Class information for:
Level 1: MINIMAL DISPLACEMENT//MORSE SARD THEOREM//C 1 SMOOTH FUNCTION

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
24581 307 15.8 25%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
249 3       MATHEMATICS//JOURNAL OF OPERATOR THEORY//MATH 46542
3377 2             LINEABILITY//SPACEABILITY//ALGEBRABILITY 1662
24581 1                   MINIMAL DISPLACEMENT//MORSE SARD THEOREM//C 1 SMOOTH FUNCTION 307

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 MINIMAL DISPLACEMENT authKW 621638 3% 63% 10
2 MORSE SARD THEOREM authKW 541519 2% 78% 7
3 C 1 SMOOTH FUNCTION authKW 497316 2% 100% 5
4 GRADIENT RANGE authKW 414428 2% 83% 5
5 INTERMEDIATE POINT authKW 223791 1% 75% 3
6 FINITE GEOMETRICAL TYPE authKW 198926 1% 100% 2
7 LIEN SCI TECH address 198926 1% 100% 2
8 MORSE SARD PROPERTY authKW 198926 1% 100% 2
9 OPTIMAL RETRACTIONS authKW 198926 1% 100% 2
10 SOLUTION FUNNEL authKW 198926 1% 100% 2

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Mathematics 11779 83% 0% 256
2 Mathematics, Applied 1848 31% 0% 96
3 Physics, Mathematical 50 4% 0% 13
4 Statistics & Probability 22 3% 0% 8
5 Mathematics, Interdisciplinary Applications 19 2% 0% 7
6 Multidisciplinary Sciences 5 1% 0% 3
7 Engineering, General 3 1% 0% 4
8 Computer Science, Cybernetics 2 0% 0% 1
9 Instruments & Instrumentation 2 2% 0% 5
10 Social Sciences, Mathematical Methods 1 0% 0% 1

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 LIEN SCI TECH 198926 1% 100% 2
2 ANALISI MATEMAT 99463 0% 100% 1
3 BANGKOK EXCELLENCE MATH CHE 99463 0% 100% 1
4 EMNERGING MARKETS TRADING 99463 0% 100% 1
5 MAECH MATH 99463 0% 100% 1
6 MATEMAT CAIXA 99463 0% 100% 1
7 UMR 5467 CNRS 99461 1% 50% 2
8 ESCUELA TECN SUPER TELECOMUNICAC 49731 0% 50% 1
9 INVEST MICROELECT CIME 49731 0% 50% 1
10 MADI 49731 0% 50% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 AMERICAN MATHEMATICAL MONTHLY 19464 7% 1% 23
2 STUDIA MATHEMATICA 4101 4% 0% 11
3 ELECTRONIC RESEARCH ANNOUNCEMENTS OF THE AMERICAN MATHEMATICAL SOCIETY 2943 1% 1% 2
4 SIBERIAN MATHEMATICAL JOURNAL 2658 3% 0% 9
5 PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 2122 6% 0% 19
6 RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS 2025 1% 1% 4
7 JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 1870 7% 0% 20
8 TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS 1522 1% 1% 3
9 INDIANA UNIVERSITY MATHEMATICS JOURNAL 1495 2% 0% 6
10 MATHEMATICAL NOTES 1265 3% 0% 8

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 MINIMAL DISPLACEMENT 621638 3% 63% 10 Search MINIMAL+DISPLACEMENT Search MINIMAL+DISPLACEMENT
2 MORSE SARD THEOREM 541519 2% 78% 7 Search MORSE+SARD+THEOREM Search MORSE+SARD+THEOREM
3 C 1 SMOOTH FUNCTION 497316 2% 100% 5 Search C+1+SMOOTH+FUNCTION Search C+1+SMOOTH+FUNCTION
4 GRADIENT RANGE 414428 2% 83% 5 Search GRADIENT+RANGE Search GRADIENT+RANGE
5 INTERMEDIATE POINT 223791 1% 75% 3 Search INTERMEDIATE+POINT Search INTERMEDIATE+POINT
6 FINITE GEOMETRICAL TYPE 198926 1% 100% 2 Search FINITE+GEOMETRICAL+TYPE Search FINITE+GEOMETRICAL+TYPE
7 MORSE SARD PROPERTY 198926 1% 100% 2 Search MORSE+SARD+PROPERTY Search MORSE+SARD+PROPERTY
8 OPTIMAL RETRACTIONS 198926 1% 100% 2 Search OPTIMAL+RETRACTIONS Search OPTIMAL+RETRACTIONS
9 SOLUTION FUNNEL 198926 1% 100% 2 Search SOLUTION+FUNNEL Search SOLUTION+FUNNEL
10 STARLIKE BODY 198926 1% 100% 2 Search STARLIKE+BODY Search STARLIKE+BODY

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 BOURGAIN, J , KOROBKOV, MV , KRISTENSEN, J , (2013) ON THE MORSE-SARD PROPERTY AND LEVEL SETS OF SOBOLEV AND BV FUNCTIONS.REVISTA MATEMATICA IBEROAMERICANA. VOL. 29. ISSUE 1. P. 1 -23 14 82% 6
2 NIKONOROV, YG , (2012) ASYMPTOTIC BEHAVIOR OF SUPPORT POINTS FOR PLANAR CURVES.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. VOL. 391. ISSUE 1. P. 147-158 11 100% 0
3 CASINI, E , GOEBEL, K , (2010) WHY AND HOW MUCH BROUWER'S FIXED POINT THEOREM FAILS IN NONCOMPACT SETTING?.MILAN JOURNAL OF MATHEMATICS. VOL. 78. ISSUE 2. P. 371-394 11 100% 0
4 HAJLASZ, P , KOROBKOV, MV , KRISTENSEN, J , (2017) A BRIDGE BETWEEN DUBOVITSKII-FEDERER THEOREMS AND THE COAREA FORMULA.JOURNAL OF FUNCTIONAL ANALYSIS. VOL. 272. ISSUE 3. P. 1265 -1295 16 55% 0
5 KOROBKOV, MV , KRISTENSEN, J , (2014) ON THE MORSE-SARD THEOREM FOR THE SHARP CASE OF SOBOLEV MAPPINGS.INDIANA UNIVERSITY MATHEMATICS JOURNAL. VOL. 63. ISSUE 6. P. 1703 -1724 12 75% 1
6 BOURGAIN, J , KOROBKOV, MV , KRISTENSEN, J , (2015) ON THE MORSE-SARD PROPERTY AND LEVEL SETS OF W-N,W- (1) SOBOLEV FUNCTIONS ON R-N.JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK. VOL. 700. ISSUE . P. 93 -112 10 83% 1
7 YOMDIN, Y , (2005) SEMIALGEBRAIC COMPLEXITY OF FUNCTIONS.JOURNAL OF COMPLEXITY. VOL. 21. ISSUE 1. P. 111 -148 15 68% 5
8 JIMENEZ-SEVILLA, M , (2008) A NOTE ON THE RANGE OF THE DERIVATIVES OF ANALYTIC APPROXIMATIONS OF UNIFORMLY CONTINUOUS FUNCTIONS ON C(0).JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. VOL. 348. ISSUE 2. P. 573-580 10 91% 1
9 YOMDIN, Y , COMTE, G , (2004) TAME GEOMETRY WITH APPLICATION IN SMOOTH ANALYSIS.TAME GEOMETRY WITH APPLICATION IN SMOOTH ANALYSIS. VOL. 1834. ISSUE . P. 1 -+ 35 29% 0
10 AZAGRA, D , BOISO, MC , (2004) UNIFORM APPROXIMATION OF CONTINUOUS MAPPINGS BY SMOOTH MAPPINGS WITH NO CRITICAL POINTS ON HILBERT MANIFOLDS.DUKE MATHEMATICAL JOURNAL. VOL. 124. ISSUE 1. P. 47 -66 9 100% 4

Classes with closest relation at Level 1


Rank Class id link
1 23273 NUMERICAL INDEX//DAUGAVET PROPERTY//BISHOP PHELPS BOLLOBAS THEOREM
2 22267 DISCONTINUOUS SELECTIONS//IMPLICIT ELLIPTIC EQUATIONS//DISCONTINUOUS DIFFERENTIAL EQUATIONS
3 19373 RANDOM FIXED POINT//RANDOM OPERATOR//RANDOM COINCIDENCE POINT
4 33509 SCALING AND SQUARING TECHNIQUE//DC POWER CONVERSION//STATIC INVERTER
5 36676 CONVERGENCE IN THE SENSE OF RESOLVENT//DISCRETE HYPERBOLIC SYSTEM//ELLIPTIC LIKE REGULARIZATION
6 23850 HADAMARD MANIFOLD//RIEMANNIAN OPTIMIZATION//MONOTONE VECTOR FIELDS
7 23915 MINKOWSKI CONTENT//COMPLEX DIMENSIONS//FRACTAL STRING
8 17204 HENSTOCK KURZWEIL INTEGRAL//MCSHANE INTEGRAL//KURZWEIL HENSTOCK INTEGRAL
9 21405 LINEABILITY//SPACEABILITY//ALGEBRABILITY
10 12387 FRAGMENTABILITY//RENORMING//PROJECTIONAL SKELETON

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