in this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. also necessary and sufficient conditions for existenceof solution are given. some numerical examples illustrate the efficiencyof the method.

We introduce a basis of the symmetric functions that evaluates to (irreducible) characters group, just as Schur evaluate irreducible G L n modules. Our main result gives three different characterizations for this basis. One shows structure coefficients (outer) product these are stable Kronecker coefficients. The results in paper focus on developing fundamental properties

We investigate Buchbaum and Eisenbud's construction of the second symmetric power $s_R(X)$ of a chain complex $X$ of modules over a commutative ring $R$. We state and prove a number of results from the folklore of the subject for which we know of no good direct references. We also provide several explicit computations and examples. We use this construction to prove the following vers...

key distribution is an important problem in wireless sensor networks where sensor nodesare randomly scattered in adversarial environments.due to the random deployment of sensors, a list of keys must be pre-distributed to each sensor node before deployment. to establish a secure communication, two nodes must share common key from their key-rings. otherwise, they can find a key- path in which ens...

locally extended affine lie algebras were introduced by morita and yoshii in [j. algebra 301(1) (2006), 59-81] as a natural generalization of extended affine lie algebras. after that, various generalizations of these lie algebras have been investigated by others. it is known that a locally extended affine lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...

Background: The dosimetric performance of Eclipse 6.5 three dimensional treatment planning system (3DTPS) is evaluated by comparing the calculated and measured dose in two dimensions following the guide lines of American Association for Physicists in Medicine Task Group 53. Materials and Methods: The calculations were performed by the 3DTPS for symmetric as well as asymmetric fields for standar...