Given a topological group G, and a finitely generated group Γ, a homomorphism π : Γ→G is locally rigid if any nearby by homomorphism π is conjugate to π by a small element of G. In 1964, Weil gave a criterion for local rigidity of a homomorphism from a finitely generated group Γ to a finite dimensional Lie group G in terms of cohomology of Γ with coefficients in the Lie algebra of G. Here we ge...

Thirty-two samples of chocolate products were analysed by HPLC for caffeine and theobromine contents. Defatted residues of samples were extracted with 80% aqueous acetone. After extraction into boiling water, the methylxanthines were identified and quantified with the use of μ-Bondapak column and mobile phase of methanol:water:acetic acid (20:79:1). Levels of caffein and theobromine in 32 sampl...

We study effects of nonlocality in the nuclear force on the G-matrix elements for finite nuclei. Nuclear G-matrix elements for 16O are calculated in the harmonic oscillator basis from a nonlocal potential which models quark exchange effects between two nucleons. We employ a simple form of potential that gives the same phase shifts as a realistic local nucleon potential. The G-matrix elements ca...

In this assay, edible cattle tissues from local markets of Ardabil, a Province of Iran, were examined for residues of tetracycline antibiotics (tetracycline, oxytetracycline and chlortetracycline). In total, 110 samples of triceps, gluteal muscle, diaphragm, kidney and liver were randomly obtained from the local markets of the city of Ardabil. Solid-phase extraction (SPE) and high-performance l...

G is a well-covered graph provided all its maximal stable sets are of the same size (Plummer, 1970). S is a local maximum stable set of G, and we denote by S ∈ Ψ(G), if S is a maximum stable set of the subgraph induced by S ∪ N(S), where N(S) is the neighborhood of S. In 2002 we have proved that Ψ(G) is a greedoid for every forest G. The bipartite graphs and the trianglefree graphs, whose famil...

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We study a local version of gap vertex-distinguishing edge coloring. From an edge labeling f : E(G) → {1, . . . , k} of a graph G, an induced vertex coloring c is obtained by coloring the vertices with the greatest difference between incident edge labels. The local gap chromatic number χ∆(G) is ∗ Partially funded by NSF GK-12 Transforming Experiences Grant DGE-0742434. † Partially funded by Sim...

We provide an algebraic formulation of the moving frame method for constructing local smooth invariants on a manifold under an action of a Lie group. This formulation gives rise to algorithms for constructing rational and replacement invariants. The latter are algebraic over the field of rational invariants and play a role analogous to Cartan’s normalized invariants in the smooth theory. The al...