Post-harvest operations have been used in order to increase the efficiency of product production. In the case of walnuts, one of the important processes for improving quality is peeling the walnut’ s shell. Because of the amount of walnuts produced in Iran and the necessity to reduce the loss of products, a device for quick removal of the walnut’ s shell is needed. This study examined and compa...

In this paper, using the Weyl-Wigner-Moyal formalism for quantum mechanics, we develop a quantum-deformed exterior calculus on the phase-space of an arbitrary hamiltonian system. Introducing additional bosonic and fermionic coordinates we construct a supermanifold which is closely related to the tangent and cotangent bundle over phase-space. Scalar functions on the super-manifold become equival...

We consider compound matrices and exterior products in order to generalize a fundamental relation between the eigenspace of a matrix A corresponding to a simple eigenvalue λ and certain minors of A − λI of order n − 1. By means of the Laplace Expansion Theorem, we show that if the geometric multiplicity of λ is k > 1, then the exterior product of k linearly eigenvectors corresponding to λ is un...

We write the fermionic q-Fock space representation of Uq(ŝln) as an infinite extended braided tensor product of finite-dimensional fermionic Uq(sln)-quantum planes or exterior algebras. Using braided geometrical techniques developed for such quantum exterior algebras, we provide a new approach to the Kashiwara-Miwa-Stern action of the Heisenberg algebra on the q-fermionic Fock space, obtaining ...

We review the notion of the deformation of the exterior wedge product. This allows us to construct the deformation of the algebra of exterior forms over a vector space and also over an arbitrary manifold. We relate this approach to the generalized statistics. we study quons, as a particular case of these generalized statistics. We also give their statistical properties. A large part of the work...

Let V be a four-dimensional real vector space with a fixed orientation. Then the wedge product can be viewed, up to a positive factor, as a canonical quadratic form of signature (3, 3) on the six-dimensional space ΛV . This gives a homomorphism from the identity component of the general linear group GL(V ) to the conformal group of the indefinite form, which is a local isomorphism. The signific...

The Hodge dual operator ∗ is one of the 3 basic operations on differential forms. (The other 2 are wedge product ∧ and exterior differentiation d.) However most treatments consider only positive-definite inner products, and there are at least 2 standard ways of generalizing this to inner products of arbitrary signature. We outline here a construction of the Hodge dual operator which works for a...