Search results for "algebra"

showing 10 items of 4129 documents

Nilpotent and perfect groups with the same set of character degrees

2014

We find a pair of finite groups, one nilpotent and the other perfect, with the same set of character degrees.

Set (abstract data type)Discrete mathematicsNilpotentPure mathematicsAlgebra and Number TheoryCharacter (mathematics)Applied MathematicsNilpotent groupUnipotentCentral seriesMathematicsJournal of Algebra and Its Applications
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Algebraic Structures of Rough Sets

1994

This paper deals with some algebraic and set-theoretical properties of rough sets. Our considerations are based on the original conception of rough sets formulated by Pawlak [4, 5]. Let U be any fixed non-empty set traditionally called the universe and let R be an equivalence relation on U. The pair A = (U, R) is called the approximation space. We will call the equivalence classes of the relation R the elementary sets. We denote the family of elementary sets by U/R. We assume that the empty set is also an elementary set. Every union of elementary sets will be called a composed set. We denote the family of composed sets by ComR. We can characterize each set X ⊆ U using the composed sets [5].

Set (abstract data type)Discrete mathematicsRelation (database)Algebraic structureEquivalence relationEmpty setRough setAlgebraic numberSpace (mathematics)Mathematics
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On a projective representation of chain geometries

1984

We define a distance d on the set of r-spaces of an n-space. By the transfer of d to the GrasmannianG=G(n, r) we obtain a distinguished class of normal rational curves of order 1, the “1-distance lines’, 1=1,..., r, which are in 1–1-correspondence to the so-called “generalized reguli of type (r, 1)”.

Set (abstract data type)Discrete mathematicsTransfer (group theory)Class (set theory)Pure mathematicsChain (algebraic topology)Order (group theory)Geometry and TopologyType (model theory)Rational normal curveProjective representationMathematicsJournal of Geometry
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A primal-dual algorithm for the fermat-weber problem involving mixed gauges

1987

We give a new algorithm for solving the Fermat-Weber location problem involving mixed gauges. This algorithm, which is derived from the partial inverse method developed by J.E. Spingarn, simultaneously generates two sequences globally converging to a primal and a dual solution respectively. In addition, the updating formulae are very simple; a stopping rule can be defined though the method is not dual feasible and the entire set of optimal locations can be obtained from the dual solution by making use of optimality conditions. When polyhedral gauges are used, we show that the algorithm terminates in a finite number of steps, provided that the set of optimal locations has nonepty interior an…

Set (abstract data type)Fermat's Last TheoremMathematical optimizationSimple (abstract algebra)General MathematicsNumerical analysisApplied mathematicsWeber problemFinite setSoftwareCounterexampleDual (category theory)MathematicsMathematical Programming
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Sylow Normalizers and Brauer Character Degrees

2000

Suppose that G is a finite group. In this note, we show that a local condition about Sylow normalizers is equivalent to a global condition on the degrees of certain irreducible Brauer characters of G. Theorem A. Let G be a finite ”p; q•-solvable group, and let Q ∈ SylqG‘ and P ∈ SylpG‘. Then every irreducible p-Brauer character of G of q′degree has p′-degree if and only if NGQ‘ is contained in some G-conjugate of NGP‘. Theorem A needs a solvability hypothesis. If p = 7, then the irreducible p-Brauer characters of the group G = PSL2; 27‘ have degrees ”1; 13; 26; 28•. If we set q = 2, then each q′-degree is also a p′-degree.

Set (abstract data type)Finite groupPure mathematicsAlgebra and Number TheoryBrauer's theorem on induced charactersCharacter (mathematics)Group (mathematics)If and only ifSylow theoremsMathematicsJournal of Algebra
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Parameter Identification of a Winding Function Based Model for Fault Detection of Induction Machines

2018

Prediction of machines' faulty parts is important in industrial applications in order to reduce productivity losses. As far as electrical machines are considered, a model-based fault diagnosis approach is usually used for this purpose. The model is derived from the modified winding function theory and hence, it requires a considerable amount of parameters at various operating conditions in order to be successfully used. However, the complete set of parameters is difficult to be obtained, as manufacturers of electric machines normally provide only the parameters that describe simple motor models (e.g. T-equivalent circuit at rated conditions). Therefore, the current work presents a method th…

Set (abstract data type)Identification (information)Bar (music)Control theorySimple (abstract algebra)Computer scienceWork (physics)Fault (power engineering)Induction motorFault detection and isolation2018 Eighth International Conference on Information Science and Technology (ICIST)
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Nature log-analytique du volume des sous-analytiques

2000

Using a preparation theorem for subanalytic functions and Lipschitz stratification for compact subanalytic sets we prove that volumes of slices of globally subanalytic sets and density have a log-analytic nature. We also prove that the set of parameters for which the volume of fiber is finite is globally subanalytic.

Set (abstract data type)Mathematics::LogicMathematics::Algebraic GeometryMathematics::Complex VariablesFiber (mathematics)General MathematicsMathematical analysisLipschitz continuityStratification (mathematics)MathematicsVolume (compression)Illinois Journal of Mathematics
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Approximation of Feasible Parameter Set in worst case identification of block-oriented nonlinear models

2003

Abstract The estimation of the Feasible Parameter Set for block-oriented nonlinear models in a worst case setting is considered. A bounding procedure is determined both for polytopic and ellipsoidie sets, consisting in the projection of the FPS ⊂ R MN of the extended parameter vector onto suitable M or N-dimensional subspaces and in the solution of convex optimization problems which provide the extreme points of the Parameter Uncertainties Intervals of the model parameteres. Bounds obtained are tighter then in the previous approaches.

Set (abstract data type)Nonlinear systemMathematical optimizationBounding overwatchConvex optimizationApplied mathematicsExtreme pointLinear subspaceProjection (linear algebra)MathematicsBlock (data storage)
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Testing Independence: A New Approach

2000

In time series analysis and modelling, testing for independence allows us to determine if the estimated model is correctly specified. In this work, we present a very simple method to test for serial independence, based on the two-dimensional embedding vectors (the so-called “2-histories”), and we analyse the power and size of such a procedure against a wide set of linear and nonlinear alternatives.

Set (abstract data type)Nonlinear systemSimple (abstract algebra)Independence (mathematical logic)EmbeddingMartingale difference sequenceWhite noiseTime seriesAlgorithmMathematics
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MATHEMATICS AS A QUASI-EMPIRICAL SCIENCE

2006

The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T1, ..., T n in which Ti+1, for 1 ≤ i < n, supersedes T i . This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, like the theories belonging to the empirical sciences, are fallible and that, consequently, mathematical knowledge has a quasi-empirical nature. The way I have chosen to provide evidence in favour of the correctness of the main thesis of t…

Set (abstract data type)Philosophy of mathematicsPhilosophy of scienceMultidisciplinaryCorrectnessHistory and Philosophy of ScienceSimple (abstract algebra)Universal setSet theoryNaive set theoryquasi-empiricism and mathematics Lakatos mathematical research programmes Cantor-Zermelo set theory philosophy of mathematics mathematical knowledgeMathematicsEpistemology
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