5,400 research outputs found
Fixture facilitates helium leak testing of pipe welds
Fixture facilitates inspection testing of circumferential pipe welds for vacuum tightness, using helium gas as a leakage tracer in conjunction with a mass spectrometer. It consists of a split rubber torus and a mating clamping ring with a vacuum hose fitting
On the record: tapping technology for immigration enforcement: a conversation with Lisa Roney
Immigration consultant Lisa Roney, former director of Research and Evaluation in the U.S. Citizenship and Immigration Services' Office of Policy and Strategy, discusses the government's E-Verify program.Emigration and immigration ; Immigrants ; Technological innovations
Carriage-rail assembly for high-resolution mechanical positioning
Carriage-rail assembly effects extreme resolution and position accuracy with little friction, and is applicable to such apparatus as optical benches, inspection fixtures, machine tools, and photographic equipment. Directions for assembly construction are given
A note on the probability of generating alternating or symmetric groups
We improve on recent estimates for the probability of generating the
alternating and symmetric groups and . In
particular we find the sharp lower bound, if the probability is given by a
quadratic in . This leads to improved bounds on the largest number
such that a direct product of copies
of can be generated by two elements
Constructive homomorphisms for classical groups
Let Omega be a quasisimple classical group in its natural representation over
a finite vector space V, and let Delta be its normaliser in the general linear
group. We construct the projection from Delta to Delta/Omega and provide fast,
polynomial-time algorithms for computing the image of an element. Given a
discrete logarithm oracle, we also represent Delta/Omega as a group with at
most 3 generators and 6 relations. We then compute canonical representatives
for the cosets of Omega. A key ingredient of our algorithms is a new,
asymptotically fast method for constructing isometries between spaces with
forms. Our results are useful for the matrix group recognition project, can be
used to solve element conjugacy problems, and can improve algorithms to
construct maximal subgroups
Coprime invariable generation and minimal-exponent groups
A finite group is \emph{coprimely-invariably generated} if there exists a
set of generators of with the property that the orders
are pairwise coprime and that for all
the set generates .
We show that if is coprimely-invariably generated, then can be
generated with three elements, or two if is soluble, and that has zero
presentation rank. As a corollary, we show that if is any finite group such
that no proper subgroup has the same exponent as , then has zero
presentation rank. Furthermore, we show that every finite simple group is
coprimely-invariably generated.
Along the way, we show that for each finite simple group , and for each
partition of the primes dividing , the product of the
number of conjugacy classes of -elements satisfies
$\prod_{i=1}^u k_{\pi_i}(S) \leq \frac{|S|}{2| Out S|}.
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