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Topic: Continuous linear form

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	Linear
		We are often concerned with bounded linear functions[?], which is equivalent to continuous ones.
		The concept of linearity can be extended to linear operators which are linear if they satisfy the superposition and homogenity relations.
		When a differential equation can be expressed in linear form, it is particularly easy to solve by breaking the equation up into smaller pieces, solving each of those pieces, and adding the solutions up.
	www.ebroadcast.com.au /lookup/encyclopedia/li/Linear.html (311 words)

	Summary: Dunes, Linear/Seif
		Linear dunes cover more desert area than any other type of dune, especially in central Australia, southern Africa, the southwestern Arabian Peninsula, and parts of the Sahara, but they are not as common (in the sense of occurring in almost every desert) as are the crescentic dunes.
		Nonetheless, the long axes of linear dunes are aligned generally within 15° of the prevailing wind or with the resultant drift direction of the local winds.
		Linear dunes can be continuous for many tens and even hundreds of kilometers, and they can form parallel barriers to cross-country movement except down the interdunal passages, which are parallel to the long axes of the dunes (see photo).
	www.tec.army.mil /research/products/desert_guide/lsmsheet/lslinear.htm (864 words)

	Continuous case and seismic imaging
		Of course, the linear theory is not limited to discrete grids.
		It is interesting to consider the continuous case because of its connection to the linear integral operators commonly used in seismic imaging.
		Linear decomposition of the data into basis functions means decomposing it into the combination of impulse responses (``hyperbolas'').
	sepwww.stanford.edu /public/docs/sep107/paper_html/node26.html (227 words)

	Mathematical Programming Glossary
		In this form, U is monotonic non-decreasing (u >= 0 in the linear case), and the extension of complementary slackness is that U(g(x)) = U(0).
		When a univariate function is piece-wise linear, it has the form a(i)x + b(i) for x in the interval [c(i), c(i+1)], where a(i) is not equal to a(i+1).
		(The phrase usually means the function is continuous.) This arises in linear programming when considering the optimal value as a function of varying right-hand sides (or cost coefficients) in fixed proportions: b+td (or c+td), where d is an admissible change vector and t is the (scalar) variable.
	glossary.computing.society.informs.org /index.php?page=L.html (2349 words)

	Non Linear Thinking --- GLOBALIZATION - Not sustainable by Products ! (Site not responding. Last check: 2007-10-10)
		The majority of the loss in the linear era was thus concentrated at one point leading to structured closure or restructuring of the manufacturing plant.
		YET Linear theories remain the priority and they continue to be dependent on continuous growth in trade as the minimal need for survival.
		Linear economic and valuation formulae have never considered the cost of “renewability” of a natural product, to be a part of the cost of a natural resource.
	www.nonlinearthinking.com /ch/mngmt/global.htm (5774 words)

	Mathematical Programming Glossary
		If continuous use of the capacity is not possible (i.e., one builds a new plant or not), the model further requires v to be binary-valued (0 or 1), and F(1) is called the fixed charge.
		In linear programming the character could be an optimal basis, and the theory is concerned with whether a particular basis remains optimal when the data is changed in a prescribed direction.
		This is a (linear) integer programming model: patterns are specified, and A(i, j, k) = amount of i-th stock (e.g., sheet or roll of material) used to generate the j-th output by the k-th pattern.
	glossary.computing.society.informs.org /index.php?page=C.html (6157 words)

	Springer Online Reference Works
		Completely investigated is also the case when the quotient algebra by the radical is the algebra of continuous functions on a totally-disconnected compactum: A necessary and sufficient condition for decomposability is that the idempotents of the original algebra be uniformly bounded.
		of continuous functions on the unit circle that have an analytic continuation inside the unit disc is a maximal subalgebra of the algebra of continuous functions on the unit circle.
		This algebra is a maximal subalgebra of the algebra of all continuous functions on the torus.
	eom.springer.de /c/c023380.htm (1448 words)

	Wikinfo \| Linear (Site not responding. Last check: 2007-10-10)
		Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (or linear spaces), linear transformations, and systems of linear equations.
		In a slightly different usage to the above, a polynomial of degree 1 is said to be linear, because the graph of a function of that form is a line.
		Images, some of which are used under the doctrine of Fair use or used with permission, may not be available.
	www.wikinfo.org /wiki.php?title=linear (430 words)

	Double Moebius Strip Studies by Petresin and Robert in the Nexus Network Journal vol. 4 no. 4 (Autumn 2002) (Site not responding. Last check: 2007-10-10)
		The curious single continuous surface named after him has only one side and one edge, and is made by twisting the band by 180° then joining the two ends.
		These relations can be graphed in the form of a figure eight or a Möbius strip: when such a graphed numeric orbit flows through the inflection point (number 9) in a clockwise sense, it subsequently reverses itself into its own twin partner, continuing the flow through an anticlockwise orbit.
		Similarities in form and movement of the double Möbius strip structure can be established with the structure and the nature of formation of a vortex.
	www.nexusjournal.com /PetRob.html (3794 words)

	Initial topology - Wikipedia, the free encyclopedia
		In topology and related areas of mathematics, the initial topology (projective topology or weak topology) on a set X, with respect to a family of functions on X, is the coarsest topology on X which makes those functions continuous.
		The inverse limit of any inverse system of spaces and continuous maps is the set-theoretic inverse limit together with the initial topology determined by the canonical morphisms.
		The weak topology on a locally convex space is the initial topology with respect to the continuous linear forms of its dual space.
	en.wikipedia.org /wiki/Initial_topology (625 words)

	3.2.2. Continuous Linear Model
		The continuous linear model (CLM) is probably the most commonly used model in PPC.
		The CLM is a mathematical function that relates explanatory variables (either discrete or continuous) to a single continuous response variable.
		It is called linear because the coefficients of the terms are expressed as a linear sum.
	www.6sigma.us /handbook/ppc/section2/ppc22.htm (445 words)

	Partners: Functional Analysis and Topology by Lawrence Narici
		Identifying the dual space---the space of continuous linear functionals---of a normed space played an especially important role in the formative years of functional analysis.
		Various extensions of limit and continuity to objects other than numbers or points has been with us since the 18th century but their rigorous study---what we might call early "functional analysis", in the sense of analysis on sets whose members were functions---did not begin until around 1820.
		With the locally convex space and von Neumann and Kolmogorov's notion of bounded set (one which is contained in a sufficiently large scalar multiple of any neighborhood of 0), duality theory was transmogrified in the works of Mackey ([14], [15]), and Grothendieck ([10], [11]).
	at.yorku.ca /t/a/i/c/42.htm (1625 words)

	Springer Online Reference Works
		A linear operator mapping one locally convex space into another, and having a special form of approximation by operators of finite rank (that is, by continuous linear operators with finite-dimensional ranges).
		that is continuous in each variable separately, and the correspondence between forms of this type is one-to-one.
		An arbitrary continuous operator on a Hilbert space is nuclear if and only if it has a finite matrix trace for any orthonormal basis (see [2], [8], [9]).
	eom.springer.de /n/n067850.htm (1744 words)

	Linear functions
		A continuous linear function must have the form f(x) = ax.
		Continuity of the function is quite essential as it's possible to show [Ref. 1, 2] that the graph of any discontinuous solution to (*) is dense in the plane R
		We have just shown that a continuous additive function is necessarily linear.
	www.cut-the-knot.org /do_you_know/linear.shtml (337 words)

	Linear model order reduction
		Currently the state-space form is the most widely used for representing any LTI system because of its manageability.
		This form is usually referred to as generalized state-space form, or a descriptor form.
		may be dense, therefore it's beneficial to keep the system description in the form of a generalized state-space (2) and not convert it into the form (1).
	web.mit.edu /mor/Linear_mor.html (971 words)

	Hybrid Methods
		Usually, the 0-1 variables appear in a linear form and the continuous variables exhibit the nonlinearities.
		In the GBD algorithm, the MILP master problem is given by a dual representation of a continuous space, while in the OA method, is it given by a primal approximation.
		The discrete variables are the decision variables for the components in the superstructure to include in the optimal structure, and the continuous variables are the values of the parameters for the included components.
	www.cs.sandia.gov /opt/survey/hybrid.html (1784 words)

	Linear Encoders, Inductosyn® Sensors and Linear Transducers
		Linear Inductosyn® transducers are supplied as rigid bars or flexible tapes.
		Standard 10 inch (254 mm) bars can be mounted end to end to form continuous measuring systems of unlimited length.
		Continuous tapes to 120 feet (36.6m) or longer can be supplied.
	www.ruhle.com /linear_transducers.htm (138 words)

	Multivariate Statistics - CVA Overview
		Suppose that we have several continuous predictor variables and we wish to use the entire set to predict several criterion variables, each of which is also continuous.
		CVA simultaneously calculates a linear composite of all x variables and a linear composite of all y variables.
		Each linear combination is called a canonical variate and takes the general linear form.
	www.uwsp.edu /psych/cw/statmanual/glmcva.html (662 words)

	Open Channel Foundation: ORACLS
		For the finiteduration optimal linear regulator problem with noise-free measurements, continuous dynamics, and integral performance index, a routine is provided which implements the negative exponential method for finding both the transient and steady-state solutions to the matrix Riccati equation.
		Finally, routines are included to implement the continuous and discrete forms of the explicit (model-in-thesystem) and implicit (model-in-the-performance-index) model following theory.
		These routines generate linear control laws which cause the output of a dynamic time-invariant system to track the output of a prescribed model.
	www.openchannelfoundation.org /projects/ORACLS (594 words)

	Decimal and percentage data
		Observations may be presented for Rasch analysis in the form of percentages in the range 0-100.
		Since these are in the form of the measures produced by Winsteps, they can be compared and combined with Rasch measures using standard statistical techniques, in the same way that weight and height are analyzed.
		Though time and weight are reported in linear units, e.g., seconds and grams, their implications in the specific context is unlikely to be linear.
	www.winsteps.com /winman/decimal.htm (983 words)

	5.1.1. What is experimental design?
		It is common to begin with a process model of the `fl box' type, with several discrete or continuous input factors that can be controlled--that is, varied at will by the experimenter--and one or more measured output responses.
		Often the experiment has to account for a number of uncontrolled factors that may be discrete, such as different machines or operators, and/or continuous such as ambient temperature or humidity.
		The most common empirical models fit to the experimental data take either a linear form or quadratic form.
	www.itl.nist.gov /div898/handbook/pri/section1/pri11.htm (450 words)

	Differential Forms and Chains (Site not responding. Last check: 2007-10-10)
		This section is concerned with some algebraic preliminaries needed to give a formal definition of what we mean by a differenial form.
		The linear independense is shown analogously to the argument of Proposition 1.
		When these coordinate functions are continuous, differential, etc., we call the vector field or k-form continuous, differentiable, etc. To simplify the hypotheses, we will henceforth use the word differentiable to mean
	www.ms.uky.edu /~ken/ma570/lectures/lecture7/html/forms.htm (679 words)

	Tweaking Algorithms for -Strand Alignment
		A wildly different set of torsion angles is more likely to lead to a steric clash within the turn region, and to be true to our discretization we wish to choose angles that are relatively close to the discrete angles that are the basis of our search space.
		Since we are going to convert the main constraint into a linear function anyway, it will only affect the coefficient matrix for our system of linear equations, so we will fold it into the main constraint function.
		If none is found, or we return after searching a branch of the tree, we continue to search for partners until we reach the first amino acid.
	www.sju.edu /~sforman/thesis-html/node5.html (3869 words)

	F24 Continuous Form Laser Printers - Microplex
		An impressive print speed of 24 ppm along with 300 dpi, creates a SOLID choice to move into continuous form laser printing.
		Adjustable form lengths and fusing temperatures make the SOLID F24 a flexible printer.
		Automatic tear-off positioning enables new print jobs to start in the proper place, which eliminates wasted forms between jobs.
	www.microplex-usa.com /f24specs.htm (139 words)

	[No title]
		These notes, summarizing my limited understanding and ongoing research on the subject of continuous realization methods, were prepared for lecture presentations at the Academia Sinica in Taiwan, the Australian National University in Canberra, and various other universities during my sabbatical leave in 1996.
		In this expository series the emphasis is on using differential equation techniques as a special continuous realization process for problems arising from the field of linear algebra.
		The matrix differential equations are cast in fairly general frameworks of which special cases have been found to be closely related to important numerical algorithms.
	www4.ncsu.edu /~mtchu/Research/Lectures/Continuous/Readme.html (301 words)

	Quantum Geometry
		In terms of this identification, the topology on X coincides with the -weak topology, induced from the dual space A (by definition continuous linear functionals, it turns out that homomorphisms between C-algebras are automatically continuous, in particular characters are continuous* linear functionals).
		The same algebraic characterization holds at the smooth level, too (smooth maps between compact smooth manifolds are in a one-to-one correspondence with unital *-homomorphisms between the associated algebras of smooth functions).
		is continuous (it can be shown that in the compact case continuity of the product implies continuity of the inverse map).
	www.matem.unam.mx /~micho/qgeom2.html (828 words)

	First Order Linear Equations
		In the first section under Linearity, you learned about the general form of a linear equation.
		By looking the general form of a first order linear equation, you can derive the general rule to find the integrating factor.
		An interesting fact concerning first order linear equations is that the integrating factor, which is found by the method just discussed, turns this non exact equation into an exact one.
	homepage.mac.com /nshoffner/nsh/ODE/FirstOD.html (1197 words)

	Amazon.com: "continuous linear forms": Key Phrase page (Site not responding. Last check: 2007-10-10)
		See all pages with references to continuous linear forms.
		We consider the space C of continuous linear forms f : AA/A -4 K. We know that C is a vector space over A. Actually C is isomorphic to...
		Continuous Forms -- Custom short-run forms, checks, and more.
	amazon.com /phrase/continuous-linear-forms (540 words)

	Optimal Regulator Algorithms For The Control Of Linear Systems
		For the finite-duration optimal linear regulator problem with noise-free measurements, continuous dynamics, and integral performance index, a routine is provided which implements the negative exponential method for finding both the transient and steady-state solutions to the matrix Riccati equation.
		Finally, routines are included to implement the continuous and discrete forms of the explicit (model-in-the-system) and implicit (model-in-the-performance-index) model following theory.
		In order to apply ORACLS, the user must write an executive (driver) program which inputs the problem coefficients, formulates and selects the routines to be used to solve the problem, and specifies the desired output.
	www.pdas.com /oracls.htm (549 words)

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