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Full-Text Articles in Physical Sciences and Mathematics
Structure For Regular Inclusions, David R. Pitts
Structure For Regular Inclusions, David R. Pitts
Department of Mathematics: Faculty Publications
We study pairs (C,D) of unital C∗-algebras where D is an abelian C∗-subalgebra of C which is regular in C in the sense that the span of {v 2 C : vDv∗ [ v∗Dv D} is dense in C. When D is a MASA in C, we prove the existence and uniqueness of a completely positive unital map E of C into the injective envelope I(D) of D whose restriction to D is the identity on D. We show that the left kernel of E, L(C,D), is the unique closed two-sided ideal of C maximal with respect to having trivial …
Negative Curves On Algebraic Surfaces, Thomas Bauer, Brian Harbourne, Andreas Leopold Knutsen, Alex Kuronya, Stefan Muller-Stach, Xavier Roulleau, Tomasz Szemberg
Negative Curves On Algebraic Surfaces, Thomas Bauer, Brian Harbourne, Andreas Leopold Knutsen, Alex Kuronya, Stefan Muller-Stach, Xavier Roulleau, Tomasz Szemberg
Department of Mathematics: Faculty Publications
We study curves of negative self-intersection on algebraic surfaces. In contrast to what occurs in positive characteristics, it turns out that any smooth complex projective surface X with a surjective non-isomorphic endomorphism has bounded negativity (i.e., that C2 is bounded below for prime divisors C on X). We prove the same statement for Shimura curves on Hilbert modular surfaces. As a byproduct we obtain that there exist only finitely many smooth Shimura curves on a given Hilbert modular surface. We. also show that any set of curves of bounded genus on a smooth complex projective surface must have bounded negativity
R0 Analysis Of A Spatiotemporal Model For A Stream Population, H. W. Mckenzie, Y. Jin, J. Jacobsen, M. A. Lewis
R0 Analysis Of A Spatiotemporal Model For A Stream Population, H. W. Mckenzie, Y. Jin, J. Jacobsen, M. A. Lewis
Department of Mathematics: Faculty Publications
Water resources worldwide require management to meet industrial, agricultural, and urban consumption needs. Management actions change the natural flow regime, which impacts the river ecosystem. Water managers are tasked with meeting water needs while mitigating ecosystem im- pacts. We develop process-oriented advection-diffusion-reaction equations that couple hydraulic flow to population growth, and we analyze them to assess the effect of water flow on population persistence. We present a new mathematical framework, based on the net reproductive rate R0 for advection-diffusion-reaction equations and on related measures. We apply the measures to popula- tion persistence in rivers under various flow regimes. This …