We use non-standard analysis to define a category ?Hilb suitable for categorical quantum mechanics in arbitrary separable Hilbert spaces, and we show that standard bounded operators can be suitably embedded in it. We show the existence of unital special commutative †-Frobenius algebras, and we conclude ?Hilb to be compact closed, with partial traces and a Hilbert-Schmidt inner product on morphi...

We present a new application of affine Lie algebras to massive quantum field theory in 2 dimensions, by investigating the q → 1 limit of the q-deformed affine ŝl(2) symmetry of the sine-Gordon theory, this limit occurring at the free fermion point. Working in radial quantization leads to a quasi-chiral factorization of the space of fields. The conserved charges which generate the affine Lie alg...

We work through, in detail, the quantum cohomology of the orbifold BG, the point with action of a finite group G. We provide a simple description of algebraic structures on the state space of this theory. As a consequence, we find that multiple copies of commuting Virasoro algebras appear in this theory which completely determine the correlators of the theory. For the Proceedings of the Mathema...

While the creation of convincing cityscapes from the outside is already possible, there is a lack of robust and efficient techniques for modeling the interior of buildings. In particular, we focus on challenges for the subdivision of the interior space into rooms and for placement of furniture in those rooms.

This paper is concerned with the sensitivities of function space oriented interior point approximations in parameter dependent optimization problems. For an abstract setting that covers control constrained optimal control problems, the convergence of interior point sensitivities to the sensitivities of the optimal solution is shown. Error bounds for Lq norms are derived and illustrated with num...

This paper discusses the so called holographic solution, in short ”holostar”. The holostar is the simplest exact, spherically symmetric solution of the original Einstein field equations with zero cosmological constant, including matter. The interior matter-distribution follows an inverse square law ρ = 1/(8πr). The interior principal pressures are Pr = −ρ and P⊥ = 0, which is the equation of st...

In single-photon emission computed tomography (SPECT), projection data can be truncated when the camera's field of view is smaller than the object to be imaged. Using truncated projections to reconstruct a region of interest (ROI) is a reality we must face if small detectors are used. The truncated data result in an underdetermined system of imaging equations, which may lead to non-unique solut...

The unilateral shift S acting on Hilbert space H is one of the most studied operators. Much is known about its structure, and this success is in large part due to the identification of S with the operator of multiplication by z on H — the Hardy space on the unit disk. From the function theory point of view, the commutant {S}′ is then simply H∞, the Hardy space of essentially bounded functions o...