Twisted Alexander invariant is defined for a finitely presentable group G and a representation of G and a surjective homomorphism of G to a free abelian group. In this talk, we introduce some examples and some properties of the twisted Alexander invariant. Moreover, as an application, we consider a partial order on the set of prime knots. Let K be a knot and G(K) the knot group. For two prime k...

We define the complete numerical radius norm for homomorphisms from any operator algebra into B(H), and show that this norm can be computed explicitly in terms of the completely bounded norm. This is used to show that if K is a complete Cspectral set for an operator T , then it is a complete M -numerical radius set, where M = 12 (C + C −1). In particular, in view of Crouzeix’s theorem, there is...

Identity-based encryption (IBE) is a special case of public-key encryption where user identities replace public keys. Every user is given a corresponding secret key for decryption, and encryptions for his or her identity must remain confidential even to attackers who learn the secret keys associated with other identities. Several IBE constructions are known to date, but their security relies on...

We consider basic conceptual graphs, namely simple conceptual graphs (SGs), which are equivalent to the existential conjunctive positive fragment of first-order logic. The fundamental problem, deduction, is performed by a graph homomorphism called projection. The existence of a projection from a SG Q to a SG Gmeans that the knowledge represented by Q is deducible from the knowledge represented ...

Criteria for palindromic difference equations A xi + Axi+1 = 0, where stands for either transpose or conjugate transpose, to have bounded or stably bounded solutions are given in terms of the congruent equivalent classes of the matrix A. It is proved that the set of bounded palindromic difference equations is connected in the complex case, and has two connected components corresponding to the s...

For any semifinite von Neumann algebra ${\mathcal M}$ and $1\leq p<\infty$, we introduce a natutal $S^1$-valued noncommutative $L^p$-space $L^p({\mathcal M};S^1)$. We say that bounded map $T\colon L^p({\mathcal M})\to N})$ is $S^1$-bounded (resp. $S^1$-contractive) if $T\otimes I_{S^1}$ extends to contractive) $T\overline{\otimes} from $ M};S^1)$ into N};S^1)$. show completely positive $S^1$-bo...

We show that certain canonical realizations of the complexes Hom(G,H) and Hom+(G,H) of (partial) graph homomorphisms studied by Babson and Kozlov are in fact instances of the polyhedral Cayley trick. For G a complete graph, we then characterize when a canonical projection of these complexes is itself again a complex, and exhibit several well-known objects that arise as cells or subcomplexes of ...

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