283,840 research outputs found
Super-rigidity for CR embeddings of real hypersurfaces into hyperquadrics
Let Q^N_l\subset \bC\bP^{N+1} denote the standard real, nondegenerate
hyperquadric of signature and M\subset \bC^{n+1} a real, Levi
nondegenerate hypersurface of the same signature . We shall assume that
there is a holomorphic mapping H_0\colon U\to \bC\bP^{N_0+1}, where is
some neighborhood of in \bC^{n+1}, such that
but . We show that if then, for any , any holomorphic mapping H\colon U\to \bC\bP^{N+1} with and must be the standard linear embedding
of into up to conjugation by automorphisms of
and
Lower bounds for identifying subset members with subset queries
An instance of a group testing problem is a set of objects \cO and an
unknown subset of \cO. The task is to determine by using queries of
the type ``does intersect '', where is a subset of \cO. This
problem occurs in areas such as fault detection, multiaccess communications,
optimal search, blood testing and chromosome mapping. Consider the two stage
algorithm for solving a group testing problem. In the first stage a
predetermined set of queries are asked in parallel and in the second stage,
is determined by testing individual objects. Let n=\cardof{\cO}. Suppose that
is generated by independently adding each x\in \cO to with
probability . Let () be the number of queries asked in the
first (second) stage of this algorithm. We show that if
, then \Exp(q_2) = n^{1-o(1)}, while there
exist algorithms with and \Exp(q_2) =
o(1). The proof involves a relaxation technique which can be used with
arbitrary distributions. The best previously known bound is q_1+\Exp(q_2) =
\Omega(p\log(n)). For general group testing algorithms, our results imply that
if the average number of queries over the course of ()
independent experiments is , then with high probability
non-singleton subsets are queried. This
settles a conjecture of Bill Bruno and David Torney and has important
consequences for the use of group testing in screening DNA libraries and other
applications where it is more cost effective to use non-adaptive algorithms
and/or too expensive to prepare a subset for its first test.Comment: 9 page
Nonnilpotent subsets in the susuki groups
Let G be a group and N be the class of nilpotent groups. A subset A of G is
said to be nonnilpotent if for any two distinct elements a and b in A, ha, bi
62 N. If, for any other nonnilpotent subset B in G, |A| ? |B|, then A is said
to be a maximal nonnilpotent subset and the cardinality of this subset (if it
exists) is denoted by !(NG). In this paper, among other results, we obtain
!(NSuz(q)) and !(NPGL(2,q)), where Suz(q) is the Suzuki simple group over the
field with q elements and PGL(2, q) is the projective general linear group of
degree 2 over the finite field of size q, respectively.Comment: submitte
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