APPROACH We sketch a more abstract version of the proof of the smoothness of CG.H/. LEMMA 16.24. Let G and H be algebraic groups over k. Let R be a k-algebra, let R0 D R=I with I 2 D 0, and let 0 denote base change R! R0. The obstruction to lifting a homomorphism u0WH0!G0 to R is a class in H .H0;Lie.G0/ ̋I ); if the class is zero, then the set of lifts modulo the action of Ker.G.R/!G.R0// by co...

The superstability of a dynamical motion is defined with existence of a minus infinity Lyapunouv exponent, this mean that this motion is attractive. There are several methods for constructing 1-D polynomial mappings with attracting cycles or superstable cycles [1,2] based on Lagrange and Newton interpolations. Superstable phenomena in some 1-D maps embedded in circuits and systems are studied i...

The concept of information distance in non-commutative setting is re-considered. Additive information, such as Kullback-Leibler divergence, is defined using convex functional with gradient having the property of homomorphism between multiplicative and additive subgroups. We review several geometric properties, such as the logarithmic law of cosines, Pythagorean theorem and a lower bound given b...

We discuss Hedetniemi's conjecture in the context of categories of relational structures under homomorphisms. In this language Hedetniemi's conjecture says that if there are no homomor-phisms from the graphs G and H to the complete graph on n vertices then there is no homomorphism from G x H to the complete graph. If an object in some category has just this property then it is called multiplica...

Abstract: The focal point of this paper is the design of fixed-order controllers for persistent disturbance rejection. It is shown that optimal controller design can, in this case, be formulated as a generalized eigenvalue problems. The results in this paper rely on an extension of the concepts of equalized performance and superstability to the case of multiinput/multi-output systems described ...

Suppose A is a C*-algebra and B is a Banach algebra such that it can be continuously imbedded in B(H), the Banach algebra of bounded linear operators on some Hubert space H. It is shown that if 6 is a compact algebra homomorphism from A into B, then 6 is a finite rank operator, and the range of 0 is spanned by a finite number of idempotents. If, moreover, B is commutative, then 9 has the form 8...

‎Bucket recursive trees are an interesting and natural‎ ‎generalization of ordinary recursive trees and have a connection‎ to mathematical chemistry‎. ‎In this paper‎, ‎we give the lower and upper bounds for the moment generating‎ ‎function and moments of the multiplicative Zagreb indices in a‎ ‎randomly chosen bucket recursive tree of size $n$ with maximal bucket size $bgeq1$‎. Also, ‎we consi...

We consider the group $(\mathcal{G},*)$ of unitized multiplicative functions in incidence algebra non-crossing partitions, where ``$*$'' denotes convolution operation. introduce a larger $(\widetilde{\mathcal{G}},*)$ from same algebra, which satisfy weaker condition being ``semi-multiplicative''. The natural action $\widetilde{\mathcal{G}}$ on sequences multilinear functionals non-commutative p...