We study infinitesimal deformations of autodual and hyper-holomorphic connections on complex vector bundles on hyper-Kähler manifolds of arbitrary dimension. In particular, we describe the DG Lie algebra controlling this deformation problem. Moreove...
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Let (f_n) be a mean zero vector valued martingale sequence. Then there exist vector valued functions (d_n) from [0,1]^n such that int_0^1 d_n(x_1,...,x_n) dx_n = 0 for almost all x_1,...,x_{n-1}, and such that the law of (f_n) is the same as the la...
In this paper we propose MA-DV2F: Multi-Agent Dynamic Velocity Vector Field. It is a framework for simultaneously controlling a group of vehicles in challenging environments. DV2F is generated for each vehicle independently and provides a map of refe...
In this Note we establish a relation between sections in globally generated holomorphic vector bundles on Kähler manifolds, isotropic with respect to a non-degenerate quadratic form, and totally geodesic foliations on Euclidean open domains. We find...
The purpose of the paper is to prove an analogous correspondence for the above prehomogeneous vector space (1)-(3). For case (1) the correspondence is bijective. However, it turns out that the correspondence is not bijective for cases (2), (3). We...
In this paper, we give an introduction to the rationality of the equivariant Morse stratification, and state the author's results on zeta functions of prehomogeneous vector spaces....
This is part one of a series of papers. In this series of papers, we consider problems analogous to the Oppenheim conjecture from the viewpoint of prehomogeneous vector spaces....
In this note, we prove that if $(G,V)$ is a prehomogeneous vector space over any field $k$ such that the stabilizer of a generic point is reductive, the set of semi-stable points is a single orbit over the separable closure of $k$....
Let (G,V) be an irreducible prehomogeneous vector space defined over a number field k, P in k[V] a relative invariant polynomial, and X a rational character of G such that P(gx)=X(g)P(x). Let V_k^{ss}={x \in V_k such that P(x) is not equal to 0}. F...
In this paper, we consider the most non-split parabolic D_4 type prehomogeneous vector space. The vector space is an analogue of the space of Hermitian forms. We determine the principal part of the zeta function....
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We define a turning of a rank-$2k$ vector bundle $E \to B$ to be a homotopy of bundle automorphisms $ψ_t$ from $\mathbb{Id}_E$, the identity of $E$, to $-\mathbb{Id}_E$, minus the identity, and call a pair $(E, ψ_t)$ a turned bundle. We investigate...
On a given manifold M, the Nijenhuis bracket makes the superspace of vector-valued differential forms into a Lie superalgebra that can be interpreted as the centralizer of the exterior differential considered as a vector field on the supermanifold...
We define a free uniformly complete vector lattice over a set of generators and give its concrete representation as a space of continuous positively homogeneous functions....
Soit $X$ une hypersurface lisse de degré $δ\geq 4$ dans $\pp ^3$ telle que $Pic(X)=Z$. On désigne par $M_X(c_2)$ l'espace de modules des fibrés vectoriels sur $X$ de classes de Chern $c_1 = 0$ et $c_2$, semi-stables par rapport au diviseur hype...
By using the Reggeometric Pomeron model for vector meson production which successfully describes the high energy lepton-nucleon data, we analyse the light meson production in ultra-peripheral heavy ion collisions at the Large Hadron Collider (LHC). T...