arXiv research

We review the basic definitions and properties concerning smooth structures, convenient spaces, diffeological spaces and tangent structures. The relation betwen them is described. A tangent structure is constructed for each pre-convenient space. This one is proved to be convenient iff the space and the tangent fibres c…

Extends Dirac structures to infinite dimensions, focusing on convenient Lie algebroids and manifolds.

The paper extends Nambu-Poisson structures to infinite dimensions.

Study projective and direct limits of Banach structures with connections to $G$-structures.

Introduces partial Jacobi manifolds in convenient spaces.

Survey on Nambu-Poisson structures in infinite dimensions.

The study explains why signature methods work in commodity futures term structure classification.

Extends Dirac structures to infinite dimensions for mechanical systems.

Lie algebras of quotient groups defined under specific conditions.

New risk measures incorporate economic states to assess crude oil derivatives.

We equip the direct limit of tangent bundles of paracompact finite dimensional manifolds with a structure of convenient vector bundle with structural group $GL(\infty,\mathbb{R}) =\underrightarrow{\lim}GL(\mathbb{R}^{n})$.

We prove that direct limits of finite dimensional Lie algebroids and their prolongations can be endowed with structures of convenient spaces.

Defines and extends Lie algebroid prolongations in convenient settings.

Introduces three types of partial bihamiltonian structures.

We define the notion of strong projective limit of Banach Lie algebroids. We study the associated structures of Fréchet bundles and the compatibility with the different morphisms. This kind of structure seems to be a convenient framework for various situations.

Paper examines floating exercise boundaries for American options in time-inhomogeneous models.

Cube category simplifies set modeling.

Kernelized PCovR reveals structure-property relations in chemistry and materials.

Discuss various definitions of vector fields on manifolds leading to Lie algebras.

We introduce the concept of partial Poisson structure on a manifold $M$ modelled on a convenient space. This is done by specifying a (weak) subbundle $T^{\prime}M$ of $T^{\ast}M$ and an antisymmetric morphism $P:T^{\prime}M\rightarrow TM$ such that the bracket $\{f,g\}_{P}=-<df,P(dg)>$ defines a Poisson bracket on the …

Co-Euler structures were studied by Burghelea and Haller on closed manifolds as dual objects to Euler structures. We extend the notion of co-Euler structures to the situation of compact manifolds with boundary. As an application, by studying their variation with respect to smooth changes of the Riemannian metric, co-Eu…

We consider the problem of constructing Poisson brackets on smooth manifolds $M$ with prescribed Casimir functions. If $M$ is of even dimension, we achieve our construction by considering a suitable almost symplectic structure on $M$, while, in the case where $M$ is of odd dimension, our objective is achieved by using …

A new multi-factor model improves commodity pricing accuracy.

Generalizes Dolbeault cohomology computation to Levi-flat CR structures on compact Lie groups.

Overview of manifolds of mappings for continuum mechanics.

This paper is devoted to the framework of direct limit of anchored Banach bundles over a convenient manifold which is a direct limit of Banach manifold. In particular we give a criterion of integrability for distributions on such convenient manifolds which are locally direct limits of particular sequences of Banach anc…

In this paper it is shown that for any network there is a uniquely determined network based on a structure tree that provides a convenient way of determining a minimal cut separating a pair $s, t$ where each of $s, t$ is either a vertex or an end in the original network. A Max-Flow Min-Cut Theorem is proved for any net…

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally con…

Clarifies structures in link homology theories using Frobenius extensions.

Study shows how Poisson brackets factor on infinite dimensional manifolds.

Introduces Q-structures for mechanics using advanced geometry.

Rigging technique introduced in \cite{bi0} is a convenient way to address the study of null hypersurfaces. It offers in addition the extra benefit of inducing a Riemannian structure on the null hypersurface which is used to study geometric and topological properties on it. In this paper we develop this technique showin…

Caratheodory's axiom limits arbitrage in resource-limited systems.

We examine the space of solutions to the affine quasi--Einstein equation in the context of homogeneous surfaces. As these spaces can be used to create gradient Yamabe solitions, conformally Einstein metrics, and warped product Einstein manifolds using the modified Riemannian extension, we provide very explicit descript…

Constructs a triple on an Atiyah algebroid with connection.

This is the first in a series of papers showing that Haken manifolds have hyperbolic structures; this first was published, the second two have existed only in preprint form, and later preprints were never completed. This eprint is only an approximation to the published version, which is the definitive form for part I, …

In this paper we study collapsing sequences M_{i}-> X of Riemannian manifolds with curvature bounded or bounded away from a controlled subset. We introduce a structure over X which in an appropriate sense is dual to the N-structure of Cheeger, Fukaya and Gromov. As opposed to the N-structure, which live over the M_{i} …

Hierarchical structure is ubiquitous in data across many domains. There are many hierarchical clustering methods, frequently used by domain experts, which strive to discover this structure. However, most of these methods limit discoverable hierarchies to those with binary branching structure. This limitation, while com…

We show that isotopy classes of simple closed curves in any oriented surface admit a quandle structure with operations induced by Dehn twists, the Dehn quandle of the surface. We further show that the monodromy of a Lefschetz fibration can be conveniently encoded as a quandle homomorphism from the knot quandle of the b…

Machine learning classifies braids and discovers new invariants.

In this paper we develop a tractable structural model with analytical default probabilities depending on some dynamics parameters, and we show how to calibrate the model using a chosen number of Credit Default Swap (CDS) market quotes. We essentially show how to use structural models with a calibration capability that …

It is well known that the category of Frolicher spaces and smooth mappings is Cartesian closed. The principal objective in this paper is to show that the full subcategory of Frolicher spaces that believe in fantasy that every Weil functor is really an exponentiation by the corresponding infinitesimal object is also Car…

A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infi…

The aim of this paper is to study self-similar solutions to the symplectic cuvature flow on 6-dimensional nilmanifolds. For this purpose, we focus our attention in the family of symplectic Two- and Three-step nilpotent Lie algebras admitting a "minimal compatible metric" and we give a complete classification of these a…

Web browser autofill predicts form field labels for convenience.

In this new version, we correct some typos. For the readers' convenience, we also added some footnotes and more details for certain lemmas and theorems.

With a view towards applications in the theory of infinite-dimensional representations of finite-dimensional Lie supergroups, we introduce a new category of supermanifolds. In this category, supermanifolds of `maps' and `fields' (fibre bundle sections) exist. In particular, loop supergroups can be realised globally in …

We proved that the solutions of $C^2$ class of certain ODEs or PDEs belong to a class of harmonic maps between two convenient generalized Lagrange spaces.