Characteristic polynomials of supertropical matrices

Supertropical matrix theory was investigated in [6], whose terminology we follow. In this work we investigate eigenvalues, characteristic polynomials and coefficients of characteristic polynomials of supertropical matrices and their powers, and obtain the analog to the basic property of matrices that any power of an eigenvalue of a matrix is an eigenvalue of the corresponding power of the matrix.Comment: Department of Mathematics, Bar-Ilan University, Ramat Gan 52900, Israel. Email: [email protected]. This paper is part of the author's Ph.D thesis, which was written at Bar-Ilan University under the supervision of Prof. L. H. Rowe

Cultural Criminology: The Time is Now

Cultural criminology understandscrime and its control asproductsofmeaning. It exploressimultaneously the macro-, meso-and micro-levels of social life, sensitive tothe operation of power, in order to produce critical analyses that are politically potent and germane to contemporary circumstances. The cultural criminological project is broad and inclusive, but focused and urgent. It relishes coalition and collaboration, clarity of thought and purpose,praxis and intervention. In its relatively short history,it has carved out a distinctive identity whilst contributing something to the development of a host of other perspectives. This article begins by offeringa contemporary definition of cultural criminology, including some reflection on its antecedentsand theresponses that have recently been addressed toits critics. This is followed by a discussion of the concerns cultural criminology shares with a variety of complementary perspectives and how it can be used to address malign structures and discourses. Finally, the relationship thatthe sub-discipline might form with transformative politicsisexploredbriefly. As truth and meaning have become the theatresof struggle between fundamentally opposed political positionspromising radically different visions of crime, criminalisation, criminal justice and everyday life,never has cultural criminology been more prescient and necessary. Thetime for cultural criminology is now

C*-algebras of Hilbert module product systems

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of quasihomomorphisms, we prove that those algebras are $K$-contractible. One special case is closely related to the Rieffel-Wiener-Hopf extension of a crossed product by R considered by Rieffel and by Pimsner and Voiculescu, and can be used to produce a new proof of Connes' analogue of the Thom isomorphism and in particular of Bott periodicity. Another special case is closely related to Arveson's spectral C*-algebras, and is used to settle Arveson's problem of computing their K-theory, extending earlier results of Zacharias to cover the general case.Comment: 11 pages (added an example and an appendix, corrected typos and improved exposition