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Supremum and Infimum - Florida State University - Department ...

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Supremum and Infimum - Florida State University - Department ...

Supremum and Infimum Characterizations of Sup and of Inf. Mika Seppälä: Sup and Inf Distance in the Set of Real Numbers The of a number is defined by setting if 0 a

http://www.math.fsu.edu/~seppala/Calculus-2004/HowTo/Supremum/sup.pdf

Date added: August 28, 2013 - Views: 12

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Supremum and Infimum - Florida State University - Department ...

1 Supremum and Infimum Mika Seppälä Mika Seppälä: Sup and Inf Distance in the Set of Real Numbers The of a number is defined by setting

http://www.math.fsu.edu/~seppala/Calculus-2004/HowTo/sup%20and%20inf%20OBSOLETE/ho-sup.pdf

Date added: July 18, 2013 - Views: 9

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Supremum and Infimum

Supremum and Infimum Characterizations of Sup and of Inf. Mika Seppälä: Sup and Inf Index FAQ Distance in the Set of Real Numbers The of a number is defined by setting if 0 a

http://www.webalt.net/Calculus-2004/HowTo/Supremum/sup.pdf

Date added: December 19, 2013 - Views: 4

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The Infimum, Supremum, and Geodesic Length of a Braid ...

The Infimum, Supremum, and Geodesic Length of a Braid Conjugacy Class JoanS.Birman1 1 PartiallysupportedbyNSFGrantsDMS-9705019andDMS-9973232. DepartmentofMathematics,ColumbiaUniversity,NewYork,NewYork10027 E-mail:[email protected] and

http://www.math.columbia.edu/~jb/inf-sup-j.pdf

Date added: April 4, 2012 - Views: 4

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Invexity of supremum and infimum functions

BULL. AUSTRAL. MATH SOC 26A51. 90C30 , VOL. 65 (2002) [289-306] INVEXITY OF SUPREMUM AND INFIMUM FUNCTIONS NGUYEN XUAN HA AND DO VAN LUU Under suitable assumptions we establis theh formulas for calculating generalised

http://journals.cambridge.org/download.php?file=%2FBAZ%2FBAZ65_02%2FS0004972700020335a.pdf&code=bc49ba401b52de6eead73b8e039e5e6c

Date added: August 27, 2014 - Views: 1

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Infimum and supremum completeness properties of ordered sets ...

Infimum and supremum completeness properties 33 Proof. By the corresponding definitions and Theorem 1.1, it is clear that inf (∅)=max lb(∅) =max(X)=X ∩ ub(X)=ub(X).

http://www.anstuocmath.ro/mathematics/pdf16/BOROS-SZAS-Comp1c.pdf

Date added: July 1, 2012 - Views: 3

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1 Supremum and Infimum 2 Sequences, accumulation points ...

Some fact about sup, inf, limsup and liminf 1 Supremum and Infimum For a set X of real numbers, the number ξ = supX, the supremum of X ( or least upper

http://people.math.umass.edu/~lr7q/ps_files/teaching/math623/sup1.pdf

Date added: September 12, 2014 - Views: 1

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Solved Problems on Supremum and Infimum

Solved Problems on Supremum and Infimum () () + +− + == +− + … 2 2 1 11 Let 1,2,3, . 12 Determine sup and inf .

http://www.webalt.net/Calculus-2004/SolvedProblems/Sup/SupProblems.pdf

Date added: November 24, 2012 - Views: 4

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Max, Min, Sup, Inf - Purdue University

The supremum, if it exists, (“sup”, “LUB,” “least upper bound”) of S is the smallest 81. 82 6. MAX, MIN, SUP, INF upper bound for S. An upper bound which actually belongs to the set is called a maximum. Proving that a certain number M is the LUB of a set S is often

http://www.math.purdue.edu/academic/files/courses/2007fall/MA301/MA301Ch6.pdf

Date added: March 12, 2012 - Views: 8

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Given a set, to compute the supremum and infimum of the set,

Given a set, to compute the supremum and infimum of the set, (Step 1) Find out the upper bound and lower bound (if any) of the set (Step 2) Show they are the desired supremum and infimum by applying the theorems

http://www.math.ust.hk/faculty/makyli/202_2007-8FaSp/TNt_07.pdf

Date added: July 18, 2013 - Views: 4

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N p () A p () B - University of Arkansas at Little Rock

Hyper-random variables and functions may be described by and the infimum bounds of the the supremum distribution function. Among the bounds of the distribution function there is a zone of the ambiguity. Random and chaotic phenomena are the degenerate hyper-random phenomena. 3.

http://ualr.edu/jdberleant/intprob/16.pdf

Date added: August 29, 2013 - Views: 1

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complete lattice/5 where the supremum V and infinum A of a ...

complete lattice/5 where the supremum V and infinum A of a subset $ of P are given by = The partially ordered set P can be embedded into its MacNeille completion • and this embedding is both supremum and infimum dense. That is to say

http://www.math.nmsu.edu/~jharding/1993%20Any%20Lattice%20can%20be%20Reg%20Embedded%20into%20MacNeille%20Comp%20of%20Distrib.pdf

Date added: December 19, 2013 - Views: 2

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Vector Optimization with Infimum and Supremum - Löhne, Preamble

Preface In mum and supremum are indispensable concepts in optimization. Never-theless their role in vector optimization has been rather marginal.

http://www.beck-shop.de/fachbuch/vorwort/9783642183508_Intro_001.pdf

Date added: October 2, 2014 - Views: 1

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Infimum and Supremum of the Set of Real Numbers. Measure Theory

INFIMUM AND SUPREMUM OF THE SET OF REAL. . . 2 (Def. 4) I1 =−∞. One can verify that there exists a set which is negative infinite number-like.

http://www.mizar.org/JFM/pdf/supinf_1.pdf

Date added: August 28, 2013 - Views: 1

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1.3 The Completeness Axiom and some Consequences ...

B. The Supremum and Infimum 1. Definition 1. A nonempty set is bounded above if there exists such that for all , . In this case is said to be

http://math.gmu.edu/~dwalnut/teach/Math315/Summer10/Sec%201.3.pdf

Date added: January 27, 2013 - Views: 5

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Introduction to Real Analysis - Rowan University

2.5 Supremum and infimum 2.5.1 A bounded set has a unique least upper bound . 2.6 The Bolzno- Weierstrass Theorem . 3.0 . Continuity and the Riemann Integral. 3.1 Limits of functions 3.1.1 Definition of continuity based on sequences

http://www.rowan.edu/colleges/las/departments/math/facultystaff/wright/Introduction%20to%20Real%20Analysis%20SPRING%202011.pdf

Date added: October 18, 2012 - Views: 12

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Real numbers - Department of Mathematics, University of Toronto

Supremum and infimum Limits and real numbers Page 5. Definition. A sequence of real numbers is called (strictly) increasing if A sequence of real numbers is called (strictly) decreasing if A ...

http://www.math.toronto.edu/ilia/Teaching/MAT378.2010/Limits%20and%20real%20numbers.pdf

Date added: October 17, 2011 - Views: 6

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Supremum and infimum in Example - KU

Supremum and infimum in [−∞,∞] Axiom + Observation: For all sets A ⊂ [−∞,∞] there is a smallest number larger than all numbers in A called supA – the supremum of A.

http://www.math.ku.dk/~richard/download/courses/Sand1MI_2008/week37monPrint.pdf

Date added: July 18, 2013 - Views: 7

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Infimum and Supremum of the Set of Real Numbers. Measure Theory

Infimum and Supremum of the Set of Real ... 167 Let X be a non-empty subset of . The functor X yields a non-empty subset of and is defined by:

http://fm.mizar.org/1991-2/pdf2-1/supinf_1.pdf

Date added: August 29, 2013 - Views: 2

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2.3 Bounds of sets of real numbers - Ohio State University

2.3 Bounds of sets of real numbers 2.3.1 Upper bounds of a set; the least upper bound (supremum) Consider S a set of real numbers. S is called bounded above if there is a number M so that any x ∈ S is

http://math.osu.edu/~costin.10/H161/supremum%20copy.pdf

Date added: January 21, 2014 - Views: 3

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SOUTHERN UNIVERSITY AND A&M COLLEGE DEPARTMENT OF MATHEMATICS ...

theorems: Axioms of the real numbers, supremum, infimum, upper limits, open and closed sets in nR, compactness, the Bolzano-Weierstrass and Heine-Borel Theorems, continuity and differentiability of functions, the Riemann Integral, The

http://www.subr.edu/assets/mathematics/Syllabi/MATH462REALANALYSIS.pdf

Date added: May 11, 2013 - Views: 2

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The Supremum of Some Canonical Processes - LK - Wiadomości

The Supremum of Some Canonical Processes Author(s): Michel Talagrand Source: American Journal of Mathematics, Vol. 116, No. 2 (Apr., 1994), pp. 283-325 ... where the infimum is taken over all the increasing sequences of partitions of T,

http://students.mimuw.edu.pl/~tt249057/other/ksiazki%20i%20papery/talagrand-supremum%20of%20some%20canonical%20processes.pdf

Date added: January 8, 2014 - Views: 4

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Chapter2

Chapter2 The supremum and infimum We review the definition of the supremum and and infimum and some of their properties that we use in defining and analyzing the Riemann integral.

https://www.math.ucdavis.edu/~hunter/m125b/ch2.pdf

Date added: October 2, 2014 - Views: 1

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Metric spaces - Department of Mathematics, University of Toronto

A metric space is called complete if every Cauchy sequence converges to a limit. Already know: ... By the definition of supremum and infimum, for any we have Let be a continuous function. Then is bounded (i.e. is a bounded set). Moreover, it ...

http://www.math.toronto.edu/ilia/Teaching/MAT378.2010/Metric%20Spaces.pdf

Date added: October 31, 2011 - Views: 7

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EKSISTENSI SUPREMUM DAN INFIMUM DENGAN TEOREMA CANTOR ...

EKSISTENSI SUPREMUM DAN INFIMUM DENGAN TEOREMA CANTOR DEDEKIND Nursiya Bito Staf Dosen Jurusan Matematika dan IPA Universitas Negeri Gorontalo ABSTRACT: In this paper, we will try to proof existence of supremum and infimum with Cantor

http://ejurnal.ung.ac.id/index.php/ST/article/download/369/361

Date added: January 21, 2014 - Views: 1

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UNIFORM APPROXIMATION BY CLASSES OF FUNCTIONS CLOSED UNDER ...

closed under pointwise supremum and infimum, respectively. Concerning the interpretation - of the functional hulls 7 and 1, a favorable case is when t,he classes Iio and Lo can be easily identified as, for example, bvhen Iio is the class of continuous functions on a - metric ...

http://www.tandfonline.com/doi/pdf/10.1080/01630569108816413

Date added: June 27, 2014 - Views: 2

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On the infimum attained by the reflected fractional Brownian ...

On the infimum attained by the reflected fractional Brownian motion for the whole range of the parameter H. By comparing them with Eq. 1, he observed

http://link.springer.com/content/pdf/10.1007%2Fs10687-014-0188-7.pdf

Date added: October 2, 2014 - Views: 1

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Section B Properties of Upper and Lower Bounds

Chapter 5 Real Numbers 12 Section B Properties of Upper and Lower Bounds By the end of this section you will be able to • prove properties of the supremum and infimum of a set

http://mathsforall.co.uk/userfiles/5B%20Properties%20of%20Upper%20and%20Lower%20Bounds.pdf

Date added: October 19, 2012 - Views: 5

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COMPLETE LATTICES - San Francisco State University

subset of X has an infimum, for the supremum of a set is then the infimum of the set of all its upper bounds. Dually, you could just verify that every subset of X has a supremum. A nonempty family F of sets is called a Moore family if it has a maximum member

http://math.sfsu.edu/smith/Math800/Units/CompleteLattices.pdf

Date added: July 18, 2013 - Views: 3

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Fast infimum-supremum interval operations for double-double ...

Fast infimum-supremum interval operations for double-double arithmetic in rounding-to-nearest Naoya Yamanaka (Waseda University) Shin’ichi Oishi

http://conf.nsc.ru/files/conferences/scan2012/141503/Yamanaka-scan2012.pdf

Date added: January 21, 2014 - Views: 2

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Southern University and A&M College - Department of ...

theorems: Axioms of the real numbers, supremum, infimum, upper limits, open and closed sets in n R, compactness, the Bolzano-Weierstrass and Heine-Borel Theorems, the Lebesgue Measure; Lebesgue measurable functions; Lebesgue integration.

http://www.math.subr.edu/syllabus/Math%20565%20Javier.pdf

Date added: July 18, 2013 - Views: 2

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2.4 The Completeness Property of R - Kennesaw State University

Supremum and In–mum of a Set De–nition 143 (Supremum and in–mum) Let Sbe a subset of R 1. If Sis bounded above, then an upper bound of Sis said to be a supremum denoted supSor a least upper bound denoted lubSif it is less than any

http://math.kennesaw.edu/~plaval/math4381/lubprop.pdf

Date added: July 16, 2014 - Views: 1

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Inhoud Editorial - GEWIS

(An infimum is a funny or stupid quote by either student or professor.) Like Dutch in- ... Finally, the Supremum editorial staff would like to thank Frans Mar-tens for his contributions to the Su-premum. In his texts, referred to as

http://www.gewis.nl/~supremum/archief/pdf/sup42.1.pdf

Date added: July 18, 2013 - Views: 1

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SYLLABUS FOR ENTRANCE EXAMINATION FOR M - Maths Panache

system as a complete ordered field, Archimedean property, supremum, infimum. Sequence and series, Convergence, limsup, liminf. Bolzano Weierstrass theorem, Heine Borel theorem. Continuity, Uniform continuity, Intermediate value theorem, Differentiability, Mean value ...

http://www.mathspanache.com/PDF/du_Syllabus.pdf

Date added: July 28, 2014 - Views: 1

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The Law of the Supremum of a Stable Lévy Process with No ...

The Annals of Probability 2008, Vol. 36, No. 5, 1777-1789 DOI: 10.1214/07-AOP376 ? Institute of Mathematical Statistics, 2008 THE LAW OF THE SUPREMUM OF A STABLE LEVY PROCESS

http://www.jstor.org/stable/25450628

Date added: July 31, 2013 - Views: 1

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Suprema/In ma Review Sheet - Michigan State University

to have a supremum or in mum in the event that it is not bounded, or is empty. We will extend the de nitions of sup and inf to these cases by using the following conventions: (1)If A is not bounded above, we de ne supA = +1.

http://math.msu.edu/~siefring/mth421_s10/sup_inf.pdf

Date added: October 13, 2013 - Views: 4

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Southern University and A&M College - Department of ...

SOUTHERN UNIVERSITY AND A&M COLLEGE Baton Rouge, Louisiana DEPARTMENT OF MATHEMATICS COURSE SYLLABUS Real Analysis I. Descriptive Information ... numbers by finding supremum and infimum of sets and using the completeness property of real numbers.

http://www.math.subr.edu/syllabus/MATH%20462%20REAL%20ANALYSIS%20(U).pdf

Date added: June 18, 2012 - Views: 5

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THE LOCAL SUPREMUM PRINCIPLE FOR OPTIMUM CONTROL PROBLEMS ...

THE LOCAL SUPREMUM PRINCIPLE FOR OPTIMUM CONTROL PROBLEMS WITH NONSCALAR-VALUED PERFORMANCE CRITERION By ... (infimum) in form of the local supremum principle for optimum control problems with nonscalar-valued performance criterion.

http://www.pp.bme.hu/ee/article/download/4924/4029

Date added: June 27, 2014 - Views: 1

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SUPERMODULARITY AND SUPERMODULAR GAMES - IESE Business School

supremum (resp., infimum) of A is a least upper bound (resp., greatest lower bound); it is denoted sup A (resp., inf A). A lattice is a partially ordered set (X, )≥ in which any two elements have a supremum and an infimum.

http://blog.iese.edu/xvives/files/2013/11/Vives-2007-Palgrave-supermodularity-IESE-WP.pdf

Date added: January 21, 2014 - Views: 1

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Yi Shen Title: Stationarity and Random Locations

locations including, for example, the location of the path supremum/infimum over an interval, the first/last hitting time, among many others. On one hand, it is proved that under stationarity, the

http://www.orie.cornell.edu/orie/upload/Yi-Shen-abstract.pdf

Date added: January 21, 2014 - Views: 1

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The Riemann Integral

upper integral of 𝑓 (on the interval [𝑎, 𝑏]) is the infimum of 𝑈(𝑓, 𝑃), taken over all partitions 𝑃. Likewise, 𝐿(𝑓), the lower integral of 𝑓 (on the interval [𝑎, 𝑏]) is the supremum of 𝐿(𝑓, 𝑃), taken over all partitions 𝑃.

http://math.la.asu.edu/~boerner/bridge/The%20Riemann%20Integral.pdf

Date added: February 20, 2014 - Views: 1

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log w(o s[s d(] d

THE SUPREMUM AND INFIMUM OF THE POISSON PROCESS' BY RONALD PYKE Columbia University 1. Introduction. Let {X(t); t ? 0} be a separable Poisson process with shift

http://www.jstor.org/stable/2237099

Date added: August 27, 2014 - Views: 1

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Answer on Question #44204 Math - Real Analysis Solution

Answer on Question #44204 – Math - Real Analysis Find the supremum and infimum of the set {(-1)^n(1+1/n): n is natural Solution Under even n the terms of this sequence become (1+1

http://www.assignmentexpert.com/free-answers/Math-Answer-44204.pdf

Date added: October 2, 2014 - Views: 1

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EXACT COMPUTATION OF THE INFIMUM IN H co-OPTIMIZATION VIA ...

INFIMUM IN H co-OPTIMIZATION VIA STATE FEEDBACK* B. M. CHEN, 1 A. SABERIl AND U.-L. Ly2 Abstract. This paper presents a simple and non-iterative procedure for the ... The supremum of the complex stability radii that can be achieved by stabilizing

http://vlab.ee.nus.edu.sg/~bmchen/papers/ctat-2.pdf

Date added: May 19, 2013 - Views: 2

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The New Palgrave Dictionary of Economics Online

A supremum (resp., infimum) of A is a least upper bound (resp., greatest lower bound); it is denoted sup A (resp., inf A). A lattice is a partially ordered set (X,≥) in which any two elements have a supremum and an infimum. Any interval of the real line

http://blog.iese.edu/xvives/files/2011/09/130.pdf

Date added: January 23, 2013 - Views: 6

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Jaworski, B. (Ed.) Proceedings of the British Society for ...

THE CONCEPT OF SUPREMUM/INFIMUM OF A SET: A PROBLEMATIC OVERTURE TO THE CONCEPT OF LIMIT? Elena Nardi School of Education, University of East Anglia

http://www.bsrlm.org.uk/IPs/ip20-12/BSRLM-IP-20-12-20.pdf

Date added: August 27, 2014 - Views: 1

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∈𝐍

Find the infimum and supremum of the set S = 1 + 2 n: n ∈𝐍 ∪ 4 −2q q: q ∈𝐐∩(1, ∞)) (Step 1) IDEA: We first find out the upper bound and lower bound of each set and combine them . Upper Bound Lower Bound A = 1 + 2 n: n ∈𝐍

http://www.math.ust.hk/~makyli/202_2007-8FaSp/TNt_08.pdf

Date added: January 21, 2014 - Views: 1

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SPECTRAL-LIKE DUALITY FOR DISTRIBUTIVE HILBERT ALGEBRAS WITH ...

SPECTRAL-LIKE DUALITY FOR DISTRIBUTIVE HILBERT ALGEBRAS WITH INFIMUM SERGIO A. CELANI AND MAR IA ESTEBAN Abstract. Distributive Hilbert Algebras with in mum, or DH^-algebras, are

http://www.ub.edu/grlnc/docs/Hilbert-Infimo.pdf

Date added: August 27, 2014 - Views: 1

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Problems and Comments on Relations Chapter 8

least upper bound is called the supremum of S. Infimum is similarly defined as the largest lower bound of a set S. The open interval 0,1 of real numbers has infimum 0 and supremum 1. It is an axiom for real numbers that any subset S of real numbers which has an upper

http://www.math.uh.edu/~klaus/discrete_math_chapter_7.pdf

Date added: January 14, 2013 - Views: 3

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6, 1994 58 I Algorithms for the Decomposition Gray-Scale ...

supremum, infimum, erosion and dilation. The results obtained apply to a broad range of useful operations. Basis decom- position of binary morphological operations is obtained as a particular case of the gray-scale theory. Basic ...

http://www.icst.pku.edu.cn/course/ImageProcessing/2014/resource/jones1994.pdf

Date added: April 4, 2014 - Views: 1