522 research outputs found
The Geometry of Self-dual 2-forms
We show that self-dual 2-forms in 2n dimensional spaces determine a
dimensional manifold and the dimension of the maximal linear
subspaces of is equal to the (Radon-Hurwitz) number of linearly
independent vector fields on the sphere . We provide a direct proof
that for odd has only one-dimensional linear submanifolds.
We exhibit dimensional subspaces in dimensions which are multiples of
, for . In particular, we demonstrate that the seven dimensional
linear subspaces of also include among many other interesting
classes of self-dual 2-forms, the self-dual 2-forms of Corrigan, Devchand,
Fairlie and Nuyts and a representation of
given by octonionic multiplication. We discuss the relation of the linear
subspaces with the representations of Clifford algebras.Comment: Latex, 15 page
A search on Dirac equation
The solutions, in terms of orthogonal polynomials, of Dirac equation with
analytically solvable potentials are investigated within a novel formalism by
transforming the relativistic equation into a Schrodinger like one. Earlier
results are discussed in a unified framework and certain solutions of a large
class of potentials are given.Comment: 9 page
Self-dual Yang-Mills fields in eight dimensions
Strongly self-dual Yang-Mills fields in even dimensional spaces are characterised by a set of constraints on the eigenvalues of the Yang-Mills fields F_{\mu \nu}. We derive a topological bound on {\bf R}^8, \int_{M} ( F,F )^2 \geq k \int_{M} p_1^2 where p_1 is the first Pontrjagin class of the SO(n) Yang-Mills bundle and k is a constant. Strongly self-dual Yang-Mills fields realise the lower bound
Assessment Of The Curriculum Of Turkish Language Teaching In The 2nd Grade Of Primary Education In Terms Of Critical Thinking Skills
AbstractThis study aims to assess Turkish language teaching program of the 2nd grade primary school in terms of critical thinking skills. The document examination method, a qualitative research method, was employed in the research. Giving information on the general structure, and content of Turkish language teaching program (6-7-8), gains there from were reviewed. These gains were classified under the titles of critical thinking skills. In the reviewed Turkish language teaching program (6-7-8), 158 gains among the total of 228 under the fields of âreading, listening/following, speaking, writing, learning, and grammarâ were found to be intended for critical thinking skills. It was further ascertained that, these gains were intended more for âapplicationâ and âanalyzingâ skills than those of critical thinking
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