Selected Problems on Experimental Mathematics

Edited by
Roman WITUŁA
Beata BAJORSKA-HARAPIŃSKA
Edyta HETMANIOK
Damian SŁOTA
Tomasz TRAWIŃSKI

WYDAWNICTWO POLITECHNIKI ŚLĄSKIEJ
GLIWICE 2017

ISBN 978-83-7880-476-5



Preface
p. 5-6
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Marek J. ŚMIETAŃSKI
New algorithms for solving unconstrained optimization problems based on the generalized Newton method involving simple quadrature rules
pp. 7-16
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Sergei S. SHERBAKOV, Michael A. ZHURAVKOV and Leonid A. SOSNOVSKIY
Contact interaction, volume damageability and multicriterial limiting states of multielement tribo-fatigue systems
pp. 17-38
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Edyta HETMANIOK, Jakub J. LUDEW and Mariusz PLESZCZYŃSKI
Examination of stability of the computer tomography algorithms in case of the incomplete information for the objects with non-transparent elements
pp. 39-60
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Tomasz TRAWIŃSKI, Sebastian BARTEL, Marcin SZCZYGIEŁ, Damian SŁOTA and Roman WITUŁA
A chosen form of a block matrix in the mathematical model of the induction squirrel-cage motors
pp. 61-72
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Edyta HETMANIOK, Michał RÓŻAŃSKI, Damian SŁOTA, Marcin SZWEDA, Tomasz TRAWIŃSKI and Roman WITUŁA
Determinants of the block arrowhead matrices
pp. 73-88
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Marcin SOWA
Error computation strategies in an adaptive step size solver for time fractional problems
pp. 89-102
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Radosław GRZYMKOWSKI, Edyta HETMANIOK and Mariusz PLESZCZYŃSKI
A novel algorithm for solving the ordinary differential equations
pp. 103-112
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Wojciech M. KEMPA and Rafał MARJASZ
Distribution of the time to butter overflow in the single-server queueing model with multiple vacation policy
pp. 113-128
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Bożena PIĄTEK and Alicja SAMULEWICZ
Gluing Busemann spaces
pp. 129-148
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Rafał ZDUŃCZYK
Sets with small differences and big sums in finite groups
pp. 149-166
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Beata BAJORSKA-HARAPIŃSKA
How programming was used to determine factorizations of self-similar groups associated to the first Grigorchuk group
pp. 167-180
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Beata BAJORSKA-HARAPIŃSKA, Mariusz PLESZCZYŃSKI, Damian SŁOTA and Roman WITUŁA
A few properties of Ramanujan cubic polynomials and Ramanujan cubic polynomials of the second kind
pp. 181-200
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Piotr LORENC, Jakub J. LUDEW, Mariusz PLESZCZYŃSKI, Alicja SAMULEWICZ and Roman WITUŁA
Iterated integrals of Faulhaber polynomials and some properties of their roots
pp. 201-218
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Edyta HETMANIOK, Bożena PIĄTEK, Mariusz PLESZCZYŃSKI and Roman WITUŁA
Identities for the inverses of central binomial coefficients
pp. 219-232
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Beata BAJORSKA-HARAPIŃSKA, Mariusz PLESZCZYŃSKI, Michał RÓŻAŃSKI, Marcin SZWEDA and Roman WITUŁA
Generalizations of Kaprekar’s transformations and Kaprekar-style transformations
pp. 233-258
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Hanna HANSLIK, Edyta HETMANIOK, Mariusz PLESZCZYŃSKI, Ireneusz SOBSTYL and Roman WITUŁA
On the orbits of Kaprekar’s transformations by discussing the numerical results
pp. 259-274
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Edyta HETMANIOK, Alicja SAMULEWICZ, Ireneusz SOBSTYL, Marcin SZWEDA and Roman WITUŁA
Triangles with ideal proportions of sides
pp. 275-288
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Grzegorz SITEK
About bi-lines of regression
pp. 289-297
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Created by Ewelina Domalik