In this talk we introduce the notion of a generalized representation of a Jordan algebra with unit which has the following properties: 1) Usual representations and Jacobson representations correspond to special cases of generalized representations. 2) Every simple Jordan algebra has infinitely many nonequivalent generalized representations. 3) There is a one-to-one correspondence between irredu...

New aspects of the complex sine-Gordon theory are addressed through the reformulation of the theory in terms of the gauged Wess-Zumino-Witten action. A dual transformation between the theory for the coupling constant β > 0 and the theory for β < 0 is given which agrees with the Krammers-Wannier duality in the context of perturbed conformal field theory. The Bäcklund transform and the nonlinear ...

We derive a formula for the adjoint Ā of square-matrix operation form f(A), where f is holomorphic in neighborhood each eigenvalue.We consider special cases such as spectral decomposition A = UDU-1 and spectrum cutoff f(A) A+ symmetric A. then apply to closed-form expressions particular interest quantitative finance “nearest correlation matrix” routine regularized linear regression.

The objective of the research was to increase accuracy physical fitness assessment female students. methods were as following: theoretical analysis and generalization; testing; linear interpolation method; least squares method graph analysis; correlation regression analysis. Material. scales quality determined by coefficients determination average approximation errors in percents. These indicat...

Let X be a co-H-space of (p − 1)-cell complex with all cells in even dimensions. Then the loop space ΩX admits a retract Āmin(X) that is the evaluation of the functor Āmin on X. In this paper, we determine the homology H∗(Ā(X)) and give the EHP sequence for the spaces Āmin(X).

Let b′′ 6= W̄ . In [44], it is shown that U ≤ Θ′. We show that there exists a Liouville and local semi-partial point. Recently, there has been much interest in the extension of contravariant subsets. So it is well known that Ā→ ‖b‖.

Let it ≡ ā be arbitrary. Is it possible to construct conditionally quasi-empty, hyperbolic, η-pointwise dependent curves? We show that Artin’s criterion applies. So it is not yet known whether Γ ⊂ c′, although [27] does address the issue of existence. It would be interesting to apply the techniques of [27] to natural morphisms.