Search results for " function"

showing 10 items of 9395 documents

Examples of Indexed PIP-Spaces

2009

This chapter is devoted to a detailed analysis of various concrete examples of pip-spaces. We will explore sequence spaces, spaces of measurable functions, and spaces of analytic functions. Some cases have already been presented in Chapters 1 and 2. We will of course not repeat these discussions, except very briefly. In addition, various functional spaces are of great interest in signal processing (amalgam spaces, modulation spaces, Besov spaces, coorbit spaces). These will be studied systematically in a separate chapter (Chapter 8).

AlgebraSequencesymbols.namesakeModulation spaceMeasurable functionComputer scienceBergman spaceBanach spacesymbolsHilbert spaceHardy spaceSequence space
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Double point curves for corank 2 map germs from C2 to C3

2012

Abstract We characterize finite determinacy of map germs f : ( C 2 , 0 ) → ( C 3 , 0 ) in terms of the Milnor number μ ( D ( f ) ) of the double point curve D ( f ) in ( C 2 , 0 ) and we provide an explicit description of the double point scheme in terms of elementary symmetric functions. Also we prove that the Whitney equisingularity of 1-parameter families of map germs f t : ( C 2 , 0 ) → ( C 3 , 0 ) is equivalent to the constancy of both μ ( D ( f t ) ) and μ ( f t ( C 2 ) ∩ H ) with respect to t , where H ⊂ C 3 is a generic plane.

AlgebraSymmetric functionPure mathematicsDouble pointPlane (geometry)Scheme (mathematics)Geometry and TopologyMilnor numberMathematicsTopology and its Applications
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Star representations of E(2)

1990

We give a complete and explicit realization of the unitary irreducible representations of the universal covering group G of E(2), the Euclidean group in two dimensions, by deformation of the algebra of functions on the dual g* of the Lie algebra of G. We define an adapted Fourier transform for G which gives a natural description of the harmonic analysis of G.

AlgebraUnitary representationRepresentation theory of SURepresentation theory of the Lorentz groupCovering groupZonal spherical functionStatistical and Nonlinear PhysicsUniversal enveloping algebra(gK)-moduleGroup algebraMathematical PhysicsMathematicsLetters in Mathematical Physics
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Multiplication of Distributions in One Dimension: Possible Approaches and Applications to δ-Function and Its Derivatives

1995

We introduce a new class of multiplications of distributions in one dimension merging two different regularizations of distributions. Some of the features of these multiplications are discussed in detail. We use our theory to study a number of examples, involving products between Dirac delta functions and its successive derivatives. © 1995 Academic Press. All rights reserved.

Algebrasymbols.namesakePure mathematicsApplied MathematicssymbolsAnalysiDirac delta functionSettore MAT/07 - Fisica MatematicaAnalysisMathematicsJournal of Mathematical Analysis and Applications
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On many-sorted algebraic closure operators

2004

A theorem of Birkhoff-Frink asserts that every algebraic closure operator on an ordinary set arises, from some algebraic structure on the set, as the corresponding generated subalgebra operator. However, for many-sorted sets, i.e., indexed families of sets, such a theorem is not longer true without qualification. We characterize the corresponding many-sorted closure operators as precisely the uniform algebraic operators. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Algebraic cycleDiscrete mathematicsGeneral MathematicsAlgebraic surfaceReal algebraic geometryAlgebraic extensionDimension of an algebraic varietyAlgebraic functionOperator theoryAlgebraic closureMathematicsMathematische Nachrichten
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On the Estimation of the Volatility-Growth Link

2012

It is common practice to estimate the volatility-growth link by specifying a standard growth equation such that the variance of the error term appears as an explanatory variable in this growth equation. The variance in turn is modeled by a second equation. Hardly any of existing applications of this framework includes exogenous controls in this second variance equation. Our theoretical findings suggest that the absence of relevant explanatory variables in the variance equation leads to a biased and inconsistent estimate of the volatility-growth link. Our simulations show that this effect is large. Once the appropriate controls are included in the variance equation consistency is restored. I…

Algebraic formula for the varianceOne-way analysis of varianceStatisticsVariance decomposition of forecast errorsEconometricsVariance-based sensitivity analysisControl variatesLaw of total varianceVariance functionMathematicsFraction of variance unexplainedSSRN Electronic Journal
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Asymptotically good codes from generalized algebraic-geometry codes

2005

We consider generalized algebraic-geometry codes, based on places of the same degree of a fixed algebraic function field over a finite field. In this note, using a method similar to the Justesen's one, we construct a family of such codes which is asymptotically good.

Algebraic function fieldBlock codeDiscrete mathematicsFunction field of an algebraic varietyApplied MathematicsReal algebraic geometryAlgebraic extensionAlgebraic functionLinear codeExpander codeComputer Science ApplicationsMathematics
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ON AUTOMORPHISMS OF GENERALIZED ALGEBRAIC-GEOMETRY CODES.

2007

Abstract We consider a class of generalized algebraic-geometry codes based on places of the same degree of a fixed algebraic function field over a finite field F / F q . We study automorphisms of such codes which are associated with automorphisms of F / F q .

Algebraic function fieldDiscrete mathematicsAlgebraic cycleFinite fieldFunction field of an algebraic varietyAlgebra and Number TheoryAutomorphisms of the symmetric and alternating groupsAlgebraic extensionAlgebraic geometryAutomorphismMathematics
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Skaitļu teorija: lekcijas, lasītas Latvijas Universitātes Matemātikas un dabas zinātņu fakultātē

1936

Lekcijas sakārtojis Fogels, Ernests ; rediģējis Lūsis, Arvīds.

Algebraic number theoryNumber theoryAritmētiskās funkcijas:MATHEMATICS::Applied mathematics::Numerical analysis [Research Subject Categories]Arithmetic functionsNumbers rationalMatemātikaKongruenti skaitļiAlgebriskā skaitļu teorijaSkaitļu teorijaSkaitļi racionālie
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An improved algorithm for thermal dynamic simulation of walls using Z-transform coefficients

2003

The Transfer Function Method (TFM), recommended by American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE), is one of the most modern tools available to solve heat transfer problems in building envelopes and environments. TFM utilises Z-transform to solve the equations system that describes the heat transfer in a multi-layered wall. Due to an analogy with an electric circuit, it is possible to write the equations system in a matrix suitable to be solved by computer. Authors carried out an analysis on an historical building placed in the south of Italy to test the reliability and the quality of the thermal dynamic simulation using TFM. The analysis is performed usi…

AlgorithmProblem solvingSettore ING-IND/11 - Fisica Tecnica AmbientaleMathematical operatorTransfer functionsBuildingMathematical transformationComputer simulationMatrix algebra
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