Extended abstracts written for Zentralblatt
  

see also:


contact data
CV data
with Czech version:
česká stránka


papers 2000 and older ones, typically on

  SOLVABLE MODELS


  PT SYMMETRIC QM


  DIRAC EQUATION


  PERTURBATION THEORY


  QUANTUM MECHANICS IN 2 DIMENSIONS

  NUMERICAL METHODS

  RELATIVISTIC CORRECTIONS

(returning to the

results once more?)


What I read recently
for inspiration

  • 15. 4. 2004:
    dalsi posledni: dvakrat vic Combese

  • 6. 4. 2004:
    druhy postposledni: Jacobi and semiboundedness

  • 6. 4. 2004:
    postposledni: Jacobi and Levinson

  • 27. 10. 2003:
    posledni, a o mne

  • 27. 10. 2003:
    Newton spatne

  • 27. 10. 2003:
    Pauli QES

  • 12. 9. 2003:
    delta by smooth - strong resolven conv.

  • 12. 9. 2003:
    iterations for much less than third eigenvalues (generalized)

  • 12. 9. 2003:
    N-body QES gr. st. sol.

  • 12. 9. 2003:
    appr. sol. a la Bogolyubov

  • 31. 7. 2003:
    graded manifolds and var. principles

  • 31. 7. 2003:
    integrable systems - re-telling the story

  • 31. 7. 2003:
    the best approximant for a given matrix - formulae

  • 31. 7. 2003:
    simultaneous closeness of the lower and upper eigenvalue estimates

  • 7. 7. 2003:
    re-construct Jacobi matrix from its off-diagonal Green function element

  • 7. 7. 2003:
    OK, completeness, but what if there is a strong singularity inside?

  • 7. 7. 2003:
    matrix ord. dif. eqs. conserving spectrum (appl. to inv. eigv. problem)

  • 7. 7. 2003:
    take trace and norm, get both bounds for eigenvalues

  • 30. 5. 2003:
    expand in eigenstates of nelin. Sturm Liouville

  • 29. 5. 2003:
    elliptic Calogero-Sutherland is QES

  • 28. 5. 2003:
    change of variables in Sturm Liouville if nonlinear

  • 5. 5. 2003:
    epsilon spectrum

  • 5. 5. 2003:
    inverse iterations globally

  • 5. 5. 2003:
    pencil, inverse-free

  • 5. 5. 2003:
    non-symmetric Jacobi-Davidson

  • 24. 3. 2003:
    M functions for 2n-th Schroedingerlikes

  • 4. 3. 2003:
    Strichartz for non-smooth Schroedingers

  • 27. 2. 2003:
    Dirac spectrum

  • 3. 2. 2003:
    proof of optimality of estimates (for singular cont. spectra) using pasted periodic examples V

  • 8. 1. 2003:
    proof of absol. cont. spectra for periodic V and x-dependent m(x) in 2 dim.

  • 8. 1. 2003:
    proof of Anderson localization

  • 2. 12. 2002:
    string with frequency-dependent friction, matricized

  • 20. 11. 2002:
    decay estimate

  • 1. 11. 2002:
    inverse eigenvalue problem I (bi-antisym. A) and II (same as approx.)

  • 30. 10. 2002:
    Markov and existence of Green

  • 14. 10. 2002:
    unitary Hessenberg = cubic conv. of QR

  • 7. 10. 2002:
    iterations with triangular-matrix (even-up, odd=down) pre-conditioning

  • 27. 9. 2002:
    pseudospektra

  • 27. 9. 2002:
    Dirichlet and Neumann ground-state estimates, bothsided

  • 5. 9. 2002:
    chybejici Kreinuv dukaz (boundedness for periodic) for ground-state estimates

  • 22. 8. 2002:
    Exnerova hluboka delta smycka (s Yoshitomim)

  • 21. 8. 2002:
    Double well V via instantons

  • 21. 8. 2002:
    V of M(any) exp i x

  • 5. 7. 2002:
    Newton method and happy birthday to T. Y.

  • 5. 7. 2002:
    Cr. and annih. of many bosons and fermions in superfluidity

  • 2. 7. 2002:
    Cr. and annih. of two bosons in PT SUSY

  • 2. 7. 2002:
    Solvable Heiseberg once more, the dipole's sin phi via cr. and annih. of two bosons

  • 21. 5. 2002:
    Solve Heiseberg!

  • 20. 5. 2002:
    Escape of particles - lower estimates

  • 20. 5. 2002:
    see 13. 5., part II

  • 13. 5. 2002:
    The (biorthogonal) series (convergence) compared with the trigonometric (Fourier) for a differential operator (of 2n-th order) (giving 'generalized sinuses')

  • 7. 5. 2002:
    Laplace, but b.c. = superp. of derivatives at a rational set

  • 6. 5. 2002:
    From Hilbert to Krein and return (the Sturm Liouvillean case)

  • 6. 5. 2002:
    Decadic oscillator spectrum lattice.

  • 22. 4. 2002:
    Singular-continuous spectra and Weyl-Titchmarsh m-function inequalities (using subordinacy a la Gilbert-Pearson)

  • 16. 3. 2002:
    m-dimensional quasi-Dirac bound states in pseudo-exponential matrix potentials

  • 19. 2. 2002:
    Computation method SER (subspace iterations, degeneracy friendly)

  • 12. 2. 2002:
    Computational physics (plus biology) textbook

  • 19. 12.:
    All matrix roots of a matrix polynomial (by deflation)

  • 18. 12.:
    So called oscillatory (= a root of totally positive) matrix from its spectrum

  • 18. 12.:
    Necessary and sufficient inequalities between eigenvalues and singular values, for real matrices in particular

  • 3. 12.:
    Low-rank approximations with and without column-wise partitioning.

  • 3. 12.:
    Bad Cholesky, Newton-improved. When and how.

  • 3. 12.:
    Conv. theorems for parallelized iterative method.

  • 3. 12.:
    Book on stochastic, circulant and Bell's (=formal-series) matrices [in the second case, cf. M. Znojil, Circular vectors and toroidal matrices, Rendiconti del Circolo Matematico di Palermo Serie II - Suppl. 39 (1996) 143-8]

  • 13. 11.:
    NLS wave propagation (solvable semi-classical ZS)

  • 7. 11.:
    Green's functions for shock waves

  • 2. 11.:
    NLS, discretized

  • 15. 10.:
    Non-Hermitian Zakharov Shabat: asymptotical eigenvalues

  • 21. 8.:
    ODE: block-Toeplitz preconditioning

  • 21. 8.:
    tridiagonalization: stability through incompleteness

  • 21. 8.:
    two-parameteric pencils homotopically

  • 21. 8.:
    silicon via density functional

  • 2. 7.:
    superfeynman weylovsko fujiwarovsky

  • 14. 5.:
    Marcelo's marvelous book on pert. th.

  • 14. 5.:
    new proof for Hill's asymptotic eigenvalues (no smoothness of V(x) required)

  • 14. 5.:
    Darboux made n-dimensional, gives singularities only on hyperplanes.

  • 28. 3.:
    they adapt telescope mirrors to atmospheric turbulences

  • 28. 3.:
    we minimize traces

  • 28. 3.:
    upper bounds for the perturbative turn of subspace

  • 28. 3.:
    soft billiard and section method

  • 28. 3.:
    selfsimilar everything

  • 26. 3.:
    tokamak stability parallelized

  • 15. 2.:
    matrix compression avoiding SVD - Lanczos modon

  • 15. 2.:
    search for generalized perigeum

  • 15. 2.:
    exporatory data analysis (Lasso)

  • 14. 2.:
    sparse and indefinite system

  • 26. 1.:
    Kato and Rellich for the Banach-space-many couplings

  • 15. 1.:
    Complex symmetric matrices: Hankel (and Lanczos)

  • 4. 1.:
    Lombardovo další vylepšování marešovských nerovností.

  • 3. 1.:
    Ito and Monte Carlo for square well.

  • 3. 1.:
    Renormalized strong coupling series (numerically)

  • 11. 12.:
    Jordan form algorithm (plus Weierstrass for pencils)

  • 11. 12.:
    Non-Hermitian in a basis can have an ill-conditioned eigenvalue problem

  • 11. 12.:
    Stable deflation of eigenpairs from a pencil

  • 11. 12.:
    Arnoldi method: using the redundant last Krylov state

  • 19.11.:
    Newton method: minimal Toeplitz eigenvalue

  • 18.11.:
    Stable method: polygon from moments

  • 17.11.:
    Improved algorithm on singular values.

  • 16.11.:
    a textbook on mathematical methods.