Class information for:
Level 1: POSITIVE POLYNOMIALS//POSITIVSTELLENSATZ//SUM OF SQUARES

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
13892 807 20.6 42%


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
1108 2             COMPOSITION OPERATOR//TOEPLITZ OPERATOR//INTEGRAL EQUATIONS AND OPERATOR THEORY 9756
13892 1                   POSITIVE POLYNOMIALS//POSITIVSTELLENSATZ//SUM OF SQUARES 807

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 POSITIVE POLYNOMIALS authKW 1094529 6% 64% 45
2 POSITIVSTELLENSATZ authKW 1019589 4% 84% 32
3 SUM OF SQUARES authKW 795236 8% 32% 65
4 POLYNOMIAL OPTIMIZATION authKW 648967 5% 42% 41
5 REAL ALGEBRAIC GEOMETRY authKW 633867 4% 49% 34
6 SUMS OF SQUARES authKW 560493 5% 37% 40
7 TRUNCATED MOMENT PROBLEM authKW 454028 2% 67% 18
8 SEMIDEFINITE PROGRAMMING authKW 433245 14% 10% 112
9 MOMENT MATRIX EXTENSION authKW 416204 1% 100% 11
10 NONCOMMUTATIVE POLYNOMIAL authKW 411993 2% 78% 14

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 16361 61% 0% 493
2 Mathematics, Applied 10180 45% 0% 360
3 Operations Research & Management Science 3452 15% 0% 122
4 Computer Science, Software Engineering 500 6% 0% 50
5 Computer Science, Theory & Methods 221 5% 0% 42
6 Automation & Control Systems 195 4% 0% 29
7 COMPUTER APPLICATIONS & CYBERNETICS 54 0% 0% 2
8 Computer Science, Cybernetics 15 0% 0% 4
9 Physics, Mathematical 8 2% 0% 13
10 Statistics & Probability 4 1% 0% 9

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 HBEREICH MATH STAT 388601 5% 24% 43
2 UPORABNO MATEMAT 227020 1% 100% 6
3 FAK NARAVOSLOVJE MATEMAT 222561 1% 59% 10
4 MATH EECS 121076 0% 80% 4
5 FAK MATEMAT FIZ 83490 1% 28% 8
6 FB MATH 12 63054 1% 33% 5
7 LAAS 58978 7% 3% 58
8 URA D751 56752 0% 50% 3
9 ODDELEK MATEMAT MATEMAT 50448 0% 67% 2
10 URA D 751 50448 0% 67% 2

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 SIAM JOURNAL ON OPTIMIZATION 63764 7% 3% 55
2 MATHEMATICAL PROGRAMMING 19406 5% 1% 40
3 JOURNAL OF GLOBAL OPTIMIZATION 9011 3% 1% 23
4 MATHEMATICA SCANDINAVICA 5342 2% 1% 14
5 JOURNAL OF SYMBOLIC COMPUTATION 4269 2% 1% 16
6 POSITIVITY 3848 0% 3% 4
7 INTEGRAL EQUATIONS AND OPERATOR THEORY 3786 2% 1% 15
8 JOURNAL OF PURE AND APPLIED ALGEBRA 3705 3% 0% 24
9 JOURNAL OF OPERATOR THEORY 3563 1% 1% 11
10 TRENDS IN MATHEMATICS 3310 1% 1% 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 POSITIVE POLYNOMIALS 1094529 6% 64% 45 Search POSITIVE+POLYNOMIALS Search POSITIVE+POLYNOMIALS
2 POSITIVSTELLENSATZ 1019589 4% 84% 32 Search POSITIVSTELLENSATZ Search POSITIVSTELLENSATZ
3 SUM OF SQUARES 795236 8% 32% 65 Search SUM+OF+SQUARES Search SUM+OF+SQUARES
4 POLYNOMIAL OPTIMIZATION 648967 5% 42% 41 Search POLYNOMIAL+OPTIMIZATION Search POLYNOMIAL+OPTIMIZATION
5 REAL ALGEBRAIC GEOMETRY 633867 4% 49% 34 Search REAL+ALGEBRAIC+GEOMETRY Search REAL+ALGEBRAIC+GEOMETRY
6 SUMS OF SQUARES 560493 5% 37% 40 Search SUMS+OF+SQUARES Search SUMS+OF+SQUARES
7 TRUNCATED MOMENT PROBLEM 454028 2% 67% 18 Search TRUNCATED+MOMENT+PROBLEM Search TRUNCATED+MOMENT+PROBLEM
8 SEMIDEFINITE PROGRAMMING 433245 14% 10% 112 Search SEMIDEFINITE+PROGRAMMING Search SEMIDEFINITE+PROGRAMMING
9 MOMENT MATRIX EXTENSION 416204 1% 100% 11 Search MOMENT+MATRIX+EXTENSION Search MOMENT+MATRIX+EXTENSION
10 NONCOMMUTATIVE POLYNOMIAL 411993 2% 78% 14 Search NONCOMMUTATIVE+POLYNOMIAL Search NONCOMMUTATIVE+POLYNOMIAL

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 NIE, JW , (2015) LINEAR OPTIMIZATION WITH CONES OF MOMENTS AND NONNEGATIVE POLYNOMIALS.MATHEMATICAL PROGRAMMING. VOL. 153. ISSUE 1. P. 247 -274 25 93% 5
2 CURTO, RE , FIALKOW, LA , (2008) AN ANALOGUE OF THE RIESZ-HAVILAND THEOREM FOR THE TRUNCATED MOMENT PROBLEM.JOURNAL OF FUNCTIONAL ANALYSIS. VOL. 255. ISSUE 10. P. 2709-2731 27 100% 12
3 CURTO, RE , YOO, S , (2015) NON-EXTREMAL SEXTIC MOMENT PROBLEMS.JOURNAL OF FUNCTIONAL ANALYSIS. VOL. 269. ISSUE 3. P. 758 -780 25 89% 0
4 KUMMER, M , (2017) DETERMINANTAL REPRESENTATIONS AND B,ZOUTIANS.MATHEMATISCHE ZEITSCHRIFT. VOL. 285. ISSUE 1-2. P. 445 -459 15 83% 1
5 CURTO, RE , FIALKOW, LA , (2005) TRUNCATED K-MOMENT PROBLEMS IN SEVERAL VARIABLES.JOURNAL OF OPERATOR THEORY. VOL. 54. ISSUE 1. P. 189-226 28 90% 46
6 CURTO, RE , YOO, S , (2014) CUBIC COLUMN RELATIONS IN TRUNCATED MOMENT PROBLEMS.JOURNAL OF FUNCTIONAL ANALYSIS. VOL. 266. ISSUE 3. P. 1611 -1626 23 92% 0
7 GHASEMI, M , KUHLMANN, S , (2016) MOMENT PROBLEM IN INFINITELY MANY VARIABLES.ISRAEL JOURNAL OF MATHEMATICS. VOL. 212. ISSUE 2. P. 989 -1012 19 95% 0
8 FIALKOW, LA , (2015) LIMITS OF POSITIVE FLAT BIVARIATE MOMENT MATRICES.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. VOL. 367. ISSUE 4. P. 2665 -2702 17 100% 0
9 JEYAKUMAR, V , LI, GY , (2017) EXACT CONIC PROGRAMMING RELAXATIONS FOR A CLASS OF CONVEX POLYNOMIAL CONE PROGRAMS.JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. VOL. 172. ISSUE 1. P. 156 -178 18 90% 0
10 FALKOW, LA , (2011) SOLUTION OF THE TRUNCATED MOMENT PROBLEM WITH VARIETY Y = X(3).TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. VOL. 363. ISSUE 6. P. 3133-3165 19 95% 0

Classes with closest relation at Level 1


Rank Class id link
1 17040 COMPLETELY POSITIVE MATRICES//COPOSITIVE MATRICES//COPOSITIVE PROGRAMMING
2 16040 WITT EQUIVALENCE//SPECIAL GROUPS//REAL PLACES
3 25038 ALMOST EVERYWHERE STABILITY//DOMAIN OF ATTRACTION//BORGS CRITERION
4 30061 2 VARIABLE WEIGHTED SHIFTS//HYPONORMAL//SUBNORMAL PAIRS
5 25790 WEIGHTED SHIFT ON A DIRECTED TREE//SUBNORMAL OPERATOR//KATEDRA ZASTOSOWAN MATEMAT
6 19111 FRACTIONAL MOMENTS//MOMENT PROBLEM//ENTHALPY DISTRIBUTION
7 2750 INTERIOR POINT METHODS//POLYNOMIAL COMPLEXITY//INTERIOR POINT ALGORITHM
8 11418 CUTTING PLANES//LIFT AND PROJECT//SPLIT CUTS
9 4303 ROW CONTRACTION//INVARIANT SUBSPACE//M ISOMETRY
10 8890 PARAMETER DEPENDENT LYAPUNOV FUNCTION//LINEAR PARAMETER VARYING SYSTEMS//LINEAR PARAMETER VARYING LPV SYSTEMS

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