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## Graybill, Franklin A.

Compute Distance To:
 Author ID: graybill.franklin-a Published as: Graybill, F. A.; Graybill, Franklin A. External Links: MGP · Wikidata
 Documents Indexed: 56 Publications since 1953, including 7 Books Biographic References: 2 Publications
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#### Co-Authors

 7 single-authored 9 Burdick, Richard K. 4 Ting, Naitee 3 Connell, Terrence L. 3 Kazempour, Mohammad K. 3 Milliken, George A. 3 Weeks, David L. 2 Hultquist, Robert A. 2 Jeyaratnam, Sakthivel 2 Johnson, Dallas E. 2 Lu, Tai-Fang C. 2 Maric, Nebojsa 2 Mood, Alexander McFarlane 2 Wang, Chih-Ming 1 Arteaga, Carmen 1 Birch, Nancy J. 1 Boardman, Thomas J. 1 Boes, Duane C. 1 Deal, R. B. 1 Fayyad, Rana 1 Folks, John Leroy 1 Gui, Rongde 1 Iyer, Hariharan K. 1 Kingman, Albert 1 Kopitzke, R. 1 Leiva, Ricardo Aníbal 1 Maqsood, Farooq 1 Marsaglia, George 1 Meyer, Carl Dean jun. 1 Mohmand, Adam Khan 1 Morrison, Robert D. 1 Mosier, Michael C. 1 Painter, Richard J. 1 Pruitt, William E. 1 Sen, Bhabesh 1 Seshadri, Vikram 1 Wortham, A. W.
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#### Serials

 10 Annals of Mathematical Statistics 8 Journal of the American Statistical Association 5 Communications in Statistics. Theory and Methods 3 Biometrical Journal 3 Biometrics 3 Journal of Statistical Planning and Inference 3 Communications in Statistics. Simulation and Computation 2 Sankhyā. Series A. Methods and Techniques 1 The American Statistician 1 The Arabian Journal for Science and Engineering 1 The Australian Journal of Statistics 1 Biometrika 1 Technometrics 1 Statistics & Probability Letters 1 Journal of Statistical Computation and Simulation 1 SIAM Review 1 Computational Statistics and Data Analysis 1 Statistics: Textbooks and Monographs
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#### Fields

 32 Statistics (62-XX) 2 General and overarching topics; collections (00-XX) 2 Probability theory and stochastic processes (60-XX) 2 Numerical analysis (65-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX)

#### Citations contained in zbMATH

45 Publications have been cited 1,173 times in 1,027 Documents Cited by Year
Introduction to the theory of statistics. 3rd ed. Zbl 0277.62002
Mood, Alexander M.; Graybill, Franklin A.; Boes, Duane C.
1974
Theory and application of the linear model. Zbl 0371.62093
Graybill, Franklin A.
1976
Matrices with applications in statistics. 2nd ed. Zbl 0496.15002
Graybill, Franklin A.
1983
An introduction to linear statistical models. Vol. 1. Zbl 0121.35605
Graybill, F. A.
1961
Quadratic forms and idempotent matrices with random elements. Zbl 0188.51601
Graybill, F. A.; Milliken, G.
1969
Combining unbiased estimators. Zbl 0096.34503
Graybill, Franklin A.; Deal, R. B.
1959
Confidence intervals on variance components. Zbl 0755.62055
Burdick, Richard K.; Graybill, Franklin A.
1992
An analysis of a two-way model with interaction and no replication. Zbl 0254.62042
Johnson, Dallas E.; Graybill, Franklin A.
1972
Theorems concerning Eisenhart’s model II. Zbl 0109.37501
Graybill, F. A.; Hultquist, R. A.
1961
Extensions of the general linear hypothesis model. Zbl 0195.48503
Milliken, George A.; Graybill, Franklin A.
1970
Regression analysis: concepts and applications. Zbl 0868.62056
Graybill, Franklin A.; Iyer, Hariharan K.
1994
Idempotent matrices and quadratic forms in the general linear hypothesis. Zbl 0080.35502
Graybill, Franklin A.; Marsaglia, George
1957
The present status of confidence interval estimation on variance components in balanced and unbalanced random models. Zbl 0648.62072
Burdick, Richard K.; Graybill, Franklin A.
1988
A note on uniformly best unbiased estimators for variance components. Zbl 0070.14503
Graybill, Franklin A.; Wortham, A. W.
1956
Confidence intervals on the intraclass correlation in the unbalanced one- way classification. Zbl 0613.62046
Burdick, Richard K.; Maqsood, Farooq; Graybill, Franklin A.
1986
Small samples confidence intervals on common mean of two normal distributions with unequal variances. Zbl 0408.62029
Maric, Nebojsa; Graybill, Franklin A.
1979
Sample size required for estimating the variance within $$d$$ units of the true value. Zbl 0126.34502
Graybill, Franklin A.; Connell, Terrence L.
1964
On quadratic estimates of variance components. Zbl 0055.37604
Graybill, Franklin A.
1954
Confidence intervals on ratios of linear combinations for non-disjoint sets of expected mean squares. Zbl 0839.62029
Gui, Rongde; Graybill, Franklin A.; Burdick, Richard K.; Ting, Naitee
1995
Sample size required to estimate the parameter in the uniform density within d units of the true value. Zbl 0121.13901
Graybill, F. A.; Connell, T. L.
1964
Confidence intervals on a difference of expected mean squares. Zbl 0656.62039
Lu, Tai-Fang C.; Graybill, Franklin A.; Burdick, Richard K.
1988
Confidence intervals on measures of variability in an unbalanced two-fold nested design with equal subsampling. Zbl 0614.62037
Burdick, Richard K.; Birch, Nancy J.; Graybill, Franklin A.
1986
Confidence intervals for variance components in the balanced two way model with interaction. Zbl 0606.62031
Leiva, Ricardo A.; Graybill, Franklin A.
1986
Confidence intervals for proportions of variability in two-factor nested variance component models. Zbl 0432.62048
Graybill, Franklin A.; Wang, Chih-Ming
1979
Minimal sufficient statistics for the two-way classification mixed model design. Zbl 0132.13204
Hultquist, R. A.; Graybill, F. A.
1965
Combining inter-block and intra-block information in balanced incomplete blocks. Zbl 0094.33001
Graybill, Franklin A.; Weeks, David L.
1959
Confidence intervals for proportions of total variance in the two-way cross component of variance model. Zbl 0515.62066
Arteaga, Carmen; Jeyaratnam, S.; Graybill, Franklin A.
1982
Confidence intervals on a ratio of variances in the two-factor nested components of variance model. Zbl 0474.62071
Wang, Chih-Ming; Graybill, Franklin A.
1981
Estimation of $$\sigma^2$$ in a two-way classification model with interaction. Zbl 0237.62048
Johnson, Dallas E.; Graybill, Franklin A.
1972
A minimal sufficient statistic for a general class of designs. Zbl 0108.31802
Weeks, D. L.; Graybill, F. A.
1962
On the unbiasedness of Yates’ method of estimation using interblock information. Zbl 0092.36101
Graybill, Franklin A.; Seshadri, V.
1960
Determining sample size for a specified width confidence interval. Zbl 0087.34201
Graybill, Franklin A.
1958
Confidence intervals on ratios of positive linear combinations of variance components. Zbl 0724.62069
Ting, Naitee; Burdick, Richard K.; Graybill, Franklin A.
1991
Confidence intervals on the ratio of expected mean squares $$(\theta _ 1-d\theta _ 2)/\theta _ 3$$. Zbl 0666.62035
Lu, Taifang C.; Graybill, Franklin A.; Burdick, Richard K.
1989
Confidence bounds for proportion of $$\sigma{}^ 2_ E$$ in unbalanced two-way crossed models. Zbl 0735.62067
Kazempour, Mohammad K.; Graybill, Franklin A.
1989
Confidence intervals on variance components in three-factor cross- classification models. Zbl 0468.62068
Jeyaratnam, S.; Graybill, Franklin A.
1980
Least squares programs - a look at the square root procedure. Zbl 0361.62061
Kopitzke, R.; Boardman, T. J.; Graybill, F. A.
1975
Note on the computation of the generalized inverse of a matrix. Zbl 0149.36801
Graybill, F. A.; Meyer, Carl D. jun.; Painter, R. J.
1966
Minimal sufficient statistics for the balanced incomplete block design under an Eisenhart model II. Zbl 0106.12807
Weeks, David L.; Graybill, Franklin A.
1961
A note on exact tests for variance components in unbalanced random and mixed linear models. Zbl 0880.62070
Fayyad, Rana; Graybill, Franklin A.; Burdick, Richard K.
1996
Evaluation of a method for setting confidence intervals on the common mean of two normal populations. Zbl 0444.62046
Maric, Nebojsa; Graybill, Franklin A.
1979
A non-linear characterization of the normal distribution. Zbl 0267.60013
Kingman, Albert; Graybill, Franklin A.
1970
Sample size for a specified width confidence interval on the variance of a normal distribution. Zbl 0097.34702
Graybill, Franklin A.; Morrison, Robert D.
1960
The staircase design: Theory. Zbl 0086.34901
Graybill, Franklin A.; Pruitt, William E.
1958
Heterogeneity of error variances in a randomized block design. Zbl 0077.33701
Graybill, Franklin A.; Folks, John Leroy
1957
A note on exact tests for variance components in unbalanced random and mixed linear models. Zbl 0880.62070
Fayyad, Rana; Graybill, Franklin A.; Burdick, Richard K.
1996
Confidence intervals on ratios of linear combinations for non-disjoint sets of expected mean squares. Zbl 0839.62029
Gui, Rongde; Graybill, Franklin A.; Burdick, Richard K.; Ting, Naitee
1995
Regression analysis: concepts and applications. Zbl 0868.62056
Graybill, Franklin A.; Iyer, Hariharan K.
1994
Confidence intervals on variance components. Zbl 0755.62055
Burdick, Richard K.; Graybill, Franklin A.
1992
Confidence intervals on ratios of positive linear combinations of variance components. Zbl 0724.62069
Ting, Naitee; Burdick, Richard K.; Graybill, Franklin A.
1991
Confidence intervals on the ratio of expected mean squares $$(\theta _ 1-d\theta _ 2)/\theta _ 3$$. Zbl 0666.62035
Lu, Taifang C.; Graybill, Franklin A.; Burdick, Richard K.
1989
Confidence bounds for proportion of $$\sigma{}^ 2_ E$$ in unbalanced two-way crossed models. Zbl 0735.62067
Kazempour, Mohammad K.; Graybill, Franklin A.
1989
The present status of confidence interval estimation on variance components in balanced and unbalanced random models. Zbl 0648.62072
Burdick, Richard K.; Graybill, Franklin A.
1988
Confidence intervals on a difference of expected mean squares. Zbl 0656.62039
Lu, Tai-Fang C.; Graybill, Franklin A.; Burdick, Richard K.
1988
Confidence intervals on the intraclass correlation in the unbalanced one- way classification. Zbl 0613.62046
Burdick, Richard K.; Maqsood, Farooq; Graybill, Franklin A.
1986
Confidence intervals on measures of variability in an unbalanced two-fold nested design with equal subsampling. Zbl 0614.62037
Burdick, Richard K.; Birch, Nancy J.; Graybill, Franklin A.
1986
Confidence intervals for variance components in the balanced two way model with interaction. Zbl 0606.62031
Leiva, Ricardo A.; Graybill, Franklin A.
1986
Matrices with applications in statistics. 2nd ed. Zbl 0496.15002
Graybill, Franklin A.
1983
Confidence intervals for proportions of total variance in the two-way cross component of variance model. Zbl 0515.62066
Arteaga, Carmen; Jeyaratnam, S.; Graybill, Franklin A.
1982
Confidence intervals on a ratio of variances in the two-factor nested components of variance model. Zbl 0474.62071
Wang, Chih-Ming; Graybill, Franklin A.
1981
Confidence intervals on variance components in three-factor cross- classification models. Zbl 0468.62068
Jeyaratnam, S.; Graybill, Franklin A.
1980
Small samples confidence intervals on common mean of two normal distributions with unequal variances. Zbl 0408.62029
Maric, Nebojsa; Graybill, Franklin A.
1979
Confidence intervals for proportions of variability in two-factor nested variance component models. Zbl 0432.62048
Graybill, Franklin A.; Wang, Chih-Ming
1979
Evaluation of a method for setting confidence intervals on the common mean of two normal populations. Zbl 0444.62046
Maric, Nebojsa; Graybill, Franklin A.
1979
Theory and application of the linear model. Zbl 0371.62093
Graybill, Franklin A.
1976
Least squares programs - a look at the square root procedure. Zbl 0361.62061
Kopitzke, R.; Boardman, T. J.; Graybill, F. A.
1975
Introduction to the theory of statistics. 3rd ed. Zbl 0277.62002
Mood, Alexander M.; Graybill, Franklin A.; Boes, Duane C.
1974
An analysis of a two-way model with interaction and no replication. Zbl 0254.62042
Johnson, Dallas E.; Graybill, Franklin A.
1972
Estimation of $$\sigma^2$$ in a two-way classification model with interaction. Zbl 0237.62048
Johnson, Dallas E.; Graybill, Franklin A.
1972
Extensions of the general linear hypothesis model. Zbl 0195.48503
Milliken, George A.; Graybill, Franklin A.
1970
A non-linear characterization of the normal distribution. Zbl 0267.60013
Kingman, Albert; Graybill, Franklin A.
1970
Quadratic forms and idempotent matrices with random elements. Zbl 0188.51601
Graybill, F. A.; Milliken, G.
1969
Note on the computation of the generalized inverse of a matrix. Zbl 0149.36801
Graybill, F. A.; Meyer, Carl D. jun.; Painter, R. J.
1966
Minimal sufficient statistics for the two-way classification mixed model design. Zbl 0132.13204
Hultquist, R. A.; Graybill, F. A.
1965
Sample size required for estimating the variance within $$d$$ units of the true value. Zbl 0126.34502
Graybill, Franklin A.; Connell, Terrence L.
1964
Sample size required to estimate the parameter in the uniform density within d units of the true value. Zbl 0121.13901
Graybill, F. A.; Connell, T. L.
1964
A minimal sufficient statistic for a general class of designs. Zbl 0108.31802
Weeks, D. L.; Graybill, F. A.
1962
An introduction to linear statistical models. Vol. 1. Zbl 0121.35605
Graybill, F. A.
1961
Theorems concerning Eisenhart’s model II. Zbl 0109.37501
Graybill, F. A.; Hultquist, R. A.
1961
Minimal sufficient statistics for the balanced incomplete block design under an Eisenhart model II. Zbl 0106.12807
Weeks, David L.; Graybill, Franklin A.
1961
On the unbiasedness of Yates’ method of estimation using interblock information. Zbl 0092.36101
Graybill, Franklin A.; Seshadri, V.
1960
Sample size for a specified width confidence interval on the variance of a normal distribution. Zbl 0097.34702
Graybill, Franklin A.; Morrison, Robert D.
1960
Combining unbiased estimators. Zbl 0096.34503
Graybill, Franklin A.; Deal, R. B.
1959
Combining inter-block and intra-block information in balanced incomplete blocks. Zbl 0094.33001
Graybill, Franklin A.; Weeks, David L.
1959
Determining sample size for a specified width confidence interval. Zbl 0087.34201
Graybill, Franklin A.
1958
The staircase design: Theory. Zbl 0086.34901
Graybill, Franklin A.; Pruitt, William E.
1958
Idempotent matrices and quadratic forms in the general linear hypothesis. Zbl 0080.35502
Graybill, Franklin A.; Marsaglia, George
1957
Heterogeneity of error variances in a randomized block design. Zbl 0077.33701
Graybill, Franklin A.; Folks, John Leroy
1957
A note on uniformly best unbiased estimators for variance components. Zbl 0070.14503
Graybill, Franklin A.; Wortham, A. W.
1956
On quadratic estimates of variance components. Zbl 0055.37604
Graybill, Franklin A.
1954
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#### Cited by 1,477 Authors

 12 Graybill, Franklin A. 10 Krishnamoorthy, Kalyanam 9 Burdick, Richard K. 8 Bonett, Douglas G. 8 Dutilleul, Pierre 8 Khuri, André I. 8 Udwadia, Firdaus E. 7 Sinha, Bimal Kumar 6 Alpargu, Gülhan 6 Buonaccorsi, John P. 6 Knapp, Guido 6 Liao, Chen-Tuo 6 Maris, Eric 6 Milliken, George A. 6 Tian, Yongge 5 Baksalary, Jerzy K. 5 Boik, Robert J. 5 Jiang, Bo 5 Kapadia, C. H. 5 Kubokawa, Tatsuya 5 Lee, Sik-Yum 5 Li, Xinmin 5 Shah, Kirti R. 5 Shinozaki, Nobuo 4 Baltagi, Badi H. 4 Bhattacharya, C. G. 4 Burch, Brent D. 4 Candel, Math J. J. M. 4 Chang, Yuan-Tsung 4 da Motta Singer, Julio 4 Dahlhaus, Rainer 4 El Bassiouni, Mohamed Y. 4 Hartung, Joachim G. 4 Heiligers, Berthold 4 Heun Song, Seuck 4 Kalaba, Robert E. 4 Kumar, Somesh 4 Meredith, William 4 Mukhopadhyay, Nitis 4 Özkale, M. Revan 4 Pitselis, Georgios 4 Puri, Madan Lal 4 Rukhin, Andrew L. 4 Sackrowitz, Harold B. 4 Scariano, Stephen M. 4 Seely, Justus F. 4 Tong, Yung Liang 4 Van Breukelen, Gerard J. P. 4 Woodward, J. Arthur 3 Addy, Cheryl L. 3 Arellano-Valle, Reinaldo Boris 3 Arendacká, Barbora 3 Bentler, Peter M. 3 Birkes, David S. 3 Browne, Michael W. 3 Brunner, Edgar 3 Carriere, Jacques F. 3 Chang, Fu-Chuen 3 Chang, Kuang-Chao 3 Cohen, Arthur 3 Cornelius, Paul L. 3 Csenki, Attila 3 Davenport, James Melton 3 De Boeck, Paul 3 Díaz-García, José A. 3 Gunst, Richard F. 3 Hardin, James W. 3 Huang, Deng-Yuan 3 Iyer, Hari K. 3 Iyer, Hariharan K. 3 Jeyaratnam, Sakthivel 3 Johnson, Dallas E. 3 Kabaila, Paul V. 3 Kabe, Dattatraya Govind 3 Kaçıranlar, Selahattin 3 Kharrati-Kopaei, Mahmood 3 Kuriki, Satoshi 3 Lee, Youngjo 3 Lewis, T. O. 3 Lu, Yong 3 Lui, Kung-Jong 3 Ma, Tiefeng 3 Mathew, Thomas 3 Neill, James W. 3 Özdemir, Halim 3 Pal, Nabendu 3 Patera, Anthony T. 3 Phohomsiri, Phailaung 3 Ronning, Gerd 3 Searle, Shayle Robert 3 Seyedsadr, Mahmoud S. 3 Stahlecker, Peter 3 Strawderman, William Edward 3 Thangjai, Warisa 3 Ting, Naitee 3 Vajda, Igor 3 van Zyl, J. Martin 3 Wang, Songgui 3 Wu, Mixia 3 Wulff, Shaun S. ...and 1,377 more Authors
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#### Cited in 179 Serials

 157 Communications in Statistics. Theory and Methods 95 Journal of Statistical Planning and Inference 49 Psychometrika 43 Communications in Statistics. Simulation and Computation 43 Journal of Statistical Computation and Simulation 40 Statistics & Probability Letters 39 Computational Statistics and Data Analysis 37 Journal of Multivariate Analysis 27 Linear Algebra and its Applications 24 Annals of the Institute of Statistical Mathematics 23 Journal of Econometrics 18 Applied Mathematics and Computation 16 Journal of Applied Statistics 12 Metrika 11 Statistics 11 European Journal of Operational Research 10 Biometrics 10 Statistical Papers 9 Economics Letters 8 Computers & Mathematics with Applications 8 The Annals of Statistics 8 Insurance Mathematics & Economics 7 Trabajos de Estadistica y de Investigacion Operativa 6 Mathematical Biosciences 6 Journal of Mathematical Psychology 6 Statistische Hefte. Neue Folge 6 American Journal of Mathematical and Management Sciences 6 Journal of Agricultural, Biological, and Environmental Statistics 5 The Canadian Journal of Statistics 5 Linear and Multilinear Algebra 5 Automatica 5 Journal of Optimization Theory and Applications 5 Journal of Time Series Analysis 5 Stochastic Processes and their Applications 5 Mathematical Geology 4 Computer Methods in Applied Mechanics and Engineering 4 Journal of Mathematical Analysis and Applications 4 Scandinavian Journal of Statistics 4 Biometrical Journal 4 Mathematics and Computers in Simulation 4 Sequential Analysis 4 Computers & Operations Research 4 Computational Statistics 4 Applied Mathematical Modelling 4 Statistische Hefte 4 Test 4 Journal of the Korean Statistical Society 3 Discrete Mathematics 3 International Journal of Mathematical Education in Science and Technology 3 Journal of Computational Physics 3 Journal of the Franklin Institute 3 Journal of Mathematical Biology 3 Journal of Economic Theory 3 Kybernetika 3 Metroeconomica 3 Metron 3 Statistica Neerlandica 3 Theoretical Population Biology 3 Acta Mathematicae Applicatae Sinica. English Series 3 Econometric Reviews 3 Mathematical and Computer Modelling 3 Games and Economic Behavior 3 Journal of Biopharmaceutical Statistics 3 Journal of Nonparametric Statistics 3 International Journal of Applied Mathematics and Computer Science 3 Journal of Statistical Theory and Practice 3 Electronic Journal of Statistics 3 Journal of Theoretical Biology 2 Biological Cybernetics 2 Computer Physics Communications 2 Discrete Applied Mathematics 2 International Journal of Systems Science 2 Bulletin of Mathematical Biology 2 Blätter (Deutsche Gesellschaft für Versicherungsmathematik) 2 Fuzzy Sets and Systems 2 Journal of Computational and Applied Mathematics 2 Journal of Mathematical Economics 2 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Journal of Information & Optimization Sciences 2 Mathematical Social Sciences 2 Applied Numerical Mathematics 2 Optimization 2 Statistical Science 2 Journal of Economics 2 Journal of Economic Dynamics & Control 2 Stochastic Hydrology and Hydraulics 2 Australian & New Zealand Journal of Statistics 2 International Journal of Theoretical and Applied Finance 2 Brazilian Journal of Probability and Statistics 2 Scandinavian Actuarial Journal 2 Advances and Applications in Statistics 2 Statistical Methodology 2 AStA. Advances in Statistical Analysis 2 Pesquisa Operacional 2 GEM - International Journal on Geomathematics 2 Special Matrices 2 Open Mathematics 1 Acta Mechanica 1 Applicable Analysis 1 Artificial Intelligence ...and 79 more Serials
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#### Cited in 37 Fields

 825 Statistics (62-XX) 142 Numerical analysis (65-XX) 68 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 63 Linear and multilinear algebra; matrix theory (15-XX) 53 Probability theory and stochastic processes (60-XX) 39 Biology and other natural sciences (92-XX) 35 Operations research, mathematical programming (90-XX) 21 Computer science (68-XX) 15 Systems theory; control (93-XX) 11 Combinatorics (05-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 7 Information and communication theory, circuits (94-XX) 6 Mechanics of particles and systems (70-XX) 6 Geophysics (86-XX) 4 Approximations and expansions (41-XX) 4 Fluid mechanics (76-XX) 3 History and biography (01-XX) 3 Mathematical logic and foundations (03-XX) 3 Ordinary differential equations (34-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Operator theory (47-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Associative rings and algebras (16-XX) 2 Functions of a complex variable (30-XX) 2 Special functions (33-XX) 2 Partial differential equations (35-XX) 2 Convex and discrete geometry (52-XX) 2 Differential geometry (53-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Number theory (11-XX) 1 Real functions (26-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) 1 Mechanics of deformable solids (74-XX)