extended abstracts 1999 - 2007 written for Mathematical Reviews (review journal of AMS) 28. 12. 2007 lip brat Krylova oboustr. ( here in pdf and here in pdf, zipped) 28. 12. 2007 symmetry inherited for fine mesh ( here in pdf and here in pdf, zipped) 9. 11. 2007 quaternionic matrices ( here in pdf and here in pdf, zipped) 16. 10. 2007 t-dep pseudo H ( here in pdf and here in pdf, zipped) 2. 10. 2007 QR(3) PDM in SIGMA ( here in pdf and here in pdf, zipped) 1. 10. 2007 one-state QES 3-body, separabilized ( here in pdf and here in pdf, zipped) 23. 8. 2007 (gen.) Krylov orthogonalized ( here in pdf and here in pdf, zipped) 18. 8. 2007 PT Hulthen KG ( here in pdf) 30. 7. 2007 hle nove PT dejiny 2 x 2 (Grass. CS) ( here in pdf) 30. 7. 2007 Poeschl Dirac blabol ( here in pdf) 30. 7. 2007 Morse Dirac Riccati ( here in pdf) 30. 6. 2007 path for -x^4 ( here in pdf) 25. 6. 2007 ix ( here in pdf) 14. 5. 2007 zamena base v differencnich rov. ( here in pdf) 19. 4. 2007 YM diagon. ( here in pdf) 26. 2. 2007 matrix cont. fractions ( here in pdf) 23. 2. 2007 Ali M. on delta ( here in pdf) 12. 2. 2007 Frieder on product ( here in pdf) 12. 2. 2007 Levai on scarfs ( here in pdf) 12. 2. 2007 Cannata and Ventura on scattering ( here in pdf) 8. 2. 20067 Ali Mostafazadeh on weak pseudo-Hermiticity ( here in pdf) 5. 12. 2006 Sokolov, Andrianova and Cannata on self-orthogonality ( here in pdf) 27. 11. 2006 Geza Levai on Scarf I ( here in pdf) 27. 11. 2006 Mondragon et al on EP (unbound states) ( here in pdf) 14. 11. 2006 Zafar Ahmed on WKB ( here in pdf) 13. 11. 2006 Fei on integrability ( here in pdf) 25. 5. 2006 next iter. conv. 15. 5. 2006 diag. tridiag. matr. 11. 5. 2006 diag. large matr. ( here in pdf) 3. 4. 2006 Solve ODE (reson.)? HEG! ( here in pdf) 3. 4. 2006 Solve OD-DE? Insert Taylor ansatz! ( here in pdf) 3. 3. 2006 WKB, PT-way ( here in pdf) 2. 1. 2006 ekvidiskretizace Laplac. ( here in pdf) 22. 12. 2005 A t-dep. PT-sym." Ham. ( here in pdf) 20. 12. 2005 A t-dep. PT-sym." Ham. ( here in pdf) 20. 12. 2005 recurrences made stable by rotation ( here in pdf) 30. 11. 2005 crazy diagon. ( here in pdf) 3. 11. 2005 Hulthen Diracque ( here in pdf) 4. 10. 2005 Newton for more var. ( here in pdf) 5. 9. 2005 Tomio: delta multiprime ( here in pdf) 5. 9. 2005 Leach in Greece: correct BCs for HO ( here in pdf) 5. 9. 2005 Voros in Japan: zeta for pert. ( here in pdf) 27. 7. 2005 rozdil stop ( here in pdf) 1. 6. 2005 imkub a Swans. by Hugh ( here in pdf) 27. 5. 2005 Dirac Woods Saxon ( here in pdf) 26. 5. 2005 singularity a la Lie (PGL) ( here in pdf) 19. 5. 2005 singularity a la Lie (PGL, ctd.) ( here in pdf) 12. 5. 2005 order of smallness of densities (d=2) ( here in pdf) 25. 4. 2005 E-reality for V ~ x^{4r+2}+igx^{2r-1} ( here in pdf) 21. 4. 2005 Barbanis potential, class. and quant. chaos ( here in pdf) 18. 4. 2005 x-dependent mass for W II ( here in pdf) 25. 3. 2005 PT symmetry, Weigert's (=classical) way in pdf 17. 3. 2005 SUSY PT Levai in pdf 1. 3. 2005 m-polynomial Heisenberg algebra ( here in pdf) 1. 3. 2005 Liouville-Green trig. ( here in pdf) 5. 2. 2005 PT band spectrum, solvable model 5. 2. 2005 re-factorization (I = T/T) in susy qm 5. I. 2005 erroneous exact solution ( here and ( here in pdf) 23. XII. 2004 KG (A. M.) for Burdik ( here in pdf - older) ( here in pdf - newer) 2. XI. 2004 Schroedinger with fractional time derivative ( here in pdf) 31. 8. 2004 V=1/x^2 discretely ( here in pdf) 23. 8. 2004 energy dependence 19. 8. 2004 vectorial continued fractions ( here in pdf) 20. 7. 2004 exceptional points for pendula ( here in pdf) 24. 6. 2004 discrete Volterra periodic ( here in pdf) 31. 5. 2004 pseudounitary Ali 13. 5. 2004 CF's ( here in pdf) 6. 4. 2004 DFT ( here in pdf) 16. 2. 2004 diskr. Green ( here in pdf) 5. 1. 2004 nelin. podgonka (in pdf - and in ps) 5. 1. 2004 delta prime (in pdf - and in ps) 12. 9. 2003, A times v: having both negative and positive components 3. 6. 2003, re-Hermitization via new scalar product (corrected) 28. 5. 2003, PT symmetric Henon Heiles II (also in pdf) 28. 5. 2003, matrix continued fractions for square roots (also in pdf) 5. 5. 2003, existence of solutions for special 2D Hartree Fock 20. 3. 2003, CNO: 1946969 Kaushal, R. S. ; Parthasarathi : "Quantum mechanics of complex Hamiltonian systems in one dimension" J. Phys. A 35 (2002), no. 41, 8743--8761. 19. 2. 2003, CNO: 1934444 Edwards, John T. ; Ford, Neville J. : "Boundedness and stability of solutions to difference equations. " J. Comput. Appl. Math. 140 (2002), no. 1-2, 275--289 [Proceedings of the 9th International Congress on Computational and Applied Mathematics (Leuven, 2000)]. 19. 2. 2003, CNO: 1940450 Mostafazadeh, Ali: "Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians" J. Math. Phys. 43 (2002), no. 12, 6343--6352. 3. 2. 2003, CNO: 1937098 Scolarici, G. ; Solombrino, L. : "Pseudo-Hermitian Hamiltonians, time-reversal invariance and Kramers degeneracy. " Phys. Lett. A 303 (2002), no. 4, 239--242. 3. 2. 2003, CNO: 1936965 Mostafazadeh, Ali: "On the pseudo-Hermiticity of a class of PT-symmetric Hamiltonians in one dimension." Modern Phys. Lett. A 17 (2002), no. 30, 1973--1977. 3. 2. 2003, CNO: 1937095 Dmitrieva, L. A. ; Pyatkin, D. A.: "Elliptic finite-gap densities of the polar operator." Phys. Lett. A 303 (2002), no. 1, 37--44 16. 1. 2003, CNO: 1921181 Buslaeva, S. F.: "On Perron's theorem for compositions of linear-fractional transformations." (in Russian) in Teor. Nablizh. funkc. Zast.", Pracy Inst. Mat. Nats. Akad. Nauk Ukr. 31 (2000) 65--71 13. 12. 2002, CNO: 1927992 Bagchi, B. ; Quesne, C.: "Pseudo-Hermiticity, weak pseudo-Hermiticity and $\eta$-orthogonality condition." Phys. Lett. A 301 (2002), no. 3-4, 173--176. 5. 12. 2002, CNO: 1928019 Jia, Chun-Sheng ; Li, Shu-Chuan ; Li, Yun ; Sun, Liang-Tian: "Pseudo-Hermitian potential models with PT symmetry" Phys. Lett. A 300 (2002), no. 2-3, 115--121. 2. 12. 2002, CNO: 1928032 Lévai, G. ; Cannata, F. ; Ventura, A.: "PT symmetry breaking and explicit expressions for the pseudo-norm in the Scarf II potential." Phys. Lett. A 300 (2002), no. 2-3, 271--281. 2. 12. 2002, CNO: 1927440 Bagchi, B. ; Quesne, C.: "Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework" Phys. Lett. A 300 (2002), no. 1, 18--26. 6. 11. 2002, CNO: 1923128 Ahmed, Zafar: "Pseudo-Hermiticity of Hamiltonians under gauge-like transformation: real spectrum of non-Hermitian Hamiltonians." Phys. Lett. A 294 (2002), no. 5-6, 287--291. 4. 10. 2002, CNO: 1916363 Lévai, G. ; Cannata, F. ; Ventura, A.: "PT-symmetric potentials and the so(2,2) algebra." J. Phys. A 35 (2002), no. 24, 5041--5057. 27. 9. 2002, CNO: 1886432 Kéri, Gerzson: "The Sherman-Morrison formula for the determinant and its application for optimizing quadratic functions on condition sets given by extreme generators." Optimization theory (Mátraháza, 1999), 119--138, Appl. Optim., 59, Kluwer Acad. Publ., Dordrecht, 2001. 27. 9. 2002, CNO: 1914178 Choi, Jeong-Ryeol; Zhang, Shou: "Thermodynamics of the standard quantum harmonic oscillator of time-dependent frequency with and without inverse quadratic potential." J. Phys. A 35 (2002), no. 12, 2845--2855. 4. 9. 2002, CNO: 1910625 Miyazaki, Mitoshi; Tsutsui, Izumi: "Quantum tunneling and caustics under inverse square potential." Ann. Physics 299 (2002), no. 1, 78--87. 4. 9. 2002, CNO: 1904984 Albeverio, Sergio; Fei, Shao-Ming; Kurasov, Pavel: "Point interactions: PT-Hermiticity and reality of the spectrum." Lett. Math. Phys. 59 (2002), no. 3, 227--242. 21. 8. 2002, CNO: 1891813 Jafarpour, Mojtaba; Afshar, Davood: "Calculation of energy eigenvalues for the quantum anharmonic oscillator with a polynomial potential." J. Phys. A 35 (2002), no. 1, 87--92. 4. 7. 2002, CNO: 1876174 Xu, Xiu-wei; Zhang, Yong-de; Hou, Guang: "General solution for multi-dimensional time-dependent coupled quantum oscillator." Nuovo Cimento Soc. Ital. Fis. B (12) 116 (2001), no. 6, 713--718. 4. 7. 2002, CNO: 1866593 Dorodnitsyn, Vladimir: "Noether-type theorems for difference equations." Appl. Numer. Math. (special issue: Themes in geometric integration) 39 (2001), no. 3-4, 307--321. 17. 4. 2002, CNO: 1872877 Kaushal, R. S.: "On the quantum mechanics of complex Hamiltonian systems in one dimension." J. Phys. A 34 (2001), no. 49, L709--L714. 12. 4. 2002, CNO: 1876902 Mondal, Chandan Kumar; Maji, Kaushik; Bhattacharyya, S. P. : "On the eigenvalues and dynamics of non-Hermitian PT symmetric Hamiltonians in finite basis spaces." Phys. Lett. A 291 (2001), no. 4-5, 203--207. 20. 3. 2002, CNO: 1873185 Handy, C. R.; Wang, Xiao Qian: Extension of a spectral bounding method to complex rotated Hamiltonians, with application to $p\sp 2-ix\sp 3$. " J. Phys. A 34 (2001), no. 40, 8297--8307. 20. 2. 2002, CNO: 1855381 Handy, C. R.: Generating converging bounds to the (complex) discrete states of the $P\sp 2+iX\sp 3+i\alpha X$ Hamiltonian." J. Phys. A 34 (2001), no. 24, 5065--5081. 20. 2. 2002, CNO: 1862637 Trzaska, Zdzislaw W.: On discrepancies between solutions to discrete models for hyperbolic systems of conservation laws: continued fractions approach." Commun. Anal. Theory Contin. Fract. 9 (2001), 76--88. 29. 1. 2002, CNO: 1863255 Yeon, Kyu-Hwang; Kim, Suk-Sung; Moon, Young-Mo; Hong, Suc-Kyoung; Um, Chung-In; George, Thomas F.: The quantum under-, critical- and over-damped driven harmonic oscillators." J. Phys. A 34 (2001), no. 37, 7719--7732. 7. 1. 2002, CNO: 1862079 Bagchi, B., Mallik, S., Quesne, C. and Roychoudhury, R.: A PT symmetric QES partner to the Khare-Mandal potential." Phys. Lett. A 289 (2001) 34 - 38. 4. 12. 2001, CNO: 1686010 Buslaev, V. I.: On Poincaré's theorem and its applications to problems of the convergence of continued fractions." (Russian) Mat. Sb. 189 (1998), no. 12, 13--28; translation in Sb. Math. 189 (1998), no. 11-12, 1749--1764. 2. 10. 2001, CNO: 1837992 Huy, Nguyen Thieu; Minh, Nguyen Van: Exponential dichotomy of difference equations and applications to evolution equations on the half-line."" Advances in difference equations, III. Comput. Math. Appl. 42 (2001), no. 3-5, 301--311. 10. 9. 2001, CNO: 1833986 Aptekarev, A. I.; Kastro Smirnova, M. : Convergence of vector Stieltjes continued fractions. (Russian)" Dokl. Akad. Nauk 375 (2000), no. 6, 727--729. 22. 8. 2001, CNO: 1826028 Lévai, G.; Cannata, F.; Ventura, A. : Algebraic and scattering aspects of a $\scr{PT}$-symmetric solvable potential." J. Phys. A 34 (2001), no. 4, 839--844. 22.8.. 2001, CNO: 1826875 Kaushal, R. S.:  Quantum analogue of Ermakov systems and the phase of the quantum wave function." Internat. J. Theoret. Phys. 40 (2001), no. 4, 835--847. 21. 6. 2001, CNO: 1815225 Dhillon, H. S.; Kusmartsev, F. V.; Kürten, K. E.: Fractal and chaotic solutions of the discrete nonlinear Schrödinger equation in classical and quantum systems" J. Nonlinear Math. Phys. 8 (2001), no. 1, 38--49. 13. 6. 2001, CNO: 1798005 de Castro, Antonio Soares; Franklin, Jerrold: Exact solutions of the Dirac equation for modified Coulombic potentials" Internat. J. Modern Phys. A 15 (2000), no. 27, 4355--4360. 14. 5. 2001, CNO: 1805176 Abramov, S. A.; Barkatou, M. A. : Rational solutions of first order linear difference systems" Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation (Rostock), 124--131 (electronic), ACM, New York, 1998. 14. 5. 2001, CNO: 1810688 Hou, Guang; Xu, Xiuwei; Zhang, Yongde: To solve quantum quadratic systems depends on time" Nuovo Cimento Soc. Ital. Fis. B (12) 115 (2000), no. 10, 1217--1226. 14. 5. 2001, CNO: 1804893 Ran, Yangqiang; Xue, Lihui; Hu, Sizhu; Su, Ru-Keng: On the Coulomb-type potential of the one-dimensional Schrödinger equation" J. Phys. A 33 (2000), no. 50, 9265--9272. 11. 4. 2001, CNO: 1806092 Mavromatis, Harry A. : A Hamiltonian decomposition technique for improving the convergence of perturbation series" Amer. J. Phys. 68 (2000), no. 12, 1134--1138. 5. 4. 2001, CNO: 1803158 Ganguly, Asish. : Associated Lamé equation, periodic potentials and ${\rm sl}(2,\bold R)$." Modern Phys. Lett. A 15 (2000), no. 31, 1923--1930. 23.3. 2001, CNO: 1801744 Selg, Matti.: Exactly solvable potential with a pronounced maximum." Proc. Estonian Acad. Sci. Phys. Math. 49 (2000), no. 4, 233--250. 8. 2. 2001 Maamache, M.; Choutri, M.: Exact evolution of the generalized damped harmonic oscillator." J. Phys. A 33 (2000), no. 35, 6203--6210. 26. 1. 2001 Jia, Chun-Sheng; Wang, Jia-Ying; He, Su; Sun, Liang-Tian: Shape invariance and the supersymmetry WKB approximation for a diatomic molecule potential." J. Phys. A 33 (2000), no. 39, 6993--6998. 11. 12. 2000 Child, Mark S.; Dong, Shi-Hai; Wang, Xiao-Gang; Quantum states of a sextic potential: hidden symmetry and quantum monodromy." J. Phys. A 33 (2000), no. 32, 5653--5661. 11.12. 2000 Mustafa, Omar; Odeh, Maen: Part of the D-dimensional spiked harmonic oscillator spectra." (shifted-l expansions) J. Phys. A 33 (2000), no. 29, 5207--5217. 15.11. 2000 Álvarez, Gabriel; Casares, Carmen: Exponentially small corrections in the asymptotic expansion of the eigenvalues of the cubic anharmonic oscillator." (Two-scale perturbation series, all orders) J. Phys. A 33 (2000), no. 29, 5171--5182. 15.11. 2000 Szmytkowski, Rados\l aw; \.Zywicka-Mo\.zejko, Bo\.zena: Sturmian basis functions for the harmonic oscillator". Beware of the well upside down! (Phys. Rev. A (3) 62 (2000), no. 2, 022104, 6 pp). 2.11. 2000 Dong, Shi-Hai: Exact solutions of the two-dimensional Schrödinger equation with certain central potentials". Rediscovery that the sextic, Coulomb and inverse sextic anharmonicities are QES (Internat. J. Theoret. Phys. 39 (2000), no. 4, 1119--1128). 27.10. 2000 Khare, Avinash; Mandal, Bhabani Prasad: A PT-invariant potential with complex QES eigenvalues" for even M (and real ones for odd M) (Phys. Lett. A 272 (2000), no. 1-2, 53--56). 27.9. 2000 Avdelas, G.; Simos, T. E.:Embedded eighth order methods for the numerical solution of the Schrödinger equation" (=Numerov-like) do well for Lennard Jones phases (J. Math. Chem. 26 (1999), no. 4, 327--341). 6.9. 2000 Lam, C. S.: Time ordering, energy ordering, and factorization" are mutally interrelated (J. Math. Phys. 41 (2000), no. 7, 4497--4507). 6.9. 2000 de Castro, A. S.; de Souza Dutra, A.: Approximate ... (= energies) of a ... (= quartic) potential ..." = simply interpolation (Phys. Lett. A 269 (2000), no. 5-6, 281--286). 28. 8. 2000 Iachello, F. and Del Sol Mesa, A: A class of exactly solvable matrix models" like Hueckel (J. Math. Chem. 25 (1999) 345 - 363). 23. 8. 2000 Xu, Xiu-wei: Exactly solving a two-dimensional time-dependent coupled quantum oscillator" in closed form, via Bogoljubov trasformation (J. Phys. A 33 (2000), no. 12, 2447--2452). 23. 8. 2000 Lu, Huaixin; Zhang, Yongde: Eigenvalue and eigenfunction of $n$-mode boson quadratic Hamiltonian" in compact form, via Bogoljubov trasformation (Internat. J. Theoret. Phys. 39 (2000), no. 2, 447--454). 21. 8. 2000 Bjerrum-Bohr, Niels Emil Jannik shows that and how 1/N expansions in nonrelativistic quantum mechanics" do diverge (J. Math. Phys. 41 (2000), no. 5, 2515--2536). 10. 8. 2000 Bender Wu formula - another resurgent proof. 25. 7. Feshbach-Villars two-component reformulation of a solvable Klein-Gordon model. 25. 7. 2000 Infinite systems of nonlinear difference equations and the existence of their periodic solutions 1. 7. Efimov effect in a discrete model 13. 6. Nonlinear difference equations and the existence and properties of their continuous and bounded solutions 13. 6. Lowering of order (i.e., riccatization giving nonlinear superposition formulae) for discrete (and Hamiltonian, i.e., symplectic) dynamical systems 26. 5. Review of numerical methods (plus a new one) for the long-time quantum evolutions 12. 4. Three hundred years after Jacopo Francesco Riccati (1676 - 1754) ... 27. 3. My own example (square rooted harmonic oscillator) revisited via shifted-l expansion (ground state). 15. 3. Nodal hypersurfaces. 4. 2. Ionization threshold for deuterium. 3. 2. Lewis Leach pre-quantized 31. 1. 2000 Nonlinear Schroedinger discretized. 30. 11. 1999 Hydrogen raising and lowering list. 17. 11. Arrow-Hurwitz algorithm is universal" 21. 10. Linear version of Calogero equation 15. 9. On a proof of convergence of finite elements 28. 7. On paper on special transformation brackets 15. 6. MR 2000 a : 81256 On paper on evaluation of self-energies 15. 6. MR 99 m : 81049 Coulomb wave functions related to Heun equation 28. 5. Given the binding energy, they re-construct potentials! 28. 5. MR 99 m : 81041 On a math. study of time-dependence of bound states 24. 5. MR 99 m : 65026 Continued fractions reviewed 21. 4. MR 99 j : 65059 Generalized eigenvalue problem: Fixing the norm of a resolvent on a vector one gets a pseudo-eigenvalue" 17. 3. MR 2000 a : 31010 Discretizing PDE 15. 2. MR 99 h : 81028 Equal tractability of the bound and scattering (Coulomb) states 18. 1. 1999 MR 99 h : 81038 The so called chiral oscillators