Let $G$ be a fct Lie group and let $U$ $V$ finite-dimensional real $G$-modules with $V^G=0$. A theorem of Marzantowicz, de Mattos dos Santos estimates the covering dimension zero-set $G$-map from unit sphere in to when is an elementary abelian $p$-group for some prime $p$ or torus. In this note, classical Borsuk-Ulam will used give refinement their result estimating that part on which acts free...

1.1. We denote by V a connected ^-dimensional complete Riemannian manifold, by d = d(V) the diameter of V, and by c = c(V) and c~ = c~(V), respectively, the upper and lower bounds of the sectional curvature of V. We set c = c(V) = max (| c1, | c~ |). We say that F i s ε-flat, ε > 0, if cd < ε. 1.2. Examples. a. Every compact flat manifold is ε-flat for any ε > 0. b. Every compact nil-manifold p...

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...

Let q be a prime power and Fq be the finite field with q elements. A q-ary m-sequence is a linear recurrence sequence of elements from Fq with the maximum possible period. A covering array CA(N ; t, k, v) of strength t is a N ×k array with entries from an alphabet of size v, with the property that any N×m subarray has at least one row equal to every possible m-tuple of the alphabet. The coverin...

A singl~ change neighbor design SCN(v, k) is a way of selecting a sequence of cycles of length k from a complete graph on v vertices with the properties: any cycle is derived from the preceding one by changing one vertex; and every· edge is covered in at least one cycle. Some properties of these designs are investigated. In particular, designs with the smallest possible number of cycles are con...

We give a proof of a general construction of a (2m,3,m−1)-uncovering, which is equivalent to a (2m,2m−3,m−1)-covering design. Furthermore, we calculate the Schönheim Bound explictly for these parameters, and show that our construction gives uncoverings within a constant factor of this bound. We also give an induced construction for (2m−1,4,m−2)-uncovering. 1 Coverings and uncoverings Covering d...

Let λ : G̃ → G be the non-trivial double covering of the symplectic group G = Sp(V, ω) of the symplectic vector space (V, ω) by the metaplectic group G̃ = Mp(V, ω). In this case, λ is also a representation of G̃ on the vector space V and thus, it gives rise to the representation of G̃ on the space of exterior forms ∧• V by taking wedge products. Let S be the minimal globalization of the Harish-Chan...