arXiv research

A new proof of an extension theorem with bounded generators.

Solves division problem for L. Hörmander's systems.

Proves Skoda's Division Theorem using degeneration and positivity of direct image bundles.

The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.

The paper revisits Rokhlin's divisibility theorem and its significance.

Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on the trivial bundle, our results recover Skoda's division theorem for holomorphic …

Geodesic connectedness proved for statistical manifolds with divisible cubic forms.

Uniform convexity in divisible domains leads to hyperbolic geometry.

An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts co-compactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are strictly convex, have $C^1$ boundary, and have word hyperbolic divid…

It is proved that the Wedderburn Theorem on finite division rings implies that all knots and links in the smooth 4-dimensional manifolds are trivial.

Completeness theorem for flat pseudo-Riemannian manifolds of signature (2,2).

Proves generic surjectivity of vector bundles via degeneration.

Proves divisibility relations for symplectic curve polynomials.

v2: An additional assumption was added in Theorem 4.8. In order to show that a connected abelian group is admissible on the site of locally compact spaces we must in addition assume that it is locally topologically divisible. This condition is used in the proof of Lemma 4.62.

Paper tackles division difficulty, proposing new methods to improve accuracy.

In contrast to the many examples of convex divisible domains in real projective space, we prove that up to projective isomorphism there is only one convex divisible domain in the Grassmannian of $p$-planes in $\mathbb{R}^{2p}$ when $p > 1$. Moreover, this convex divisible domain is a model of the symmetric space associ…

Division algorithm for surface group rings yields standard complexes and cohomological dimensions.

Adopting a zonal structure of electricity market requires specification of zones' borders. In this paper we use social welfare as the measure to assess quality of various zonal divisions. The social welfare is calculated by Market Coupling algorithm. The analyzed divisions are found by the usage of extended Locational …

New proof of divisibility property for certain algebraic varieties.

The paper sets lower bounds on envy-free divisions in cake-cutting problems.

Researchers infer gene activity in dividing cells, accounting for protein inheritance and division history.

Paper finds local normal forms for wavefronts in flat coordinates.

Furuta's ``10/8-th's'' theorem gives a bound on the magnitude of the signature of a smooth spin 4-manifold in terms of the second Betti number. We show that in the presence of a Z/2^p action, his bound can be strengthened. As applications, we give new genus bounds on classes with divisibility and we give a classificati…

Algorithm learns fair division from noisy feedback in uncertain markets.

Study of characteristic numbers in 24-dimensional String manifolds.

If all but two vertices of a triangulated sphere have degrees divisible by $k$, then the exceptional vertices are not adjacent. This theorem is proved for $k=2$ with the help of the coloring monodromy. For $k = 3, 4, 5$ colorings by the vertices of platonic solids have to be used. With a coloring monodromy one can asso…

In this note we introduce a construction which assigns to an arbitrary manifold bundle its fiberwise orientation covering. This is used to show that the zeta classes of unoriented surface bundles are not divisible in the stable range.

Generalizes Rochlin's theorem to 4-manifolds with boundary and arbitrary 3-manifold boundaries.

Study shows non-symmetric convex sets have full boundary limits.

Supersymmetry is deeply related to division algebras. Nonabelian Yang-Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green-Schwarz superstring. In both cases, supersymmetry relies on the vanishing of a certain tr…

Since most of the traded options on individual stocks is of American type it is of interest to generalize the results obtained in semi-static trading to the case when one is allowed to statically trade American options. However, this problem has proved to be elusive so far because of the asymmetric nature of the positi…

We consider the Alexander polynomial of a plane algebraic curve twisted by a linear representation. We show that it divides the product of the polynomials of the singularity links, for unitary representations. Moreover, their quotient is given by the determinant of its Blanchfield intersection form. Specializing in the…

We present a short proof of the following Pontryagin theorem, whose original proof was complicated and has never been published in details: {\bf Theorem.} Let $M$ be a connected oriented closed smooth 3-manifold. Let $L_1(M)$ be the set of framed links in $M$ up to a framed cobordism. Let $°:L_1(M)\to H_1(M;\Z)$ be the…

Study of congestion in negative curvature manifolds using fair-division algorithms.

LLMs can collude in market divisions, maximizing profits.

Constructs modular forms and proves divisibility results for odd-dimensional manifolds.

New invariants from divisibility of Lee classes for slice-torus.

This a free translation with additional explanations of {\em Processus à Accroissement Independants Chapitre I: La Décomposition de Paul Lévy}, by J.L. Bretagnolle, in {\em Ecole d'Eté de Probabilités}, Lecture Notes in Mathematics 307, Springer 1973. The Lévy-Khintchine representation of infinitely divisible distribut…

In this article we consider a version of the geography question for simply-connected symplectic 4-manifolds that takes into account the divisibility of the canonical class as an additional parameter. We also find new examples of 4-manifolds admitting several symplectic structures, inequivalent under deformation and sel…

In this work, we examine the process of Tropical Polynomial Division, a geometric method which seeks to emulate the division of regular polynomials, when applied to those of the max-plus semiring. This is done via the approximation of the Newton Polytope of the dividend polynomial by that of the divisor. This process i…

We prove that some symetric semi-riemannian manifolds do not admit a proper domain which is divisible by the action of a discrete group of isometries. In other words, if a closed semi-riemannian manifold is locally isometric to such a model, and if its developing map is injective, then the manifold is actually geodesic…

HiPart offers an efficient, interactive tool for hierarchical clustering.

In this short article we give a geometric meaning of the divisibility of $KO$-theoretical Euler classes for given two spin modules. We are motivated by Furuta's 10/8-inequality for a closed spin $4$-manifold. The role of the reducibles is clarified in the monopole equations of Seiberg-Witten theory, as done by Donaldso…

New algorithms for fair item allocation with limited copies.

A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite divisible distribution, and particularly elliptical tempered stable distribution, w…

Classically, isothermic surfaces are characterized as those surfaces which are "divisible into infinitesimal squares by their curvature lines". This characterization is the direct analogue to the definition of discrete isothermic nets. In order to understand the relations between the discrete and the smooth theory bett…

Proves positive Euler characteristic for certain manifolds with positive second intermediate Ricci curvature.

The paper connects polygon spaces with quotient spaces using spin actions and normed division algebras.