Geometric crossover is a representation-independent generalization of the traditional crossover defined using the distance of the solution space. By choosing a distance firmly rooted in the syntax of the solution representation as basis for geometric crossover, one can design new crossovers for any representation. In previous work we have applied geometric crossover to simple permutations. In t...

      The French law, contrary to the Iranian law, has given the mother a kind of representation for guardianship and training of the child. This is a development that was established in France in 1970, and in Article 6 of the Iranian Family Protection Act of 2012, the granting of representation to the mother over the legal procedure for demand of the child or the incompetent has been entrusted...

we regard the shearlet group as a semidirect product group andshow that its standard representation is,typically, a quasiregu-lar representation. as a result we can characterize irreducibleas well as square-integrable subrepresentations of the shearletgroup.

This paper develops recursive solution methods for linear rational expectations models. The underlying structural model is transformed into a state-space representation, which can then be used to solve the model and to form the Gaussian likelihood function. The recursive solution method has several advantages over other approaches. First, the set of solutions to the model are summarized by a se...

For the evolutionary algorithm, the representation of the electronic circuit has two methods, one kind is code with the electronic circuit solution space, the other is code with the problem space. How one representation quality weighs may think the following questions? The first is the code method should as far as possible complete, it is say for the significance solution circuit or the optimiz...

This paper shows how to compute a second-order accurate solution of a non-linear rational expectation model using algorithms developed for the solution of linear rational expectation models. The result is a state-space representation for the realized values of the variables of the model. This state-space representation can easily be used to compute impulse responses as well as conditional and u...

A c-number path integral representation is constructed for the solution of the Dirac equation. The integration is over the real trajectories in the continuous three-space and other two canonical pairs of compact variables controlling the dynamics of the spin and the chirality flips. The problems to overcome in order to find a c-number path integral representation for the solution of the Dirac e...

We study the automorphic theta representation $Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$‎. ‎This representation is obtained from the residues of Eisenstein series on this group‎. ‎If $r$ is odd‎, ‎$nle r

This paper deals with representation and solution of asymmetric decision problems. We describe a new representation called sequential valuation networks that is a hybrid of Covaliu and Oliver’s sequential decision diagrams and Shenoy’s valuation networks. The solution algorithm is based on the idea of decomposing a large asymmetric problem into smaller symmetric subproblems and then using Sheno...