The Newest Release of the Ortocartan Set of Programs for Algebraic Calculations in Relativity

The program Ortocartan for algebraic calculations in relativity has just been implemented in the Codemist Standard Lisp and can now be used under the Windows 98 and Linux operating systems. The paper describes the new facilities and subprograms that have been implemented since the previous release in 1992. These are: the possibility to write the output as Latex input code and as Ortocartan's input code, the calculation of the Ellis evolution equations for the kinematic tensors of flow, the calculation of the curvature tensors from given (torsion-free) connection coefficients in a manifold of arbitrary dimension, the calculation of the lagrangian from a given metric by the Landau-Lifshitz method, the calculation of the Euler–Lagrange equations from a given lagrangian (only for sets of ordinary differential equations) and the calculation of first integrals of sets of ordinary differential equations of second order (the first integrals are assumed to be polynomials of second degree in the first derivatives of the functions).     

Drying Induced Stresses in a Swelling Porous Wall

The present paper is concerned with the stresses generated in a capillary-porous wall saturated from the bottom and dried naturally on its side planes. The upper cross-section of the wall is totally isolated and no heat and moisture transfer occurs through it, while the bottom one has an a priori determined temperature and moisture content. The vertical planes of the wall are surrounded by air having different temperatures and moisture contents on the left and the right sides. The problem is solved numerically based on a mechanistic model of drying earlier developed by the authors. The distributions of temperature, moisture content, and the drying induced stresses are determined. The variation of temperature on the wall left and right surfaces is analysed dependent on the surroundings temperature. The influence of boundary conditions on the stress distribution in the wall is discussed.     

A Criterion for Compatibility of Conformal and Projective Structures

In a space-time M, a conformal structure is defined by the distribution of light-cones. Geodesics are traced by freely falling particles, and the collection of all unparameterized geodesics determines the projective structure of M. The article contains a formulation of the necessary and sufficient conditions for these structures to be compatible, i.e. to come from a metric tensor which is then unique up to a constant factor. The theorem applies to all dimensions and signatures.     

The t-Tone Chromatic Number of Random Graphs

A proper 2-tone k-coloring of a graph is a labeling of the vertices with elements from \({\binom{[k]}{2}}\) such that adjacent vertices receive disjoint labels and vertices distance 2 apart receive distinct labels. The 2-tone chromatic number of a graph G, denoted τ ₂(G) is the smallest k such that G admits a proper 2-tone k coloring. In this paper, we prove that w.h.p. for \({p\geq Cn^{-1/4} {\rm ln}^{9/4}n, \tau_2(G_{n, p}) = (2 + o(1))\chi(G_{n, p})}\) where \({\chi}\) represents the ordinary chromatic number. For sparse random graphs with p = c/n, c constant, we prove that \({\tau_2(G_{n, p}) = \lceil{({\sqrt{8\Delta + 1} + 5})/{2}}}\) where Δ represents the maximum degree. For the more general concept of t-tone coloring, we achieve similar results.     

Robust Markov perfect equilibria

In this paper we study a Markov decision model with quasi-hyperbolic discounting and transition probability function depending on an unknown parameter. Assuming that the set of parameters is finite, the sets of states and actions are Borel and the transition probabilities satisfy some additivity conditions and are atomless, we prove the existence of a non-randomised robust Markov perfect equilibrium.     

Metallomesogens: enaminoketone derivatives of the 3-oxa, 3-thia- and 3-selena-butyric amides

Liquid crystalline Ni(II) and Cu(II) complexes of tetradentate ligands, enaminoketones and 3-oxa; 3-thia- and 3-selena-butyramides were synthesized and examined. The compounds show very low C ₁ symmetry resulting from the chiral donor atoms — oxygen, sulphur and selenium — incorporated in the butyric amide moiety. This chirality can be observed in NMR studies. The complexes exhibit enantiotropic as well as monotropic calamitic SmA and N phases.     

Microsynthesis of Dianhydrohexitols

Abstract

Conditions have been established for the microsyntheses of dianhydro-hexitols by reaction of 1, 4-monoanhydro-D, L-galactitols and 1, 5-monoanhydro-D-galactitol as well as of 1, 4- and 1, 5-monoanhydro-D-glucitols and -D-mannitols with tosyl chloride in pyridine followed by cyclization of the resulting 6-O-tosyl derivatives in methanolic solution of sodium methoxide. The dianhydrohexitols were formed by intramolecular nucleophilic substitution of the C-6 O-tosyl group with a properly stereochemically oriented hydroxyl group.

Components of the mixtures were separated by capillary gas chromato-graphy using columns coated with SP-2340 and identified by GC-MS. The identities of the synthesized dianhydrohexitols were confirmed by comparison with the GC retention times and mass spectra of authentic samples.     

Supramolecular synthons and pattern recognition in adenine amides – synthesis,structures and thermal properties

An effective method for the synthesis of novel adenine amides was developed and successfully implemented, leading to 4-propyloxy-N-(9H-purin-6-yl)benzamide (1) and 4-dodecyloxy-N-(9H-purin-6-yl)benzamide (2). The compounds were fully characterised by means of spectroscopic (¹H NMR, ¹³C NMR, FT-IR) and thermal (TG, DSC) analysis. The crystallographic analysis revealed that the formation of supramolecular chains relies on hydrogen bonding between amide functionalities. All supramolecular synthons found in the crystal structure of 1 were confirmed with the temperature-dependent IR method. The temperature-dependent IR method is useful in determining supramolecular interactions for compound 2, for which the crystal structure could not be obtained. A detailed analysis of temperature-dependent FT-IR spectra was used for the first time to identify the hydrogen bonds that exist in the solid state of our compounds; it can therefore be considered a promising method for the pattern recognition of hydrogen bonding in supramolecular chemistry.     

Correction of Characteristics of Subsystems of Torsionally Vibrating Complex Mechatronic Systems as an Introduction to Solution of Their Inverse Task

In this paper the analysis of torsionally vibrating subsystem of complex mechanical and mechatronic systems by using the the exact and approximate methods were the main purposes to solve the task of assignment of frequency-modal analysis and characteristics of mechatronic system. The characteristic of the elementary subsystems using the exact and approximate methods has been determined according to accepted frequencies and the correction coefficient. The frequencies were chosen from the spectrum in which the synthesis of complex systems will be conducted. It is very important that the difference of flexibility values in the spectrum was minimal. The coefficient of the correction has been determined according to the flexibility values of chosen points and it is equal to quotient of flexibility calculated using the exact method across the flexibility delivered by using the approximate method. The coefficient of the correction is the zero-dimensional quantity. After determination of the correction coefficient the medium value which has been afterwards considered in correlation of dynamic characteristics has been calculated. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)