Class information for:
Level 1: P REGULARITY//ABNORMAL POINT//P FACTOR OPERATOR

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
31974 145 14.1 26%


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
244 3       MATHEMATICS, APPLIED//MATHEMATICS//BLOW UP 46988
4124 2             P REGULARITY//ABNORMAL POINT//P FACTOR OPERATOR 557
31974 1                   P REGULARITY//ABNORMAL POINT//P FACTOR OPERATOR 145

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 P REGULARITY authKW 2787216 10% 88% 15
2 ABNORMAL POINT authKW 2105899 7% 100% 10
3 P FACTOR OPERATOR authKW 1263539 4% 100% 6
4 2 REGULARITY authKW 748755 6% 44% 8
5 LYUSTERNIK THEOREM authKW 658090 3% 63% 5
6 2 NORMAL MAPPING authKW 631770 2% 100% 3
7 INDEX OF QUADRATIC FORM authKW 631770 2% 100% 3
8 ABNORMAL PROCESSES authKW 421180 1% 100% 2
9 DIFFERENT EQUAT FUNCT ANAL address 421180 1% 100% 2
10 DORONICYN COMP address 421180 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 3249 64% 0% 93
2 Mathematics, Applied 2217 49% 0% 71
3 Operations Research & Management Science 208 9% 0% 13
4 Automation & Control Systems 67 5% 0% 7
5 Physics, Mathematical 58 6% 0% 9
6 Multidisciplinary Sciences 52 3% 0% 5
7 Computer Science, Software Engineering 7 2% 0% 3
8 Computer Science, Cybernetics 6 1% 0% 1
9 Imaging Science & Photographic Technology 2 1% 0% 1
10 Computer Science, Information Systems 1 1% 0% 2

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 DIFFERENT EQUAT FUNCT ANAL 421180 1% 100% 2
2 DORONICYN COMP 421180 1% 100% 2
3 DORODNICYN COMP 179927 16% 4% 23
4 AREA ESTADIST INVEST OPERAT 126349 2% 20% 3
5 ECON METODOS CUANTITAT HA ECON 120334 1% 29% 2
6 ECON METODOS CUANTITATIVOS H ECON 105294 1% 50% 1
7 DIFFERENTIAL EQUAT FUNCT ANAL 84233 1% 20% 2
8 DORODNITSYN COMP 53712 3% 5% 5
9 SYST 48208 19% 1% 27
10 CONTROL DYNAM SYST 107 81 35097 1% 17% 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 DOKLADY MATHEMATICS 27551 14% 1% 20
2 MATEKON 11082 1% 5% 1
3 COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 9283 6% 0% 9
4 MATHEMATICAL NOTES 5107 8% 0% 11
5 USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 4503 3% 1% 4
6 MATHEMATISCHE NACHRICHTEN 4250 6% 0% 9
7 NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2808 3% 0% 5
8 SBORNIK MATHEMATICS 2173 3% 0% 4
9 RUSSIAN MATHEMATICAL SURVEYS 2136 3% 0% 5
10 NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2105 8% 0% 11

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 P REGULARITY 2787216 10% 88% 15 Search P+REGULARITY Search P+REGULARITY
2 ABNORMAL POINT 2105899 7% 100% 10 Search ABNORMAL+POINT Search ABNORMAL+POINT
3 P FACTOR OPERATOR 1263539 4% 100% 6 Search P+FACTOR+OPERATOR Search P+FACTOR+OPERATOR
4 2 REGULARITY 748755 6% 44% 8 Search 2+REGULARITY Search 2+REGULARITY
5 LYUSTERNIK THEOREM 658090 3% 63% 5 Search LYUSTERNIK+THEOREM Search LYUSTERNIK+THEOREM
6 2 NORMAL MAPPING 631770 2% 100% 3 Search 2+NORMAL+MAPPING Search 2+NORMAL+MAPPING
7 INDEX OF QUADRATIC FORM 631770 2% 100% 3 Search INDEX+OF+QUADRATIC+FORM Search INDEX+OF+QUADRATIC+FORM
8 ABNORMAL PROCESSES 421180 1% 100% 2 Search ABNORMAL+PROCESSES Search ABNORMAL+PROCESSES
9 HIGH ORDER NECESSARY CONDITIONS FOR OPTIMALITY 421180 1% 100% 2 Search HIGH+ORDER+NECESSARY+CONDITIONS+FOR+OPTIMALITY Search HIGH+ORDER+NECESSARY+CONDITIONS+FOR+OPTIMALITY
10 HIGH ORDER TANGENT SETS 421180 1% 100% 2 Search HIGH+ORDER+TANGENT+SETS Search HIGH+ORDER+TANGENT+SETS

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 BREZHNEVA, O , TRET'YAKOV, AA , (2010) COME BACK TO LAGRANGE. THE P-FACTOR ANALYSIS OF OPTIMALITY CONDITIONS.NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION. VOL. 31. ISSUE 8. P. 871-891 14 100% 1
2 ARUTYUNOV, AV , (2012) SMOOTH ABNORMAL PROBLEMS IN EXTREMUM THEORY AND ANALYSIS.RUSSIAN MATHEMATICAL SURVEYS. VOL. 67. ISSUE 3. P. 403 -457 18 72% 0
3 ARUTYUNOV, AV , AVAKOV, ER , IZMAILOV, AF , (2008) NECESSARY OPTIMALITY CONDITIONS FOR CONSTRAINED OPTIMIZATION PROBLEMS UNDER RELAXED CONSTRAINT QUALIFICATIONS.MATHEMATICAL PROGRAMMING. VOL. 114. ISSUE 1. P. 37-68 14 93% 5
4 BREZHNEVA, OA , TRET'YAKOV, AA , (2003) OPTIMALITY CONDITIONS FOR DEGENERATE EXTREMUM PROBLEMS WITH EQUALITY CONSTRAINTS.SIAM JOURNAL ON CONTROL AND OPTIMIZATION. VOL. 42. ISSUE 2. P. 729-745 14 100% 18
5 AVAKOV, ER , (2015) STABILITY THEOREM AND EXTREMUM CONDITIONS FOR ABNORMAL PROBLEMS.PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS. VOL. 291. ISSUE 1. P. 4 -23 9 82% 0
6 AVAKOV, ER , ARUTYUNOV, AV , KARAMZIN, DY , (2014) AN INVESTIGATION OF SMOOTH MAPS IN A NEIGHBOURHOOD OF AN ABNORMAL POINT.IZVESTIYA MATHEMATICS. VOL. 78. ISSUE 2. P. 213 -250 7 100% 0
7 HERNANDEZ-JIMENEZ, B , OSUNA-GOMEZ, R , ROJAS-MEDAR, M , DOS SANTOS, LB , (2013) GENERALIZED CONVEXITY FOR NON-REGULAR OPTIMIZATION PROBLEMS WITH CONIC CONSTRAINTS.JOURNAL OF GLOBAL OPTIMIZATION. VOL. 57. ISSUE 3. P. 649-662 9 75% 1
8 PRUSINSKA, A , TRET'YAKOV, AA , (2011) ON THE EXISTENCE OF SOLUTIONS TO NONLINEAR EQUATIONS INVOLVING SINGULAR MAPPINGS WITH NON-ZERO P-KERNEL.SET-VALUED AND VARIATIONAL ANALYSIS. VOL. 19. ISSUE 3. P. 399-416 7 100% 2
9 MEDAK, B , TRET'YAKOV, AA , (2015) EXISTENCE OF PERIODIC SOLUTIONS TO NONLINEAR P-REGULAR BOUNDARY VALUE PROBLEM.BOUNDARY VALUE PROBLEMS. VOL. . ISSUE . P. - 7 88% 0
10 MEDAK, B , TRET'YAKOV, AA , (2015) P-REGULAR NONLINEAR DYNAMICS.TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. VOL. 46. ISSUE 1. P. 283 -301 6 100% 0

Classes with closest relation at Level 1


Rank Class id link
1 33884 JOURNAL OF COMPUTER AND SYSTEMS SCIENCES INTERNATIONAL//ACTUAL COMPUTING WORKLOAD//AEROKOSMOS
2 19397 NORMAL NECESSARY CONDITIONS//DISCRETE APPROXIMATIONS//MIXED CONSTRAINTS
3 28238 CONICAL APPROXIMATIONS//DUBOVITSKII MILYUTIN THEOREM//DISTRIBUTED CONTROL PROBLEMS
4 3266 METRIC REGULARITY//CODERIVATIVE//SUBDIFFERENTIAL
5 25628 MULTIPARAMETER EIGENVALUE PROBLEM//TWO PARAMETER//NONLINEAR STURM LIOUVILLE
6 17049 IMPLICITLY DEFINED CURVE//BIALTERNATE PRODUCT//UNILATERAL DYNAMIC CONTACT
7 32881 ABSOLUTE VALUE EQUATION//GENERALIZED NEWTON METHOD//A POSTERIORI PROCESSING
8 8178 SUPERLINEAR CONVERGENCE//NONLINEAR PROGRAMMING//GLOBAL CONVERGENCE
9 29467 CYCLIC POLYGON//EQUIDISSECTION//MECHANICAL LINKAGE
10 25647 PROPAGATION FAILURE//LATTICE DIFFERENTIAL EQUATIONS//MIXED TYPE FUNCTIONAL DIFFERENTIAL EQUATIONS

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