Let S be a discrete semigroup, m (S) the space of all bounded real functions on S with the usualsupremum norm. Let Acm (S) be a uniformly closed left invariant subalgebra of m (S) with 1 c A. We say that A is extremely left amenable if there isamultiplicative left invariant meanon A. Let P = {h ?A: h =|g-1,g | forsome g ?A, s ?S}. It isshown that . A is extremely left amenable if and only ...

Despite the central importance often placed on expectations in defining norms, are routinely invoked a fleeting manner. When they are, utilised many different ways, without anyone acknowledging this, which creates confusion. The article argues that should not be viewed as playing singular role norm process. Instead, it puts forward three roles play dynamics: (i) norms embody expectations, (ii),...

Keeping order in the classroom, modifying students’ behavioral problems, and implementing regulations codified at schools are among the issues in education involving the minds of headmasters and teachers. Following adolescence appropriate behavioral patterns plays a key role in bringing about the adolescents’ positive social behavior. This study aimed to investigate the predictors o...

we introduce a homological invariant of a manifold known as Gromov’s norm. Gromov’s norm of hyperbolic manifolds will be seen to be proportional to the volume of the manifold. The first striking consequence of this result is that the volume of a hyperbolic manifold is a topological invariant. Intuitively, Gromov’s norm measures the efficiency with which multiples of a homology class can be repr...

This paper describes a fuzzy union based approach for automatically evaluating machine generated extract summaries. The proposed method represents every sentence within a machine generated summary as a fuzzy set. Sentences in the reference summary are assigned membership grades in each of these fuzzy sets using cosine distance measure. Finally Fuzzy union (s-norm operation) is used to compute a...

concern over the depletion of natural resources in general, and water scarcity in particular, has stimulated the development and implementation of some policies aimed at changing farmers' behavior in terms of conserving water. in this regard, government has recently begun to invest on researches supporting the technical solutions on conserving water in the agricultural sector as the bigges...

For an m × N underdetermined system of linear equations with independent pre-Gaussian random coefficients satisfying simple moment conditions, it is proved that the s-sparse solutions of the system can be found by `1-minimization under the optimal condition m ≥ c s ln(eN/s). The main ingredient of the proof is a variation of a classical Restricted Isometry Property, where the inner norm becomes...

If v is a norm on en, let H(v) denote the set of all norm-Hermitians in e nn. Let S be a subset of the set of real diagonal matrices D. Then there exists a norm v such that S = H(v) (or S = H(v) n D) if and only if S contains the identity and S is a subspace of D with a basis consisting of rational vectors. As a corollary, it is shown that, for a diagonable matrix h with distinct eigenvalues .1...