Low-temperature series for renormalized operators: The ferromagnetic square-lattice Ising model

A method for computing low-temperature series for renormalized operators in the two-dimensional Ising model is proposed. These series are applied to the study of the properties of the truncated renormalized Hamiltonians when we start at very low temperature and zero field. The truncated Hamiltonians for majority rule, Kadanoff transformation, and decimation for 2×2 blocks depend on the how we approach the first-order phase-transition line. The renormalization group transformations are multivalued and discontinuous at this first-order transition line when restricted to some finite-dimensional interaction space.     

5‐Methyl­sulfanyl‐3H‐1,2,3‐triazolo[4,5‐d]pyrimidin‐7(6H)‐one (2‐methyl­thio‐8‐aza­xanthine) monohydrate

The title compound, C₅H₅N₅OS·H₂O, crystallizes as the monohydrate. Disorder of the H atoms that participate in the hydrogen bonds implies that two different tautomers are present in the crystal structure, one of them with both acidic H atoms attached to the imidazole ring and the other with one acidic H atom on each ring.     

Rigid motions in relativity

Starting with a simple characterization of pairs of rigidly joined straight world lines, successive generalizations are obtained up to the most general case which allows us to establish the various definitions of rigid motions in relativity (both special and general).     

A Structure Theorem for Free Temporal Algebras

In this paper an algebraic version for temporal algebras of the logical filtrations for modal and temporal logics is analysed. A structure theorem for free temporal algebras and also some results with regard to the variety of temporal algebras are obtained.     

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.     

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.