arXiv research

Paper defines spectral triple and computes functional for nonminimal de Rham-Hodge operator.

In this paper, we get a Kastler-Kalau-Walze type theorem associated to nonminimal de Rham-Hodge operators on compact manifolds with boundary. We give two kinds of operator-theoretic explanations of the gravitational action in the case of four dimensional compact manifolds with flat boundary.

The paper proves formulas and theorems for statistical de Rham Hodge operators on manifolds with boundary.

The paper studies perturbations of de Rham Hodge operators on manifolds with or without boundaries.

Promotes spectral functionals to noncommutative fields and proves a theorem.

Paper introduces a new multilinear functional for spectral triples and computes its properties.

What is the suitable Laplace operator on vector fields for the Navier-Stokes equation on a Riemannian manifold? In this note, by considering Nash embedding, we will try to elucidate different aspects of different Laplace operators such as de Rham-Hodge Laplacian as well as Ebin-Marsden's Laplacian. A probabilistic repr…

Unified method for analyzing evolving manifolds using de Rham-Hodge theory.

Introduces a new Hodge theory using vector fields on manifolds.

Recent years have witnessed a trend that advanced mathematical tools, such as algebraic topology, differential geometry, graph theory, and partial differential equations, have been developed for describing biological macromolecules. These tools have considerably strengthened our ability to understand the molecular mech…

These lecture notes in the De Rham-Hodge theory are designed for a 1-semester undergraduate course (in mathematics, physics, engineering, chemistry or biology). This landmark theory of the 20th Century mathematics gives a rigorous foundation to modern field and gauge theories in physics, engineering and physiology. The…

The paper bounds bandwidth and focal radius for manifolds with positive isotropic curvature.

Discretizes Hodge-Dirac operators on a torus.

New method for manifold topological learning avoids remeshing issues.

We look at several problems in even dimensional conformal geometry based around the de Rham complex. A leading and motivating problem is to find a conformally invariant replacement for the usual de Rham harmonics. An obviously related problem is to find, for each order of differential form bundle, a ``gauge'' operator …

Computer algebra methods are applied to investigation of spectral asymptotics of elliptic differential operators on curved manifolds with torsion and in the presence of a gauge field. In this paper we present complete expressions for the second coefficient (E_2) in the heat kernel expansion for nonminimal operator on m…

Study biharmonic conformal immersions into anti-de Sitter space, proving rigidity and local existence.

Study biharmonic conformal immersions into anti-de Sitter space, proving rigidity and local existence.

In this paper we construct examples of Weil-Petersson geodesics with nonminimal ending laminations which have 1-dimensional limit sets in the Thurston compactification of Teichmüller space.

In the current paper the Lagrangian of a classical, relativistic point particle is obtained whose conjugate momentum satisfies the dispersion relation of a quantum wave packet that is subject to Lorentz violation based on a particular coefficient of the nonminimal Standard-Model Extension (SME). The properties of this …

New solutions found to Ginzburg-Landau equations on surfaces.

New solutions found for Ginzburg-Landau equations on complex manifolds.

Given a smooth hermitean vector bundle $V$ of fiber $\mathbb{C}^N$ over a compact Riemannian manifold and $\nabla$ a covariant derivative on $V$, let $P = -(\lvert g \rvert^{-1/2} \nabla_μ\lvert g \rvert^{1/2} g^{μν} u \nabla_ν+ p^μ\nabla_μ+q)$ be a nonminimal Laplace type operator acting on smooth sections of $V$ wher…

Spirals are not shortest paths in certain sub-Riemannian geometries.

Witten- Helffer-Sjöstrand theory is a considerable addition to the De Rham- Hodge theory for Riemannian manifolds and can serve as a general tool to prove results about comparison of numerical invariants associated to compact manifolds analytically, i.e. by using a Riemannian metric, or combinatorially, i.e by using a …

Formulas derived for operators on forms in anti-de Sitter spaces.

Let $P$ be a Laplace type operator acting on a smooth hermitean vector bundle $V$ of fiber $\mathbb{C}^N$ over a compact Riemannian manifold given locally by $P= - [g^{μν} u(x)\partial_μ\partial_ν+ v^ν(x)\partial_ν+ w(x)]$ where $u,\,v^ν,\,w$ are $M_N(\mathbb{C})$-valued functions with $u(x)$ positive and invertible. F…

We give a locally minimal, but not globally minimal bridge position of a knot, that is, an unstabilized, nonminimal bridge position of a knot. It implies that a bridge position cannot always be simplified so that the bridge number monotonically decreases to the minimal.

We prove existence and uniqueness of a sequence of differential intertwining operators for spherical principal series representations, which are realized on boundaries of anti de Sitter spaces. Algebraically, these operators correspond to homomorphisms of generalized Verma modules. We relate these families to the asymp…

We show that some curvature operators are locally invertible, in some weithted sobolev spaces, near the euclidian metric. (Nous montrons que certains opérateurs affines en la courbure de Ricci sont localement inversibles, dans des espaces de Sobolev à poids, au voisinage de la métrique euclidienne.)

We obtain an off-diagonal upper bound for Green and heat kernel of Laplace type operator on symmetric spaces.

We extend the study of the de Rham operator with ideal boundary conditions from the case of isolated conic singularities, as analyzed by Cheeger, to the case of arbitrary stratified pseudomanifolds. We introduce a class of ideal boundary operators and the notion of mezzoperversity, which intermediates between the stand…

New projection operators for multipatch spaces with stable properties.

Study reveals how boundary wave operator determines metric properties on anti-de Sitter spacetimes.

New Lipschitz de Rham theorem for $L_p$-cohomology.

Research resolves sign conventions in Floer theory for Morse-Bott case.

Study on sine-cones' spectra and stability under Ricci-de Turck flow.

This paper questions some current ideas about the practice of specific capital market operations - the so-called day trading operations. The text advanced from theoretical propositions to a detailed analysis of the study entitled "Is it possible to live by day-trading?" (CHAGUE and GIOVANNETTI, 2019), to which it offer…

The aim of this paper is to propose an operational two-dimensional parametric adjustment for laws of maintenance in disability. The method suggested rests on splines in dimension 2; it is applied to a real data set, and the scale of reserving which results from it is compared with the scale of reference of the BCAC.

The paper classifies and proves properties of symmetry breaking operators for specific groups.

We consider the notion of the De Rham operator on finite-dimensional diffeological spaces such that the diffeological counterpart Λ^1(X) of the cotangent bundle, the so-called pseudo-bundle of values of differential 1-forms, has bounded dimension. The operator is defined as the composition of the Levi-Civita connection…

We are interested in the spectrum of the Hodge-de Rham operator on a cyclic covering $X$ over a compact manifold $M$ of dimension $n+1$. Let $Σ$ be a hypersurface in $M$ which does not disconnect $M$ and such that $M-Σ$ is a fundamental domain of the covering. If the cohomology group $H^{n/2 (Σ)$ is trivial, we can con…

A new method de-randomizes MCMC dynamics using the Stein operator.

We present Distributed Equivalent Substitution (DES) training, a novel distributed training framework for large-scale recommender systems with dynamic sparse features. DES introduces fully synchronous training to large-scale recommendation system for the first time by reducing communication, thus making the training of…

Algorithm computes eigenvalues and eigenforms on Calabi-Yau threefolds.

Study polynomial structures on generalized tangent bundles and their compatibility with operators.

We prove an analogue of the de Rham theorem for the extended L^2-cohomology introduced by M. Farber. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of A-modules over a finite von Neumann algebra A is chain-homotopy equivalent (with bound…

Constructs a support-preserving homotopy for differential forms with boundary decay estimates.