Paweł Karczmarek | John Paul II Catholic University of Lublin (original) (raw)

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Papers by Paweł Karczmarek

Research paper thumbnail of Application of Faber polynomials to the approximate solution of a generalized boundary value problem of linear conjugation in the theory of analytic functions

Computers & Mathematics with Applications, 2014

Research paper thumbnail of A study in facial regions saliency: A fuzzy measure approach

Soft Computing, 2014

People recognize familiar faces in a similar way by using interior facial features (facial region... more People recognize familiar faces in a similar way by using interior facial features (facial regions) such as eyes, nose, mouth, etc. However, the importance of these regions in the realization of face identification and a quantification of the impact of such regions on the recognition process could vary from one region to another. An intuitively appealing observation is that of monotonicity: the more regions are taken into account in the recognition process, the better. From a formal point of view, the relevance of the facial regions and an aggregation of these pieces of experimental evidence can be described in the formal setting of fuzzy measures. Fuzzy measures are of particular interest with this regard given their monotonicity property (which stands in a clear contrast with the more restrictive additivity property inherent to probability-like measures). In this study, we concentrate on the construction of fuzzy measures (more specifically, k-fuzzy measure) and characterize their performance in the problem of face recognition using a collection of experimental data.

Research paper thumbnail of Singular integral equations with multiplicative regular and Cauchy kernels

Computer Algebra Systems in Teaching and Research, 2013

Research paper thumbnail of Singular Integral Equations with Multiplicative Cauchy-type Kernels

Fasciculi Mathematici, 2013

In this paper we consider singular integral equations of the first kind with multiplicative Cauch... more In this paper we consider singular integral equations of the first kind with multiplicative Cauchy-type kernels defined on n-dimensional domains. We give their general solutions in the class of Hölder continuous functions and propose the statements of uniqueness problem.

Research paper thumbnail of Local descriptors in application to the aging problem in face recognition

Pattern Recognition, 2013

Research paper thumbnail of Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel

Annales Universitatis Mariae Curie–Skłodowska. Sectio A. Mathematica, 2012

In the present paper, we give the exact solutions of a singular equation with logarithmic singula... more In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.

Research paper thumbnail of Numerical Solution of Singular Integral Equation in the Half–Plane

Computer Algebra Systems in Teaching and Research. Differential Equations, Dynamical Systems and Celestial Mechanics, 2011

Research paper thumbnail of Cauchy–type singular integral equation with constant coefficients on the real line

Applied Mathematics and Computation, 2010

Research paper thumbnail of Generalized characteristic singular integral equation with Hilbert kernel

Opuscula Mathematica

In this paper an explicit solution of a generalized singular integral equation with a Hilbert ker... more In this paper an explicit solution of a generalized singular integral equation with a Hilbert kernel depending on indices of characteristic operators is presented.

Research paper thumbnail of Approximate solution of a singular integral equation with a multiplicative Cauchy kernel in the half–plane

Opuscula Mathematica, 2008

In this paper, Jacobi and trigonometric polynomials are used to construct the approximate solutio... more In this paper, Jacobi and trigonometric polynomials are used to construct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

Research paper thumbnail of Application of Chebyshev and trigonometric polynomials to the approximation of a solution of a singular integral equation with a multiplicative Cauchy kernel in the half–plane

Computational Methods in Applied Mathematics, 2008

In this article Chebyshev and trigonometric polynomials are used to construct an approximate solu... more In this article Chebyshev and trigonometric polynomials are used to construct an approximate solution of a singular integral equation with a multiplicative Cauchy kernel in the half-plane.

Research paper thumbnail of Singular integral equation with a multiplicative Cauchy kernel in the half–plane

Opuscula Mathematica, 2008

In this paper the explicit solutions of singular integral equation with a multiplicative Cauchy k... more In this paper the explicit solutions of singular integral equation with a multiplicative Cauchy kernel in the half-plane are presented.

Research paper thumbnail of Application of Jacobi polynomials to approximate solution of a singular integral equation with Cauchy kernel

Applied Mathematics and Computation, 2006

In this paper, exact solution of the characteristic equation with Cauchy kernel on the interval [... more In this paper, exact solution of the characteristic equation with Cauchy kernel on the interval [À1, 1] is presented. Next, Jacobi polynomials are used to derive approximate solutions of the characteristic and general Cauchy-type singular integral equations. Moreover, estimations of errors of the approximated solutions are presented and proved.

Research paper thumbnail of Application of Faber polynomials to the approximate solution of a generalized boundary value problem of linear conjugation in the theory of analytic functions

Computers & Mathematics with Applications, 2014

Research paper thumbnail of A study in facial regions saliency: A fuzzy measure approach

Soft Computing, 2014

People recognize familiar faces in a similar way by using interior facial features (facial region... more People recognize familiar faces in a similar way by using interior facial features (facial regions) such as eyes, nose, mouth, etc. However, the importance of these regions in the realization of face identification and a quantification of the impact of such regions on the recognition process could vary from one region to another. An intuitively appealing observation is that of monotonicity: the more regions are taken into account in the recognition process, the better. From a formal point of view, the relevance of the facial regions and an aggregation of these pieces of experimental evidence can be described in the formal setting of fuzzy measures. Fuzzy measures are of particular interest with this regard given their monotonicity property (which stands in a clear contrast with the more restrictive additivity property inherent to probability-like measures). In this study, we concentrate on the construction of fuzzy measures (more specifically, k-fuzzy measure) and characterize their performance in the problem of face recognition using a collection of experimental data.

Research paper thumbnail of Singular integral equations with multiplicative regular and Cauchy kernels

Computer Algebra Systems in Teaching and Research, 2013

Research paper thumbnail of Singular Integral Equations with Multiplicative Cauchy-type Kernels

Fasciculi Mathematici, 2013

In this paper we consider singular integral equations of the first kind with multiplicative Cauch... more In this paper we consider singular integral equations of the first kind with multiplicative Cauchy-type kernels defined on n-dimensional domains. We give their general solutions in the class of Hölder continuous functions and propose the statements of uniqueness problem.

Research paper thumbnail of Local descriptors in application to the aging problem in face recognition

Pattern Recognition, 2013

Research paper thumbnail of Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel

Annales Universitatis Mariae Curie–Skłodowska. Sectio A. Mathematica, 2012

In the present paper, we give the exact solutions of a singular equation with logarithmic singula... more In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.

Research paper thumbnail of Numerical Solution of Singular Integral Equation in the Half–Plane

Computer Algebra Systems in Teaching and Research. Differential Equations, Dynamical Systems and Celestial Mechanics, 2011

Research paper thumbnail of Cauchy–type singular integral equation with constant coefficients on the real line

Applied Mathematics and Computation, 2010

Research paper thumbnail of Generalized characteristic singular integral equation with Hilbert kernel

Opuscula Mathematica

In this paper an explicit solution of a generalized singular integral equation with a Hilbert ker... more In this paper an explicit solution of a generalized singular integral equation with a Hilbert kernel depending on indices of characteristic operators is presented.

Research paper thumbnail of Approximate solution of a singular integral equation with a multiplicative Cauchy kernel in the half–plane

Opuscula Mathematica, 2008

In this paper, Jacobi and trigonometric polynomials are used to construct the approximate solutio... more In this paper, Jacobi and trigonometric polynomials are used to construct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

Research paper thumbnail of Application of Chebyshev and trigonometric polynomials to the approximation of a solution of a singular integral equation with a multiplicative Cauchy kernel in the half–plane

Computational Methods in Applied Mathematics, 2008

In this article Chebyshev and trigonometric polynomials are used to construct an approximate solu... more In this article Chebyshev and trigonometric polynomials are used to construct an approximate solution of a singular integral equation with a multiplicative Cauchy kernel in the half-plane.

Research paper thumbnail of Singular integral equation with a multiplicative Cauchy kernel in the half–plane

Opuscula Mathematica, 2008

In this paper the explicit solutions of singular integral equation with a multiplicative Cauchy k... more In this paper the explicit solutions of singular integral equation with a multiplicative Cauchy kernel in the half-plane are presented.

Research paper thumbnail of Application of Jacobi polynomials to approximate solution of a singular integral equation with Cauchy kernel

Applied Mathematics and Computation, 2006

In this paper, exact solution of the characteristic equation with Cauchy kernel on the interval [... more In this paper, exact solution of the characteristic equation with Cauchy kernel on the interval [À1, 1] is presented. Next, Jacobi polynomials are used to derive approximate solutions of the characteristic and general Cauchy-type singular integral equations. Moreover, estimations of errors of the approximated solutions are presented and proved.