This paper outlines a proof of the Jordan Normal Form Theorem. First we show that a complex, finite dimensional vector space can be decomposed into a direct sum of invariant subspaces. Then, using induction, we show the Jordan Normal Form is represented by several cyclic, nilpotent matrices each plus an eigenvalue times the identity matrix – these are the Jordan

The theorems of this paper show that the main results in the structure and representation theory of Jordan algebras and of alternative algebras are valid for a larger class of algebras defined by simple identities which obviously hold in the Jordan and alternative cass. A new unification of the Jordan and associative theories is also achieved.

Leaders create meaning out of events and relationships that devastate nonleaders. Even when battered by experience, leaders do not see themselves as helpless or find themselves paralyzed. They look at the same events that unstring those less capable and fortunate and see something useful, and often a plan of action as well. A powerful example is that of Vernon E. Jordan, civil rights pioneer an...

In the present paper, we propose a mean field approach for spin ladders based upon the Jordan-Wigner transformation along an elaborately ordered path. We show on the mean field level that ladders with even number legs open a energy gap in their low energy excitation with a magnitude close to the corresponding experimental values, whereas the low energy excitation of the odd-number-leg ladders a...

The dynamic susceptibility χ Q (ω) of the isotropic XY-model (s=1/2) on the alternating superlattice (closed chain) in a transverse field h is obtained exactly at arbitrary temperatures. It is determined from the results obtained for the dynamic correlations < S jn(t)S z lm(0) >, which have been calculated by introducing the generalized Jordan-Wigner transformation, by using Wick’s theorem and ...

Multicomponent KdV-systems are defined in terms of a set of structure constants and, as shown by Svinolupov, if these define a Jordan algebra the corresponding equations may be said to be integrable, at least in the sense of having higher-order symmetries, recursion operators and hierarchies of conservation laws. In this paper the dispersionless limits of these Jordan KdV equations are studied,...

The structure of the set of compact constant mean curvature surfaces whose boundary is a given Jordan curve in R seems far from being understood. We shall consider a simple, but interesting, situation concerning this problem: Assume that M be an embedded compact H-surface in R+ = {x3 ≥ 0} with ∂M = Γ ⊂ P = {x3 = 0}. Then, there is little known about the geometry and topology of M in terms of Γ....

As long ago as 1962 Nitsche conjectured that a harmonic homeomorphism h: A(r, R) onto −→A(r∗, R∗) between planar annuli exists if and only if R∗ r∗ 1 2 ( R r + r R ) . We prove this conjecture when the domain annulus is not too wide; explicitly, when R e3/2r. We also treat the general annuli A(r, R), 0 < r < R < ∞, and obtain the sharp Nitsche bound under additional assumption that either h or ...

OBJECTIVE The physiological effects of cigarette smoking have been widely studied, however, little is known regarding the effects of smoking hubble-bubble. We examined the acute effects of hubble-bubble smoking on heart rate, systolic, diastolic, and mean arterial blood pressure and maximum end-expiratory carbon monoxide. METHODS This study was carried out in the student laboratory, School of...

We investigate the spectral geometry of the exceptional Jordan algebra and its extensions. We examine the spectrum of the exceptional Jordan algebra over the sixteen-dimensional space of primitive idempotents, where it exhibits three real eigenvalues. We interpret the spectrum as coordinates for a coincident D-brane system where the real eigenvalues correspond to positions of three D0-branes on...