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Yr Athro Karl Schmidt
Timau a rolau for Karl Schmidt
Trosolwg
Diddordebau ymchwil
Mae fy ymchwil yn disgyn i sawl maes gwahanol o fathemateg bur a chymhwysol, wedi'i ddal gyda'i gilydd gan y syniad arweiniol o ddadansoddi sbectrol matricsau a gweithredwyr llinol.
- Theori sbectrol - gweithredwyr differol, dadansoddiad swyddogaethol, theori gweithredwyr, dadansoddiad asymptotig, hafaliadau differol, theori sbectrol gyfrifiadurol
- Ystadegau amlamrywiol - dadansoddiad sbectrwm unigol o gyfresi amser, dulliau mathemategol mewn geneteg feddygol
- Theori rhifau cyfunol ac algebra llinol - cymesureddau matrics, systemau swm cyfanrifau, ffwythiannau rhannwr cyffredinol, cyfres Dirichlet
Addysgu
Rwyf wedi dysgu ystod eang o bynciau mathemategol, yn amrywio o ddadansoddi mathemategol, hafaliadau differol cyffredin a rhannol, dadansoddiad swyddogaethol, theori sbectrol, topoleg i ddadansoddiad rhifiadol, mecaneg cwantwm a mecaneg glasurol.
Mae fy addysgu presennol yn cynnwys cyfres o fodiwlau ar ddadansoddi swyddogaethol a harmonig (Blwyddyn 3) a theori sbectrol gweithredwyr hunan-gydweithredol (Blwyddyn 4 / MSc) yn ogystal â modiwl lefel PhD ar theori sbectrol hafaliadau differol cyffredin ar gyfer consortiwm MAGIC.
Rwy'n goruchwylio prosiectau israddedig (Blwyddyn 3 a Blwyddyn 4) yn rheolaidd ar bynciau mewn theori sbectrol, dadansoddi mathemategol a mathemateg tymer cerddorol.
Ffwythiannau gweinyddol
Arweinydd Astudiaethau Ymchwil Ôl-raddedig, COMAT
Cyhoeddiad
2026
- Yao, K. et al. 2026. 78. Joint modelling of polygenic risk and rare variants enhances liability-based disease prediction [Abstract]. European Neuropsychopharmacology 111 (Supple) 113105. (10.1016/j.euroneuro.2026.113105)
- Escott-Price, V. , Leonenko, G. and Schmidt, K. M. 2026. Positioning personal polygenic risk score against the population background. Research in Statistics 4 (1) 2685935. (10.1080/27684520.2026.2685935)
2025
- Law, A. D. , Lettington, M. C. and Schmidt, K. M. 2025. Multifactorisations and divisor functions. UTILITAS MATHEMATICA 125 , pp.43-60. (10.61091/um125-03)
- Schmidt, K. M. and Umeda, T. 2025. On the resolvent convergence of discrete Dirac operators on 3D cubic lattices. Journal of Mathematical Analysis and Applications 546 (2) 129247. (10.1016/j.jmaa.2025.129247)
- Jameel, G. S. and Schmidt, K. M. 2025. Eigenvalue bounds for perturbed periodic Dirac operators. Journal of Spectral Theory 15 (3), pp.1279-1303. (10.4171/jst/556)
- Higham, N. J. , Lettington, M. C. and Schmidt, K. M. 2025. Symmetry decomposition and matrix multiplication. Linear Algebra and its Applications 710 , pp.310-335. (10.1016/j.laa.2025.01.041)
2023
- Escott-Price, V. and Schmidt, K. M. 2023. Pitfalls of predicting age related traits by polygenic risk scores. Annals of Human Genetics 87 (5), pp.203-209. (10.1111/ahg.12520)
- Schmidt, K. M. and Umeda, T. 2023. Continuum limits for discrete Dirac operators on 2D square lattices. Analysis and Mathematical Physics 13 (46)(10.1007/s13324-023-00809-7)
- Simmonds, E. et al. 2023. What does heritability of Alzheimer’s disease represent?. PLoS ONE 18 (4) e0281440. (10.1371/journal.pone.0281440)
- Lettington, M. and Schmidt, K. 2023. On the sum of left and right circulant matrices. Linear Algebra and its Applications 658 , pp.62-85. (10.1016/j.laa.2022.10.024)
2021
- Brown, B. M. et al. 2021. The inverse problem for a spectral asymmetry function of the Schrödinger operator on a finite interval. Mathematika 67 (4), pp.788-806. (10.1112/mtk.12105)
- Escott-Price, V. and Schmidt, K. M. 2021. Correction to: Probability of Alzheimer's disease based on common and rare genetic variants. Alzheimer's Research and Therapy 13 (1) 156. (10.1186/s13195-021-00898-1)
- Escott-Price, V. and Schmidt, K. M. 2021. Probability of Alzheimer’s disease based on common and rare genetic variants. Alzheimer's Research & Therapy 13 140. (10.1186/s13195-021-00884-7)
- Higham, N. J. , Lettington, M. C. and Schmidt, K. M. 2021. Integer matrix factorisations, superalgebras and the quadratic form obstruction. Linear Algebra and its Applications 622 , pp.250-267. (10.1016/j.laa.2021.03.028)
- Escott-Price, V. and Schmidt, K. M. 2021. Challenges of adjusting Single-Nucleotide Polymorphism effect sizes for linkage disequilibrium. Human Heredity 85 (1), pp.24-34. (10.1159/000513303)
2020
- Lettington, M. C. and Schmidt, K. M. 2020. Divisor functions and the number of sum systems. Integers 20 A61.
- Hill, S. L. et al. 2020. Some properties and applications of non-trivial divisor functions. Ramanujan Journal 51 (10.1007/s11139-018-0093-9)
2019
- Huxley, M. N. , Lettington, M. C. and Schmidt, K. M. 2019. On the structure of additive systems of integers. Periodica Mathematica Hungarica 78 , pp.178-199. (10.1007/s10998-018-00275-w)
- Phillips, T. R. L. , Schmidt, K. M. and Zhigljavsky, A. 2019. Extension of the Schoenberg theorem to integrally conditionally positive definite functions. Journal of Mathematical Analysis and Applications 470 (1), pp.659-678. (10.1016/j.jmaa.2018.10.032)
- Vivian-Griffiths, T. et al. 2019. Predictive modeling of schizophrenia from genomic data: Comparison of polygenic risk score with kernel support vector machines approach. American Journal of Medical Genetics Part B: Neuropsychiatric Genetics 180 (1), pp.80-85. (10.1002/ajmg.b.32705)
2018
- Baker, E. et al. 2018. POLARIS: polygenic LD-adjusted risk score approach for set-based analysis of GWAS data. Genetic Epidemiology 42 (4), pp.366-377. (10.1002/gepi.22117)
- Hill, S. , Lettington, M. C. and Schmidt, K. M. 2018. Block representations and spectral properties of constant sum matrices. Electronic Journal of Linear Algebra 34 , pp.170-190. (10.13001/1081-3810.3530)
- Phillips, T. and Schmidt, K. M. 2018. On unbounded positive definite functions. Mathematica Pannonica 26 (2), pp.33-51.
2017
- Lettington, M. C. , Schmidt, K. M. and Hill, S. 2017. On superalgebras of matrices with symmetry properties. Linear and Multilinear Algebra 66 (8), pp.1538-1563. (10.1080/03081087.2017.1363153)
- Vronskaya-Robl, M. and Schmidt, K. M. 2017. On perturbation stability of SSA and MSSA forecasts and the supportiveness of time series. Statistics and Its Interface 10 (1), pp.33-46.
2016
- Schmidt, K. M. 2016. On the asymptotics of the spectral density of radial Dirac operators with divergent potential. Integral Equations and Operator Theory 85 , pp.137-149. (10.1007/s00020-015-2276-8)
2015
- Schmidt, K. M. and Umeda, T. 2015. Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials. Letters in Mathematical Physics 105 , pp.1479-1497. (10.1007/s11005-015-0799-1)
2014
- Brunnock, R. , Lettington, M. C. and Schmidt, K. M. 2014. On square roots and norms of matrices with symmetry properties. Linear Algebra and its Applications 459 , pp.175-207. (10.1016/j.laa.2014.06.054)
- Hughes, D. and Schmidt, K. M. 2014. Absolutely continuous spectrum of Dirac operators with square-integrable potentials. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144 (3), pp.533-555. (10.1017/S0308210512001187)
- Escott-Price, V. , Ghodsi, M. and Schmidt, K. M. 2014. How allele frequency and study design affect association test statistics with misrepresentation errors. Biostatistics 15 (2), pp.311-326. (10.1093/biostatistics/kxt048)
- Schmidt, K. M. and Umeda, T. 2014. Spectral properties of massless Dirac operators with real-valued potentials. Presented at: Spectral and scattering theory and related topics Kyoto University, Japan 14-16 December 2011. RIMS Kôkyûroku Bessatsu B45: Spectral and Scattering Theory and Related Topics. Kyoto, Japan: , pp.25-30.
2013
- Brown, B. M. , Eastham, M. S. P. and Schmidt, K. M. 2013. Periodic differential operators. Operator Theory: Advances and Applications Vol. 230Basel: Birkhäuser.
- Kerfriden, P. et al. 2013. Statistical extraction of process zones and representative subspaces in fracture of random composites. International Journal for Multiscale Computational Engineering 11 (3), pp.253-287. (10.1615/IntJMultCompEng.2013005939)
- Schmidt, K. M. and Zhigljavsky, A. A. 2013. An extremal property of the generalized arcsine distribution. Metrika 76 (3), pp.347-355. (10.1007/s00184-012-0391-y)
2012
- Brown, B. M. and Schmidt, K. M. 2012. On the HELP Inequality for Hill Operators on Trees. In: Brown, B. M. , Lang, J. and Wood, I. G. eds. Spectral Theory, Function Spaces and Inequalities: New Techniques and Recent Trends. Operator Theory: Advances and Applications Vol. 219.Basel: Springer. , pp.21-36. (10.1007/978-3-0348-0263-5_2)
- Escott-Price, V. et al. 2012. Permutation-based approaches do not adequately allow for linkage disequilibrium in gene-wide multi-locus association analysis. European Journal of Human Genetics 20 (8), pp.890-896. (10.1038/ejhg.2012.8)
2011
- Korotyaev, E. L. and Schmidt, K. M. 2011. On the resonances and eigenvalues for a 1D half-crystal with localised impurity. Journal für die reine und angewandte Mathematik (Crelles Journal) 2012 (670), pp.217-248. (10.1515/CRELLE.2011.153)
2010
- Schmidt, K. M. 2010. Spectral properties of rotationally symmetric massless dirac operators. Letters in Mathematical Physics 92 (3), pp.231-241. (10.1007/s11005-010-0393-5)
2009
- Brown, B. M. , Christiansen, J. S. and Schmidt, K. M. 2009. Spectral properties of a q-Sturm–Liouville Operator. Communications in Mathematical Physics 287 (1), pp.259-274. (10.1007/s00220-008-0623-1)
- Evans, W. D. and Schmidt, K. M. 2009. A discrete Hardy-Laptev-Weidl type inequality and associated Schrödinger-type operators. Revista Matemática Complutense 22 (1), pp.75-90.
- Schmidt, K. M. and Zhigljavsky, A. A. 2009. A characterization of the arcsine distribution. Statistics & Probability Letters 79 (24), pp.2451-2455. (10.1016/j.spl.2009.08.018)
2008
- Escott-Price, V. and Schmidt, K. M. 2008. On multiple-testing correction in genome-wide association studies. Genetic Epidemiology 32 (6), pp.567-573. (10.1002/gepi.20331)
- Aumann, S. , Brown, B. M. and Schmidt, K. M. 2008. A Hardy-Littlewood-type inequality for the p-Laplacian. Bulletin of the London Mathematical Society 40 (3), pp.525-531. (10.1112/blms/bdn035)
- Brown, B. M. , Langer, M. and Schmidt, K. M. 2008. The HELP inequality on trees. Presented at: Isaac Newton Institute for Mathematical Sciences Cambridge, UK 8 January - 29 June 2007. Published in: Exner, P. et al., Analysis on Graphs and Its Applications. Proceedings of Symposia in Pure Mathematics Vol. 77. Providence, RI: American Mathematical Society. , pp.337-354.
- Eastham, M. S. P. and Schmidt, K. M. 2008. Asymptotics of the spectral density for radial dirac operators with divergent potentials. Publications of the Research Institute for Mathematical Sciences 44 (1), pp.107-129. (10.2977/prims/1207921078)
2007
- Monaquel, S. J. and Schmidt, K. M. 2007. On M-functions and operator theory for non-self-adjoint discrete Hamiltonian systems. Journal of Computational and Applied Mathematics 208 (1), pp.82-101. (10.1016/j.cam.2006.10.043)
2006
- Schmidt, K. M. 2006. Exceptional coupling constants for the Coulomb-Dirac operator with anomalous magnetic moment. Journal of Computational and Applied Mathematics 194 (1), pp.17-25. (10.1016/j.cam.2005.06.022)
- Escott-Price, V. and Schmidt, K. M. 2006. Individual SNP Allele Reconstruction from Informative Markers Selected by a Non-Linear Gauss-Type Algorithm. Human Heredity 62 (2), pp.97-106. (10.1159/000096097)
- Escott-Price, V. and Schmidt, K. M. 2006. Susceptibility of Biallelic Haplotype and Genotype Frequencies to Genotyping Error. Biometrics 62 (4), pp.1116-1123. (10.1111/j.1541-0420.2006.00563.x)
2005
- Eastham, M. S. P. and Schmidt, K. M. 2005. Absence of high-energy spectral concentration for Dirac systems with divergent potentials. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135 (4), pp.689-702. (10.1017/S0308210500004078)
- Escott-Price, V. et al. 2005. Design of Case-controls Studies with Unscreened Controls. Annals of Human Genetics 69 (5), pp.566-576. (10.1111/j.1529-8817.2005.00175.x)
2004
- Kalf, H. and Schmidt, K. M. 2004. Spectral stability of the Coulomb-Dirac Hamiltonian with anomalous magnetic moment. Journal of Differential Equations 205 (2), pp.408-423. (10.1016/j.jde.2004.04.009)
- Brown, B. M. et al. 2004. Distribution of eigenvalues in gaps of the essential spectrum of Sturm-Liouville operators - a numerical approach. Journal Of Computational Analysis And Applications 6 (1), pp.85-95.
- Schmidt, K. M. 2004. On the integrability of differential equations by quadratures according to Maximovič. Journal of Computational and Applied Mathematics 171 (1-2), pp.393-410. (10.1016/j.cam.2004.01.021)
2003
- Escott-Price, V. and Schmidt, K. M. 2003. Approximate projectors in singular spectrum analysis. SIAM Journal on Matrix Analysis and Applications (SIMAX) 24 (4), pp.932-942. (10.1137/S0895479801398967)
- Schmidt, K. M. 2003. Eigenvalue asymptotics of perturbed periodic Dirac systems in the slow-decay limit. Proceedings Of The American Mathematical Society 131 (4), pp.1205-1214.
- Schmidt, K. M. 2003. Spectral properties of Dirac systems with coefficients infinite at infinity. RIMS Kokyuroku 1315 , pp.24-31.
2002
- Schmidt, K. M. 2002. Eigenvalues in gaps of perturbed periodic Dirac operators: numerical evidence. Journal of Computational and Applied Mathematics 148 (1), pp.169-181. (10.1016/S0377-0427(02)00580-0)
- Schmidt, K. M. 2002. A short proof for Bargmann-type inequalities. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 458 (2027), pp.2829-2832. (10.1098/rspa.2002.1021)
2001
- Schmidt, K. M. 2001. A remark on a paper by Evans and Harris on the point spectra of Dirac operators. Proceedings Of The Royal Society Of Edinburgh Section A-Mathematics 131 (A), pp.1237-1243. (10.1017/S0308210500001360)
- Schmidt, K. M. 2001. An Application of Gesztesy–Simon–Teschl Oscillation Theory to a Problem in Differential Geometry. Journal of Mathematical Analysis and Applications 261 (1), pp.61-71. (10.1006/jmaa.2001.7471)
2000
- Schmidt, K. M. 2000. A Remark on The Essential Spectra of Dirac Systems. Bulletin of the London Mathematical Society 32 (1), pp.63-70. (10.1112/S0024609399006463)
- Schmidt, K. M. 2000. Critical Coupling Constants and Eigenvalue Asymptotics of Perturbed Periodic Sturm-Liouville Operators. Communications in Mathematical Physics 211 (2), pp.465-485. (10.1007/s002200050822)
- Schmidt, K. M. 2000. Relative Oscillation–Non-Oscillation Criteria for Perturbed Periodic Dirac Systems. Journal of Mathematical Analysis and Applications 246 (2), pp.591-607. (10.1006/jmaa.2000.6821)
1999
- Schmidt, K. M. 1999. Oscillation of the perturbed Hill equation and the lower spectrum of radially periodic Schrodinger operators in the plane. Proceedings of the American Mathematical Society 127 (8), pp.2367-2374.
1998
- Brown, B. M. et al. 1998. Welsh Eigenvalues of radially periodic Schrödinger operators. Journal of Mathematical Analysis and Applications 225 (1), pp.347-357. (10.1006/jmaa.1998.6048)
- Schmidt, K. M. and Yamada, O. 1998. Spherically symmetric dirac operators with variable mass and potentials infinite at infinity. Publications Of The Research Institute For Mathematical Sciences 34 (3), pp.211-227.
1997
- Schmidt, K. M. 1997. Absolutely continuous spectrum of Dirac systems with potentials infinite at infinity. Mathematical Proceedings of the Cambridge Philosophical Society 122 (2), pp.377-384.
1996
- Schmidt, K. M. 1996. Dense point spectrum for the one-dimensional Dirac operator with an electrostatic potential. Proceedings of the Royal Society of Edinburgh, Section: A Mathematics 126 (5), pp.1087-1096. (10.1017/S0308210500023271)
1995
- Schmidt, K. M. 1995. A remark on boundary value problems for the Dirac operator. Quarterly Journal of Mathematics 46 (184), pp.509-516.
- Schmidt, K. M. 1995. Dense point spectrum and absolutely continuous spectrum in spherically symmetric Dirac operators. Forum Mathematicum 7 (7), pp.459-475. (10.1515/form.1995.7.459)
1993
- Schmidt, K. M. 1993. On the essential spectrum of Dirac operators with spherically symmetric potentials. Mathematische Annalen 297 (1), pp.117-131. (10.1007/BF01459491)
- Schmidt, K. M. 1993. On the genericity of nonvanishing instability intervals in periodic Dirac systems. Annales De L'Institut Henri Poincare-Physique Theorique 59 (3), pp.315-326.
Adrannau llyfrau
- Brown, B. M. and Schmidt, K. M. 2012. On the HELP Inequality for Hill Operators on Trees. In: Brown, B. M. , Lang, J. and Wood, I. G. eds. Spectral Theory, Function Spaces and Inequalities: New Techniques and Recent Trends. Operator Theory: Advances and Applications Vol. 219.Basel: Springer. , pp.21-36. (10.1007/978-3-0348-0263-5_2)
Cynadleddau
- Schmidt, K. M. and Umeda, T. 2014. Spectral properties of massless Dirac operators with real-valued potentials. Presented at: Spectral and scattering theory and related topics Kyoto University, Japan 14-16 December 2011. RIMS Kôkyûroku Bessatsu B45: Spectral and Scattering Theory and Related Topics. Kyoto, Japan: , pp.25-30.
- Brown, B. M. , Langer, M. and Schmidt, K. M. 2008. The HELP inequality on trees. Presented at: Isaac Newton Institute for Mathematical Sciences Cambridge, UK 8 January - 29 June 2007. Published in: Exner, P. et al., Analysis on Graphs and Its Applications. Proceedings of Symposia in Pure Mathematics Vol. 77. Providence, RI: American Mathematical Society. , pp.337-354.
Erthyglau
- Yao, K. et al. 2026. 78. Joint modelling of polygenic risk and rare variants enhances liability-based disease prediction [Abstract]. European Neuropsychopharmacology 111 (Supple) 113105. (10.1016/j.euroneuro.2026.113105)
- Escott-Price, V. , Leonenko, G. and Schmidt, K. M. 2026. Positioning personal polygenic risk score against the population background. Research in Statistics 4 (1) 2685935. (10.1080/27684520.2026.2685935)
- Law, A. D. , Lettington, M. C. and Schmidt, K. M. 2025. Multifactorisations and divisor functions. UTILITAS MATHEMATICA 125 , pp.43-60. (10.61091/um125-03)
- Schmidt, K. M. and Umeda, T. 2025. On the resolvent convergence of discrete Dirac operators on 3D cubic lattices. Journal of Mathematical Analysis and Applications 546 (2) 129247. (10.1016/j.jmaa.2025.129247)
- Jameel, G. S. and Schmidt, K. M. 2025. Eigenvalue bounds for perturbed periodic Dirac operators. Journal of Spectral Theory 15 (3), pp.1279-1303. (10.4171/jst/556)
- Higham, N. J. , Lettington, M. C. and Schmidt, K. M. 2025. Symmetry decomposition and matrix multiplication. Linear Algebra and its Applications 710 , pp.310-335. (10.1016/j.laa.2025.01.041)
- Escott-Price, V. and Schmidt, K. M. 2023. Pitfalls of predicting age related traits by polygenic risk scores. Annals of Human Genetics 87 (5), pp.203-209. (10.1111/ahg.12520)
- Schmidt, K. M. and Umeda, T. 2023. Continuum limits for discrete Dirac operators on 2D square lattices. Analysis and Mathematical Physics 13 (46)(10.1007/s13324-023-00809-7)
- Simmonds, E. et al. 2023. What does heritability of Alzheimer’s disease represent?. PLoS ONE 18 (4) e0281440. (10.1371/journal.pone.0281440)
- Lettington, M. and Schmidt, K. 2023. On the sum of left and right circulant matrices. Linear Algebra and its Applications 658 , pp.62-85. (10.1016/j.laa.2022.10.024)
- Brown, B. M. et al. 2021. The inverse problem for a spectral asymmetry function of the Schrödinger operator on a finite interval. Mathematika 67 (4), pp.788-806. (10.1112/mtk.12105)
- Escott-Price, V. and Schmidt, K. M. 2021. Correction to: Probability of Alzheimer's disease based on common and rare genetic variants. Alzheimer's Research and Therapy 13 (1) 156. (10.1186/s13195-021-00898-1)
- Escott-Price, V. and Schmidt, K. M. 2021. Probability of Alzheimer’s disease based on common and rare genetic variants. Alzheimer's Research & Therapy 13 140. (10.1186/s13195-021-00884-7)
- Higham, N. J. , Lettington, M. C. and Schmidt, K. M. 2021. Integer matrix factorisations, superalgebras and the quadratic form obstruction. Linear Algebra and its Applications 622 , pp.250-267. (10.1016/j.laa.2021.03.028)
- Escott-Price, V. and Schmidt, K. M. 2021. Challenges of adjusting Single-Nucleotide Polymorphism effect sizes for linkage disequilibrium. Human Heredity 85 (1), pp.24-34. (10.1159/000513303)
- Lettington, M. C. and Schmidt, K. M. 2020. Divisor functions and the number of sum systems. Integers 20 A61.
- Hill, S. L. et al. 2020. Some properties and applications of non-trivial divisor functions. Ramanujan Journal 51 (10.1007/s11139-018-0093-9)
- Huxley, M. N. , Lettington, M. C. and Schmidt, K. M. 2019. On the structure of additive systems of integers. Periodica Mathematica Hungarica 78 , pp.178-199. (10.1007/s10998-018-00275-w)
- Phillips, T. R. L. , Schmidt, K. M. and Zhigljavsky, A. 2019. Extension of the Schoenberg theorem to integrally conditionally positive definite functions. Journal of Mathematical Analysis and Applications 470 (1), pp.659-678. (10.1016/j.jmaa.2018.10.032)
- Vivian-Griffiths, T. et al. 2019. Predictive modeling of schizophrenia from genomic data: Comparison of polygenic risk score with kernel support vector machines approach. American Journal of Medical Genetics Part B: Neuropsychiatric Genetics 180 (1), pp.80-85. (10.1002/ajmg.b.32705)
- Baker, E. et al. 2018. POLARIS: polygenic LD-adjusted risk score approach for set-based analysis of GWAS data. Genetic Epidemiology 42 (4), pp.366-377. (10.1002/gepi.22117)
- Hill, S. , Lettington, M. C. and Schmidt, K. M. 2018. Block representations and spectral properties of constant sum matrices. Electronic Journal of Linear Algebra 34 , pp.170-190. (10.13001/1081-3810.3530)
- Phillips, T. and Schmidt, K. M. 2018. On unbounded positive definite functions. Mathematica Pannonica 26 (2), pp.33-51.
- Lettington, M. C. , Schmidt, K. M. and Hill, S. 2017. On superalgebras of matrices with symmetry properties. Linear and Multilinear Algebra 66 (8), pp.1538-1563. (10.1080/03081087.2017.1363153)
- Vronskaya-Robl, M. and Schmidt, K. M. 2017. On perturbation stability of SSA and MSSA forecasts and the supportiveness of time series. Statistics and Its Interface 10 (1), pp.33-46.
- Schmidt, K. M. 2016. On the asymptotics of the spectral density of radial Dirac operators with divergent potential. Integral Equations and Operator Theory 85 , pp.137-149. (10.1007/s00020-015-2276-8)
- Schmidt, K. M. and Umeda, T. 2015. Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials. Letters in Mathematical Physics 105 , pp.1479-1497. (10.1007/s11005-015-0799-1)
- Brunnock, R. , Lettington, M. C. and Schmidt, K. M. 2014. On square roots and norms of matrices with symmetry properties. Linear Algebra and its Applications 459 , pp.175-207. (10.1016/j.laa.2014.06.054)
- Hughes, D. and Schmidt, K. M. 2014. Absolutely continuous spectrum of Dirac operators with square-integrable potentials. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144 (3), pp.533-555. (10.1017/S0308210512001187)
- Escott-Price, V. , Ghodsi, M. and Schmidt, K. M. 2014. How allele frequency and study design affect association test statistics with misrepresentation errors. Biostatistics 15 (2), pp.311-326. (10.1093/biostatistics/kxt048)
- Kerfriden, P. et al. 2013. Statistical extraction of process zones and representative subspaces in fracture of random composites. International Journal for Multiscale Computational Engineering 11 (3), pp.253-287. (10.1615/IntJMultCompEng.2013005939)
- Schmidt, K. M. and Zhigljavsky, A. A. 2013. An extremal property of the generalized arcsine distribution. Metrika 76 (3), pp.347-355. (10.1007/s00184-012-0391-y)
- Escott-Price, V. et al. 2012. Permutation-based approaches do not adequately allow for linkage disequilibrium in gene-wide multi-locus association analysis. European Journal of Human Genetics 20 (8), pp.890-896. (10.1038/ejhg.2012.8)
- Korotyaev, E. L. and Schmidt, K. M. 2011. On the resonances and eigenvalues for a 1D half-crystal with localised impurity. Journal für die reine und angewandte Mathematik (Crelles Journal) 2012 (670), pp.217-248. (10.1515/CRELLE.2011.153)
- Schmidt, K. M. 2010. Spectral properties of rotationally symmetric massless dirac operators. Letters in Mathematical Physics 92 (3), pp.231-241. (10.1007/s11005-010-0393-5)
- Brown, B. M. , Christiansen, J. S. and Schmidt, K. M. 2009. Spectral properties of a q-Sturm–Liouville Operator. Communications in Mathematical Physics 287 (1), pp.259-274. (10.1007/s00220-008-0623-1)
- Evans, W. D. and Schmidt, K. M. 2009. A discrete Hardy-Laptev-Weidl type inequality and associated Schrödinger-type operators. Revista Matemática Complutense 22 (1), pp.75-90.
- Schmidt, K. M. and Zhigljavsky, A. A. 2009. A characterization of the arcsine distribution. Statistics & Probability Letters 79 (24), pp.2451-2455. (10.1016/j.spl.2009.08.018)
- Escott-Price, V. and Schmidt, K. M. 2008. On multiple-testing correction in genome-wide association studies. Genetic Epidemiology 32 (6), pp.567-573. (10.1002/gepi.20331)
- Aumann, S. , Brown, B. M. and Schmidt, K. M. 2008. A Hardy-Littlewood-type inequality for the p-Laplacian. Bulletin of the London Mathematical Society 40 (3), pp.525-531. (10.1112/blms/bdn035)
- Eastham, M. S. P. and Schmidt, K. M. 2008. Asymptotics of the spectral density for radial dirac operators with divergent potentials. Publications of the Research Institute for Mathematical Sciences 44 (1), pp.107-129. (10.2977/prims/1207921078)
- Monaquel, S. J. and Schmidt, K. M. 2007. On M-functions and operator theory for non-self-adjoint discrete Hamiltonian systems. Journal of Computational and Applied Mathematics 208 (1), pp.82-101. (10.1016/j.cam.2006.10.043)
- Schmidt, K. M. 2006. Exceptional coupling constants for the Coulomb-Dirac operator with anomalous magnetic moment. Journal of Computational and Applied Mathematics 194 (1), pp.17-25. (10.1016/j.cam.2005.06.022)
- Escott-Price, V. and Schmidt, K. M. 2006. Individual SNP Allele Reconstruction from Informative Markers Selected by a Non-Linear Gauss-Type Algorithm. Human Heredity 62 (2), pp.97-106. (10.1159/000096097)
- Escott-Price, V. and Schmidt, K. M. 2006. Susceptibility of Biallelic Haplotype and Genotype Frequencies to Genotyping Error. Biometrics 62 (4), pp.1116-1123. (10.1111/j.1541-0420.2006.00563.x)
- Eastham, M. S. P. and Schmidt, K. M. 2005. Absence of high-energy spectral concentration for Dirac systems with divergent potentials. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 135 (4), pp.689-702. (10.1017/S0308210500004078)
- Escott-Price, V. et al. 2005. Design of Case-controls Studies with Unscreened Controls. Annals of Human Genetics 69 (5), pp.566-576. (10.1111/j.1529-8817.2005.00175.x)
- Kalf, H. and Schmidt, K. M. 2004. Spectral stability of the Coulomb-Dirac Hamiltonian with anomalous magnetic moment. Journal of Differential Equations 205 (2), pp.408-423. (10.1016/j.jde.2004.04.009)
- Brown, B. M. et al. 2004. Distribution of eigenvalues in gaps of the essential spectrum of Sturm-Liouville operators - a numerical approach. Journal Of Computational Analysis And Applications 6 (1), pp.85-95.
- Schmidt, K. M. 2004. On the integrability of differential equations by quadratures according to Maximovič. Journal of Computational and Applied Mathematics 171 (1-2), pp.393-410. (10.1016/j.cam.2004.01.021)
- Escott-Price, V. and Schmidt, K. M. 2003. Approximate projectors in singular spectrum analysis. SIAM Journal on Matrix Analysis and Applications (SIMAX) 24 (4), pp.932-942. (10.1137/S0895479801398967)
- Schmidt, K. M. 2003. Eigenvalue asymptotics of perturbed periodic Dirac systems in the slow-decay limit. Proceedings Of The American Mathematical Society 131 (4), pp.1205-1214.
- Schmidt, K. M. 2003. Spectral properties of Dirac systems with coefficients infinite at infinity. RIMS Kokyuroku 1315 , pp.24-31.
- Schmidt, K. M. 2002. Eigenvalues in gaps of perturbed periodic Dirac operators: numerical evidence. Journal of Computational and Applied Mathematics 148 (1), pp.169-181. (10.1016/S0377-0427(02)00580-0)
- Schmidt, K. M. 2002. A short proof for Bargmann-type inequalities. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 458 (2027), pp.2829-2832. (10.1098/rspa.2002.1021)
- Schmidt, K. M. 2001. A remark on a paper by Evans and Harris on the point spectra of Dirac operators. Proceedings Of The Royal Society Of Edinburgh Section A-Mathematics 131 (A), pp.1237-1243. (10.1017/S0308210500001360)
- Schmidt, K. M. 2001. An Application of Gesztesy–Simon–Teschl Oscillation Theory to a Problem in Differential Geometry. Journal of Mathematical Analysis and Applications 261 (1), pp.61-71. (10.1006/jmaa.2001.7471)
- Schmidt, K. M. 2000. A Remark on The Essential Spectra of Dirac Systems. Bulletin of the London Mathematical Society 32 (1), pp.63-70. (10.1112/S0024609399006463)
- Schmidt, K. M. 2000. Critical Coupling Constants and Eigenvalue Asymptotics of Perturbed Periodic Sturm-Liouville Operators. Communications in Mathematical Physics 211 (2), pp.465-485. (10.1007/s002200050822)
- Schmidt, K. M. 2000. Relative Oscillation–Non-Oscillation Criteria for Perturbed Periodic Dirac Systems. Journal of Mathematical Analysis and Applications 246 (2), pp.591-607. (10.1006/jmaa.2000.6821)
- Schmidt, K. M. 1999. Oscillation of the perturbed Hill equation and the lower spectrum of radially periodic Schrodinger operators in the plane. Proceedings of the American Mathematical Society 127 (8), pp.2367-2374.
- Brown, B. M. et al. 1998. Welsh Eigenvalues of radially periodic Schrödinger operators. Journal of Mathematical Analysis and Applications 225 (1), pp.347-357. (10.1006/jmaa.1998.6048)
- Schmidt, K. M. and Yamada, O. 1998. Spherically symmetric dirac operators with variable mass and potentials infinite at infinity. Publications Of The Research Institute For Mathematical Sciences 34 (3), pp.211-227.
- Schmidt, K. M. 1997. Absolutely continuous spectrum of Dirac systems with potentials infinite at infinity. Mathematical Proceedings of the Cambridge Philosophical Society 122 (2), pp.377-384.
- Schmidt, K. M. 1996. Dense point spectrum for the one-dimensional Dirac operator with an electrostatic potential. Proceedings of the Royal Society of Edinburgh, Section: A Mathematics 126 (5), pp.1087-1096. (10.1017/S0308210500023271)
- Schmidt, K. M. 1995. A remark on boundary value problems for the Dirac operator. Quarterly Journal of Mathematics 46 (184), pp.509-516.
- Schmidt, K. M. 1995. Dense point spectrum and absolutely continuous spectrum in spherically symmetric Dirac operators. Forum Mathematicum 7 (7), pp.459-475. (10.1515/form.1995.7.459)
- Schmidt, K. M. 1993. On the essential spectrum of Dirac operators with spherically symmetric potentials. Mathematische Annalen 297 (1), pp.117-131. (10.1007/BF01459491)
- Schmidt, K. M. 1993. On the genericity of nonvanishing instability intervals in periodic Dirac systems. Annales De L'Institut Henri Poincare-Physique Theorique 59 (3), pp.315-326.
Llyfrau
- Brown, B. M. , Eastham, M. S. P. and Schmidt, K. M. 2013. Periodic differential operators. Operator Theory: Advances and Applications Vol. 230Basel: Birkhäuser.
Ymchwil
Ar ôl dechrau fy mywyd academaidd mewn ffiseg fathemategol, yn benodol mewn mecaneg cwantwm, rwyf wedi datblygu diddordebau ymchwil mewn amrywiaeth o feysydd mathemateg. Os oes thema gyffredin, bydd yn ddadansoddiad sbectrol - datgloi'r wybodaeth sydd wedi'i guddio yn eigenvalues a phriodweddau sbectrol mwy cyffredinol matricsau a gweithredwyr llinol.
Theori sbectrol
Mae gen i ddiddordeb mewn dadansoddi priodweddau gweithredwyr llinol, gweithredwyr differol fel arfer - megis gweithredwyr Schrödinger a Dirac o fecaneg cwantwm a gweithredwyr eraill ffiseg fathemategol -, gweithredwyr integrol a matricsau anfeidrol, gan gyfuno cysyniadau pwerus dadansoddiad swyddogaethol a theori gweithredwyr gyda'r astudiaeth fwy technegol o hafaliadau differol, yn enwedig priodweddau ansoddol ac asymptotig eu datrysiadau (nad ydynt fel arfer yn hygyrch mewn ffurf benodol), a gyda dadansoddiad mathemategol cyffredinol.
Ystadegau aml-amrywiol
Rwy'n dod â fy ngwybodaeth o ddadansoddi mathemategol i wahanol gymwysiadau yn yr astudiaeth o ddata real. Un maes o'r fath yw dadansoddi sbectrwm unigol, dull o ddadansoddi cyfres amser sy'n seiliedig ar ddadelfennu gwerth unigol matricsau cysylltiedig.
Mewn cydweithrediad hirsefydlog â'r Athro Valentina Escott-Price, rwy'n cyfrannu at y defnydd o dechnegau mathemategol mewn geneteg feddygol, gan ddatblygu dulliau newydd o ddadansoddi data ystadegol cydberthynol mewn setiau data mawr iawn a dimensiwn uchel a herio methodoleg bresennol yn y maes.
Theori rhifau cyfunol ac algebra llinol
Gyda Dr Matthew Lettington, rwy'n astudio dadelfennu cymesuredd matricsau a chwestiynau dilynol o gyfuniad ychwanegion, ffwythiannau rhannwr cyffredinol a chyfresi Dirichlet cyfatebol.
Grŵp ymchwil
Addysgu
Israddedig / ôl-raddedig a addysgir - semester yr hydref
- MA4010 / MAT020 Theori a Chymwysiadau Sbectrol
Israddedig - semester y gwanwyn
- MA3005 Dadansoddiad Swyddogaethol a Fourier
Lefel ymchwil ôl-raddedig - semester yr hydref
- MAGIC057 Theori Sbectrol Gweithredwyr Differol Cyffredin
Bywgraffiad
Cymwysterau
- 1990 Dipl. phys. (Ludwig-Maximilians-Universität München)
- 1992 Dr. rer. nat. (Ludwig-Maximilians-Universität München)
- 1999 Habilitation (Ludwig-Maximilians-Universität München)
Swyddi academaidd
- 1992 - 1993 Cymrawd ymchwil (Mathematisches Institut, LMU München)
- 1993 - 2000 Darlithydd (Mathematisches Institut, LMU München)
- 1994 - 1995 Cydymaith Gwadd (Adran Mathemateg, Sefydliad Technoleg California, Pasadena)
- 2000 - 2003 Darlithydd (Ysgol Mathemateg, Caerdydd)
- 2003 - 2009 Uwch Ddarlithydd (Ysgol Mathemateg, Caerdydd)
- 2009 - 2017 Darllenydd (Ysgol Mathemateg, Caerdydd)
- 2017 - presennol Athro (Ysgol/Adran Mathemateg, Caerdydd)
Anrhydeddau
- 2020 Cymrawd Etholedig Cymdeithas Ddysgedig Cymru
Meysydd goruchwyliaeth
Goruchwyliaeth gyfredol
Prosiectau'r gorffennol
- S Monaquel (cyd-oruchwyliaeth gyda W D Evans) - Rhai Problemau sy'n Gysylltiedig â Hafaliadau Differol a Gwahaniaeth, PhD 2004
- S Aumann (cyd-oruchwyliaeth gyda B M Brown) - Anghydraddoldeb Math Hardy-Littlewood i'r p-Laplacian, MPhil 2007
- M Ghodsi (goruchwyliaeth ar y cyd â V Moskvina) - Dadansoddiad o Brosesau Deinamig ar gyfer Asesu Prawf mewn Geneteg Feddygol, PhD 2012
- D Hughes - Dadansoddiad Sbectrol o Weithredwyr Dirac o dan Amodau Integradwyedd, PhD 2012
- M Vronskaya (goruchwyliaeth ar y cyd ag A Zhigljavsky) - Sefydlogrwydd Dadansoddiad Sbectrwm Unigol ac Achosoldeb mewn Cyfres Amser, PhD 2014
- S Hill (goruchwyliaeth ar y cyd â M C Lettington) - Problemau sy'n gysylltiedig â Theori Rhif: Systemau Swm a Phellter, Matricsau Sgwariau Cildroadwy a Ffwythiannau Divisor, PhD 2018
- E Baker (ar y cyd â V Escott-Price (prif oruchwylydd) et al, MEDIC) - Ymchwilio i Strategaethau Newydd ar gyfer Nodi Mecanweithiau Achosol mewn Clefyd Alzheimer Cymryd Dulliau Biowybodeg y Tu Hwnt i GWAS, PhD 2018
- T Phillips (goruchwyliaeth ar y cyd ag A Zhigljavsky) - Ar Ffwythiannau Pendant Cadarnhaol ac Amodol Negyddol gyda Singularity yn Sero, a'u Cymwysiadau mewn Theori Potensial, PhD 2018
- M Lewis (goruchwyliaeth ar y cyd â K Cherednichenko, Caerfaddon) - Sefydlogrwydd Datrysiadau Hafaliad p-Laplace Un-dimensiwn gyda Photensial Cyfnodol, PhD 2019
- Cyfraith (goruchwyliaeth ar y cyd â M C Lettington) - Ar bynciau sy'n gysylltiedig â systemau swm, PhD 2023
- G S Jameel - Dadansoddiad Cymhleth o Weithredwyr Differol nad ydynt yn Hunan-Hunangysylltiol, PhD 2026
Contact Details
[email protected]
+44 29208 76778
Abacws, Ystafell 2.18, Ffordd Senghennydd, Cathays, Caerdydd, CF24 4AG
+44 29208 76778
Abacws, Ystafell 2.18, Ffordd Senghennydd, Cathays, Caerdydd, CF24 4AG