Class information for:
Level 1: BETHE SOMMERFELD CONJECTURE//ASYMPTOTIC BEHAVIOR OF VIRTUAL EIGENVALUES//VIRTUAL EIGENVALUES

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
20434 461 19.7 33%


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
549 3       MATHEMATICS//STURM LIOUVILLE OPERATOR//ANNALES HENRI POINCARE 18286
1111 2             ANNALES HENRI POINCARE//COMMUNICATIONS IN MATHEMATICAL PHYSICS//SCHRODINGER OPERATOR 9740
20434 1                   BETHE SOMMERFELD CONJECTURE//ASYMPTOTIC BEHAVIOR OF VIRTUAL EIGENVALUES//VIRTUAL EIGENVALUES 461

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 BETHE SOMMERFELD CONJECTURE authKW 264945 1% 100% 4
2 ASYMPTOTIC BEHAVIOR OF VIRTUAL EIGENVALUES authKW 198709 1% 100% 3
3 VIRTUAL EIGENVALUES authKW 198709 1% 100% 3
4 DENSE POINT SPECTRUM authKW 176627 1% 67% 4
5 SPECTRAL SHIFT FUNCTION authKW 174213 2% 24% 11
6 MAGNETIC SCHRODINGER OPERATOR authKW 168578 3% 18% 14
7 SCHRODINGER OPERATOR authKW 137070 7% 6% 33
8 BAND FUNCTIONS authKW 132472 0% 100% 2
9 LG ANGEW STOCHAST address 132472 0% 100% 2
10 SOBOLEV LIEB THIRRING INEQUALITIES authKW 132472 0% 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 10716 65% 0% 301
2 Physics, Mathematical 3725 25% 0% 117
3 Mathematics, Applied 2090 27% 0% 126
4 Physics, Multidisciplinary 163 10% 0% 47
5 Physics, Particles & Fields 43 4% 0% 19
6 Multidisciplinary Sciences 17 1% 0% 6
7 Mathematical & Computational Biology -0 0% 0% 1
8 Mathematics, Interdisciplinary Applications -1 0% 0% 1
9 Mechanics -1 1% 0% 3
10 Computer Science, Theory & Methods -2 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 LG ANGEW STOCHAST 132472 0% 100% 2
2 FR 2254 66236 0% 100% 1
3 FR CNRS 2254 66236 0% 100% 1
4 MABUMR 5466 MATH BORDEAUX 66236 0% 100% 1
5 TRANSPORT THEORY MATH PHYS 66236 0% 100% 1
6 UA 758 66236 0% 100% 1
7 UDMURTIA SCI 44155 0% 33% 2
8 GRP PROJECT PN II ID PCE 2011 3 0075 33117 0% 50% 1
9 MAT ANAL ITS PLICAT 33117 0% 50% 1
10 UA 760 22077 0% 33% 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 JOURNAL OF SPECTRAL THEORY 62728 3% 8% 12
2 ANNALES HENRI POINCARE 21664 4% 2% 18
3 COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 14451 5% 1% 23
4 FUNCTIONAL ANALYSIS AND ITS APPLICATIONS 13800 4% 1% 19
5 ST PETERSBURG MATHEMATICAL JOURNAL 7732 2% 2% 7
6 INTEGRAL EQUATIONS AND OPERATOR THEORY 7569 3% 1% 16
7 ASYMPTOTIC ANALYSIS 5589 2% 1% 10
8 JOURNAL OF FUNCTIONAL ANALYSIS 5372 5% 0% 23
9 COMMUNICATIONS IN MATHEMATICAL PHYSICS 5062 5% 0% 25
10 JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS 3840 1% 2% 3

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 BETHE SOMMERFELD CONJECTURE 264945 1% 100% 4 Search BETHE+SOMMERFELD+CONJECTURE Search BETHE+SOMMERFELD+CONJECTURE
2 ASYMPTOTIC BEHAVIOR OF VIRTUAL EIGENVALUES 198709 1% 100% 3 Search ASYMPTOTIC+BEHAVIOR+OF+VIRTUAL+EIGENVALUES Search ASYMPTOTIC+BEHAVIOR+OF+VIRTUAL+EIGENVALUES
3 VIRTUAL EIGENVALUES 198709 1% 100% 3 Search VIRTUAL+EIGENVALUES Search VIRTUAL+EIGENVALUES
4 DENSE POINT SPECTRUM 176627 1% 67% 4 Search DENSE+POINT+SPECTRUM Search DENSE+POINT+SPECTRUM
5 SPECTRAL SHIFT FUNCTION 174213 2% 24% 11 Search SPECTRAL+SHIFT+FUNCTION Search SPECTRAL+SHIFT+FUNCTION
6 MAGNETIC SCHRODINGER OPERATOR 168578 3% 18% 14 Search MAGNETIC+SCHRODINGER+OPERATOR Search MAGNETIC+SCHRODINGER+OPERATOR
7 SCHRODINGER OPERATOR 137070 7% 6% 33 Search SCHRODINGER+OPERATOR Search SCHRODINGER+OPERATOR
8 BAND FUNCTIONS 132472 0% 100% 2 Search BAND+FUNCTIONS Search BAND+FUNCTIONS
9 SOBOLEV LIEB THIRRING INEQUALITIES 132472 0% 100% 2 Search SOBOLEV+LIEB+THIRRING+INEQUALITIES Search SOBOLEV+LIEB+THIRRING+INEQUALITIES
10 THE CARLEMAN OPERATOR AND ITS PERTURBATIONS 132472 0% 100% 2 Search THE+CARLEMAN+OPERATOR+AND+ITS+PERTURBATIONS Search THE+CARLEMAN+OPERATOR+AND+ITS+PERTURBATIONS

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 KUCHMENT, P , (2016) AN OVERVIEW OF PERIODIC ELLIPTIC OPERATORS.BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY. VOL. 53. ISSUE 3. P. 343 -414 66 40% 1
2 DANILOV, LI , (2011) ON ABSOLUTE CONTINUITY OF THE SPECTRUM OF A 3D PERIODIC MAGNETIC DIRAC OPERATOR.INTEGRAL EQUATIONS AND OPERATOR THEORY. VOL. 71. ISSUE 4. P. 535-556 16 100% 1
3 MIRANDA, P , (2016) EIGENVALUE ASYMPTOTICS FOR A SCHRODINGER OPERATOR WITH NON-CONSTANT MAGNETIC FIELD ALONG ONE DIRECTION.ANNALES HENRI POINCARE. VOL. 17. ISSUE 7. P. 1713 -1736 19 73% 0
4 MOROZOV, S , PARNOVSKI, L , SHTERENBERG, R , (2014) COMPLETE ASYMPTOTIC EXPANSION OF THE INTEGRATED DENSITY OF STATES OF MULTIDIMENSIONAL ALMOST-PERIODIC PSEUDO-DIFFERENTIAL OPERATORS.ANNALES HENRI POINCARE. VOL. 15. ISSUE 2. P. 263-312 12 100% 1
5 DANILOV, LI , (2009) ON ABSOLUTE CONTINUITY OF THE SPECTRUM OF A PERIODIC MAGNETIC SCHRODINGER OPERATOR.JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. VOL. 42. ISSUE 27. P. - 14 93% 3
6 PARNOVSKI, L , SOBOLEV, AV , (2010) BETHE-SOMMERFELD CONJECTURE FOR PERIODIC OPERATORS WITH STRONG PERTURBATIONS.INVENTIONES MATHEMATICAE. VOL. 181. ISSUE 3. P. 467-540 12 100% 6
7 DIMASSI, M , DUONG, AT , (2014) TRACE ASYMPTOTICS FORMULA FOR THE SCHRODINGER OPERATORS WITH CONSTANT MAGNETIC FIELDS.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. VOL. 416. ISSUE 1. P. 427-448 14 78% 0
8 SHIRAI, S , (2005) STRONG-ELECTRIC-FIELD EIGENVALUE ASYMPTOTICS FOR THE IWATSUKA MODEL.JOURNAL OF MATHEMATICAL PHYSICS. VOL. 46. ISSUE 5. P. - 13 100% 1
9 DANILOV, LI , (2010) ON ABSOLUTE CONTINUITY OF THE SPECTRUM OF THREE- AND FOUR-DIMENSIONAL PERIODIC SCHRODINGER OPERATORS.JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. VOL. 43. ISSUE 21. P. - 11 100% 3
10 PUSHNITSKI, A , (2011) THE BIRMAN-SCHWINGER PRINCIPLE ON THE ESSENTIAL SPECTRUM.JOURNAL OF FUNCTIONAL ANALYSIS. VOL. 261. ISSUE 7. P. 2053-2081 13 81% 2

Classes with closest relation at Level 1


Rank Class id link
1 11187 LIMITING ABSORPTION PRINCIPLE//MOURRE ESTIMATE//RELATIVISTIC SCHRODINGER OPERATORS
2 13318 STAT MECH MATH PHYS//STAT MECH MATH PHYS THEORET CHEM//ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE
3 14256 QUANTUM ERGODICITY//DCAIN//EIGENFUNCTION ESTIMATES
4 4794 RANDOM SCHRODINGER OPERATORS//INTEGRATED DENSITY OF STATES//ABSOLUTELY CONTINUOUS SPECTRUM
5 7203 DOPPLER//TRAPPED MODES//POINT INTERACTIONS
6 13336 GROSS PITAEVSKII HIERARCHY//MEAN FIELD LIMIT//UMR 8088
7 31773 ASTIGMATIC BEAM//LENSGUIDES//OAO LOMO
8 29481 UNSATURATED NUMERICAL METHOD//DOUBLE DEGENERATION//OPERATOR POTENTIAL
9 28890 FBI BARGMANN TRANSFORM//COMPLEX PERTURBATION//INFINITE CURVATURE
10 13757 UNIVERSAL INEQUALITIES//EIGENVALUE RATIO//LIEB THIRRING INEQUALITIES

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