Wheeled PROPs, graph complexes and the master equation

We introduce and study wheeled PROPs, an extension of the theory of PROPs which can treat traces and, in particular, solutions to the master equations which involve divergence operators. We construct a dg free wheeled PROP whose representations are in one-to-one correspondence with formal germs of SP-manifolds, key geometric objects in the theory of Batalin-Vilkovisky quantization. We also construct minimal wheeled resolutions of classical operads Com and Ass as rather non-obvious extensions of Com_infty and Ass_infty, involving, e.g., a mysterious mixture of associahedra with cyclohedra. Finally, we apply the above results to a computation of cohomology of a directed version of Kontsevich's complex of ribbon graphs.Comment: LaTeX2e, 63 pages; Theorem 4.2.5 on bar-cobar construction is strengthene

Frobenius manifold structures on the spaces of abelian integrals

Frobenius manifold structures on the spaces of abelian integrals were constructed by I. Krichever. We use D-modules, deformation theory, and homological algebra to give a coordinate-free description of these structures. It turns out that the tangent sheaf multiplication has a cohomological origin, while the Levi-Civita connection is related to 1-dimensional isomonodromic deformations.Comment: Expanded version. The case of an abelian integral with multiple poles is treated. Other minor improvements. Final versio

Weak localization of holes in high-mobility heterostructures

Theory of weak localization is developed for two-dimensional holes in semiconductor heterostructures. Ballistic regime of weak localization where the backscattering occurs from few impurities is studied with account for anisotropic momentum scattering of holes. The transition from weak localization to anti-localization is demonstrated for long dephasing times. For stronger dephasing the conductivity correction is negative at all hole densities due to non-monotonous dependence of the spin relaxation time on the hole wavevector. The anomalous temperature dependent correction to the conductivity is calculated. We show that the temperature dependence of the conductivity is non-monotonous at moderate hole densities.Comment: 5 pages, 4 figure

Interval total colorings of graphs

A total coloring of a graph $G$ is a coloring of its vertices and edges such that no adjacent vertices, edges, and no incident vertices and edges obtain the same color. An \emph{interval total $t$-coloring} of a graph $G$ is a total coloring of $G$ with colors $1,2,\...,t$ such that at least one vertex or edge of $G$ is colored by $i$, $i=1,2,\...,t$, and the edges incident to each vertex $v$ together with $v$ are colored by $d_{G}(v)+1$ consecutive colors, where $d_{G}(v)$ is the degree of the vertex $v$ in $G$. In this paper we investigate some properties of interval total colorings. We also determine exact values of the least and the greatest possible number of colors in such colorings for some classes of graphs.Comment: 23 pages, 1 figur

Inducing Barbero-Immirzi Connections along SU(2)-reductions of Bundles on Spacetime

We shall present here a general apt technique to induce connections along bundle reductions which is different from the standard restriction. This clarifies and generalizes the standard procedure to define Barbero-Immirzi (BI) connection, though on spacetime. The standard spacial BI connection used in LQG is then obtained by its spacetime version by standard restriction. The general prescription to define such a reduced connection is interesting from a mathematical viewpoint and it allows a general and direct control on transformation laws of the induced object. Moreover, unlike what happens by using standard restriction, we shall show that once a bundle reduction is given, then any connection induces a reduced connection with no constraint on the original holonomy as it happens when connections are simply restricted.Comment: 6 pages, some comments adde

Coordination Methods and Forms

The problem of behavior, action-reaction coordination remains its actuality for regulation and managing  by social subjects. The decision by different methodology approaches in sciences and practice seeks its true efficiency proofing. Efficiency providing needs by management tasks technology rationality. Classifying measures became a ground coordination problem solution

Classification and Volume Coordination Tasks of Organization Activity and Behavior

Based on the process approach, the article classifes the types of coordination tasks of different complexity and forms. Factors of influence on labor intensity of coordination tasks of activities and behavior are identifed. It is proposed to group factors of influence on the standard of manageability in connection with the solution of coordination tasks. The need and composition of the tasks of using informal relations and structure in coordination are justifed

Long-term Dynamics of the Electron-nuclear Spin System of a Semiconductor Quantum Dot

A quasi-classical theoretical description of polarization and relaxation of nuclear spins in a quantum dot with one resident electron is developed for arbitrary mechanisms of electron spin polarization. The dependence of the electron-nuclear spin dynamics on the correlation time $\tau_c$ of electron spin precession, with frequency $\Omega$, in the nuclear hyperfine field is analyzed. It is demonstrated that the highest nuclear polarization is achieved for a correlation time close to the period of electron spin precession in the nuclear field. For these and larger correlation times, the indirect hyperfine field, which acts on nuclear spins, also reaches a maximum. This maximum is of the order of the dipole-dipole magnetic field that nuclei create on each other. This value is non-zero even if the average electron polarization vanishes. It is shown that the transition from short correlation time to $\Omega\tau_c>1$ does not affect the general structure of the equation for nuclear spin temperature and nuclear polarization in the Knight field, but changes the values of parameters, which now become functions of $\Omega\tau_c$. For correlation times larger than the precession time of nuclei in the electron hyperfine field, it is found that three thermodynamic potentials ($\chi$, $\bm{\xi}$, $\varsigma$) characterize the polarized electron-nuclear spin system. The values of these potentials are calculated assuming a sharp transition from short to long correlation times, and the relaxation mechanisms of these potentials are discussed. The relaxation of the nuclear spin potential is simulated numerically showing that high nuclear polarization decreases relaxation rate.Comment: RevTeX 4, 12 pages, 9 figure

Structural adaptation of Salsola soda L. (Chenopodiaceae) from inland and maritime saline area

The microscopic analysis of leaf and stem in two populations of Salsola soda was carried out in order to examine mechanism of anatomical adaptations to environmental condition on saline habitats and to determine if there exists a morpho-anatomical differentiation between populations from maritime and inland saline area. Analysis included 26 quantitative characters of leaf and stem. The results showed that both populations exhibited halomorphic and xeromorphic adaptations, which refered to ecological plasticity and adaptations of plants to their habitats. Our research also showed that S. soda had quite a stable morphoanatomical structure, since only quantitative changes were recorded. [Projekat Ministarstva nauke Republike Srbije, br. 173002

One-dimensional Chern-Simons theory

We study a one-dimensional toy version of the Chern-Simons theory. We construct its simplicial version which comprises features of a low-energy effective gauge theory and of a topological quantum field theory in the sense of Atiyah.Comment: 37 page