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Topic: F sigma set

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	[No title] (Site not responding. Last check: 2007-09-07)
		E is equal to a G_delta set with a null set removed.
		E is equal to a F_sigma set with a null set removed.
		E is equal to a finite union of intervals with a null set removed.
	www.math.ucla.edu /~tao/java/MultipleChoice/measurable.txt (554 words)

	Straightening Bases for Tensor Products
		Let ${\cal T}_f$ be the set of all pairs $[{\bf T}, T']$ of tableaux of shape $\lambda=(\lambda_1, \ldots, \lambda_k)$, where ${\bf T}$, with entries consisting of the multiset $\{f(1),\, \ldots\,, f(n)\}$, $\lambda_1+\cdots + \lambda_k = n$, is row-strict-column-weak, and $T'$, with entries consisting of the set $\b n=\{1, \ldots, n\}$, is row-strict-column-strict.
		Alternatively, the monotone function $f$ is referred to as a ``multiset'' of the set $\b d$ of size $n$ and of {\it type} $\alpha=(\alpha_1, \ldots, \alpha_d)$.
		Alternatively, $f$ is a multiset of $\b 5$ of size $8$ and type $(2, 1, 0, 3, 2, 0, 0, 0)$.
	www-cse.ucsd.edu /users/gill/Research/StrBasTeX.html (5259 words)

	F-sigma set - Wikipedia, the free encyclopedia
		set (said F-sigma set) is a countable union of closed sets.
		The notation originated in France with F for fermé (French:closed) and σ for somme (French:union).
		In metrizable spaces, every open set is an F
	en.wikipedia.org /wiki/F-sigma_set (79 words)

	[No title]
		On the other hand, the property of not belonging to the set {x: (d- not= d+) or (D- not= D+)} does not distribute over pointwise subtraction, and so the analogous set for f-g might not be contained in the union of the corresponding sets for f and g.
		Then the set of nondecreasing functions (not necessarily continuous) which are not finitely differentiable at any point of E is residual in the space of nondecreasing functions (sup norm) if and only if E is contained in an F_sigma Lebesgue measure zero set.
		Then the set of absolutely continuous functions which are not finitely differentiable at any point of E is residual in the space of absolutely continuous functions (variational norm) if and only if E is contained in an F_sigma Lebesgue measure zero set.
	www.math.niu.edu /~rusin/known-math/00_incoming/diff_essay (2153 words)

	PlanetMath: $F_\sigma$ set
		set if it equals the union of a countable collection of closed sets.
		set because it can be expressed as the union of a countable set of lines:
		Cross-references: lines, rational, plane, complement, closed sets, collection, countable, union, topological space, subset
	planetmath.org /encyclopedia/F_sigmaSet.html (67 words)

	[No title]
		If D is a regular domain in the complex plane and f is a continous function on the boundary of D, then there exists a unique harmonic function f on D such that h(z)=f(z) for all boundary points of D. Dirichlet problem +------------------------------------------------------------ Let K be a compact subset of the complex plane.
		Let P(K) the set of all Borel probability measure on K. A measure nu maximizing the potential theoretical energy in P(K) is called an equilibrium measure of K. Properties: every compact K has an equilibrium measure.
		connected sets of cardinality larger than 1 are non-thin at every point of their closure A domain S is thin at a point z in S if and only if z is regular.
	www.math.harvard.edu /~knill/sofia/data/potential.txt (536 words)

	Sigma 18-50 mm f/2.8 DC EX Lens Review
		The Sigma 18-50mm f/2.8 lens is an autofocus lens optimized for APS-sized digital sensors that provides an extremely useful range that is 35mm equivalent of 28.8mm to 80mm.
		The Sigma lens is particularly appealing not only for its large constant aperture, but also for its very compact, convenient size (3.3 inches long, 15.6 ounces).
		Sigma 18-50mm vs. Carl Zeiss Planar 50mm A head-to-head test comparing the Sigma to one of the best fixed lenses.
	topicpoint.com /sigma_18-50mm (900 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		The first set shows pictures of results for tossing a fair coin n times for n = 1, 2, 3, 4, 5, 10, 20, 50, 100, and 500 For each n, there is a pair of pictures showing the same data in two ways.
		The first set of plots is for a fair coin, the second set for the biased coin, and the third set for the biased die.
		The most general statement of the Central limit theorem does not require that the values of f_i be integers, or even that all the f_i have the same distribution!) We will sketch a proof of this in a simple case, fair coin flipping.
	www.cs.berkeley.edu /~demmel/ma55/LectureNotes/Lecture_23_Apr_20.txt (1626 words)

	Popular Photography Magazine: Sigma 500mm f/4.5 EX APO AF (Site not responding. Last check: 2007-09-07)
		Sigma supplies a shoulder strap, carrying case, protective front-element boot, bayonetting reversible hood, and nonremovable tripod collar.
		The tripod collar's foot is grooved to double as a grip for off-pod, handheld operation.
		Finally, Sigma designed a lensmount filter drawer (46mm filters) that rotates for convenient positioning of the (supplied) circular polarizing filter.
	www.popphoto.com /article.asp?section_id=2&article_id=274 (487 words)

	Sigma 18-125mm f/3.5-5.6 DC review
		Newly designed by Sigma as a wide angle to short-medium telephoto for use as a general purpose, walk-around lens, we take a look at how it performs.
		Sigma have learnt well how to control chromatic aberrations and none of their new designs have suffered from the anomaly.
		This shot, taken at 51mm and 1/500sec at f/8 on a Sigma SD10 is around the middle of the range.
	www.ephotozine.com /equipment/tests/testdetail.cfm?test_id=377 (807 words)

	[No title]
		The image of a set is the set of things that the elements of the set are mapped to.
		The preimage of a set is the set of things that are mapped into that set.
		Note that the preimage of an open set under a continuous function is open, but that the image of an open set need not be.
	www.math.unl.edu /~webnotes/src/classes-1995/class24.wfy (885 words)

	Ixypuls (Site not responding. Last check: 2007-09-07)
		The pulse is applied only to spins which have had their spin flags set to TRUE to the function call (see Class Spin System).
		sigma = sigma_eq(AMX); // set the density matrix to equilibrium for AMX sigma = sigma_eq(AMX); // set the density matrix to equilibrium for AMX sigma = Ixypuls(AMX, sigma, 90.0, 270.0); // Pulse all spins by 90 degrees on the -y axis.
		sigma = Ixypuls(AMX, sigma, "19F", 90.0, 90.); // Pulse all fluorines by 90 degrees on the y axis.
	gamma.magnet.fsu.edu /html/modules/hslib/pulseia3.htm (546 words)

	shutterbug: Sigma AF 105mm f/2.8 EX Macro Lens
		Remember to set the ring to the correct position when autofocusing; this speeds up the operation and avoids the risk of damage to the motor during.
		Sigma includes a screw-in lens hood, although it is not really necessary except in extreme sidelighting.
		Setting the precise point of focus proved to be easy and convenient with the AF 105mm f/2.8 EX Macro.
	www.shutterbug.net /test_reports/0899sb_sigma (2026 words)

	Sigma AF70-200mm f/2.8 APO HSM EX (Site not responding. Last check: 2007-09-07)
		Sigma AF70-200mm f/2.8 APO HSM EX by Yuri Vilin
		Looks like Sigma did pretty good job deploying the ultrasonic technologies, which is certainly a big advantage for their products.
		Sigma also tends to hunt during focusing, so the possibility to correct autofocus manually might be useful in this case.Probably, lens will focus differently with another camera (like EOS 3/5, or even EOS 1), I don't know.
	www.photozone.de /2Equipment/reviews/sigma70200ex.htm (1106 words)

	Sigma Equation - (Site not responding. Last check: 2007-09-07)
		The nonlinear [sigma] model is considered to be useful in describing hadrons (Skyrmions) in low energy hadron physics and the approximate behavior of the global texture.^Here we investigate the properties of the static solution of the nonlinear [...
		The pair $(X, \sigma)$ is a real Riemann surface and the quotient $X/\langle\sigma\rangle$ by the action of $\sigma$ is a closed Klein surface.
		Unification of the general non-linear sigma model and the Virasoro master equation Unification of the general non-linear sigma model and the Virasoro master equation The Virasoro master equation describes a large set of conformal field theories...
	equation.fabca.com /index.php?k=sigma-equation (837 words)

	[No title] (Site not responding. Last check: 2007-09-07)
		A map-germ $f : (N, S) \lra (P, y_o)$ is {\bf generically TQ}, GTQ for short, if there is a dense subset $C$ of its critical set $\Sigma(f)$ such that $f_x$ is TQ for all $x \in C$.
		Thus the set $V_{\x, k} = \{z \in \Sigma_r : d_\x(z) \ge k\}$ is $\{z \in \Sigma_r : d'_\x(z) \ge k\}$, and is thus defined by the vanishing of matrices whose entries are polynomial with the coefficients of $p^r(z)$, thus with respect to coordinates in $J^r(n, 2)$.
		Moreover $f$ is $(k + 1)$-$\a$-determined; it is easy to show that any change in terms of degree $\ge k + 2$ does not change the diffeomorphism type of the critical set.
	home.imf.au.dk /esn/preprints/001 (6458 words)

	shutterbug: Sigma’s 24-60mm f/2.8 EX DG
		But there’s more to it than that—what Sigma has done is to take what they’ve learned about the required corrections for digital photography and applied them to their new line-up of film/digital camera lenses.
		Setting the Canon EOS 20D to ISO 800, I was able to hand hold at f/2.8 at 1/125 sec.
		Bridge: This shot of the Alte Brucke (old bridge) in Heidelberg at sunset was made with the Sigma 24-60mm on a Canon EOS 20D with an exposure of 1/60 sec at f/6.3 with the lens set at 24mm (about 40mm, 35mm equivalent).
	www.shutterbug.com /features/0305firstlook (828 words)

	BirdForum - Sigma 600mm f/8 Mirror Telephoto Lens (Site not responding. Last check: 2007-09-07)
		However, one thing to keep in mind is that while the lens is set to focus at "macro" range, very close, the results from less than about 25 or 30 feet are inevitably disappointing.
		This is taken with a Canon 10D and a Sigma F/8 600 mirror lens handheld.
		The main thing to keep in mind is that given the high magnification and the slow aperture of a mirror lens, it's advisable to use a high ISO (1000 or 1250) and to shoot in good light.
	www.birdforum.net /showthread.php?t=9353 (2107 words)

	XDSCONV: Output Formats
		The test-flag is set by XDSCONV to 1 for test-reflections and to 0 for reflections in the working set.
		Reflection intensities related by crystallographic symmetry as well as Friedel pairs are averaged and the mean intensity is converted to F. The file is sorted with respect to these indices.
		F = weighted mean of all reflection amplitudes which have the same unique indices h,k,l; Sigma(F) = standard deviation of F DF = 0 because there is no anomalous scattering effect Sigma(DF)= 0 standard deviation of DF is theoretically 0.0 3)Sigma(DF)<0 Some data are missing in this record.
	www.esrf.fr /exp_facilities/px_soft/XDS_html_doc/xdsconv_formats.html (744 words)

	Wilmott Forums - sigma algebras
		The sigma algebra induced by any discrete random variable taking up countably infinite values is countably infinite.
		So F is an algebra of sets, but not a sigma-algebra.
		If you list all the sets in F then you'll find that there are 8 sets and so F is a "countable" union of sets as you wanted to see.
	www.wilmott.com /messageview.cfm?catid=3&threadid=25475 (331 words)

	Transition Systems
		So a transition system is a set together with a transition structure on it.
		Tfam (A,B) = (Sigma a : A) B a -> A : Set
		Each successive family of sets is a "internal refinement" or restriction of its predecessor.
	homepages.inf.ed.ac.uk /v1phanc1/transition_systems.html (2191 words)

	Sigma Albegra - Physics Help and Math Help - Physics Forums (Site not responding. Last check: 2007-09-07)
		A sigma-albegra F over the set X is a subsets of X which is closed under contable set operations.
		The empty set is in F. If E is in F, then the complement of E is also in F. If E1, E2,..., En is a sequence in F, then their contable union is also in F. This is the def.
		That means that if you perform a countable set operation on elements of F, you produce another element of F, not F itself.
	www.physicsforums.com /showthread.php?p=794790#post794790 (640 words)

	Interaction Systems
		So an interaction system is a set together with an interaction structure on it.
		A : Set B : A -> Set C : (Pi a : A) B a -> Set d : (Pi a : A, b : B a)C a b -> A
		the set of Petersonn-Synek parse trees for that state (or in terms of rule sets, the closed derivation trees for that statement).
	homepages.inf.ed.ac.uk /v1phanc1/interactive_systems.html (1926 words)

	FM Reviews - 20mm f/1.8 EX DG Aspherical RF (Site not responding. Last check: 2007-09-07)
		Sigma 20mm f1.8 EX DG Aspherical RF is one of several EX Series lenses.
		Second one again from Sigma UK was slightly better but still had the same basic issues as the first.
		Sigma have not released a new and updated version of this lens, probably because they'd probably prefer the people who care about the noise and speed to go out and buy a better (and more expensive) Sigma lens.
	www.fredmiranda.com /reviews/showproduct.php?product=125&sort=7&thecat=13 (2412 words)

	Sigma 150mm f/2.8 HSM macro
		Does anyone have any experience with the Sigma 150mm f/2.8 macro EX My dillema is this: I have a Canon 28/1.8 and a Tamron 90/2.8 macro.
		Size and weight is similar too and the 50mm missing from the Sigma to the Canon is not that bad.
		Sigma's recent past is a major concern to some, myself included.
	www.photo.net /bboard/q-and-a-fetch-msg?msg_id=00DRP8 (964 words)

	Simplex (Site not responding. Last check: 2007-09-07)
		Rather than using standard set notation to denote an affine chain, it is instead the standard practice to use plus signs to separate each member in the set.
		In this case, both the summation convention for denoting the set, and the boundary operation commute with the embedding.
		The boundary operation commutes with the mapping because, in the end, the chain is defined as a set and little more, and the set operation always commutes with the map operation (by definition of a map).
	www.worldhistory.com /wiki/S/Simplex.htm (897 words)

	[No title]
		A "language" over Sigma is any set of strings over Sigma (in other words, a language is any subset of Sigma*).
		For example, {e} is a language containing only the empty string, {0,1,6} is a language, {e,0,00,000,...} is a language, and {} (the empty set) is a language.
		Sigma must be a subset of Gamma, and Gamma must include a "blank" symbol 'b' that is not in Sigma.
	www.cs.toronto.edu /~fpitt/2000W/CSC366/LN07.txt (1045 words)

	[No title]
		This combined with truncation of the series in (\ref{f.fourier}) (which is orthogonal projection, as we've discussed in detail) will yield an effective and practical method for approximating $f$, assuming that $f$ is uniformly bounded.
		Now, as stated at the top, the goal is to arrive at a practical and effective method for approximating $f$ by, say, $f_n$, by approximately computing the orthogonal projection of $f$ upon $\trigs_n$.
		It is called the ``Fourier matrix'', and (\ref{dft}) is referred to as the ``Discrete Fourier Transform'' DFT (of degree $n$) of $f$.
	www-math.bgsu.edu /~gwade/ma669/dft/dft.tex~ (1265 words)

	Canon EOS Beginners' FAQ III - Lenses
		Newer Sigma lenses seem to be a bit sturdier, judging by anecdotal evidence.
		And Sigma has regrettably a long history of older lenses turning out to be incompatible with later EOS cameras.
		It can be very annoying to set a filter to achieve the effect you want, touch up the focus, and find that the polarizing or graduated ND effect has changed because the end of the lens has rotated.
	photonotes.org /articles/beginner-faq/lenses.html (15154 words)

	[No title]
		But, given an $\scr F_\sigma$ set $E$ of measure zero there is a function $f$ continuous on the dyadic group whose Walsh-Fourier series diverges everywhere on $E$ (Harris \cite{30}).
		The empty set (Walsh \cite{61}) and every countable set (Fine \cite{18}) is a set of uniqueness, but some sets of measure zero are sets of uniqueness and others are not (Shne\u\i der \cite{46}).
		In fact, a set of uniqueness is not determined by its set theoretic properties but by its algebraic and number theoretic properties.
	www.ams.org /journals/bull/pre-1996-data/199226-2/Wade (3063 words)

	shutterbug: Sigma AF 14mm f/2.8 EX Aspherical HSM
		This Sigma 14mm lens came in handy whenever my 20mm was too long to include all important areas of a subject or scene.
		Do note that the Sigma AF 14mm f/2.8 EX Aspherical HSM is not a fisheye, but a true rectilinear lens.
		Sigma now offers the Hypersonic focus technology in several lenses, including this 14mm f/2.8 EX Aspherical HSM model, in Canon, Nikon (D), and Sigma AF mount.
	www.shutterbug.net /test_reports/0599sb_sigma (1970 words)

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