Let m∗(n) be the minimum number of edges in an n-uniform simple hypergraph that is not two colorable. We prove that m∗(n) = Ω(4n/ ln(n)). Our result generalizes to r-coloring of b-simple uniform hypergraphs. For fixed r and b we prove that a maximum vertex degree in b-simple n-uniform hypergraph that is not r-colorable must be Ω(rn/ ln(n)). By trimming arguments it implies that every such graph...

We first investigate the algebraic structure of vertex algebroids B when are simple Leibniz algebras. Next, we use these to construct indecomposable non-simple C2-cofinite N-graded algebras VB?. In addition, classify irreducible VB?-modules and examine conformal vectors

In this paper a class of simple theories, called the low theories is developed, and the following is proved. Theorem Let T be a low theory, A a set and a; b elements realizing the same strong type over A. Then, a and b realize the same Lascar strong type over A. The reader is expected to be familiar with forking in simple theories, as developed in Kim's thesis Kim]. The Lascar strong type of a ...

protein structural flexibility is important for catalysis, binding, protein design, and allostery. some simple methods have recently been introduced to compute protein flexibility directly from the protein structure without any mechanical models. for example the atomic mean square displacement (or b-factor) is related to the number of neighboring atoms. the protein structure can be modeled as a...

cellulose sulfuric acid was used as an efficient biopolymer-based catalyst for the synthesis of tetrahydropyrimido[4,5-b]quinoline-2,4,6-triones and hexahydro-2h-pyrazolo[5,4-b]quinoline-6-ones via three component reaction of aldehyde, 5,5-dimethyl-1,3-cyclohexadione and 6-amino-1,3-dimethyluracil or 5-amino-3-methyl-1-phenypyrazole under solvent-free conditions at 90 oc. the major advantages o...