We give a finite presentation by generators and relations for the group O_n(Z[1/2]) of n-dimensional orthogonal matrices with entries in Z[1/2]. then obtain similar form M/sqrt(2)^k, where k is nonnegative integer M an matrix. Both groups arise study quantum circuits. In particular, when dimension power 2, elements latter are precisely unitary that can be represented circuit over universal gate...

We discuss an approach to minimizing the group variability of generation in a system intermittent renewable sources using portfolio theory. The total that can be modeled various parameters as goal-functions is minimized given any desired level expected long-term generation. An extensive analysis was carried out on set time series measured data obtained from twenty wind plants Croatia over five ...

A loop (Q; ·) is called a Basarab if the identities: (x · yxρ)(xz) = x yz and (yx) (xλz x) hold. It was shown that left, right middle nuclei of coincide, nucleus set elements whose inner mapping Tx are automorphisms. The generators group were refined in terms one total loop. Necessary su_cient condition(s) (associators) for to be established. discovered loop: ↦ an endomorphism only left (right)...

We find generators of the group of birational automorphisms of the Hessian surface of a general cubic surface. Its nonsingular minimal model is a K3 surface with the Picard lattice of rank 16 which embeds naturally in the even unimodular lattice II1,25 of rank 26 and signature (1, 25). The generators are related to reflections with respect to some Leech roots. A similar observation was made fir...

We give the center of the elliptic quantum group in general case. Based on the Dynamic Yang-Baxter Relation and the fusion method, we prove that the center commute with all generators of the elliptic quantum group. Then for a kind of assumed form of these generators, we find that the coefficients of these generators form a new type closed algebra. We also give the center for the algebra.