arXiv research

Improved indefinite Kasparov modules for non-elliptic operators.

We use computer algebra to demonstrate the existence of a multilinear polynomial identity of degree 8 satisfied by the bilinear operation in every Lie-Yamaguti algebra. This identity is a consequence of the defining identities for Lie-Yamaguti algebras, but is not a consequence of anticommutativity. We give an explicit…

Paper establishes maximum principles for weakly 1-coercive operators.

The intertwining operator constructed in [Sz1,Sz2] does not appear in the right form. It is established there by using only the anticommutators. The correct operator must involve all endomorphisms, which are unified by the Z-Fourier transform. Although some of the correct elements of the previous constructions are kept…

We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature invariants decay at infinity, identifying a conformally invariant tensor which serves a…

The study examines weakly Einstein Lie groups and proves non-existence for certain types.

The paper studies hypersurfaces in specific nearly Kähler manifolds and their properties.

We study the lightlike foliations that appear on Lorentzian manifolds with weakly irreducible not irreducible holonomy algebra. We give global structure equations for the foliation that generalize the Gauss and Weingarten equations for one lightlike hypersurface. This gives us some global operators on the manifold. Usi…

The Bergman-Szegő kernel is analyzed for weakly pseudoconvex CR manifolds of finite type.

A linear different operator L is called weakly hypoelliptic if any local solution u of Lu=0 is smooth. We allow for systems, that is, the coefficients may be matrices, not necessarily of square size. This is a huge class of important operators which cover all elliptic, overdetermined elliptic, subelliptic and parabolic…

We re-examine classical mechanics with both commuting and anticommuting degrees of freedom. We do this by defining the phase dynamics of a general Lagrangian system as an implicit differential equation in the spirit of Tulczyjew. Rather than parametrising our basic degrees of freedom by a specified Grassmann algebra, w…

We present new results concerning the solvability, of lack thereof, in the Cauchy problem for the debar operator, with initial values assigned on a weakly pseudoconvex hypersurface, and provide illustrative examples.

A gauged bi-differential calculus over an associative (and not necessarily commutative) algebra A is an N-graded left A-module with two covariant derivatives acting on it which, as a consequence of certain (e.g., nonlinear differential) equations, are flat and anticommute. As a consequence, there is an iterative constr…

We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The class of noncommutative spaces studied is very rich. Non-anticommutative superspa…

Let $G/K$ be an irreducible Hermitian symmetric spaces of compact type with the standard homogeneous complex structure. Then the real symplectic manifold $(T^*(G/K),Ω)$ has the natural complex structure $J^-$. We construct all $G$-invariant Kähler structures $(J,Ω)$ on homogeneous domains in $T^*(G/K)$ anticommuting wi…

Using a supergeometric interpretation of field functionals developed in previous papers, we show that for quite a large class of systems of nonlinear field equations with anticommuting fields, infinite-dimensional supermanifolds (smf) of classical solutions can be constructed. Such systems arise in classical field mode…

Let P be a knot in a solid torus, K a knot in 3-space and P(K) the satellite knot of K with pattern P. This defines an operator on the set of knot types and induces a satellite operator P:C--> C on the set of smooth concordance classes of knots. There has been considerable interest in whether certain such functions are…

We prove that the empirical risk of most well-known loss functions factors into a linear term aggregating all labels with a term that is label free, and can further be expressed by sums of the loss. This holds true even for non-smooth, non-convex losses and in any RKHS. The first term is a (kernel) mean operator --the …

Disk surgery on primitive disks of genus-3 Heegaard splittings of 3-sphere yields no primitive disks.

New single-loop algorithm tackles weakly convex constraints in stochastic optimization.

A Lie-admissible algebra gives by anticommutativity a Lie algebra. In this work we study remarkable classes of Lie-admissible algebras such as Vinberg, PreLie algebras. We compute the corresponding binary quadratic operads and study their Koszul duality. Considering Lie algebras as Lie-admissible algebras we can define…

This work is motivated by numerical solutions to Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVIs) associated with combined stochastic and impulse control problems. In particular, we consider (i) direct control, (ii) penalized, and (iii) semi-Lagrangian discretization schemes applied to the HJBQVI proble…

Sharp bounds derived for eigenvalues on specific geometric spaces.

Free differential algebras (FDA's) provide an algebraic setting for field theories with antisymmetric tensors. The "presentation" of FDA's generalizes the Cartan-Maurer equations of ordinary Lie algebras, by incorporating p-form potentials. An extended Lie derivative along antisymmetric tensor fields can be defined, an…

EM algorithm converges slowly for weakly identifiable Gaussian mixtures.

Quaternionic analysis proves minimum of Willmore functional on Riemann surfaces.

We investigate geometric invariants of the one parameter family of Mukai threefolds that admit $\mathbb C^{*}$ action. In particular we find the invariant divisors in the anticanonical system, and thus establish a bound on the log canonical thresholds. Furthermore we find an explicit description of such threefolds in t…

The homotopy groups of the (stabilized) group of invertible pseudodifferential operators of order zero acting on a closed manifold X are computed in terms of the K-theory of the cosphere bundle S*X. At the same time, we show that the subgroup of invertible compact perturbations of the identity is weakly retractable ins…

Active learning improves inspection systems by using weakly labeled data.

Extends compactness theory to variable-coefficient pseudo-differential operators on manifolds.

Weakly Einstein Kähler surfaces are characterized and classified.

We consider a class of abstract nonlinear evolution equations in supermanifolds (smf's) modelled over Z_2-graded locally convex spaces. We show uniqueness, local existence, smoothness, and an abstract version of causal propagation of the solutions. If an a-priori estimate prevents the solutions from blowing-up then an …

Classifies weakly Einstein submanifolds in space forms satisfying specific equalities.

New differential operator helps characterize non-collapsed RCD spaces.

Fixed points of mean section operators found in convex bodies.

The study explores weakly $p$-Kähler hyperbolic manifolds.

Positive surgery on knots in weakly fillable 3-manifolds yields weakly fillable contact structures.

Develops Poisson structures on weak Sobolev loop spaces for integrable systems.

We discuss of the conceptual difficulties connected with the anticommutativity of classical fermion fields, and we argue that the "space" of all classical configurations of a model with such fields should be described as an infinite-dimensional supermanifold M. We discuss the two main approaches to supermanifolds, and …

Study weakly weighted Einstein-Finsler metrics, showing specific curvature properties and characterizing them.

The paper provides examples of keen weakly reducible bridge spheres for links in b-bridge position.

Novel boundary integral equations for Dirac operators in 3D Lipschitz domains.

Researchers create a method to join hyperboloidal data sets without violating the shear-free condition.

ParPIC clusters directed graphs using random walks and diffusion operators.

The study examines weakly Einstein metrics on specific types of manifolds.

The first isospectral pairs of metrics are constructed on balls and spheres. This long standing problem, concerning the existence of such pairs, has been solved by a new method called "Anticommutator Technique." Among the wide range of such pairs, the most striking examples are provided on (4k-1)-dimensional spheres, w…

Minimal displacement set in weakly systolic complexes is systolic and embeds isometrically.

Study on extended weakly symmetric spaces, classifying and providing an example.