where B ∈ C, C ∈ C are fixed matrices and ∆ is an element of a subset ∆ of C. It is assumed that ∆ is closed, connected and contains the zero matrix. The size of a perturbation ∆ ∈ ∆ is measured by a norm ‖ · ‖ on C. (a) The structued pseudospectrum (also called spectral value set) of the triple (A,B,C) with respect to the perturbation class ∆, the underlying norm ‖ · ‖ and the perturbation lev...

Planar coincidence site lattices and modules with N -fold symmetry are well understood in a formulation based on cyclotomic fields, in particular for the class number one case, where they appear as certain principal ideals in the corresponding ring of integers. We extend this approach to multiple coincidences, which apply to triple or multiple junctions. In particular, we give explicit results ...

We develop a general framework to describe dualities from algebraic, differential, and noncommutative geometry, as well as physics. We pursue a relationship between the Baum-Connes conjecture in operator K-theory and derived equivalence statements in algebraic geometry and physics. We associate to certain data, reminiscent of spectral triple data, a differential graded category in such a way th...

satellite imagery was used as a rapid and spatially explicit method to delineate crop residue cover and to estimate the use and intensity of conservation tillage. the potential of multispectral high-spatial resolution of worldview-2 local data was evaluated using 11 satellite spectral indices and linear spectral unmixing analysis (lsua). experimental plots were examined; residue cover was measu...

A semifinite spectral triple for an algebra canonically associated to canonical quantum gravity is constructed. The algebra is generated by based loops in a triangulation and its barycentric subdivisions. The underlying space can be seen as a gauge fixing of the unconstrained state space of Loop Quantum Gravity. This paper is the second of two papers on the subject. email: johannes.aastrup@uni-...

We investigate conditions on a graph C∗-algebra for the existence of a faithful semifinite trace. Using such a trace and the natural gauge action of the circle on the graph algebra, we construct a smooth (1,∞)-summable semfinite spectral triple. The local index theorem allows us to compute the pairing with K-theory. This produces invariants in the K-theory of the fixed point algebra, and these ...

In this work, the double and triple poles soliton solutions for Gerdjikov-Ivanov(GI) type of derivative nonlinear Schr\"{o}dinger equation with zero boundary conditions(ZBCs) nonzero conditions(NZBCs) are studied via Riemann-Hilbert (RH) method. Though spectral problem analysis, we first give out Jost function scattering matrix under ZBCs NZBCs. Then according to analyticity, symmetry asymptoti...

As a generalization of the triple I method, the universal triple Imethod is investigated from the viewpoints of both fuzzy reasoningand fuzzy controller. The universal triple I principle is putforward, which improves the previous triple I principle. Then,unified form of universal triple I method is established based onthe (0,1)-implication or R-implication. Moreover, the reversibilityproperty o...

1. The telescope conjecture and Bousfield localization 4 1.1. Telescopes 4 1.2. Bousfield localization and Bousfield classes 6 1.3. The telescope conjecture 8 1.4. Some other open questions 9 2. Some variants of the Adams spectral sequence 10 2.1. The classical Adams spectral sequence 11 2.2. The Adams-Novikov spectral sequence 12 2.3. The localized Adams spectral sequence 15 2.4. The Thomified...

Let S⊂L2⊂S∗ be the Gel'fand triple over Bernoulli space, where elements of S∗ are called generalized functionals. In this paper, we define integrals functionals with respect to a spectral measure (projection operator-valued measure) in framework S⊂L2⊂S∗, and examine their fundamental properties. New notions introduced, several results obtained examples also shown.