Related papers: Geometrically Constrained Localized Configurations…
These are pedagogical notes on the Hamiltonian formulation of constrained dynamical systems. All the examples are finite dimensional, field theories are not covered, and the notes could be used by students for a preliminary study before the…
This article is a continuation of a previous work that dealt with the topological obstructions to the reductions of the bundle of linear frames on a spacetime manifold for a particular chain of subgroups of GL(4). In this article, the…
Finding the Time-Optimal Parameterization of a Path (TOPP) subject to second-order constraints (e.g. acceleration, torque, contact stability, etc.) is an important and well-studied problem in robotics. In comparison, TOPP subject to…
A two dimensional Poincar$\acute{e}$-invariant self-dual field with constraints is studied in geometric way. We obtained its symplectic structure and conservative currents on space of solutions, which are also invariant under…
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
In this work, we investigate the existence of analytic solutions of static scalar fields on Lifshitz spacetimes. We evade Derrick's theorem on curved spacetimes by breaking general covariance and use first-order formalism to obtain…
Shape analysis concerns the problem of determining "shape invariants" for programs that perform destructive updating on dynamically allocated storage. In recent work, we have shown how shape analysis can be performed, using an abstract…
Higher-order topology is prized for its ability to realize lower-dimensional boundary states which are stable beyond fine-tuning. However, disorder presents a failure mechanism that can destroy topological in-gap states. Here, we…
We consider the enumeration problem of first-order queries over structures of bounded degree. It was shown that this problem is in the Constant-Delaylin class. An enumeration problem belongs to Constant-Delaylin if for an input of size n it…
Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified…
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
Using the dual of Bousfield-Friedlander localization we colocalize resolution model structures on cosimplicial objects over a left proper model category to get truncated resolution model structures. These are useful to study realization and…
Constrained Hamiltonian systems fall into the realm of presymplectic geometry. We show, however, that also Poisson geometry is of use in this context. For the case that the constraints form a closed algebra, there are two natural Poisson…
From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models…
We are dealing with the problem of space layout planning here. We present an architectural conceptual CAD approach. Starting with design specifications in terms of constraints over spaces, a specific enumeration heuristics leads to a…
Carrying out perturbations around a lattice topological field theory in two dimensions, we show that it is on a first order phase transition fixed point with multiplicity ${n(n-1)/2}$, where $n$ is the number of its independent physical…
We discuss first order optimality conditions for geometric optimization problems with Neumann boundary conditions and boundary observation. The methods we develop here are applicable to large classes of state systems or cost functionals.…
This paper proposes an algorithmic framework for various reconfiguration problems using zero-suppressed binary decision diagrams (ZDDs), a data structure for families of sets. In general, a reconfiguration problem checks if there is a…
We introduce the concept of a class of graphs, or more generally, relational structures, being locally tree-decomposable. There are numerous examples of locally tree-decomposable classes, among them the class of planar graphs and all…
We present a unified framework to construct well-posed formulations for large classes of linear operator equations including elliptic, parabolic and hyperbolic partial differential equations. This general approach incorporates known weak…