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Faculty of Science

Prof. RNDr. Josef Janyška, DSc.

Basic CV Supervisor Qualifications Publications Projects Teaching

Publications issued by MU Press

2012

Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case

JANYŠKA, Josef - MARKL, Martin.
Combinatorial differential geometry and ideal Bianchi–Ricci identities II - the torsion case. Archivum Mathematicum, Brno, Masaryk University. ISSN 0044-8753, 2012, vol. 48, no. 1, pp. 61-80.

2011

Combinatorial differential geometry and ideal Bianchi–Ricci identities

JANYŠKA, Josef - MARKL, Martin.
Combinatorial differential geometry and ideal Bianchi–Ricci identities. Advances in Geometry, de Gruyter, Germany. ISSN 1615-715X, 2011, vol. 11, no. 3, pp. 509-540.

General covariant derivatives for general connections

JANYŠKA, Josef.
General covariant derivatives for general connections. Differential Geometry and its Applications, Elsevier, The Nederlands. ISSN 0926-2245, 2011, vol. 29, no. S1, pp. "S116"-"S124".

Reduction theorem for general connections

JANYŠKA, Josef.
Reduction theorem for general connections. Annales Polonici Mathematici, Polsko, Varšava, Instytut Matematyczny PAN, Poland. ISSN 0066-2216, 2011, vol. 102, no. 3, pp. 231-254.

2010

An algebraic approach to physical scales

JANYŠKA, Josef - MODUGNO, Marco - VITOLO, Raffaele.
An algebraic approach to physical scales. Acta Applicandae Mathematicae, Kluwer, The Nederlands. ISSN 0167-8019, 2010, vol. 110, no. 3, pp. 1249-1276.

2009

Generalized geometrical structures of odd dimensional manifolds

JANYŠKA, Josef - MODUGNO, Marco.
Generalized geometrical structures of odd dimensional manifolds. Journal de Mathematiques Pures et Appliquees, Francie, Elsevier SAS, France. ISSN 0021-7824, 2009, vol. 91, no. 2, pp. 211-232.

Natural and gauge-natural bundles and natural Lagrangian structures

JANYŠKA, Josef.
Natural and gauge-natural bundles and natural Lagrangian structures. In Variations, Geometry and Physics. Vyd. 1. New York : Nova Science Publishers, 2009. in honour of Demeter Krupka's sixty-fifth birthday, ISBN 978-1-60456-920-9, pp. 143-166.

Natural principal connections on the principal gauge prolongation of a principal bundle

JANYŠKA, Josef - VONDRA, Jan.
Natural principal connections on the principal gauge prolongation of a principal bundle. REPORTS ON MATHEMATICAL PHYSICS, Elsevier SAS, Poland. ISSN 0034-4877, 2009, vol. 64, no. 3, pp. 395-415.

2008

Geometric structures of the classical general relativistic phase space

JANYŠKA, Josef - MODUGNO, Marco.
Geometric structures of the classical general relativistic phase space. International Journal of Geometrical Methods in Modern Physics, World Scientific, Great Britain. ISSN 0219-8878, 2008, vol. 5, no. 5, pp. 699-754.

2007

10th International Conference Differential Geometry and its Application

JANYŠKA, Josef.
10th International Conference Differential Geometry and its Application. 2007. CZE, Olomouc. 27.8.2007 - 31.8.2008, Worldwide Activity.

Higher order Utiyama's invariant interaction

JANYŠKA, Josef.
Higher order Utiyama's invariant interaction. REPORTS ON MATHEMATICAL PHYSICS, Elsevier SAS, Poland. ISSN 0034-4877, 2007, vol. 59, no. 1, pp. 63-81.

Utiyama's reduction method and infinitesimal symmetries of invariant Lagrangians

JANYŠKA, Josef.
Utiyama's reduction method and infinitesimal symmetries of invariant Lagrangians. In Symmetry and Preturbation Theory. Vyd. první. Londýn : World Scientific, 2007. ISBN 978-981-277-616-7, pp. 255-256. 2007, Otranto, Itálie.

2006

An outline of covariant quantum mechanics

JANYŠKA, Josef - MODUGNO, Marco.
An outline of covariant quantum mechanics. In Recent Developments in Gravitational Phzsics. USA : Amazon, Institute of Physics Conference Series, 2006. ISBN 978-0-7503-0943-1, pp. 367-384. 2002, Roma.

Geometric structures on the tangent bundle of the Einstein spacetime

JANYŠKA, Josef.
Geometric structures on the tangent bundle of the Einstein spacetime. Archivum Mathematicum, Brno, Masaryk University. ISSN 0044-8753, 2006, vol. 42, no. 2, pp. 195-203.

Graded Lie algebra of Hermitian tangent valued forms

JANYŠKA, Josef - MODUGNO, Marco.
Graded Lie algebra of Hermitian tangent valued forms. Journal de Mathematiques Pures et Appliquees, Francie, Elsevier SAS, France. ISSN 0021-7824, 2006, vol. 85, no. 5, pp. 687-697.

Hermitian vector fields and special phase functions

JANYŠKA, Josef - MODUGNO, Marco.
Hermitian vector fields and special phase functions. International Journal of Geometrical Methods in Modern Physics, World Scientific, Great Britain. ISSN 0219-8878, 2006, vol. 3, no. 4, pp. 719-754.

Higher order Utiyama-like theorem

JANYŠKA, Josef.
Higher order Utiyama-like theorem. REPORTS ON MATHEMATICAL PHYSICS, Elsevier SAS, Poland. ISSN 0034-4877, 2006, vol. 58, no. 1, pp. 93-118.

On the geometry of variational calculus on some functional bundles

JANYŠKA, Josef - KOLÁŘ, Ivan - CABRAS, Antonela.
On the geometry of variational calculus on some functional bundles. Note di Matematica, Itálie, Univerzita Lecce, Poland. ISSN 1123-2536, 2006, vol. 2006, no. 1, pp. 51-66.

Quantum operators and Hermitian vector fields

JANYŠKA, Josef - MODUGNO, Marco.
Quantum operators and Hermitian vector fields. In DIFFERENTIAL GEOMETRY AND PHYSICS. Čína : World Scientific, 2006. ISBN 978-981-270-377-4, pp. 97-106. 2005, Tianjin.

2005

Higher order valued reduction theorems for classical connections

JANYŠKA, Josef.
Higher order valued reduction theorems for classical connections. Central European Journal of Mathematics, Poland. ISSN 1644-3616, 2005, vol. 3, no. 2, pp. 294-308.

Natural connections given by general linear and classical connections

JANYŠKA, Josef.
Natural connections given by general linear and classical connections. In Differential Geometry and its Application. Vyd. první. Praha : MATFYZ PRESS, 2005. ISBN 80-86732-63-0, pp. 289-303. 2004, Praha.

2004

Functorial prolongation of some functional bundles

JANYŠKA, Josef - KOLÁŘ, Ivan - CABRAS, Antonela.
Functorial prolongation of some functional bundles. Annales Academiae Paedagogicae Cracoviensis, Studia Mathematica IV, Krakov, Pedagogická akademie, Poland. ISSN 1643-6555, 2004, vol. 2004, no. 1, pp. 17-30.

Higher order valued reduction theorems for general linear connections

JANYŠKA, Josef.
Higher order valued reduction theorems for general linear connections. Note di Matematica, Itálie, Univerzita Lecce, Poland. ISSN 1123-2536, 2004, vol. 23, no. 2, pp. 75-97.

On the curvature of tensor product connections and covariant differentials

JANYŠKA, Josef.
On the curvature of tensor product connections and covariant differentials. Supplemento di Rendiconti del Circolo Matematico di Palermo, Palermo, Italy. ISSN 0009-725X, 2004, vol. 72, no. 1, pp. 135-143.

Reduction theorems for general linear connections

JANYŠKA, Josef.
Reduction theorems for general linear connections. Differential Geometry and its Applications, Amsterdam, Elsevier Science, The Nederlands. ISSN 0926-2245, 2004, vol. 20, no. 2, pp. 177-196.

2002

Analytická geometrie

book cover HORÁK, Pavel - JANYŠKA, Josef.
Analytická geometrie. 1. dotisk 1. vydání. Brno : Masarykova univerzita v Brně, 2002. 155 pp. Obsahuje bibliografii. ISBN 80-210-1623-X.

Covariant pre-quantum operators

JANYŠKA, Josef - MODUGNO, Marco.
Covariant pre-quantum operators. In Proceedings of the International Conference on "Differential Geometry and Its Applications", eds. O. Kowalski, D. Krupka and J. Slovák. Opava : Silesian University, 2002. ISBN 80-7248-166-5, pp. 285-308. 2001, Opava (Cyech Republic), August 27 - 31, 2001.

Covariant quantum mechanics and quantum symmetries

JANYŠKA, Josef - MODUGNO, Marco - SALLER, Dirk.
Covariant quantum mechanics and quantum symmetries. In Proceedings of the International Conference on "Recent Developments in General Relativity", eds. R. Cianci, R. Collina, M. Francaviglia and P. Fre. Německo : Springer-Verlag, 2002. ISBN 80-7248-166-5, pp. 179-202. 2000, Genoa (Italy) 2000.

Covariant Schroedinger operator

JANYŠKA, Josef - MODUGNO, Marco.
Covariant Schroedinger operator. J. Phys. A: Math. Gen., UK, Institute of Physics Publishing, Great Britain. ISSN 0305-4470, 2002, vol. 35, no. 40, pp. 8407-8434.

Uniqueness results by covariance in covariant quantum mechanics

JANYŠKA, Josef - MODUGNO, Marco.
Uniqueness results by covariance in covariant quantum mechanics. In Proceedings of the Second International Symposium on "Quantum Theory and Symmetries", eds. E. Kapuscik, A. Horzela. New Jersey - London - Singapore : World Scientific, 2002. ISBN 981-02-4887-3, pp. 404-411. 2001, Krakow (Polsko), July 18 - 21, 2001.

2001

A remark on natural quantum Lagrangians and natural generalized Schroedinger operators in Galilei quantum mechanics

JANYŠKA, Josef.
A remark on natural quantum Lagrangians and natural generalized Schroedinger operators in Galilei quantum mechanics. Supplemento ai Rendiconti del Circolo Matematico di Palermo,Serie II, Palermo, Itálie, Univerzita Palermo, Italy. ISSN 0009-725X, 2001, vol. 66, no. 2, pp. 117-128.

Analytická teorie kuželoseček a kvadrik

book cover JANYŠKA, Josef - SEKANINOVÁ, Anna.
Analytická teorie kuželoseček a kvadrik. Vyd. 2. Brno : Masarykova univerzita, 2001. 178 pp. ISBN 80-210-2604-9.

Natural Poisson and Jacobi structures on the tangent bundle of a pseudo-Riemannian manifold

JANYŠKA, Josef.
Natural Poisson and Jacobi structures on the tangent bundle of a pseudo-Riemannian manifold. In Global Differential Geometry: The Mathematical Legacy of Alfred Gray. Vyd. 1. USA : American Mathematical Society, 2001. ISBN 0-8218-2750-2, pp. 343-347. September 18-23, 2000, Bilbao (Spain).

Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold

JANYŠKA, Josef.
Natural vector fields and 2-vector fields on the tangent bundle of a pseudo-Riemannian manifold. Archivum Mathematicum, Brno, MU Brno. ISSN 0044-8753, 2001, vol. 37, no. 2, pp. 143-160.

2000

Quantisable functions in general relativity

JANYŠKA, Josef - MODUGNO, Marco.
Quantisable functions in general relativity. Vyd. 1. Ciombra : University of Coimbra, 2000. 21 pp. Textos Mat. Ser. B.

1999

On the graded Lie algebra of quantisable forms

JANYŠKA, Josef - MODUGNO, Marco.
On the graded Lie algebra of quantisable forms. In Differential Geometry and Applications. Vyd. 1. Brno : Masarykova Univerzita, 1999. ISBN 80-210-2097-0, pp. 601-620.

1998

Galilei general relativistic quantum mechanics revisited

JANYŠKA, Josef - JADCZYK, Arkadius - MODUGNO, Marco.
Galilei general relativistic quantum mechanics revisited. In Geometria, Física-Matemática e outros Ensaios. Coimbra : Univerzita Coimbra, 1998. pp. 253-313.

Natural Lagrangians for quantum structures over 4-dimensional space-time

JANYŠKA, Josef.
Natural Lagrangians for quantum structures over 4-dimensional space-time. Rendiconti di Matematica, VII, Roma, Italy. ISSN 1120-7183, 1998, vol. 18, no. 4, pp. 623-648.

Professor Karel Svoboda (1918 - 1997)

JANYŠKA, Josef - KOLÁŘ, Ivan.
Professor Karel Svoboda (1918 - 1997). Archivum Mathematicum, Brno, Masaryk University. ISSN 0044-8753, 1998, vol. 1998, no. 2, i-3 pp.

1997

Analytická geometrie

book cover HORÁK, Pavel - JANYŠKA, Josef.
Analytická geometrie. Brno : Masarykova univerzita v Brně, 1997. 151 pp. ISBN 80-210-1623-.

On quantum vector fields in general relativistic quantum mechanics

JANYŠKA, Josef - MODUGNO, Marco.
On quantum vector fields in general relativistic quantum mechanics. General Mathematics, Rumunsko, Romania. ISSN 1221-5023, 1997, vol. 1997, no. 1, pp. 199-217.

1996

Analytická teorie kuželoseček a kvadrik

JANYŠKA, Josef - SEKANINOVÁ, Anna.
Analytická teorie kuželoseček a kvadrik. Vyd. 1. Brno : Masarykova univerzita, 1996. 178 pp. ISBN 80-210-1435-0.

Classical particle phase space in general relativity

JANYŠKA, Josef - MODUGNO, Marco.
Classical particle phase space in general relativity. In Differential Geometry and Applications. Brno : Masarykova Univerzita, 1996. ISBN 80-210-1369-9, pp. 573-602.

Natural symplectic stuctures on the tangent bundle of a space time

JANYŠKA, Josef.
Natural symplectic stuctures on the tangent bundle of a space time. Supplemento ai Rendiconti del Circolo Matematico di Palermo,Serie II, Italy. ISSN 0009-725X, 1996, vol. 43, no. 2, pp. 153-162.

Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibred manifold

JANYŠKA, Josef - MODUGNO, Marco.
Relations between linear connections on the tangent bundle and connections on the jet bundle of a fibred manifold. Archivum Mathematicum, Brno, MU Brno. ISSN 0044-8753, 1996, vol. 32, no. 4, pp. 281-288.

1995

Natural quantum Lagrangians in Galilei quantum mechanics

JANYŠKA, Josef.
Natural quantum Lagrangians in Galilei quantum mechanics. Rendiconti di Matematica, VII, Roma, Italy. ISSN 1120-7183, 1995, vol. 15, no. 4, pp. 457-468.

Remarks on symplectic and contact 2-forms in relativistic theories

JANYŠKA, Josef.
Remarks on symplectic and contact 2-forms in relativistic theories. Bollettino Unione Mat. Italiana (7), Italy. 1995, vol. 9-B, no. 4, pp. 587-616.

Some natural operations in general relativistic theories

JANYŠKA, Josef.
Some natural operations in general relativistic theories. 1995. 77 pp.

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