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Jerzy Grzybowski - Publications

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< //Commutative semigroups with cancellation law: a representation theorem// (with D. Pallaschke, H. Przybycień and R. Urbański), "Semigroup Forum" (2011) (published online), DOI 10.1007/s00233-011-9327-5.
< //A note on the dual of the Minkowski-Radstrom-Hormander lattices// (with D. Pallaschke and R. Urbański), "Pacific J. Optim." **6** (2) (2010), 255--262.
< //The intersection property in the family of compact convex sets// (with D. Borowska), "J. Convex Anal." **17** (1) (2010), 173--181.
< //On the amount of minimal pairs of convex sets// (with D. Pallaschke and R. Urbański), "Optim. Meth. Soft." **25** (1) (2010), 89--96.
< //Reduction of finite exhausters// (with D. Pallaschke and R. Urbański), "J. Glob. Optim." **46** (2010), 589--601.
< //Crystal growth in terms of Minkowski-Radstrom-Hormander space// (with R. Urbański), "Bull. Soc. Sci. Lettr. Łódź" **59** (1) (2009), 91--101.

to

> //On minimal representations by a family of sublinear functions//, "Journal of Global Optimization" (accepted, with M. Küçük, Y. Küçük and R. Urbański).
> //Demyanov difference in infinite dimensional spaces//, "Springer Optimization and Its Applications: Constructive Nonsmooth Analysis and Related Topics", **87** (accepted, with D. Pallaschke and R. Urbański).
> //Minkowski-Rådström-Hörmander cone//, "Pacific Journal of Optimization" (accepted, with M. Küçük, Y. Küçük and R. Urbański).
> //Separation of Finitely Many Convex Sets and Data Pre-Classification//, "Springer Optimization in Science and Engineering" (accepted, with M. Gaudioso, D. Pallaschke and R. Urbański).
> //On Simons’ version of Hahn-Banach-Lagrange theorem//, "Commentationes Mathematicae" (accepted, with H. Przybycień and R. Urbański)
> //Completeness in Minkowski-Radstrom-Hormander spaces//, "Optimization", (2013) DOI: 10.1080/02331934.2013.793330 (with H. Przybycień).
> //Decomposition of Minkowski-Rådström-Hörmander space to the direct sum of symmetric and asymmetric subspaces//, "Set-Valued and Variational Analysis" **21** (2) (2013), 201–216 (with H. Przybycień and R. Urbański).
> //Algebraic separation and shadowing of arbitrary sets//, "Commentationes Mathematicae", **53** (2) (2013), 155-164 (with D. Pallaschke and R. Urbański).
> //On max-min Representations of Ordered Median Functions//, "Optimization", (2013) DOI: 10.1080/02331934.2012.750322 (with J. Kalcsics, S. Nickel, D. Pallaschke and R. Urbański).
> //Unique metric segments in the hyperspace over a strictly convex Minkowski space//, "Beiträge zur algebra und geometrie", **54** (1) (2013), 453-467 (with A. Bogdewicz).
> //The completion of the space of convex, bounded sets with respect to the Demyanov metric//, "Demonstratio Mathematica", **46** (1) (2013), 191–196 (with A. Leśniewski i T. Rzezuchowski).
> //
Commutative semigroups with cancellation law: a representation theorem//, "Semigroup Forum" **83** (3) (2011), 447-456 (with D. Pallaschke, H. Przybycień and R. Urbański).
> //Ordered median functions and symmetries//,
"Optimization", **60** (7) (2011), 801-811 (with S. Nickel, D. Pallaschke and R. Urbański).
> //Continuous piecewise linear functions on the octants of $$\mathbb{R}^n$$//, "Optimization", **60** (1
-2) (2011), 101-112 (with D. Pallaschke and R. Urbański)
> //A note on the dual of the Minkowski-Radstrom-Hormander lattices// (with D. Pallaschke and R. Urbański), "Pacific J. Optim." **6** (2) (2010), 255-262.
> //The intersection property in the family of compact convex sets// (with D. Borowska), "J. Convex Anal." **17** (1) (2010), 173-181.
> //On the amount of minimal pairs of convex sets// (with D. Pallaschke and R. Urbański), "Optim. Meth. Soft." **25** (1) (2010), 89-96.
> //Reduction of finite exhausters// (with D. Pallaschke and R. Urbański), "J. Glob. Optim." **46** (2010), 589-601.
> //Crystal growth in terms of Minkowski-Radstrom-Hormander space// (with R. Urbański), "Bull. Soc. Sci. Lettr. Łódź" **59** (1) (2009), 91-101.

Changed:

< //Minimal pairs of bounded closed sets as minimal representations of elements of the Minkowski-Radstrom-Hormander spaces// (with D. Pallaschke and R. Urbański), "Convex and Fractal Geometry", Banach Center Publications, **84** (1) (2009), 31--55.
< //On reduction of pairs of bounded closed convex sets//, (with D. Pallaschke and R. Urbański) "Studia Math." **189** (1) (2008), 1--12.
< //Extreme points of lattice intervals in the Minkowski-Radstrom-Hormander lattice//, (with R. Urbański) "Proc. Amer. Math. Soc." **136** (11) (2008), 3957--3962.

to

> //Minimal pairs of bounded closed sets as minimal representations of elements of the Minkowski-Radstrom-Hormander spaces// (with D. Pallaschke and R. Urbański), "Convex and Fractal Geometry", Banach Center Publications, **84** (1) (2009), 31-55.
> //On reduction of pairs of bounded closed convex sets//, (with D. Pallaschke and R. Urbański) "Studia Math." **189** (1) (2008), 1-12.
> //Extreme points of lattice intervals in the Minkowski-Radstrom-Hormander lattice//, (with R. Urbański) "Proc. Amer. Math. Soc." **136** (11) (2008), 3957-3962.

Changed:

< //Decomposition of the polyhedron from Albrecht Dürer's Melencolia I to a minimal pair of compact convex sets//, "The Volume dedicated to Professor Hubert Jongen on the ocassion of his 60th birthday, Optimization", **57** (2), 2008, 337-344, (with D. Pallaschke and R. Urbański).

to

> //Decomposition of the polyhedron from Albrecht Dürer's Melencolia I to a minimal pair of compact convex sets//, "Optimization", **57** (2), 2008, 337-344, (with D. Pallaschke and R. Urbański).

Changed:

< "Dedicated to the 75th birthday of Professor Stefan Rolewicz, Control and Cybernetics", **36** (4), 2007, 911-924, (with D. Pallaschke and R. Urbański).

to

> "Control and Cybernetics", **36** (4), 2007, 911-924, (with D. Pallaschke and R. Urbański).

Changed:

< //Three criteria minimality for pairs of compact convex sets//, "The Volume dedicated to Professor Diethard Pallaschke on the ocassion of his 65th birthday, Optimization ", **55** (5-6), (2006), 569-576, (with R. Urbański).

to

> //Three criteria minimality for pairs of compact convex sets//, "Optimization ", **55** (5-6), (2006), 569-576, (with R. Urbański).

Changed:

< //Data pre-classification and the separation law for closed bounded sets//, "Special Issue dedicated to Professor Franco Giannessi on the occasion of his 70th birthday, Optimization Methods and Software", **20**, (2-3), 2005, 213-223, (with D. Pallaschke and R. Urbański).

to

> //Data pre-classification and the separation law for closed bounded sets//, "Optimization Methods and Software", **20**, (2-3), 2005, 213-223, (with D. Pallaschke and R. Urbański).


Mathematical Papers

On minimal representations by a family of sublinear functions, "Journal of Global Optimization" (accepted, with M. Küçük, Y. Küçük and R. Urbański).

Demyanov difference in infinite dimensional spaces, "Springer Optimization and Its Applications: Constructive Nonsmooth Analysis and Related Topics", 87 (accepted, with D. Pallaschke and R. Urbański).

Minkowski-Rådström-Hörmander cone, "Pacific Journal of Optimization" (accepted, with M. Küçük, Y. Küçük and R. Urbański).

Separation of Finitely Many Convex Sets and Data Pre-Classification, "Springer Optimization in Science and Engineering" (accepted, with M. Gaudioso, D. Pallaschke and R. Urbański).

On Simons’ version of Hahn-Banach-Lagrange theorem, "Commentationes Mathematicae" (accepted, with H. Przybycień and R. Urbański)

Completeness in Minkowski-Radstrom-Hormander spaces, "Optimization", (2013) DOI: 10.1080/02331934.2013.793330 (with H. Przybycień).

Decomposition of Minkowski-Rådström-Hörmander space to the direct sum of symmetric and asymmetric subspaces, "Set-Valued and Variational Analysis" 21 (2) (2013), 201–216 (with H. Przybycień and R. Urbański).

Algebraic separation and shadowing of arbitrary sets, "Commentationes Mathematicae", 53 (2) (2013), 155-164 (with D. Pallaschke and R. Urbański).

On max-min Representations of Ordered Median Functions, "Optimization", (2013) DOI: 10.1080/02331934.2012.750322 (with J. Kalcsics, S. Nickel, D. Pallaschke and R. Urbański).

Unique metric segments in the hyperspace over a strictly convex Minkowski space, "Beiträge zur algebra und geometrie", 54 (1) (2013), 453-467 (with A. Bogdewicz).

The completion of the space of convex, bounded sets with respect to the Demyanov metric, "Demonstratio Mathematica", 46 (1) (2013), 191–196 (with A. Leśniewski i T. Rzezuchowski).

Commutative semigroups with cancellation law: a representation theorem, "Semigroup Forum" 83 (3) (2011), 447-456 (with D. Pallaschke, H. Przybycień and R. Urbański).

Ordered median functions and symmetries, "Optimization", 60 (7) (2011), 801-811 (with S. Nickel, D. Pallaschke and R. Urbański).

Continuous piecewise linear functions on the octants of $$ \mathbb{R}^n $$, "Optimization", 60 (1-2) (2011), 101-112 (with D. Pallaschke and R. Urbański)

A note on the dual of the Minkowski-Radstrom-Hormander lattices (with D. Pallaschke and R. Urbański), "Pacific J. Optim." 6 (2) (2010), 255-262.

The intersection property in the family of compact convex sets (with D. Borowska), "J. Convex Anal." 17 (1) (2010), 173-181.

On the amount of minimal pairs of convex sets (with D. Pallaschke and R. Urbański), "Optim. Meth. Soft." 25 (1) (2010), 89-96.

Reduction of finite exhausters (with D. Pallaschke and R. Urbański), "J. Glob. Optim." 46 (2010), 589-601.

Crystal growth in terms of Minkowski-Radstrom-Hormander space (with R. Urbański), "Bull. Soc. Sci. Lettr. Łódź" 59 (1) (2009), 91-101.

Pairs of convex bodies in a hyperspace over a Minkowski two-dimensional space joined by a unique metric segment (with A. Bogdewicz), "Convex and Fractal Geometry", Banach Center Publications, 84 (1) (2009)

Minimal pairs of bounded closed sets as minimal representations of elements of the Minkowski-Radstrom-Hormander spaces (with D. Pallaschke and R. Urbański), "Convex and Fractal Geometry", Banach Center Publications, 84 (1) (2009), 31-55.

On reduction of pairs of bounded closed convex sets, (with D. Pallaschke and R. Urbański) "Studia Math." 189 (1) (2008), 1-12.

Extreme points of lattice intervals in the Minkowski-Radstrom-Hormander lattice, (with R. Urbański) "Proc. Amer. Math. Soc." 136 (11) (2008), 3957-3962.

Strongly monotypic polytopes in $$ \mathbb R^3 $$ (with D. Borowska), "Demonstratio Math." 41 (2008), no. 1, 165-169.

Decomposition of the polyhedron from Albrecht Dürer's Melencolia I to a minimal pair of compact convex sets, "Optimization", 57 (2), 2008, 337-344, (with D. Pallaschke and R. Urbański).

Generalized directional derivatives for locally Lipschitz functions witch satisfy Leibniz rule,
"Control and Cybernetics", 36 (4), 2007, 911-924, (with D. Pallaschke and R. Urbański).

Minkowski difference and Sallee elements in an ordered semigroup (with D. Borowska), "Comment. Math." 47 (2007), no. 1, 77-83.

Three criteria minimality for pairs of compact convex sets, "Optimization ", 55 (5-6), (2006), 569-576, (with R. Urbański).

On inclusion and summands of bounded closed convex sets, "Acta Math. Hungar.", 106 (4). 2005, 293-300, (with R. Urbański).

Minimal quasidifferential of a piecewise linear function in $$ \mathbb R^3 $$, "Z. Anal. Anwendungen", 24 (2005), no. 1, 189-202.

Data pre-classification and the separation law for closed bounded sets, "Optimization Methods and Software", 20, (2-3), 2005, 213-223, (with D. Pallaschke and R. Urbański).

On the Representation Property of Kernels Quasidifferentials, "Journal of Convex Analysis", 11 (2), 2004, 387-390, (with R. Urbański).

A geometric representation of the Morse fan, "Journal of Global Optimization", 30, 2004, 319-333, (with D. Pallaschke and R. Urbański).

Affine straight lines in family of bounded closed convex sets , "Rendiconti del Circolo Mathematico di Palermo", 53 (2), 2004, 225-230, (with R. Urbański).

On reduced pairs of bounded closed convex sets,
"Revista Mathemática Complutence", 16 (2), 2003, 59-63, (with R. Urbański).

On the number of minimal pairs of compact convex sets that are not translates of one another, "Studia Math.", 158 (1), 2003, 59-63, (with R. Urbański).

On summands of closed bounded convex sets, "Zeitschrift für Analysis und ihre Anwendungen", 21 (4), 2002, 845-850, (with H. Przybycień and R. Urbański).

General Methods of Constructing Equivalent Minimal Pairs not Unique up to Translation, "Revista Mathemática Complutence", 13 (2), 2000, 383-398, (with S. Kaczmarek and R. Urbański).

Minimal pairs representing selections of four linear functions in $$ \mathbb R^3 $$, "Journal of Convex Analysis", 7 (2), 2000, 445-452, (with D. Pallaschke and R. Urbański).

On pairs of closed bounded convex sets which lay in complementary subspaces, "Function Spaces the Fifth Conference, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, Series", 213, 2000, 165-171, (with R. Urbański).

On Common Summands and Anti-summands of Compact Convex Sets, "Bull. Polish. Acad. Sci. Math.", 47 (1), 1999, 367-377, (with R. Urbański and W. Wiernowolski).

On Convex Class of Pairs of Convex Bodies, "Proc. Amer. Math. Soc.", 125 (11), 1997, 3397-3403, (with R. Urbański).

Minimal Pairs of Bounded Closed Convex Sets, "Studia Math.", 126 (1), 1997, 95-99, (with R. Urbański).

A note on summands of compact convex sets, "Mathematika" 43 (1996), no. 2, 286-294.

Minimal pairs of convex compact sets, "Arch. Math. (Basel)" 63 (2) (1994), 173-181.

A note on (s,t)-convex modulars, "Comment. Math." 30 (2) (1991), 309-315.

On (s,t)-convex modulars over a field with valuation, "Comment. Math." 29 (1990), no. 2, 183-193.

On F-quasinorms in vector spaces over a locally compact field with valuation, "Bull. Polish Acad. Sci. Math." 36 (1988), no. 5-6, 268-272.

Analytic continuation from compact set, "Univ. Iagel. Acta Math." 27 (1988), 259-269.