On Covariant Phase Space and the Variational Bicomplex

The notion of a phase space in classical mechanics is well known. The extension of this concept to field theory however, is a challenging endeavor, and over the years numerous proposals for such a generalization have appeared in the literature. In this paper We review a Hamiltonian formulation of Lagrangian field theory based on an extension to infinite dimensions of J.-M. Souriau's symplectic approach to mechanics. Following G. Zuckerman, we state our results in terms of the modern geometric theory of differential equations and the variational bicomplex. As an elementary example, we construct a phase space for the Monge–Ampere equation.     

Steady-state analytical solutions for the lattice boltzmann equation

A general class of analytical solutions of the lattice Boltzmann equation is derived for two-dimensional, steady-state unidirectional flows. A subset of the solutions that verifies the corresponding Navier-Stokes equations is given. It is pointed out that this class includes, e.g., the Couette and the Poiseuille flow but not, e.g., the basic Kolmogorov flow. For steady-state non-unidirectional flows, first and second order solutions of the lattice Boltzmann equation are derived. Practical consequences of the analysis are mentioned. Differences between the technique applied here and those used in some earlier works are emphasized.     

Investigating and ordering Quadrilaterals and their analogies in space—problem fields with various aspects

Problem fields with one or two generating problems and possibilities of varying existing problems give a good chance for self-activities of students and can be used for reaching different general aims. In this paper some topics concerning quadrilaterals will be presented. I hope they will animate teachers for more problem orientation in mathematics education. First we will reflect about different types of convex and non-convex quadrilaterals and possibilities of ordering them. Then we focus on middle-quadrilaterals and types of quadrilaterals with special middle-quadrilaterals as well as their logical ordering. Finally we investigate the analogies in space to the parallelogram and its sub-types and order them in the “house of parallelepipeds”.     

Proteinases from Carica papaya Latex

Data on the proteinase complex from Carica papaya latex were reviewed. The properties and applications of the domestic preparation cucumazyme and known medicinal preparations based on papaya proteinases (caripazyme, lecozyme, lecopain) were compared.     

Cycloaddition of Thiourea to Tri(1-propenyl)amine

Russian Journal of General Chemistry -     

2‐connected 7‐coverings of 3‐connected graphs on surfaces

An m‐covering of a graph G is a spanning subgraph of G with maximum degree at most m. In this paper, we shall show that every 3‐connected graph on a surface with Euler genus k ≥ 2 with sufficiently large representativity has a 2‐connected 7‐covering with at most 6k ? 12 vertices of degree 7. We also construct, for every surface F² with Euler genus k ≥ 2, a 3‐connected graph G on F² with arbitrarily large representativity each of whose 2‐connected 7‐coverings contains at least 6k ? 12 vertices of degree 7. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 26–36, 2003     

Interaction of indigo carmine dye with silica modified with humic acids at solid/liquid interface

Two distinct humic acids, one extracted from Brazilian peat soil, HA_PS, and another one obtained from commercial source, HA_FL, were attachment onto silica gel modified with aminopropyltrimethoxysilane, producing two material named SiHA_PS and SiHA_FL, respectively. The ability of these materials in removing indigo carmine dye from aqueous solution was followed through series of adsorption isotherms adjusted to modified Langmuir equation. The maximum number of moles adsorbed gave 6.82 ± 0.12 × 10⁻⁴ and 2.15 ± 0.17 × 10⁻⁴ mol g⁻¹ for SiHA_PS and SiHA_FL, respectively. Same interactions were calorimetrically followed and the thermodynamic data showed endothermic enthalpic values: 12.31 ± 0.55 and 24.69 ± 1.05 kJ mol⁻¹ for SiHA_PS and SiHA_FL surfaces, respectively. Gibbs free energies for two adsorption processes of indigo carmine dye presented negative values, reflecting dye/surface interactions must be accompanied by an increased in entropy values, which are 65 ± 3 and 98 ± 5 J mol⁻¹ K⁻¹ for SiHA_PS and SiHA_FL materials, respectively. The adsorption processes for both materials were spontaneous in nature although they presented an endothermic enthalpy for the interaction, resulting in an entropically favored process.     

Mössbauer Study of Ceramic Finds from the Galería de las Ofrendas, Chavín de Huántar

Ceramic finds from the Galería de las Ofrendas at Chavín de Huántar and surface finds from the settlement of Chavín were characterised by combining the results of archaeological typology with archaeometric studies using neutron activation analysis, Mössbauer spectroscopy, X-ray diffraction and thin-section microscopy. Sherds from the pyramid Tello are included in the study as representative of local material. The analyses show that the vessels were made from different raw materials and that different firing procedures were used in their production. Sherds of certain styles largely exhibit similar types of Mössbauer patterns and in many instances also have similar element compositions. This supports the archaeological notion that the vessels were brought to Chavín from the provinces, perhaps on the occasion of a festivity.