We study the interplay between the properties of the germ of a singular variety N ⊂ Rn given in the title and the algebra of vector fields tangent to N . The Poincare lemma property means that any closed differential (p+1)-form vanishing at any point ofN is a differential of a p-form which also vanishes at any point of N . In particular, we show that the classical quasi-homogeneity is not a nec...

This paper introduces two concepts of exceptional families for a class of nonlinear projection equations which provide a uniied formulation of several special cases such as nite-dimensional variational inequalities and complementarity problems. Based on these concepts, two alternative theorems, and then two suucient existence conditions, are established for this class of nonlinear projection eq...

A (complex) Enriques surface is a projective smooth connected algebraic surface Y over C with H(Y,OY ) = H (Y,OY ) = (0), (Ω 2 Y ) ⊗ 2 ≃ OY but Ω 2 Y 6≃ OY ([CF]). In this note we give a short proof of the fact that the coarse moduli space of complex Enriques surfaces is quasi-affine. This was first shown by Borcherds [B] using the denominator function of a generalized Kac-Moody superalgebra (t...

For a quasidifferentiable function f defined on R 2 , it is proved, in the sense of Demyanov and Rubinov, that the following assertion [∂f (x),∂f (x)]∈Df (x) (∂f (x) + ∂f (x)), [∂f (x),∂f (x)]∈Df (x) (∂f (x) − ∂f (x)) ∈ Df (x) in this paper, where Df (x) denotes the set of all quasidifferentials of f at x. It is shown that this way can be viewed as an approach to determining or choosing a repre...

Golomb and Welch conjectured in 1970 that there only exist perfect Lee codes for radius t = 1 or dimension n = 1, 2. It is admitted that the existence and the construction of quasi-perfect Lee codes have to be studied since they are the best alternative to the perfect codes. In this paper we firstly highlight the relationships between subset sums, Cayley graphs, and Lee linear codes and present...

‎We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups‎. ‎We prove Arthur's conjecture‎, ‎the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group‎, ‎for quasi-split special unitary groups and their inner forms‎. ‎Furthermore‎, ‎we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms‎. ‎This w...

We consider several distances between two sets of points, which are modifications of the Hausdorff metric, and apply them to describe some fractals such as δ-quasi-self-similar sets, and some other geometric notions in Euclidean space, such as tilings with quasi-prototiles and patterns with quasi-motifs. For the δ-quasi-self-similar sets satisfying the open set condition we obtain the same resu...