this study concerns the existence and multiplicity of positive weak solutions for a class ofsemilinear elliptic systems with nonlinear boundary conditions. our results is depending onthe local minimization method on the nehari manifold and some variational techniques. alsoby using mountain pass lemma, we establish the existence of at least one solution withpositive energy.

Barendregt’s Lemma in its original form is a statement on Combinatory Logic that holds also for the lambda calculus and gives important insight into the syntactic interplay between substitution and reduction. Its origin lies in undefinablity proofs, but there are other applications as well. It is connected to the so-called Square Brackets Lemma, introduced by van Daalen in proofs of strong norm...

For our study of Faltings’ heights on abelian varieties over number fields, it will be convenient if we can compactify the “moduli space” of g-dimensional abelian varieties (over Z) such that the universal abelian scheme extends to a semi-abelian scheme over the compactification. The reason for this wish is that ideally we’d like to set up a theory for which the Faltings height of an abelian va...

The Mixture Lemma plays a central role in the study of the singularity of solutions of the Boltzmann equation. We offer a detailed proof of the lemma. The proof depends on the proper switching of the differentiations with respect to the space variables to those of the microscopic velocities, and depends on the precise regularity properties of the collision operator. Received February 16, 2010. ...

The mechanism of floral organ specification is principally conserved in angiosperms, as demonstrated by the ABC model. By contrast, mechanisms that regulate the development of organs or structures specific to a group of species remain unclear. Grasses have unique inflorescence units, comprising spikelets and florets. In the genus Oryza (rice), the single spikelet consists of a fertile floret su...

The dater equalities constitutes an appropriate tool which allows a linear description of Timed Event Graphs in the field of (max, +) algebra. This paper proposes an equivalent model in the usual algebra which can describe Timed and P-time Event Graphs. Considering 1-periodic behavior, the application of a variant of Farkas’ lemma allows the determination of upper and lower bounds of the produc...