Search results for "Empty set"

showing 6 items of 6 documents

A remark on differentiable functions with partial derivatives in Lp

2004

AbstractWe consider a definition of p,δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p,δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.

Change of variablesPure mathematicsPolish groupApplied MathematicsMathematical analysisNull set or empty setReal-valued functionHaar nullPartial derivativeAlmost everywhereCoarea formulaDifferentiable functionAnalysisMathematics
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Hard single diffraction in p̄p collisions at s=630 and 1800 GeV

2002

Using the D empty set detector, we have studied events produced in (p) over barp collisions that contain large forward regions with very little energy deposition ("rapidity gaps") and concurrent jet production at center-of-mass energies of roots = 630 and 1800 GeV. The fraction of events with forward or central jets associated with rapidity gaps is compared to predictions for hard diffraction. We also extract the momentum loss for scattered protons in such processes. (C) 2002 Elsevier Science B.V. All rights reserved.

DiffractionPhysicsParticle physicsNuclear and High Energy Physics010308 nuclear & particles physicsDetectorEmpty setHERAJet (particle physics)01 natural sciencesNuclear physicsPomeron0103 physical sciencesMomentum lossRapidityHigh Energy Physics::Experiment010306 general physicsPhysics Letters B
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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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Absolutely continuous functions in Rn

2005

Abstract For each 0 α 1 we consider a natural n-dimensional extension of the classical notion of absolute continuous function. We compare it with the Malý's and Hencl's definitions. It follows that each α-absolute continuous function is continuous, weak differentiable with gradient in L n , differentiable almost everywhere and satisfies the formula on change of variables.

Polish groupPure mathematicsChange of variablesα-regular intervalsContinuous functionApplied MathematicsMathematical analysisNull set or empty setQuasi-continuous functionAbsolute continuityWeak derivativeAbsolutely continuous functionsSobolev spaceHaar nullSobolev spacesAlmost everywhereDifferentiable functionAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Quasi-model-independent search for new physics at large transverse momentum

2001

We apply a quasi-model-independent strategy ("Sleuth") to search for new high p_T physics in approximately 100 pb^-1 of ppbar collisions at sqrt(s) = 1.8 TeV collected by the DZero experiment during 1992-1996 at the Fermilab Tevatron. Over thirty-two e mu X, W+jets-like, Z+jets-like, and 3(lepton/photon)X exclusive final states are systematically analyzed for hints of physics beyond the standard model. Simultaneous sensitivity to a variety of models predicting new phenomena at the electroweak scale is demonstrated by testing the method on a particular signature in each set of final states. No evidence of new high p_T physics is observed in the course of this search, and we find that 89% of …

PhysicsNuclear and High Energy PhysicsParticle physics010308 nuclear & particles physicsPhysics beyond the Standard ModelTevatronFOS: Physical sciencesEmpty setState (functional analysis)01 natural sciencesHigh Energy Physics - Experiment3. Good healthStandard ModelSet (abstract data type)Nuclear physicsHigh Energy Physics - Experiment (hep-ex)Experimental High Energy Physics0103 physical sciencesComputingMethodologies_DOCUMENTANDTEXTPROCESSING[PHYS.HEXP]Physics [physics]/High Energy Physics - Experiment [hep-ex]High Energy Physics::ExperimentFermilabElectroweak scale010306 general physics
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A local notion of absolute continuity in IR^n

2005

We consider the notion of p, δ-absolute continuity for functions of several variables introduced in [2] and we investigate the validity of some basic properties that are shared by absolutely continuous functions in the sense of Maly. We introduce the class $δ−BV^p_loc(\Omega,IR^m)$ and we give a characterization of the functions belonging to this class.

Class (set theory)Pure mathematicsPolish groupHaar nullGeneral MathematicsMathematical analysisNull set or empty setAlgebra over a fieldAbsolute continuityCharacterization (mathematics)Modulus of continuityMathematics
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