Related papers: Algebraic dynamics in O*-algebras: a perturbative …
Motivated by algebraic quantum field theory and our previous work we study properties of inductive systems of \ $C^*$-algebras over arbitrary partially ordered sets. A partially ordered set can be represented as the union of the family of…
A Markov approximation in open quantum dynamics can give unphysical results when a map acts on a state that is not in its domain. This is examined here in a simple example, an open quantum dynamics for one qubit in a system of two…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
This paper aims to maximize algebraic connectivity of networks via topology design under the presence of constraints and an adversary. We are concerned with three problems. First, we formulate the concave maximization topology design…
We study the geometric and dynamical structure induced by the return map associated with domains in the class \(\mathcal{O}_{C}\). This map, defined through a geometric round-trip between the convex core and the outer boundary, generates a…
This article deals with a particular class of shape and topology optimization problems: the optimized design is a region $G$ of the boundary $\partial \Omega$ of a given domain $\Omega$, which supports a particular type of boundary…
In this paper we study the lattice of restricted subalgebras of a restricted Lie algebra. In particular, we consider those algebras in which this lattice is dually atomistic, lower or upper semimodular, or in which every restricted…
Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any…
We characterize when a C*-cover admits a C*-dynamical extension of dynamics on an operator algebra in terms of the boundary ideal structure for the operator algebra in its maximal representation and show that the C*-covers that admit such…
We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursive subhomogeneous algebras, and they have an inductive…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
The weak formulation of parabolic problems with dynamic boundary conditions is rewritten in form of a partial differential-algebraic equation. More precisely, we consider two dynamic equations with a coupling condition on the boundary. This…
We consider perturbations of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator plus an indefinite potential. We consider both sublinear and superlinear perturbations and we determine how the set of positive…
It is sometimes desirable to produce for a nonlinear system of ODEs a new representation of simpler structural form, but it is well known that this goal may imply an increase in the dimension of the system. This is what happens if in this…
We consider finite approximations of a topological space $M$ by noncommutative lattices of points. These lattices are structure spaces of noncommutative $C^*$-algebras which in turn approximate the algebra $\cc(M)$ of continuous functions…
Algebraic effects are computational effects that can be represented by an equational theory whose operations produce the effects at hand. The free model of this theory induces the expected computational monad for the corresponding effect.…
In this review, we summarize the main ideas of perturbative algebraic quantum field theory, which is a rigorous framework combining some of the Haag-Kastler axioms with perturbative methods involving formal power series. It allows for the…
We consider one dimensional deformed Heisenberg algebra leading to existence of minimal length for coordinate operator and minimal and maximal uncertainty of momentum operator. For this algebra an exactly solvable Hamiltonian is…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
A finite dimensional system with a quadratic Hamiltonian constraint is Dirac quantized in holomorphic, antiholomorphic and mixed representations. A unique inner product is found by imposing Hermitian conjugacy relations on an operator…