks is known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. We show on the example of the 2-D Grover walk that one can exploit the effect of localization to construct stationary solutions. Moreover, we find full-revivals of a quantum state with a period of two steps. We prove that there cannot be longer cycles for a four-state quantum walk. Stationary states and revivals result from interference which has no counterpart in classical random walks

The cone of curves of Fano varieties of coindex four

We classify the cones of curves of Fano varieties of dimension greater or equal than five and (pseudo)index dim X -3, describing the number and type of their extremal rays.Comment: 27 pages; changed the numbering of Theorems, Definitions, Propositions, etc. in accordance with the published version to avoid incorrect reference

Log Fano varieties over function fields of curves

Consider a smooth log Fano variety over the function field of a curve. Suppose that the boundary has positive normal bundle. Choose an integral model over the curve. Then integral points are Zariski dense, after removing an explicit finite set of points on the base curve.Comment: 18 page

Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry

Assuming the standard framework of mirror symmetry, a conjecture is formulated describing how the diffeomorphism group of a Calabi-Yau manifold Y should act by families of Fourier-Mukai transforms over the complex moduli space of the mirror X. The conjecture generalizes a proposal of Kontsevich relating monodromy transformations and self-equivalences. Supporting evidence is given in the case of elliptic curves, lattice-polarized K3 surfaces and Calabi-Yau threefolds. A relation to the global Torelli problem is discussed.Comment: Approx. 20 pages LaTeX. One reference adde