Samarium Based High Surface Area Perovskite Type Oxides SmFe1-XAlXO3 (X=0.00, 0.50, 0.95). Part II, Catalytic Combustion of CH4

The catalytic combustion of methane with stoichiometric amounts of oxygen to CO₂ and H₂O has been studied over samarium based high surface area perovskite type oxides SmFe_1-xAl_xO₃ (x=0.00, 0.50 0.95) prepared via a new sol-gel method. A comparison to other lanthanum perovskites prepared by the ceramic method shows higher catalytic activity for SmFeO₃ and SmFe_0.5Al_0.5O₃ samples.     

Kinetic Formulation for Systems of Two¶Conservation Laws and Elastodynamics

For scalar conservation laws, the kinetic formulation makes it possible to generate all the entropies from a simple kernel. We show how this concept replaces and simplifies greatly the concept of Young measures, avoiding the difficulties encountered when working in L ^p . The general construction of the two kinetic functions that generate the entropies of 2 × 2 strictly hyperbolic systems is also developed here. We show that it amounts to building a “universal” entropy, i.e., one that can be truncated by a “kinetic value” along Riemann invariants. For elastodynamics, this construction can be completed and specialized using the additional Galilean invariance. This allows a full characterization of convex entropies. It yields a kinetic formulation consisting of two semi-kinetic equations which, as usual, are equivalent to the infinite family of all the entropy inequalities. Accepted May 29, 2000?Published online November 16, 2000     

Ganea comonads

We construct for all topological space X and all n∈N a natural section e ⁿ _X :G ⁿ X→G ⁿ G ⁿ X of the Ganea projection :G ⁿ G ⁿ X→G ⁿ X and show that the triple (G ⁿ ,g ⁿ ,e ⁿ ) is a comonad on Top ^*. Received: 6 March 2000     

Nanomaterials in Cementitious Composites: An Update

This review is an update about the addition of nanomaterials in cementitious composites in order to improve their performance. The most common used nanomaterials for cementitious materials are carbon nanotubes, nanocellulose, nanographene, graphene oxide, nanosilica and nanoTiO₂. All these nanomaterials can improve the physical, mechanical, thermal and electrical properties of cementitious composites, for example increase their compressive and tensile strength, accelerate hydration, decrease porosity and enhance fire resistance. Cement based materials have a very complex nanostructure consisting of hydration products, crystals, unhydrated cement particles and nanoporosity where traditional reinforcement, which is at the macro and micro scale, is not effective. Nanomaterials can reinforce the nanoscale, which wasn’t possible heretofore, enhancing the performance of the cementitious matrix.     

Stable blowup for the cubic wave equation in higher dimensions

We consider the wave equation with a focusing cubic nonlinearity in higher odd space dimensions without symmetry restrictions on the data. We prove that there exists an open set of initial data such that the corresponding solution exists in a backward light-cone and approaches the ODE blowup profile.     

A strongly polynomial algorithm for a concave production-transportation problem with a fixed number of nonlinear variables

We show that the production-transportation problem involving an arbitrary fixed number of factories with concave production cost is solvable in strongly polynomial time. The algorithm is based on a parametric approach which takes full advantage of the specific structure of the problem: monotonicity of the objective function along certain directions, small proportion of nonlinear variables and combinatorial properties implied by transportation constraints.     

Lyapunov Functionals and L 1 -Stability for Discrete Velocity Boltzmann Equations

We devise Lyapunov functionals and prove uniform L¹ stability for one-dimensional semilinear hyperbolic systems with quadratic nonlinear source terms. These systems encompass a class of discrete velocity models for the Boltzmann equation. The Lyapunov functional is equivalent to the L¹ distance between two weak solutions and non-increasing in time. They result from computations of two point interactions in the phase space. For certain models with only transversal collisional terms there exist generalizations for three and multi-point interactions.     

The Minimum Concave Cost Network Flow Problem with fixed numbers of sources and nonlinear arc costs

We prove that the Minimum Concave Cost Network Flow Problem with fixed numbers of sources and nonlinear arc costs can be solved by an algorithm requiring a number of elementary operations and a number of evaluations of the nonlinear cost functions which are both bounded by polynomials inr, n, m, wherer is the number of nodes,n is the number of arcs andm the number of sinks in the network.On leave from Institute of Mathematics, P.O. Box 631, Bo Ho, Hanoi, Vietnam.     

3,5-dinitrobenzoyl amino acid esters. Broadly applicable chiral solvating agents for NMR determination of enantiomeric purity.

Methyl esters of N-(3,5-dinitrobenzoyl)-amino acids have been used as chiral solvating agents to induce NMR spectral nonequivalence between the enantiomers of a broad array of solutes.