Related papers: Quantitative nonorientability of embedded cycles

We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…

We generalize the notion of length to an ordinal-valued invariant defined on the class of finitely generated modules over a Noetherian ring. A key property of this invariant is its semi-additivity on short exact sequences. As an…

J.H.C. Whitehead introduced the concept of crossed modules in the early 20th century. These crossed modules are crucial for algebraic models of 2-type homotopy, which involve connected spaces with no higher than second-degree homotopy…

Loop groups G as families of mappings of the complex manifold M into another complex manifold N preserving marked points $s_0\in M$ and $y_0\in N$ are investigated. Quasi-invariant measures $\mu $ on G relative to dense subgroups $G'$ are…

In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…

We show that the presence of a two-dimensional inertial manifold for an ordinary differential equation in ${\mathbb R}^{n}$ permits reducing the problem of determining asymptotically orbitally stable limit cycles to the Poincare--Bendixson…

One of the most important problems in the studying of frames and its extensions is the invariance of these systems under perturbation. The current paper is concerned with the invariance of Modular biframes for operators under some class of…

The quantum mechanical measurement problem is the difficulty of dealing with the indefiniteness of the pointer observable at the conclusion of a measurement process governed by unitary quantum dynamics. There has been hope to solve this…

In this paper some piecewise smooth perturbations of a three-dimensional differential system are considered. The existence of invariant manifolds filled by periodic orbits is obtained after suitable small perturbations of the original…

We assign some kind of invariant manifolds to a given integrable PDE (its discrete or semi-discrete variant). First, we linearize the equation around its arbitrary solution $u$. Then we construct a differential (respectively, difference)…

We define an isotopy invariant of embeddings N -> R^m of manifolds into Euclidean space. This invariant together with the \alpha-invariant of Haefliger-Wu is complete in the dimension range where the \alpha-invariant could be incomplete. We…

We present and analyze rigorously a quadratically convergent algorithm to compute an invariant circle for 2-dimensional maps along with the corresponding foliation by stable manifolds. We prove that when the algorithm starts from an initial…

Canonical metrics and conformal invariants are presented for closed oriented even-dimensional manifolds with non-degenerate conformal structures and in particular for compact Riemann surfaces.

In this paper, we investigate the space of certain weak stability conditions on the triangulated category of D0-D2-D6 bound states on a smooth projective Calabi-Yau 3-fold. In the case of a quintic 3-fold, the resulting space is interpreted…

We study harmonic and totally invariant measures in a foliated compact Riemannian manifold isometrically embedded in an Euclidean space. We introduce geometrical techniques for stochastic calculus in this space. In particular, using these…

The intrinsic unsharpness of a quantum observable is studied by introducing the notion of resolution width. This quantification of accuracy is shown to be closely connected with the possibility of making approximately repeatable…

We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.

Uncertainty estimation is critical for numerous applications of deep neural networks and draws growing attention from researchers. Here, we demonstrate an uncertainty quantification approach for deep neural networks used in inverse problems…

Electrical impedance tomography aims at reconstructing the conductivity inside a physical body from boundary measurements of current and voltage at a finite number of contact electrodes. In many practical applications, the shape of the…

In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we…