The group isomorphism problem consists in deciding whether two groups G and H given by their multiplication tables are isomorphic. An algorithm for group isomorphism attributed to Tarjan runs in time n, c.f. [Mil78]. Miller and Monk showed in [Mil79] that group isomorphism can be many-one reduced to isomorphism testing for directed graphs. For groups with n elements, the graphs have valence at ...

In this paper we examine the hard problems underlying asymmetric pairings, their precise relationships and how they affect a number of existing protocols. Furthermore, we present a new model for the elliptic curve groups used in asymmetric pairings, which allows both an efficient pairing and an efficiently computable isomorphism.

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.

The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability graphs of partially ordered sets with interval dimension 2 and height 3. In contrast, the problem is known to be solvable in polynomial time for comparabilit...

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...

Introduction Millikan’s theory of content places great reliance on the existence of isomorphisms between a system of representations and the things in the world which they represent — “the mapping requirement for being intentional signs” (Millikan 2004, p. 106). This paper asks whether those isomorphisms are doing any substantive explanatory work. Millikan’s isomorphism requirement is deployed ...

Abstract We consider two inclusions of $C^{*}$ -algebras whose small have approximate units the large and their spaces all bounded bimodule linear maps. suppose that are strongly Morita equivalent. In this paper, we shall show there exists an isometric isomorphism from one maps to other space study basic properties about isomorphism. And, using isomorphism, define Picard group for a map discuss...

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 ...