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Topic: Wedge sum

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	Wedge sum - Wikipedia, the free encyclopedia
		In topology, the wedge sum is a "one-point union" of a family of topological spaces.
		The wedge sum of the family is given by:
		Alternatively, the wedge sum can be see as the pushout of the diagram X ← {•} → Y in the category of topological spaces (where {•} is any one point space).
	en.wikipedia.org /wiki/Wedge_sum (233 words)

	Wedge sum -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		In (The configuration of a communication network) topology, the wedge sum is a "one-point union" of a family of ((mathematics) any set of points that satisfy a set of postulates of some kind) topological spaces.
		The wedge sum can be understood as the (additional info and facts about coproduct) coproduct in the (additional info and facts about category of pointed spaces) category of pointed spaces.
		Alternatively, the wedge sum can be see as the (additional info and facts about pushout) pushout of the diagram X ← → Y in the (additional info and facts about category of topological spaces) category of topological spaces (where is any one point space).
	www.absoluteastronomy.com /encyclopedia/w/we/wedge_sum.htm (271 words)

	Wedge (disambiguation) - Wikipedia, the free encyclopedia
		In phonetics, wedge is a name commonly used for the open-mid back unrounded vowel.
		In U.S. geography, the Wedge is part of the border between Delaware and Pennsylvania.
		In Westchester County, New York, a hero sandwich, submarine sandwich, or hoagie is called a wedge.
	en.wikipedia.org /wiki/Wedge (199 words)

	wikien.info: Main_Page (Site not responding. Last check: 2007-10-09)
		Wedge is a pilot who joined the Rebellion at age 17 after the deaths of his parents.
		Wedge issue is a term describing a social or political issue that is used by politicians as a ploy to "split" an opposing political party's support base and thereby entice voters to shift their support from one party to another.
		topological spaces with distinguised basepoints x0 and y0) the wedge sum of X and Y is the quotient of the disjoint union of X and Y by the identification x0 ∼ y..
	www.hostingciamca.com /browse.php?title=W/WE/WED (2366 words)

	Wedge (Site not responding. Last check: 2007-10-09)
		Technically a portable double inclined plane, a wedge is a simple machine used to separate two objects, or portions of objects, through the application of force, perpendicular to the inclined surfaces, developed by conversion of force applied to the blunt end.
		The mechanical advantage of a wedge depends on the ratio of it length to its thickness.
		In mathematics, there is something called the wedge product in exterior algebra and the wedge sum in algebraic topology.
	www.worldhistory.com /wiki/W/Wedge.htm (287 words)

	Straightening Bases for Tensor Products
		That is, $U_n$ is the vector space of all formal sums of elements of $S_n$, regarded as basis elements, with rational coefficients.
		The {\it matched sum}, $(T \rightarrow T')$, is defined to be the element of $U_n$ consisting of the sum of all permutations (i.e., elements of $U_n$) $\sigma$ such that $\sigma(T_i) = T'_i$, $1\leq i \leq k$, where $T_i$ and $T'_i$ are, respectively, the $i^{th}$ rows of $T$ and $T'$.
		Note that the expression $\otimes_{t=1}^ke_{h(\overline\lambda_{t-1}+1))} \wedge \, \cdots\, \wedge e_{h(\overline\lambda_t)}$ is exactly the representative tensor (Definition~3.1) associated with the tableau ${\bf T}$ whose $t^{th}$ row is the vector $(h(\overline\lambda_{t-1}+1), \ldots, h(\overline\lambda_t))$, $h=f\rho_T$.
	www-cse.ucsd.edu /~gill/Research/StrBasTeX.html (5259 words)

	Vector Spaces.
		wedge = sum(: sign([i,j,k]).q(i)×q(j)×q(k) ←[i,j,k] :{permutations of [0,1,2]})
		Given def(f) = wedge×wedge, we can describe wedge as a square root of det(f); given that the 3-way antisymmetrised V⊗V⊗V is one-dimensional, this square root is unique up to sign; so (aside from its sign) it won't depend on our choice of basis, and it fully determines the action of ^.
		Composing wedge with f's inverse, we obtain an antisymmetric product which combines two members of V and yields a member of V. See also: the three-dimensional vector differential operators.
	www.chaos.org.uk /~eddy/math/vector.html (1388 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		This means that $f\sigma + df \wedge \eta = 0$, and wedging with $df$ we obtain $f df \wedge \sigma = 0$.
		Since the total index is the sum of the local contributions, we obtain (3.3).
		The sum of the indices of $\tilde Y \vert_{V_\epsilon}$ is given by the multiplicity of the ideal $(f-\epsilon,f_1,\ldots,f_{2m})$, which by definition is the index $Ind_{V,{V_\epsilon},0}(Y)$.
	home.imf.au.dk /esn/preprints/112 (2740 words)

	[No title]
		Suppose that $\wedge$ is known to be a good lattice for packing spheres of radius 1 in $\Bbb{R}^n$.
		Let $\wedge$ be the set of all points of $\Bbb R^n$ with integer coordinates that are congruent mod $p$ to some codeword of $C$.
		It is easy to verify that $\wedge$ is a lattice of determinant $p^{n-k}$ and that the spheres of radius $\tfrac12 \sqrt{d}$ centred on the lattice points are nonoverlapping.
	www.ams.org /journals/bull/pre-1996-data/199329-2/Rogers (3453 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		An allocation rule $A$ is {\bf feasible} if $\forall s$, \begin{eqnarray} \sum_{i* \in \cal I} qA_i(s) & \leq & Q \\ A(s) & \leq & s \end{eqnarray*} where $\leq$ for matrices is taken element by element.
		In a game framework, a measure of efficiency may be the sum of the utilities of the players $\sum u_i(A_i(s))$, in which case $m$-efficiency is Pareto optimality.
		Thus $$m(A(s)) = \sum_{i \in \cal I} m_i(A_i(s)) = \sum_{l \in {\cal L}} \sum_{i \in {\cal I}(l)} m_i(A_i(s)),$$ is maximized iff each of the $L$ terms $\sum_{i \in {\cal I}(l)} m_i(A_i(s)))$ is independently maximized.
	www.ctr.columbia.edu /~nemo/R/auction/tree.tex~ (4255 words)

	[No title]
		In absence of the wedge, the interference should be exactly as that of a Fabry-Perot, if the wedge angle be absent and if the light be allowed to arrive at all possible angles,- i.e.
		These straight lines for a given wedge can be calibrated to give an accurate value of the imaginary part of the refractive index.
		Plot of the wedge thickness verses logarithm of the maximum value of the intensity at a given value of the imaginary part of the refractive index..
	www.physica.org /WordTeX/705.doc (1329 words)

	The cutting sticks problem
		Given a value for n, is it possible to represent all tuples as series of disjoint sums of the natural numbers from 1 to n.
		Pair up the parts summing to S/2 (and the number S/2) to form k-k1 parts summing to S and one part summing to r.
		Pair up the parts summing to (S+1)/2 together with the number (S+1)/2 to find r-k1-1 parts summing to S+1, and pair up the part summing to n1 with the number S-n1+1 which was left out to get one part summing to S+1.
	www.iwriteiam.nl /cutsticks.html (4753 words)

	Small bone X-ray densitometry
		The first macro, Wedge, takes a ROI from the wedge and determines two major parameters: the background density, D0, and the Al X-ray attenuation, mu-Al.
		The aluminum wedge must be oriented vertically, the dividing lines between the steps are horizontal.
		When selecting the wedge ROI, stay away from the wedge borders but provide enough area (make it at least 12 pixels wide) 4.
	www.haidekker.org /densitometry (723 words)

	[No title]
		Since $X=Y+Z$ (direct sum) we have a canonical identification of $X^$ with $Y^ \oplus Z^*$.
		The linear projection ${\cal P}_Y$ of the linear space ${\teneuf C}_0^X$ onto its linear subspace ${\teneuf C}_Y^X$ determined by the preceding direct sum decomposition is a morphism {\rm (}in particular it is an operator of norm 1{\rm)}.
		Denote by $\widetilde{{\teneuf C}}^X_0$ the $C^$-direct sum* of the algebras ${\teneuf C}_Y^X$ with $Y\in{\mathbb P}(X)$: \begin{equation} \label{eq3.4} \widetilde{{\teneuf C}}^X_0 = \bigoplus_{Y \in {\mathbb P}(X)} {\teneuf C}_Y^X. \end{equation} Let ${\cal P}:{\teneuf C}_0^X\rightarrow\widetilde{{\teneuf C}}^X_0$ be defined by \begin{equation}\label{eq3.400} {\cal P}[T]=\bigoplus_{Y\in{\mathbb P}(X)}{\cal P}_Y[T].
	www.ma.hw.ac.uk /EJDE/conf-proc/04/d1/damak-tex (4929 words)

	[No title]
		The proper Hilbert space, then, is Fock space, $\F$, the sum of all the original $N$-particle spaces with $N = 0, 1, 2, \dots$.
		Despite years of attention to the subject it is surprising that some of the basic properties have not been clearly stated, much less proved.
		A {\bf simple vector} in $\H^{(N)}$ is of the form $$f_1 \wedge f_2 \wedge \dots \wedge f_N := \sum \limits_{{\rm permutations}} (-)^\pi \cdot f_{\pi (1)} \otimes f_{\pi (2)} \otimes \dots \otimes f_{\pi (N)}, \eqno(2a.2)$$ where each $f_i$ is in $\H$.
	www.ma.utexas.edu /mp_arc/papers/93-334 (6276 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Thus the two have the same dimension, and so any injective linear map is a bijection.
		Earlier we also showed that \begin_inset Formula \((\Lambda _{k}(V))^{}\simeq A_{k}(V) \) \end_inset, and we can extend that to isomorphisms: \begin_inset Formula \[ \Lambda (V^{})\simeq \sum _{k=0}^{\infty }\Lambda _{k}(V^{})\simeq \sum* _{k=0}^{\infty }(\Lambda _{k}(V))^{}\simeq (\Lambda (V))^{}\simeq A(V):=\sum _{k=0}^{\infty }A_{k}(V),\] \end_inset which will all be presumed once we get over the hurdle of these conventions problems.
		However, it is really just as reasonable to choose \begin_inset Formula \((\theta ^{1}\wedge \dots \wedge \theta ^{k,v}_{1}\wedge \dots \wedge v_{k})_{\beta }:=\frac{1}{k!}det(\theta ^{1}(v_{j})).
	www.lehigh.edu /dlj0/Desktop/dlj0/courses/423f96-lect12.lyx (1498 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Summe aller 3 Sektoren der Recoil Wedge und Strip Anode if ren lt 3.
		normierte x-Koordinate des Recoil wedge and strip c c c c jetzt kartesiche Koordinate Y recoil ausrechnen : c c lda zrz !
		E-Energie gegen TAC2 endif endif endif c c generate 2-dim electron position spectra with gates on sum energy c and (TAC-windows(i.e.
	www.phys.ksu.edu /students/classes/astronomy/elektron/elre9805.evl;20 (2356 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		\layout Standard The sum of all these things, \begin_inset Formula $T(V):=\sum V_{r,s}$ \end_inset, is the \shape italic tensor algebra \shape default of \begin_inset Formula $V$ \end_inset.
		Earlier we also showed that \begin_inset Formula $(\Lambda _{k}(V))^{}\simeq A_{k}(V)$ \end_inset, and we can extend that to isomorphisms: \begin_inset Formula \[ \Lambda (V^{})\simeq \sum _{k=0}^{\infty }\Lambda _{k}(V^{})\simeq \sum* _{k=0}^{\infty }(\Lambda _{k}(V))^{}\simeq (\Lambda (V))^{}\simeq A(V):=\sum _{k=0}^{\infty }A_{k}(V),\] \end_inset which will all be presumed once we get over the hurdle of these conventions problems.
		It is, after all, redundant to permute the terms inside \begin_inset Formula $f$ \end_inset or \begin_inset Formula $g$ \end_inset around, since they are already alternating.
	www.lehigh.edu /dlj0/Desktop/dlj0/courses/423f02-lect9.lyx (1407 words)

	Strappy Wedge Sandal Items (Site not responding. Last check: 2007-10-09)
		New BALENCIAGA PARIS strappy wedge sandals 38.5 8 $495
		NW strappy wooden platform wedge leather sandals sz 39
		Sexy Strappy NEW BORN Wedge Sandals Hot Pink SZ 9
	unitpulsetheory.com /strappywedgesandal.html (397 words)

	GL Series by Allen&Heath
		Our new mic preamp has an extended 74dB gain range with massive headroom able to deal with the widest range of signals right up to +34dBu.
		Our configurable M fader lets you create an LR sum mono fill, an engineers monitor wedge feed, or a dedicated centre or sub-bass speaker mix from Aux 6 which means you can dial in exactly what you need from each channel.
		M can be configured as LR sum, Wedge, or Aux-Fed Sub or C master
	www.glseries.com /gl2400.php (558 words)

	kp densities
		note: the wedges must be in ascending order
		if wedge i has been written, the next wedge only contains k_points
		the last (specified) wedge only contains k_points not contained in the first
	www.wsi.tu-muenchen.de /nextnano3/structure/densities/kp_densities.html (480 words)

	NTU Info Centre: Pointed space (Site not responding. Last check: 2007-10-09)
		The coproduct in the category of pointed spaces is the wedge sum, which can be thought of as the one-point union of spaces.
		The smash product of two pointed spaces is essentially the quotient of the direct product and the wedge sum.
		The reduced suspension ΣX of a pointed space X is smash product of X and the pointed circle S
	www.nowtryus.com /article:Pointed_space (396 words)

	Allen & Heath - GL2400 Dual Function Live Sound Mixer - [Sam Ash]
		Engineered for modern engineering techniques, every detail in this mixer has been carefully thought out to provide the very best mixing experience.
		For example, the mono output can be configured as LR sum, wedge, or aux-fed sub or centre master.
		In Monitor mode, all six auxes are available on faders with mutes, inserts, meters and XLR drive.
	samash.com /redirect.asp?ItemID=41731&Allen+and+Heath+Mixing+Consoles (794 words)

	Shure - Sennheiser - Beyerdynamic - Trantec - Mercury Pro Audio Sales to the UK
		The mono output can be configured as LR sum, wedge, or aux-fed sub or centre master.
		The PS10 TD provides crossover, sensed-amplifier control and system equalisation optimised for the PS10 and LS500.
		One PS10 TD has two inputs and three outputs, L, R and summed sub out, minimising installation cost and complexity.
	www.mercury-av.com /sales/toc.html (5727 words)

	NTU Info Centre: Smash product (Site not responding. Last check: 2007-10-09)
		These subspaces intersect at a single point: (x
		So the union of these subspaces can be identified with the wedge sum X ∨ Y.
		The smash product is important in homotopy theory, a branch of algebraic topology.
	www.nowtryus.com /article:Smash_product (165 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		\end{equation} In particular, the wedge product of $n$ 1-forms is given explicitly by \begin{equation} \label{det} (\omega_1\wedge\ldots\wedge\omega_n)\,(\xi_1,\ldots,\xi_n) = \text{det}\,\omega_i(\xi_j)\,.
		\end{equation} Wedge product is associative and skew-commutative: \begin{equation} \label{skew} (\omega^k\wedge\omega^l)\wedge\omega^m = \omega^k\wedge(\omega^l\wedge\omega^m)\,, \ \ \ \ \ \ \ \ \ \omega^k\wedge\omega^m = (-)^{km}\,\omega^m\wedge\omega^k\,.
		\end{equation} There is another general formula for $d\omega^k$ which involves the notion of the commutator of vector fields (see (\ref{commut}) below)\,: \begin{multline} \label{d2} d\omega\,(\xi_0,\xi_1,\ldots,\xi_k) = \sum_{i=0}^{k}\,(-)^i\,\xi_i (\omega\,(\xi_0,\ldots,\xi_{i-1},\xi_{i+1},\ldots,\xi_k)) \\ + \sum_{i
	thsun1.jinr.ru /~alvladim/qft/geometry.txt (4117 words)

	Will Wilkinson / The Fly Bottle
		The lesson they each show us is that we are better off in a multitude of different ways, worse off in a few others, and as happy as we've ever been.
		The troubled and disappointed tone has come to stupefy me. It simply doesn't make sense, relative to common sense, or to the science, to think of individual happiness as an open-ended increasing sum, rather than as homeostatic, a kind of equilibrium state.
		So it's just not a mystery why our wealth or anything isn't making us a lot happier, because we've already arrived.
	willwilkinson.net /flybottle (5542 words)

	[No title]
		/ Parameter mResponse = 8 Real Response(mResponse) Integer Npe_Dose(0:mDose) Logical Debug/.true./, First/.true./, Dump_track, In_Glass Integer nDebug/0/, mDebug/5/ Logical Inside if(First) then ff = Pi * (fiber_diameter/2.)2 / fiber_spacing2 ff_EM = 0.50 * ff ff_Had = 0.25 * ff write(output,5050) beta_threshold, 1 GeV_per_pe,fiber_spacing,fiber_diameter,ff, 2 ff_EM, ff_Had 5050 format(' Big Fiber Wedge Cerenkov.
		sum Fe energy loss Response(1) = Response(1) + destep Call hFill(402,vect(7),0.,step) !
		sum TC fibers do m = 1, mGang Egang(m) = 0.
	www.public.iastate.edu /~alpha/pubs/hauptman/hf_fiber_geom.f (954 words)

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