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162 results on '"Ciesielski, Krzysztof Chris"'

6. Optimization of Max-Norm Objective Functions in Image Processing and Computer Vision

Author

Malmberg, Filip, Ciesielski, Krzysztof Chris, Strand, Robin, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Couprie, Michel, editor, Cousty, Jean, editor, Kenmochi, Yukiko, editor, and Mustafa, Nabil, editor

Published
2019
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7. Graph-Based Segmentation with Local Band Constraints

Author

de Moraes Braz, Caio, Miranda, Paulo A. V., Ciesielski, Krzysztof Chris, Cappabianco, Fábio A. M., Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Couprie, Michel, editor, Cousty, Jean, editor, Kenmochi, Yukiko, editor, and Mustafa, Nabil, editor

Published
2019
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9. Lineability, spaceability, and additivity cardinals for Darboux-like functions

Author

Ciesielski, Krzysztof Chris, Gámez-Merino, José L., Pellegrino, Daniel, and Seoane-Sepúlveda, Juan B.

Subjects
Mathematics - Functional Analysis
Abstract

We introduce the concept of {\em maximal lineability cardinal number}, $\mL(M)$, of a subset $M$ of a topological vector space and study its relation to the cardinal numbers known as: additivity $A(M)$, homogeneous lineability $\HL(M)$, and lineability $\LL(M)$ of $M$. In particular, we will describe, in terms of $\LL$, the lineability and spaceability of the families of the following Darboux-like functions on $\real^n$, $n\ge 1$: extendable, Jones, and almost continuous functions.

Published
2013

18. The Minimum Barrier Distance: A Summary of Recent Advances

Author

Strand, Robin, Ciesielski, Krzysztof Chris, Malmberg, Filip, Saha, Punam K., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Kropatsch, Walter G., editor, Artner, Nicole M., editor, and Janusch, Ines, editor

Published
2017
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21. Examples of Sierpinski–Zygmund maps in the class of Darboux-like functions

Author

Ciesielski, Krzysztof Chris and Pan, Cheng-Han

Abstract

The Darboux-like functions represent a group of maps that are continuous in a generalized sense. The algebra of subsets of RR(i.e., maps from Rto R) generated by these classes has nine atoms, that is, the smallest non-empty elements of the algebra. The subject of this work is to study the intersections of these atoms with the class SZof Sierpinski–Zygmund functions—the maps that have as little of the standard continuity as possible. Specifically, we will show that it is independent of the standard axioms of set theory that each of these atoms has a non-empty intersection with SZ. For seven of the nine atoms this has been unknown, and the constructions of the examples provide answers to the problems stated in a recent survey A century of Sierpinski–Zygmund functionsof K. C. Ciesielski and J. Seoane-Sepúlveda. Notice that lineability of the main classes of Darboux-like functions, as well as of Sierpinski–Zygmund functions, has been intensively studied. The presented work opens a possibility to study also the lineability of the nine smaller classes we discuss here.

Published
2024
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25. Fuzzy Connectedness Segmentation: A Brief Presentation of the Literature

Author

Herman, Gabor T., Kong, T. Yung, Ciesielski, Krzysztof Chris, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Barneva, Reneta P., editor, Bhattacharya, Bhargab B., editor, and Brimkov, Valentin E., editor

Published
2015
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33. Linearly continuous maps discontinuous on the graphs of twice differentiable functions.

Author

Ciesielski, Krzysztof Chris and Rodríguez-Vidanes, Daniel L.

Subjects
*DIFFERENTIABLE functions, *CONTINUOUS functions, *SET functions, *PROBLEM solving
Abstract

A function g\colon \mathbb {R}^n\to \mathbb {R} is linearly continuous provided its restriction g\restriction \ell to every straight line \ell \subset \mathbb {R}^n is continuous. It is known that the set D(g) of points of discontinuity of any linearly continuous g\colon \mathbb {R}^n\to \mathbb {R} is a countable union of isometric copies of (the graphs of) f\restriction P, where f\colon \mathbb {R}^{n-1}\to \mathbb {R} is Lipschitz and P\subset \mathbb {R}^{n-1} is compact nowhere dense. On the other hand, for every twice continuously differentiable function f\colon \mathbb {R}\to \mathbb {R} and every nowhere dense perfect P\subset \mathbb {R} there is a linearly continuous g\colon \mathbb {R}^2\to \mathbb {R} with D(g)=f\restriction P. The goal of this paper is to show that this last statement fails, if we do not assume that f'' is continuous. More specifically, we show that this failure occurs for every continuously differentiable function f\colon \mathbb {R}\to \mathbb {R} with nowhere monotone derivative, which includes twice differentiable functions f with such property. This generalizes a recent result of professor Luděk Zajíček [On sets of discontinuities of functions continuous on all lines, arxiv.org/abs/2201.00772v1, 2022] and fully solves a problem from a 2013 paper of the first author and Timothy Glatzer [Real Anal. Exchange 38 (2012/13), pp. 377–389]. [ABSTRACT FROM AUTHOR]

Published
2023
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