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...
Within finite element models of fluids, vector-valued fields such as velocity or momentum variables are commonly discretised using the Raviart-Thomas elements. However, when using the lowest-order quadrilateral Raviart-Thomas elements, standard finit...
Feb 4, 2023 · In some of these infinite-dimensional vector spaces, when they're normed, there may be Schauder Bases , where we have infinite sums, which require a notion of convergence.
We propose a novel neural network model for music signal processing using vector product neurons and dimensionality transformations. Here, the inputs are first mapped from real values into three-dimensional vectors then fed into a three-dimensional v...
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We propose a hybrid classical-quantum approach for modeling transition probabilities in health and disability insurance. The modeling of logistic disability inception probabilities is formulated as a support vector regression problem. Using a quantum...
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