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Number of items: 57.

Phillips, Tomos, Schmidt, Karl and Zhigljavsky, Anatoly 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
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Vivian-Griffiths, Timothy, Baker, Emily, Schmidt, Karl M., Bracher-Smith, Matthew, Walters, James, Artemiou, Andreas, Holmans, Peter, O'Donovan, Michael C., Owen, Michael J., Pocklington, Andrew and Escott-Price, Valentina 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

Lettington, Matthew, Schmidt, Karl, Huxley, Martin Neil and Hill, Sally 2019. Some properties and applications of non-trivial divisor functions. Ramanujan Journal 10.1007/s11139-018-0093-9

Huxley, Martin, Lettington, Matthew and Schmidt, Karl Michael 2018. On the structure of additive systems of integers. Periodica Mathematica Hungarica 10.1007/s10998-018-00275-w

Baker, Emily, Schmidt, Karl Michael, Sims, Rebecca, O'Donovan, Michael C., Williams, Julie, Holmans, Peter and Escott-Price, Valentina 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, Sally, Lettington, Matthew C. and Schmidt, Karl Michael 2018. Block representations and spectral properties of constant sum matrices. Electronic Journal of Linear Algebra 34 , pp. 170-190. 10.13001/1081-3810,1537-9582.3530

Phillips, Tomos and Schmidt, Karl Michael 2018. On unbounded positive definite functions. Mathematica Pannonica

Lettington, Matthew C., Schmidt, Karl Michael and Hill, Sally 2017. On superalgebras of matrices with symmetry properties. Linear and Multilinear Algebra 66 (8) , pp. 1538-1563. 10.1080/03081087.2017.1363153

Vronskaya-Robl, Maria and Schmidt, Karl Michael 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, Karl Michael 2016. On the asymptotics of the spectral density of radial Dirac operators with divergent potential. Integral Equations and Operator Theory 85 (1) , pp. 137-149. 10.1007/s00020-015-2276-8

Schmidt, Karl Michael and Umeda, Tomio 2015. Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials. Letters in Mathematical Physics 105 (11) , pp. 1479-1497. 10.1007/s11005-015-0799-1

Brunnock, Rochelle, Lettington, Matthew C. and Schmidt, Karl Michael 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, Daniel and Schmidt, Karl Michael 2014. Absolutely continuous spectrum of Dirac operators with square-integrable potentials. Proceedings of the Royal Society of Edinburgh, Section: A Mathematics 144 (03) , pp. 533-555. 10.1017/S0308210512001187

Escott-Price, Valentina, Ghodsi, Mansoureh and Schmidt, Karl Michael 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, Karl Michael and Umeda, Tomio 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: Research Institute for Mathematical Sciences, Kyoto University, pp. 25-30.

Schmidt, Karl Michael and Zhigljavsky, Anatoly Alexandrovich 2013. An extremal property of the generalized arcsine distribution. Metrika 76 (3) , pp. 347-355. 10.1007/s00184-012-0391-y

Kerfriden, Pierre, Schmidt, Karl Michael, Rabczuk, T. and Bordas, Stephane Pierre Alain 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

Brown, Brian Malcolm, Eastham, Michael S. P. and Schmidt, Karl Michael 2013. Periodic differential operators. Operator Theory: Advances and Applications, vol. 230. Basel: Birkhäuser.

Escott-Price, Valentina, Schmidt, Karl Michael, Vedernikov, Alexey, Owen, Michael John, Craddock, Nicholas John, Holmans, Peter Alan and O'Donovan, Michael Conlon 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

Brown, Brian Malcolm and Schmidt, Karl Michael 2012. On the HELP Inequality for Hill Operators on Trees. In: Brown, Brian Malcolm, Lang, Jan and Wood, Ian 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)

Korotyaev, Evgeny L. and Schmidt, Karl Michael 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, Karl Michael 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, Brian Malcolm, Christiansen, Jacob S. and Schmidt, Karl Michael 2009. Spectral properties of a q-Sturm–Liouville Operator. Communications in Mathematical Physics 287 (1) , pp. 259-274. 10.1007/s00220-008-0623-1

Schmidt, Karl Michael and Zhigljavsky, Anatoly Alexandrovich 2009. A characterization of the arcsine distribution. Statistics & Probability Letters 79 (24) , pp. 2451-2455. 10.1016/j.spl.2009.08.018

Evans, William Desmond and Schmidt, Karl Michael 2009. A discrete Hardy-Laptev-Weidl type inequality and associated Schrödinger-type operators. Revista Matemática Complutense 22 (1) , pp. 75-90.

Escott-Price, Valentina and Schmidt, Karl Michael 2008. On multiple-testing correction in genome-wide association studies. Genetic Epidemiology 32 (6) , pp. 567-573. 10.1002/gepi.20331

Aumann, S., Brown, Brian Malcolm and Schmidt, Karl Michael 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, Brian Malcolm, Langer, M. and Schmidt, Karl Michael 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., Keating, J. P., Kuchment, P. A., Sunada, T. and Teplyaev, A. eds. Analysis on Graphs and Its Applications. Proceedings of Symposia in Pure Mathematics , vol. 77. Providence, RI: American Mathematical Society, pp. 337-354.

Eastham, Michael S. P. and Schmidt, Karl Michael 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, Karl Michael 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, Karl Michael 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, Valentina and Schmidt, Karl Michael 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

Escott-Price, Valentina and Schmidt, Karl Michael 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

Eastham, Michael S. P. and Schmidt, Karl Michael 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, Valentina, Holmans, Peter Alan, Schmidt, Karl Michael and Craddock, Nicholas John 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, Hubert and Schmidt, Karl Michael 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, Brian Malcolm, Eastham, Michael S. P., Hinz, Andreas M. and Schmidt, Karl Michael 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, Karl Michael 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

Schmidt, Karl Michael 2003. Spectral properties of Dirac systems with coefficients infinite at infinity. RIMS Kokyuroku 1315 , pp. 24-31.

Escott-Price, Valentina and Schmidt, Karl Michael 2003. Approximate projectors in singular spectrum analysis. SIAM Journal on Matrix Analysis and Applications (SIMAX) 24 (4) , pp. 932-942. 10.1137/S0895479801398967

Schmidt, Karl Michael 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, Karl Michael 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, Karl Michael 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, Karl Michael 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, Karl Michael 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, Karl Michael 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, Karl Michael 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, Karl Michael 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, Karl Michael 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.

Schmidt, Karl Michael and Yamada, Osanobu 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.

Brown, Brian Malcolm, Eastham, M. S. P., Hinz, A. M., Kriecherbauer, Thomas, McCormack, Daniel K. R. and Schmidt, Karl Michael 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, Karl Michael 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, Karl Michael 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, Karl Michael 1995. A remark on boundary value problems for the Dirac operator. Quarterly Journal of Mathematics 46 (184) , pp. 509-516.

Schmidt, Karl Michael 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, Karl Michael 1993. On the essential spectrum of Dirac operators with spherically symmetric potentials. Mathematische Annalen 297 (1) , pp. 117-131. 10.1007/BF01459491

Schmidt, Karl Michael 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.

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