for any smooth projective variety X over a field k. Here CH(X)Q is the Chow group of codimension p algebraic cycles modulo rational equivalence on X with Q-coefficients, and DMM(X) is the bounded derived category of the (conjectural) abelian category of mixed motivic sheaves onX . By the adjoint relation for the structure morphism aX : X → Spec k, the conjecture would be equivalent to the bijec...

Domain Theory provides a denotational semantics for programming languages and calculi containing fixed point combinators and other so-called paradoxical combinators. This dissertation presents results in the category theory and type theory of Axiomatic Domain Theory. Prompted by the adjunctions of Domain Theory, we extend Benton’s linear/nonlinear dualsequent calculus to include recursive linea...

Motivated by recent theoretical results obtained by the third author for the identification problem arising in single-photon emission computerized tomography (SPECT), we propose an adjoint state method for recovering both the source and the attenuation in the attenuated X-ray transform. Our starting point is the transport-equation characterization of the attenuated X-ray transform, and we apply...

Using Voiculescu’s notion of a matricial microstate we introduce fractal dimensions and entropy for finite sets of self-adjoint operators in a tracial von Neumann algebra. We show that they possess properties similar to their classical predecessors. We relate the new quantities to free entropy and free entropy dimension and show that a modified version of free Hausdorff dimension is an algebrai...

We consider eigenvalue problems for self-adjoint Sturm-Liouville difference equations of any even order. It is well known that such problems with Dirichlet boundary conditions can be transformed into an algebraic eigenvalue problem for a banded, real-symmetric matrix, and vice versa. In this article it is shown that such a transform exists for general separated, self-adjoint boundary conditions...

Let G be a connected reductive algebraic group with Lie algebra g. The ground field k is algebraically closed and of characteristic zero. Fundamental results in invariant theory of the adjoint representation ofG are primarily associated with C. Chevalley and B. Kostant. Especially, one should distinguish the ”Chevalley restriction theorem” and seminal article of Kostant [5]. Later, Kostant and ...

We introduce the compactness locus of a geometric functor between rigidly-compactly generated tensor-triangulated categories, and describe it for several examples arising in equivariant homotopy theory and algebraic geometry. It is a subset of the tensor-triangular spectrum of the target category which, crudely speaking, measures the failure of the functor to satisfy Grothendieck-Neeman duality...

We give a construction of nonsmooth self-dual projective algebraic varieties. They appear as certain projectivized orbit closures for some linear actions of reductive algebraic groups. Applying this construction to adjoint representations, we obtain geometric characterization of distinguished nilpotent elements of semisimple Lie algebras [BC1], [BC2] (i.e., nilpotent elements whose centralizer ...

We are interested in the simulation and optimization of gas transport in networks. The gas flow through pipes can be modelled on the basis of the (isothermal) Euler equations. Further network components are described by purely algebraic equations. Depending on the data and the resulting network dynamics, models of different fidelity can be used in different regions of the network. Using adjoint...

For a graph G, we denote by P (G, λ) the chromatic polynomial of G and by h(G, x) the adjoint polynomial of G. A graph G is said to be chromatically unique if for any graph H, P (H, λ) = P (G, λ) implies H ∼= G. In this paper, we investigate some algebraic properties of the adjoint polynomials of some graphs. Using these properties, we obtain necessary and sufficient conditions for Kn − E(∪a,bT...