Split-complex number

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Topic: Split-complex number

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	Cardinal number
		It is possible to use a different formal notion for number, called ordinals, based on the ideas of counting and considering each number in turn, and we discover that the notions of cardinality and ordinality are divergent once we move out of the finite numbers.
		He also proved that the set of all ordered pairs of natural numbers is denumerably infinite, and later that the set of all algebraic numbers (every member of the set is a set of numbers of its own, like an extended ordered pair) is denumerably infinite.
		The latter cardinal number is also often denoted by c; it is the cardinality of the set of real numbers, or the continuum, whence the name.
	pedia.newsfilter.co.uk /wikipedia/c/ca/cardinal_number.html (1913 words)

	Split-complex number - Wikipedia, the free encyclopedia
		In the twentieth-century the split-complex numbers became a common platform to describe the Lorentz Boosts of special relativity, in a spacetime plane because a velocity change between frames of reference is nicely expressed by a hyperbolic rotation.
		The split-complex numbers do not form a normed algebra in the usual sense of the word since the "norm" is not positive-definite.
		The split-complex numbers are a special case of a Clifford algebra.
	www.wikipedia.org /wiki/Split-complex (1478 words)

	Complex plane - Encyclopedia, History, Geography and Biography
		Under addition, they add like vectors, and the multiplication of complex numbers can be expressed simply using polar coordinates, where the magnitude of the product is the product of those of the terms, and the angle from the real axis of the product is the sum of those of the terms.
		In mathematics, the complex plane is a way of visualising the space of the complex numbers.
		Argand diagrams are frequently used to plot the positions of poles and zeros of a function in the complex plane.
	www.arikah.com /encyclopedia/Complex_plane (370 words)

	Encyclopedia: Tessarine
		When w and z are both real numbers, then t amounts to a split-complex number.
		In mathematics, an imaginary number (or purely imaginary number) is a complex number whose square is negative or zero.
		In mathematics, the complex numbers are an extension of the real numbers by the inclusion of the imaginary unit, satisfying.
	www.nationmaster.com /encyclopedia/Tessarine (418 words)

	Number - Biocrawler
		The arithmetical operations of numbers, such as addition, subtraction, multiplication and division, are generalized in the branch of mathematics called abstract algebra; one obtains the groups, rings and fields.
		While (most) real numbers have infinitely long expansions to the right of the decimal point, one can also try to allow for infinitely long expansions to the left in base p, where p is a prime, leading to the p-adic numbers.
		Numbers should be distinguished from numerals, which are (combinations of) symbols used to represent numbers.
	www.biocrawler.com /biowiki/Number (640 words)

	Hypercomplex number - MindSharer Article Archive
		Whereas complex numbers can be viewed as points in a plane, hypercomplex numbers can be viewed as points in some higher-dimensional Euclidean space (4 dimensions for the quaternions, 4 for the tessarines, 4 for the coquaternions, 8 for the octonions, 8 for the biquaternions, 16 for the sedenions).
		In mathematics, hypercomplex numbers are extensions of the complex numbers constructed by means of abstract algebra, such as quaternions, tessarines, coquaternions, octonions, biquaternions and sedenions.
		But none of these extensions forms a field, essentially because the field of complex numbers is algebraically closed — see fundamental theorem of algebra.
	articles.mindsharer.com /html/Hypercomplex_number (153 words)

	Encyclopedia: Quaternion
		In mathematics, the quaternions are a non-commutative extension of the complex numbers.
		In mathematics, a complex number is an expression of the form a + bi, where a and b are real numbers, and i stands for the square root of minus one (âˆ’1), which cannot be represented by any real number.
		In mathematics, a normed division algebra A is a division algebra over the real or complex numbers which is also a normed vector space, with norm
	www.nationmaster.com /encyclopedia/Quaternion (653 words)

	Interactive Fly, Drosophila
		Enhancer of split complex [E(spl)-C] genes are the target of the Notch pathway.
		Enhancer of split is one of seven genes of the E(spl)-C. Signals from the Notch receptor are carried from the surface of the cell to the nucleus, by the dual function protein Suppressor of Hairless.
		An important advance of this study is the in vivo validation of a large number of biologically relevant miRNA targets that are minimally paired to miRNAs outside of the 'box:seed' region.
	flybase.net /data/allied-data/interactive-fly/neural/enhsplit.htm (5800 words)

	Biquaternion - Encyclopedia, History, Geography and Biography
		Then {a + b ι j : a, b ∈ R } is a subring of biquaternions isomorphic to the split-complex number ring.
		Let {1, i, j, k} be the basis for the (real) quaternions, and let u, v, w, x be Complex numbers, then
		Given any 2x2 complex matrix, there are complex values u, v, w, and x to put it in this form so that the matrix ring is isomorphic to the biquaternion ring.
	www.arikah.net /encyclopedia/Biquaternion (434 words)

	Split complex vectors and AltiVec FFT's
		It is possible to go between a more conventional 'interleaved' complex format and the split format using the vDSP functions ctoz and ztoc, and I had planned to use these to convert the 2D FFT back to an interleaved format to simplify zero-padding in a preliminary version.
		The FFT routine in question makes use of what Apple calls a "split complex vector" format, which is a reordering of array elements to improve performance.
		For example, if = you are doing a 2X interpolation: = = interleaved complex: = riririririririri -= riririririririri0000000000000000 = = split complex: = rrrrrrrriiiiiiii -= rrrrrrrr00000000iiiiiiii00000000 = Thanks - for some reason (and perhaps I have some other bug) this approach does not seem to work for the 2D case I am dealing with.
	www.seriousliving.net /new-1314810-1134.html (1237 words)

	Hyperbolic quaternion - tScholars.com
		The idea was criticized for its failure to conform to associativity of multiplication, but it has a legacy in Minkowski space and as an extension of split-complex numbers.
		One also notes that any subplane of the set M of hyperbolic quaternions that contains the real axis forms a plane of split-complex numbers.
		Like the quaternions, the set of hyperbolic quaternions form a vector space over the real numbers of dimension 4.
	www.tscholars.com /encyclopedia/Hyperbolic_quaternion (350 words)

	The enhancer of split complex of Drosophila includes four Notch-regulated members of the bearded gene family.
		The enhancer of split complex of Drosophila includes four Notch-regulated members of the bearded gene family.Consistent with this, both are expressed specifically in multiple settings where N signaling takes place.
		During Drosophila development, transcriptional activation of genes of the Enhancer of split Complex (E(spl)-C) is a major response to cell-cell signaling via the Notch (N) receptor.
		Finally, we present our initial studies of the structure, expression and regulation of the newest member of the Brd gene family, Ocho, which is located in the recently identified Bearded Complex.
	www.pdg.cnb.uam.es /UniPub/iHOP/gp/8425356.html (238 words)

	Real number - Biocrawler
		Perhaps the most natural extension are the complex numbers which contain solutions to all polynomial equations.
		Self-adjoint operators on a Hilbert space (for example, self-adjoint square complex matrices) generalize the reals in many respects: they can be ordered (though not totally ordered), they are complete, all their eigenvalues are real and they form a real associative algebra.
		In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line.
	www.biocrawler.com /biowiki/Real_number (2100 words)

	Drosophila tissue and organ development: Head
		In rpr mutants, the number of vesicles associated with the dorsal surface of the brain is significantly increased (Nassif, 1998).
		Based on this expression pattern, it is anticipated that the distribution of the Dpp protein in the head may be complex, and may shift during development from a dorsoventral gradient (early phase) over a posteroanterior gradient (intermediate phase) to a local point source (late phase) (Chang, 2001).
		At the same time, posterior optic lobe cells are reduced in number (Chang, 2001).
	www.flybase.net /allied-data/lk/interactive-fly/aimorph/head.htm (7706 words)

	Numbers and the number system
		Multiply and divide whole numbers and decimals by 10, 100, 1000, and explain what happens.
		Add and subtract whole numbers and decimals (with up to two decimal places) on paper.
		Round decimals to the nearest whole number or one decimal place.
	www.lgfl.net /lgfl/leas/enfield/schools/southgate/accounts/staff/dwhitfield/web/pages/level_5_checker.html (670 words)

	Minkowski space - Wikipedia, the free encyclopedia
		Furthermore, the theorem states that the number of positive and negative unit vectors in any such basis is fixed.
		This pair of numbers is called the signature of the inner product.
		There is a theorem stating that any inner product space satisfying conditions 1-3 above always has an orthonormal basis.
	en.wikipedia.org /wiki/Minkowski_space (1008 words)

	Drosophila tissue and organ development: Peripheral nervous system
		The function of proneural bHLH proteins in Drosophila PNS development is complex, since they not only activate in SOPs genes that promote the neural precursor cell fate (e.g., ac and sc themselves, sens and phyl); they also activate in non-SOPs genes involved in inhibiting this fate (e.g., genes of the Enhancer of split Complex).
		A number of mutants were isolated in an EMS mutagenesis screen for mutations on chromosome 2 that disrupt an auditory response in Drosophila adults.
		It is anticipated that a number of the SOP genes identified will prove to act similarly (Reeves, 2005).
	flybase.net /data/allied-data/interactive-fly/aimorph/pns.htm (10429 words)

	Split-complex
		The collection of all such z is called the plane of split-complex numbers D.
		is called split-complex when x and y are real numbers and
		In abstract algebra terms, this is therefore the quotient ring
	pedia.newsfilter.co.uk /wikipedia/s/sp/split_complex.html (125 words)

	Drosophila tissue and organ development: Wing
		The anterior-posterior compartment boundary splits the wing/hinge region into two equally sized compartments, but the position of the boundary in the body wall region produces a small posterior compartment representing approximately one-quarter of the total tissue.
		The phenotype was dose sensitive and directly related to the number of transgenes and length and temperature of transgene induction (Ren, 2005).
		The expression of the non-stop (not) gene decreased 3.9 fold from 24 to 40 hrs.
	www.sdbonline.org /fly/aimorph/wing.htm (5323 words)

	Constructible number
		Thus, the set K of all constructible complex numbers forms a field, a subfield of the field of algebraic numbers.
		All rational numbers are constructible, and all constructible numbers are algebraic numbers.
		In other words, the number in the last column is an element of the set in the same row, but is not constructible.
	www.info-pedia.net /about/constructible_number (862 words)

	Page
		The solution was to split complex tasks into a number of parallel channels/processors.
		Supercomputers are typically used for number crunching functions, such as extremely sophisticated simulations and analysis.
		This greatly reduces development costs as expenses are spread out over a far larger number of processors.
	www.mgmt.utoronto.ca /~fertuck/pbis/ch02c/page2.htm (918 words)

	Target Specificities of Drosophila Enhancer of split Basic Helix-Loop-Helix Proteins -- Jennings et al. 19 (7): 4600 -- Molecular and Cellular Biology
		The Enhancer of split complex and adjacent genes in the 96F region of Drosophila melanogaster are required for segregation of neural and epidermal progenitor cells.
		Genes of the Enhancer of split and achaete-scute complexes are required for a regulatory loop between Notch and Delta during lateral signalling in Drosophila.
		Seven genes of the Enhancer of split complex of Drosophila melanogaster encode helix-loop-helix proteins.
	mcb.asm.org /cgi/content/full/19/7/4600 (7393 words)

	Interactive Fly, Drosophila
		When Notch is bound by a ligand, a signal is passed across the cell membrane releasing the Suppressor of Hairless protein, freeing this protein to enter the nucleus and assume its role in activating transcription of Enhancer of split complex genes.
		For example, Notch is required to limit the number of neural precursors, limit the number of muscle precursors, limit the growth of Malpighian tubules, and regulate the growth of the ovary.
		The development and patterning of the wing in Drosophila relies on a sequence of cell interactions molecularly driven by a number of ligands and receptors.
	flybase.bio.indiana.edu /allied-data/lk/interactive-fly/neural/notch1.htm (2653 words)

	The Effect of Polymorphisms in the Enhancer of split Gene Complex on Bristle Number Variation in a Large Wild-Caught Cohort of Drosophila melanogaster -- Macdonald et al. 171 (4): 1741 -- Genetics
		The Effect of Polymorphisms in the Enhancer of split Gene Complex on Bristle Number Variation in a Large Wild-Caught Cohort of Drosophila melanogaster -- Macdonald et al.
		Articles by Macdonald, S. Articles by Long, A. The Effect of Polymorphisms in the Enhancer of split Gene Complex on Bristle Number Variation in a Large Wild-Caught Cohort of Drosophila melanogaster
		The Enhancer of split complex [E(spl)-C] in Drosophila encompasses
	www.genetics.org /cgi/content/abstract/171/4/1741 (297 words)

	The enhancer of split complex of Drosophila includes four Notch-regulated members of the bearded gene family -- Lai et al. 127 (16): 3441 -- Development
		The Effect of Polymorphisms in the Enhancer of split Gene Complex on Bristle Number Variation in a Large Wild-Caught Cohort of Drosophila melanogaster
		The enhancer of split complex of Drosophila includes four Notch-regulated members of the bearded gene family -- Lai et al.
		The enhancer of split complex of Drosophila includes four Notch-regulated members of the bearded gene family
	dev.biologists.org /cgi/content/abstract/127/16/3441 (665 words)

	Drosophila melanogaster Casein Kinase II Interacts with and Phosphorylates the Basic Helix-Loop-Helix Proteins m5, m7, and m8 Derived from the Enhancer of split Complex -- Trott et al. 276 (3): 2159 -- Journal of Biological Chemistry
		Drosophila melanogaster Casein Kinase II Interacts with and Phosphorylates the Basic Helix-Loop-Helix Proteins m5, m7, and m8 Derived from the Enhancer of split Complex -- Trott et al.
		The abbreviations used are: CKII, casein kinase II; HLH, helix-loop-helix; bHLH, basic HLH; E(spl), Enhancer of split; E(spl)C, Enhancer of split complex; Dm, D.
		Articles by Trott, R. Articles by Bidwai, A. Drosophila melanogaster Casein Kinase II Interacts with and Phosphorylates the Basic Helix-Loop-Helix Proteins m5, m7, and m8 Derived from the Enhancer of split Complex
	www.jbc.org /cgi/content/full/276/3/2159 (6314 words)

	RE: [xsl] Mike Kay's tip 8 how to use XSLT efficiently
		> > But I have a question about tip number eight: > "Split complex transformations into several stages." > > What does this mean?
		I would still strongly advocate implementing complex transformations as a pipeline (a sequence of simple transformations), but more for software engineering reasons (modularity, maintainability, reusability) than for raw performance.
		However, that's not contradictory: you can't improve performance unless you can measure it and analyze it, and that's far more likely to be feasible if you adopt a clean pipeline architecture.
	www.xslt.com /html/xsl-list/2005-04/msg00874.html (298 words)

	BioMed Central Full text Delta activity independent of its activity as a ligand of Notch
		The number of repetitions of an experiment is indicated in the figure legends.
		Sca associates with Dl Although N and Sca complexes could be immuno-precipitated [14], we, and others [23], had failed to detect Sca on S2-N cells.
		We have previously shown that Sca and N form complexes [14].
	www.biomedcentral.com /1471-213X/5/6 (6609 words)

	Local CNC programming and ethernet cuts machining: News from NC Graphics (Cambridge)
		He realised that conventional machine tools and tooling were not capable of economically producing the complex shapes required in the latest plastics components.
		The set-up sheet provides all the information required for each electrode, the X and Y position relative to the common datum, together with lift or drop for height, which is kept to a round number for simplicity.
		With this method of manufacture every job is the same, in that the sparking operation ends at Z zero, removing the need to specify a depth to spark to, the associated possibility of error, and multiple setting operations.
	www.manufacturingtalk.com /news/ncg/ncg107.html (849 words)

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Topic: Split-complex number

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In the News (Sat 18 May 13)