
	Where results make sense

Topic: Butterfly lemma

Related Topics

Formal group law

Group theory

Standard Model

Laryngeal mask airway

In the News (Thu 24 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Zassenhaus lemma - Wikipedia, the free encyclopedia
		In mathematics, the butterfly lemma or Zassenhaus lemma, named after Hans Julius Zassenhaus, is a technical result on the lattice of subgroups of a group.
		Lemma: Suppose (G,Ω) is a group with operators and A and C are subgroups.
		The 'butterfly' becomes apparent when trying to draw the Hasse diagram of the various groups involved.
	en.wikipedia.org /wiki/Zassenhaus_lemma (102 words)

	2N-Wing Butterfly Problem
		Lemma 2 is a curious result in its own right.
		However, in general, the N pairs of wings are split between a number of butterflies, one per an irreducible cycle that compose the permutation.
		This is an open question whether the butterflies are just stuck on top of each other and could be in principle separated, or whether their wings are so entangled that no separation is possible.
	www.cut-the-knot.org /Curriculum/Geometry/Butterfly.shtml (344 words)

	[No title]
		By the butterfly lemma, there exists a pair $(\pi,\pi')$ of conjugate halfplanes, say $\pi_\up$ and $\pi_\lo$, and a sign, say $+$, such that both half-planes contain an infinite clusters of this sign with positive probability.
		But the line touching lemma guarantees that the infinitely many doubly-infinite `vertical' $+$paths passing through the horizontal axis are connected to each other in $\pi_{n,\up}$ and $\pi_{n,\lo}$.
		By Lemma \ref{lss-circuits}, $\D$ is $\hat\nu$-almost surely surrounded by a $\lss$circuit, and with probability at least $1-\e$ such a $\lss$circuit can be found in a sufficiently large square $\L$.
	www.ma.utexas.edu /mp_arc/papers/99-280 (7197 words)

	\large The Spectra of Wrapped Butterfly Digraphs
		Butterfly networks have been extensively studied in the literature because of their many applications in computer architectures.
		The spectra of undirected unwrapped butterfly graphs has been determined recently in [15] by considering the hierarchical structure of the graphs.
		In this section we obtain the distance matrices of a wrapped butterfly digraph as polynomials in the adjacency matrix.
	www-ma4.upc.es /~comellas/butterfly/comellas-web.html (1664 words)

	Science Fair Projects - Zassenhaus lemma
		In mathematics, the butterfly lemma or Zassenhaus lemma is a technical result on the lattice of subgroups of a group.
		Lemma (Butterfly lemma): Say G is an Ω-group and A and C are subgroups.
		Hans Julius Zassenhaus proved this lemma specifically to give the smoothest proof of the Schreier refinement theorem.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Butterfly_lemma (256 words)

	The Lepidoptera of the Circles
		Since Howard Eves was at the time the editor of the Elementary Problem Department of the Monthly it is reasonable to assume that he was the first to notice the resemblance of the shape in the middle of the problem's diagram to the ubiquitous insect.
		The existence of the lopsided butterfly is now a well established fact largely thanks to the efforts of A. Candy (1896).
		A completely different kind of butterflies was discovered in 1997 by Qiu FaWen, a Chinese mathematics and physics teacher, and his students with the aid of Geometer's Sketchpad.
	www.maa.org /editorial/knot/Lepidoptera.html (1191 words)

	Grass Genera of the World - Plinthanthesis Steud.
		Lemmas similar in texture to the glumes to decidedly firmer than the glumes (firmly membranous to leathery); not becoming indurated; incised; 2 lobed; deeply cleft (to about halfway), or not deeply cleft (the lobes minute, or up to 4 mm long); awnless, or mucronate, or awned (shortly).
		Lemmas non-carinate (rounded on the back); without a germination flap; 7 nerved, or 9 nerved.
		Disseminule a caryopsis enclosed in but free of the lemma and palea.
	www.biologie.uni-hamburg.de /b-online/delta/grass/www/plinthan.htm (573 words)

	Citations: A butterfly subdivision scheme for surface interpolation with tension control - Dyn, Gregory, Levin ... (Site not responding. Last check: 2007-09-21)
		The butterfly subdivision step is applied as a prolongation operator, that generally generates better initial values than simple linear interpolation.
		Butterfly subdivision interpolates the vertices of the mesh, and thus, as is shown in Section 3.3.4, is especially practical for the implementation of wavelets on smooth surfaces.
		However, although the original Butterfly scheme is defined on arbitrary triangular meshes, the limit surface is not C 1 continuous at extraordinary points of valence k = 3 and k 7 [22] It is C 1 on regular meshes.
	citeseer.ist.psu.edu /cs?q=dbnum=1,GID=13804,DID=0,start=100,cluster=none,qtype=context: (3566 words)

	Citations: Layered Cross Product -- a technique to construct interconnection networks - Even, Litman (ResearchIndex) (Site not responding. Last check: 2007-09-21)
		Thus, the bounds for the FFT apply directly to BS (d) From Lemma 3.2 it follows that lower bounds for the FFT apply to P (d) because P (d) reduces to F (d) Since our pebbling strategy for the FFT graph in the standard MHG advances pebbles....
		Lemma 1.1 For any nonnegative integers j; k the subgraph of B n induced by the nodes of levels j; j 1; j k is the disjoint sum 4 of 2 n Gammak copies of B k.
		Lemma 1.2 There is an automorphism of B n which maps each level 0 n of the....
	citeseer.ist.psu.edu /context/370713/0 (866 words)

	The Butterfly Theorem
		According to Coxeter and Greitzer, one of the solutions to the Butterfly theorem was submitted in 1815 by W. Horner of Horner's method fame.
		The Butterfly theorem is a particular case of a more general Two Butterflies theorem.
		Choose one "butterfly quadrilateral" to be symmetric with respect to OM and so that its intersecting sides meet at M. The second "butterfly quadrilateral" is bound to intersect PQ at the same points as the first, i.e., symmetrically with respect to M. Proof 7
	www.cut-the-knot.org /pythagoras/Butterfly.shtml (2297 words)

	Grass Genera of the World - Dichaetaria Nees
		Lemmas decidedly firmer than the glumes; not becoming indurated (but firm, leathery); incised; awned.
		Lemmas hairless; glabrous; non-carinate (rounded on the back); without a germination flap; 3 nerved.
		Palea present (long and narrow); relatively long (equalling the lemma); entire (pointed); with apical setae; thinner than the lemma (membranous); not indurated; 2-nerved; 2-keeled.
	www.biologie.uni-hamburg.de /b-online/delta/grass/www/dichaeta.htm (531 words)

	Climate Science: Roger Pielke Sr. Research Group Weblog » More on the Butterfly Effect (Site not responding. Last check: 2007-09-21)
		What everyone is telling you is that if you look at a fixed time at a particular point, yes, the butterfly has an effect on the weather and if, as most people, you define weather as what their nose encounters at a particular moment.
		At a distance of even a few meters from a butterfly, it is impossible to distinguish its influence from another butterfly a short distance away.
		What the shadowing lemma does not state is that there is a a tube of radius delta that always stays within epsilon of the original trajectory (which would be only the case in a non-chaotic system).
	climatesci.atmos.colostate.edu /?p=70 (12683 words)

	[No title]
		chrysalis (KRIS-uh-lis) noun [plural chrysalises or chrysalides (kri-SAL-i-deez)] A pupa, especially of a moth or butterfly, enclosed in a firm case or cocoon.
		Butterflies usually emerge from their chrysalises sometime between 9:30 a.m.
		Legions of local people eke out a living by scooping up crude oil from idled wells across the republic and making what must be the world's worst gasoline." There is no butter in butterfly, but once there was a boot in bootleg.
	www.wordsmith.org /awad/archives/0698 (3738 words)

	Theoretical Analyses
		In this section we show that the new VarMC bound and MVarMC bound techniques can also be used for theoretical analyses of lower bounds on the Graph Partitioning problem and can give improved lower bounds compared with the known 1-1-MC.
		Here we consider the butterfly network without wraparound which has been studied extensively.
		The butterfly network is an example of a quite regular network where the VarMC instance gives a better lower bound on the bisection problem with equally sized partitions than the known 1-1-MC.
	www.uni-paderborn.de /cs/sensen/GraphPart/ESA_html/node5.html (571 words)

	Mathematics
		Asymptotic expansion of integrals, including: Watson's lemma, stationary phase, Laplace's method, and the method of steepest descent.
		Emergence of spatial and temporal order in biological and ecological systems: Hopf and Turing bifurcation in reaction-diffusion systems, how do zebras get their stripes, patterns on snake skins and butterfly wings, spatial organization in the visual cortex, symmetry breaking in hormonal interactions, how do the ovaries count.
		Basic techniques of mathematics are introduced and applied to significant biological phenomena that cannot be fully understood without their use.
	www.njit.edu /v2/archivecatalog/graduate/96/68.html (2081 words)

	Permutation routing in hypercubic networks
		Without loss of generality, we may start with the ordinary butterfly to explain the main problems, and all the results mentioned here apply to all the hypercubic networks.
		The following lemma shows that the bit-reversal and the transpose permutations are (up to constant factors) examples of the worst-case permutations for greedy routing on hypercubic networks with nonconstant buffers.
		What is even more important, Lemma implies that the hypercube itself is able to simulate any bounded-degree topology optimally.
	www.cs.wisc.edu /~tvrdik/10/html/Section10.html (2889 words)

	The Art of Numerology Classes
		We are releasing the old vibration of a year that has gone by and are embracing a new energy.
		This month we start to emerge like a butterfly out of a cocoon…showing more of our strength, courage, leadership ability…presenting our new Self as a result of the past year of inner growth and transformation that has taken place.
		Colleen Lemma has been teaching various classes and workshops on metaphysical subjects since 1997 including astrology, numerology, crystals, past lives and Reiki.
	www.wholisticlifeservices.com /numerology.html (530 words)

	[No title]
		Indeed from Lemma \ref{partition}, Lemma \ref{estimari} and $\by-\bz\leq \bx -\bz+\bx- \by$: $$
		\leq K\veN\frac{C}{\beta}(A\tilde{\Phi}_{j})(\bx) $$ whereof by Lemma \ref{estimari}: \begin{equation}\label{gauge} \parallel (U_{j,\ve}^{}h_{\ve}U_{j,\ve}-h_{0})U_{j,\ve}^{}\tilde{\Phi}_{j} \parallel^{2} \leq K(\veN\frac{C}{\beta^{3}})^{2}\parallel\tilde{\Phi}_{j}\parallel^{2}.
		\end{equation} and the proof of Lemma \ref{aconv} is complete.
	www.ma.utexas.edu /mp_arc/html/papers/03-399 (1695 words)

	Sorting on hypercubic networks
		The implementation exploits the recursive structure of the butterfly, precisely matching the requirements of the algorithm.
		The implementation on an N-node hypercube is straightforward by contracting the rows of the ordinary butterfly into hypercube nodes, as shown on Figure.
		Bitonic Sort has almost the same implementation on the butterfly, adjacent butterflies just sort the corresponding subsequences alternatively as ascending and descending.
	www.cs.wisc.edu /~tvrdik/17/html/Section17.html (1714 words)

	Math 210A: Modern Algebra (Site not responding. Last check: 2007-09-21)
		Class 4 (M Oct. 4): Zassenhaus (butterfly) lemma, Schreier's theorem, proof of Jordan-Holder, action of group on a set, G-action, orbit Gi, Cauchy's Theorem, isotropy group.
		Class 13 (M Nov. 8): introduction to rings: commutative ring, identity, ring homomorphisms and isomorphisms, ideal, principal ideal domain, quotient ring, isomorphism theorems for rings.
		Class 17 (M Nov. 22): Gauss' Theorem (R UFD implies R[x] UFD), Gauss' lemma(s), Eisenstein criterion, Luca's theorem.
	math.stanford.edu /~vakil/210 (570 words)

	95.409: Assignment #1 (Site not responding. Last check: 2007-09-21)
		Problem 1: Consider any four networks of your choice (e.g Hypercube, Butterfly,...) and state what are different lower bounds for any deterministic oblivious permutation routing scheme on these networks.
		Problem 3: Prove Lemma 4.5 on page 76 in Raghavan-Motwani's book.
		Don't copy the proof from the book - rather write the proof in your own words.
	www.scs.carleton.ca /~maheshwa/courses/409/ass3.html (406 words)

	Watkins, Refereed Publications
		A generalization of the Bramble-Hilbert lemma and applications to multivariate interpolation, J. Approx.
		Comparison of solutions to the thirteen-moment and standard transport equations for low-speed thermal proton flows, with R. Schunk, Planet.
		SR and SZ algorithms for the symplectic (butterfly) eigenproblem (.ps), with P. Benner and H. Fassbender, Linear Algebra Appl., 287 (1999), pp.
	www.sci.wsu.edu /math/faculty/watkins/refpub.html (793 words)

	Faculty of Science -Department of MACS-Course Synopses (Site not responding. Last check: 2007-09-21)
		Character Theory: Elementary properties of characters, class functions, sums and products of characters, Schur's lemma; orthogonality relations for matrix entries and characters, representation with the same character are isomorphic, irreducible characters.
		Decomposition of the regular representation, number of irreducible representations, number of conjugacy classes, canonical decomposition of a representation.
		Jordan Holder theorem; the anter and ascending series; Zassenhauss (butterfly) lemma; groups action on a set.
	www.nul.ls /faculties/science/macs_ugsynopses.htm (3352 words)

	MUST´VE BEEN BLIND Lyrics - by DANIEL LEMMA : Lyrics And Songs
		There are more songs by DANIEL LEMMA that are not in albums here
		You are viewing lyrics of MUST´VE BEEN BLIND by DANIEL LEMMA from the album UNKNOWN at LyricsAndSongs.COM
		Sought the pleasures, sought the pleasures of a young man's mind
	www.lyricsandsongs.com /song/511027.html (398 words)

	Fate (and the Butterfly Effect): Notes: ELISION Ensemble
		Fate (and the Butterfly Effect): Notes: ELISION Ensemble
		A Dance and a Hymn to Alexander Maconochie
		It was commissioned by the Australia Council for the Arts and written especially for Benjamin MARKS, Geoffrey MORRIS and ELISION Ensemble.
	www.elision.org.au /repertoire/notes/35000.html (182 words)

	Butterfly & Daisy Solar Stepping Stone
		This product is not available in this price set.
		The Solar Garden Store is owned & operated by Lemma Marketing.
		NOTE: It appears your browser does not support scripting (javascript).
	www.solargardenstore.com /site/1479562/product/G5085 (92 words)

	COMP 4009 Introduction to Parallel Computing
		Odd-Even Merge Sort on ButterFly, Routing on Butterfly (example using bit reversal permutation).
		Oct 31: MIDTERM in THE CLASS STARTING AT 1435.
		Nov 7: Lower and upper bound for routing on a butterfly.
	www.scs.carleton.ca /~maheshwa/courses/4009COMP/outline.html (704 words)

Try your search on: Qwika (all wikis)