Tangent algebraic subvarieties of vector fields

An algebraic commutative group is associated to any vector field on a complete algebraic variety . The group acts on and its orbits are the minimal subvarieties of which are tangent to . This group is computed in the case of a vector field on .

     

Flexible contracting theory and case examples

When companies or governmental agencies arrange for contracts that call for deliveries over extended periods of time, arrangements are often made to adjust the final prices for exogenous changes in the costs of production. This paper shows, under specified conditions, how contracts can be devised which allow for price changes but at the same time still provide incentives for the producing unit to be efficient. For example, only under very specific conditions will a “pass-through” arrangement be acceptable. We show how the techniques of Geometric Programming applied to the economic theory of production can be used to analyze such problems.     

Some Basics on Privacy Techniques,Anonymization and their Big Data Challenges

With the progress in the information and communication fields, new opportunities and technologies for statistical analysis, knowledge discovery, data mining, and many other research areas have emerged, together with new challenges for privacy and data protection. Nowadays several personal records are kept in computerized databases. Personal data is collected and kept in census databases, medical databases, employee databases, among others. There has always been an asymmetry between the benefits of computerized databases and the rights of individual data subjects. Some data protection principles can be derived from the legal framework. In this survey, we present some basic cryptographic and non-cryptographic techniques that may be used for enhancing privacy, we focus mainly on anonymization in databases and networks, discuss some differences and interactions among the well-known models of k-anonymity and differential privacy and finally present some challenges to privacy that come from big data analytics.     

Regular and chaotic dynamics of a neutral atom in a magnetic trap

In the framework of the nonlinear mechanics, we study the dynamics of a neutral atom confined in a magnetic quadrupolar trap. Owing to the axial symmetry of the system, the z-component of the angular momentum p _φ is an integral of motion and, in cylindrical coordinates, the dynamics of the atom is modeled by a two-degree of freedom Hamiltonian. The structure and evolution of the phase space as a function of the energy is explored extensively by means of numerical techniques of continuation of families of periodic orbits and Poincaré surfaces of section.     

The Cayley–Dickson process for dialgebras

We adapt the algorithm of Kolesnikov and Pozhidaev, which converts a polynomial identity for algebras into the corresponding identities for dialgebras, to the Cayley–Dickson doubling process. We obtain a generalization of this process to the setting of dialgebras, establish some of its basic properties, and construct dialgebra analogues of the quaternions and octonions.     

Palladium(II) and platinum(II) tetrakisthiourea dichloride bis(7-hydroxy-5-methyl[1,2,4]triazolo[1,5a]pyrimidine) dihydrate solvates

The title compounds palladium(II) and platinum(II) tetrakisthiourea dichloride bis(7-hydroxy-5-methyl[1,2,4]triazolo[1,5a]pyrimidine (Hmtpo)) dihydrate solvates, have been synthesized by reacting thecis-[MCl₂(Hmtpo)₂] (where M=Pt(II), Pd(II)) complexes with an excess of thiourea (tu) and the structure of the palladium compound was solved by X-ray diffraction. Crystals of [Pd(tu)₄]Cl₂·2Hmtpo·2H₂O are triclinic with space groupP and unit cell dimensionsa=7.972(1),b=9.049(1),c=11.808(2)Å, =88.20(1), =75.15(1), =76.54(1)^o. The cation [Pd(tu)₄]²⁺ is centrosymmetric involving four sulfur thiourea atoms in a near square planar environment. The triazolopyrimidine molecules, chloride anions and water molecules do not take part in the metal center coordination but interact by hydrogen bonding between them and the thiourea moieties. A comparison between powder diffraction data of palladium(II) and platinum(II) compounds clearly indicates that both compounds are isomorphous.     

Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem

We prove that theq-state Potts antiferromagnet on a lattice of maximum coordination numberr exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) wheneverq>2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay forq7), triangular lattice (q11), hexagonal lattice (q4), and Kagomé lattice (q6). The proofs are based on the Dobrushin uniqueness theorem.     

Spectroscopic,thermal, and X-ray diffraction studies of tetrakis(thiourea) palladium chloride bis (5,7-dimethyl[1,2,4]triazolo[1,5-a]pyrimidine dihydrate

The crystal and molecular structure of the title compound, ·[Pd(S=C(NH₂)₂)₄]Cl₂·2dmtp·2H₂O. has been determined and refined to a finalR=0.034. The cation is centrosymmetric with the Pd atom existing in a square planar geometry with two disparate Pd–S bond distances of 2.3129(9) and 2.292(1)Å. Interatomic parameters are reported for the first non-coordinated dmtp molecule; these suggest the predominance of a particular canonical form in the solid state. The lattice is stabilized via a series H-bonding contacts involving the thiourea. Cl^– and dmtp species. Crystals of [Pd(S=C(NH₂)₂)₄]Cl₂ · 2dmtp · 2H₂O are monoclinic with space groupP2₁/c, and unit cell dimensionsa=15.129(1),b=8.512(1),c=12.663(1) Å, =104.05(1)°.