Precise bounds and asymptotics for the first Dirichlet eigenvalue of triangles and rhombi

We study the asymptotic expansion of the first Dirichlet eigenvalue of certain families of triangles and of rhombi as a singular limit is approached. In certain cases, which include isosceles and right triangles, we obtain the exact value of all the coefficients of the unbounded terms in the asymptotic expansion as the angle opening approaches zero, plus the constant term and estimates on the remainder. For rhombi and other triangle families such as isosceles triangles where now the angle opening approaches π, we have the first two terms plus bounds on the remainder. These results are based on new upper and lower bounds for these domains whose asymptotic expansions coincide up to the orders mentioned. Apart from being accurate near the singular limits considered, our lower bounds for the rhombus improve upon the bound by Hooker and Protter for angles up to approximately 22° and in the range (31°,54°). These results also show that the asymptotic expansion around the degenerate case of the isosceles triangle with vanishing angle opening depends on the path used to approach it.     

Integrated Groups and Smooth Distribution Groups

In this paper, we prove directly that α-times integrated groups define algebra homomorphisms. We also give a theorem of equivalence between smooth distribution groups and α-times integrated groups.     

Altered protein synthesis in rat kidney cells exposed to semiconductor materials

It is thought that the extensive industrial use of arsenic, gallium and indium, which have applications as the materials for III–V semiconductors, will increase human exposure to these compounds in the near future. We have undertaken the development of new biological indicators for assessing exposure to these elements. Element-specific alterations in protein synthesis patterns were expected to occur following exposure to arsenic compounds. We examined alterations in protein synthesis in primary cultures of rat kidney proximal tubule epithelial cells by sodium arsenite, gallium chloride and indium chloride, utilizing two-dimensional gel electrophoresis. After incubation with the chemicals for 20 h, newly synthesized proteins were labeled with [³⁵S]methionine. A protein with a molecular weight (M_r) of 30 000 was markedly induced on exposure to 10 μM arsenite or 300 μM gallium chloride, and synthesis of proteins with M_r values of 85 000, 71 000, 65 000, 51 000, 38 000 and 28 000 were also increased by exposure to arsenite and gallium chloride. No significant changes were observed upon exposure to indium. Some of these increased proteins could be heat-shock proteins.     

Heuristics and look-ahead integration to solve constraint satisfaction problems efficiently

Logic programming languages, such asProlog, allow a declarative specification of Constraint Satisfaction Problems (CSPs), freeing the user from specifying more or less complex control directives. However, the price to pay for such flexibility is a loss of efficiency, which makes Logic Programming inadequate to solve CSPs of even moderate size and complexity. To extend the range of applicability of logic programming, several improvements have been proposed. The use of heuristics is one such improvement. Although this usually forces the user to specify some form of control (thus abandoning the pure declarative nature of a logic program), these specifications can be made declarative by making use of some appropriate meta-predicates. Another extension to logic programming that improves its efficiency, is the active use of constraints, as done in the various formulations of constraint logic programming languages. In particular, the use of finite domains is quite adequate to implement look-ahead schemes to efficiently solve several types of CSPs. In this paper, we discuss the complementary nature of heuristics and look-ahead schemes and present a constraint logic programming framework that integrates both these techniques. Results obtained with a time-tabling problem executed on a prototype that implements such a framework are presented, and show that significant efficiency improvements can be achieved when compared with the separate use of the two techniques.     

Purification and characterization of gamma-enolase from various mammals.

The gamma subunit of enolase (gamma-enolase) was purified from the brain tissues of cow, dog, goat, pig, rabbit, and rat. The purification was achieved in only three steps: ammonium sulfate-precipitation, DE 53 cellulose ion-exchange chromatography, and polyacrylamide gel electrophoresis (PAGE) in a preparative mode. The purification procedure was comparatively more simple than previously reported methods, and the yield of gamma-enolase was sufficient for subsequent structural and immunological analyses. In all mammals, the purified gamma-enolase migrated in sodium dodecyl sulfate-PAGE (SDS-PAGE) with a molecular mass of 46 kilodaltons (kDa), and the immunological cross-reactivity between those gamma-enolases was very strong. The structural homology of these gamma-enolases was examined by peptide mapping using cyanogen bromide cleavage and subsequent two-dimensional electrophoresis. The resulting peptide patterns were highly similar and in cow, dog, and goat, the patterns were almost identical. These results indicate that structural homology, that is, the species non-specificity of gamma-enolase, appears to be very high.     

Local solution for the Kadomtsev-Petviashvili equation with periodic conditions

In this article we prove a local existence and uniqueness theorem for the Kadomtsev-Petviashvili Equation (u _t +u _xxx +uu _x ) _x −u _yy =0) in the Sobolev spaces of orders≥3, with initial values in the same spaces, and periodic boundary conditions. This theorem improves previous results based upon the application of singular perturbation techniques.     

Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.