Discrete convexity and unimodularity. I

In this paper we develop a theory of convexity for a free Abelian group M (the lattice of integer points), which we call theory of discrete convexity. We characterize those subsets X of the group M that could be call "convex". One property seems indisputable: X should coincide with the set of all integer points of its convex hull co(X) (in the ambient vector space V). However, this is a first approximation to a proper discrete convexity, because such non-intersecting sets need not be separated by a hyperplane. This issue is closely related to the question when the intersection of two integer polyhedra is an integer polyhedron. We show that unimodular systems (or more generally, pure systems) are in one-to-one correspondence with the classes of discrete convexity. For example, the well-known class of g-polymatroids corresponds to the class of discrete convexity associated to the unimodular system A_n:={\pm e_i, e_i-ej} in Z^n.Comment: 26 pages, Late

Luminescence Solvato- and Vapochromism of Alkynyl-Phosphine Copper Clusters

The reaction of [Cu(NCMe)4][PF6] with aromatic acetylenes HC2R and triphosphine 1,1,1-tris(diphenylphosphino)methane in the presence of NEt3 results in the formation of hexanuclear Cu(I) clusters with the general formula [Cu6(C2R)4{(PPh2)3CH}2][PF6]2 (R = 4-X-C6H4 (1-5) and C5H4N (6); X = NMe2 (1), OMe (2), H (3), Ph (4), CF3 (5)). The structural motif of the complexes studied consists of a Cu6 metal core supported by two phosphine ligands and stabilized by σ- and π-coordination of the alkynyl fragments (together with coordination of pyridine nitrogen atoms in cluster 6). The solid state structures of complexes 2-6 were determined by single crystal XRD analysis. The structures of the complexes in solution were elucidated by (1)H, (31)P, (1)H-(1)H COSY NMR spectroscopy, and ESI mass spectrometry. Clusters 1-6 exhibit moderately strong phosphorescence in the solid state with quantum yields up to 17%. Complexes 1-5 were found to form solvates (acetone, acetonitrile) in the solid state. The coordination of loosely bound solvent molecules strongly affects emission characteristics and leads to solvato- and vapochromic behavior of the clusters. Thus, solvent-free and acetonitrile solvated forms of 3 demonstrate contrasting emission in orange (615 nm) and blue (475 nm) regions, respectively. The computational studies show that alkynyl-centered IL transitions mixed with those of MLCT between the Cu6 metal core and the ligand environment play a dominant role in the formation of excited states and can be considerably modulated by weakly coordinating solvent molecules leading to luminescence vapochromism.This research has been supported by St. Petersburg State University Research Grant 0.37.169.2014, and Russian Foundation for Basic Research Grants 13-03-00970, 14-03-32077, and 13-03-12411. Academy of Finland (Grant 268993/2013, I.O.K), University of Eastern Finland (strategic funding—Russian–Finnish collaborative project), is also gratefully acknowledged. The work was carried out using equipment of the Analytical Center of Nano- and Biotechnologies of SPbSPU with financial support of the Ministry of Education and Science of Russian Federation; Centers for Magnetic Resonance, X-ray Diffraction Studies, Chemical Analysis and Materials Research, Optical and Laser Materials Research; and Computer Center of St. Petersburg State University

Multivariate Lorenz dominance based on zonoids

Multivariate Lorenz order, Directional majorization, Price Lorenz order, Generalized Lorenz function, Multidimensioned Gini index,

РАЗРАБОТКА АЛГОРИТМОВ МОДЕЛИРОВАНИЯ РАБОТЫ ДАТЧИКОВ РАСХОДА ТОПЛИВА И ВЗАИМОДЕЙСТВИЯ С ТОПЛИВНОЙ МАГИСТРАЛЬЮ

In this article the construction principles of device function modeling algorithms of the fuel charge are considered. The functioning dynamic models of parameters measurement systems of fuel are submitted.Анотаці

The octahedron recurrence and RSK-correspondence

In [2] we proposed a new approach to the RSK (Robinson-Schensted-Knuth) correspondence based on bi-crystal structure of arrays. However, it was not easy to compare our construction with the classical one. The point is that the classical RSKcorrespondenc