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1

Optical feedback. I static effects

Bałuka Paweł, Mielniczek Izabela, Druz Valeriia, Chabko Jakub, Kuzma Marian

Physics for Economy

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2023

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Vol. 5, No.1

71-85

EN

The feedbacks a common phenomenon. This paper gives examples of feedback in computer science (iterations). The primary aim of this paper is to observe the effects of optical feedback in a monitor-camera system. The static effects of optical feedback are presented in this paper. The problem of symmetry of the obtained images is discussed. It is explained how a multiple three-lens copying machine generates the Sierpinski triangle, which is a basic and very well-known fractal. In the next paper ( Part II ) the dynamic effects of optical feedback will be discussed.

2

A study of a meromorphic perturbation of the sine family

Domínguez Patricia, Vázquez Josué

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

8--27

EN

We study the dynamics of a meromorphic perturbation of the family λsinz by adding a pole at zero and a parameter μ , that is, fλ,μ(z)=λsinz+μ/z , where λ,μ∈C⧹{0} . We study some geometrical properties of fλ,μ and prove that the imaginary axis is invariant under fn and belongs to the Julia set when ∣λ∣≥1 . We give a set of parameters (λ,μ) , such that the Fatou set of fλ,μ has two super-attracting domains. If λ=1 and μ∈(0,2) , the Fatou set of f1,μ has two attracting domains. Also, we give parameters λ,μ such that ±π/2 are fixed points of fλ,μ and the Fatou set of fλ,μ contains attracting domains, parabolic domains, and Siegel discs, we present examples of these domains. This paper closes with an example of fλ,μ , where the Fatou set contains two types of domains, for λ,μ given.

3

Topologies on the set of iterates of a holomorphic function in infinite dimensions

Mackey M., Mellon P.

Bulletin of the Polish Academy of Sciences. Mathematics

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2022

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Vol. 70, no. 2

151--158

EN

Let f: B→B be a compact holomorphic map on the open unit ball B of a complex Banach space Z in possibly infinite dimensions, where f compact means f(B) is relatively compact. The sequence of iterates (fn)n of f (where fn:=f∘fn−1, f1:=f) is of much interest and, since it generally does not converge, the set of all its subsequential limits for a particular topology have been studied instead. We prove that the pointwise limit of any subsequence of (fn)n is itself a holomorphic function. We show, in fact, that on the set of iterates {fn : n∈N} the topology of pointwise convergence on B coincides with any finer topology on the space H(B,Z) of holomorphic functions from B to Z. In particular, it coincides with both the compact-open topology and the topology of local uniform convergence on B. Despite the fact that these topologies are not first countable, we prove that the set of accumulation points of (fn)n coincides with the set of all its subsequential limits.

4

Iteracje we współczesnej architekturze oraz nauczaniu architektonicznym

Wawrzyniak Cezary

Zeszyty Naukowe Wyższej Szkoły Technicznej w Katowicach

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2021

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nr 13

17--26

PL

Artykuł przybliża uświadomione wykorzystywanie iteracji w kształtowaniu formy architektonicznej na wybranych przykładach: stadionu Aami Park w Melbourne oraz wieżowca Al Hamra Tower w Kuwejcie. Ważnym aspektem poruszonym w pracy jest przybliżenie doświadczeń własnych związanych iteracją i dydaktyką na uczelni wyższej na kierunku architektura. Działalność architektoniczna osadzona na pograniczu techniki i sztuki. Skomplikowanie jej natury może do tego stopnia zmieniać obraz projektowania, że proste logiczne cykle ulegają ukryciu, rozmyciu w gąszczu wszelkich zasad. Zasad tych w wielu wypadkach nie można określić prostą regułą. Doświadczony architekt stawiając przysłowiową kreską decyduje o kilkunastu aspektach jednocześnie. Przy czym znaczna ich część wynika z jego doświadczenia jednostkowego i własnej interpretacji zasad ogólnych. Nie trudno więc o opinię negującą iteracje w architekturze wśród zawodowców zajmujących się innymi zawodami, które w ogólnej ocenie mogą być do architektury bardzo podobne.

EN

The paper presents the iteration in architectural design, using selected examples: the Aami Park stadium in Melbourne and the Al Hamra Tower in Kuwait. An important aspect of the paper is the presentation of the author’s own experiences related to the introduction of iteration in the didactic process of an design course in the field of architecture. Architectural activity is set on the borderline between technology and art. The complexity of its nature can change the image of design to such an extent that simple logical cycles become hidden, blurred in the thicket of all the rules. In many cases, these principles cannot be defined by a simple rule. An experienced architect making the proverbial line decides about a dozen or so aspects at the same time. A considerable part of them results from his individual experience and his own interpretation of general principles. Therefore, it is not difficult to find an opinion negating iterations in architecture among professionals dealing with other professions, which in general assessment may be very similar to architecture.

5

Some families of sublinear correspondences

Najmadi Parvaneh, Aghajani Masoumeh

Journal of Applied Analysis

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2019

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Vol. 25, nr 1

91--95

EN

Let K be a closed convex cone in a real Banach space, H: K → cc(K) a continuous sublinear correspondence with nonempty, convex and compact values in K, and let f : ℝ → ℝ be defined by f(t) = Σ∞n =0 antn, where t ∈ ℝ, an ≥ 0, n ∈ ℕ.We show that the correspondence Ft(x) := Σ∞n =0 an tnHn(x), (x ∈ K) is continuous and sublinear for every t ≥ 0 and Ft ∘ Fs(x) ⊆ Σ∞n=0 cnHn(x), x ∈ K, where cn = Σ>sup>nk = 0 akan−k tksn−k, t, s ≥ 0.

6

Evaluation of a marine object propulsion system preliminary design process using an iteration method

Adamkiewicz A., Przybyła M.

Journal of Machine Construction and Maintenance - Problemy Eksploatacji

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2018

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no. 2

87--93

EN

The article shows the complexity of a marine object generating the necessity of multi-criteria optimization. Due to a great number of criteria and complexity of structure, the design process was classified as hierarchic with a descending structure. A spatial design spiral has been suggested, through developing a two-dimensional Evans’ spiral. Specifics of preliminary design have been discussed. A procedure of iteration calculations in designing propulsion systems of vessels resulting from the ship owner’s design requirements has been presented. An evaluation of the process has been illustrated using as an example a local optimization of a one-dimension design problem of a propeller from a propulsion system of a Ro-Pax type vessel.

PL

W artykule pokazano złożoność obiektów oceanotechnicznych generującą konieczność optymalizacji wielokryterialnej. Ze względu na mnogość kryteriów oraz złożoność budowy proces projektowania zakwalifikowano jako hierarchiczny o strukturze zstępującej. Zaproponowano przestrzenną spiralę projektową, rozwijając tym samym dwuwymiarową spiralę Evansa. Omówiono specyfikę projektowania wstępnego. Przedstawiono procedurę obliczeń iteracyjnych w projektowaniu układów ruchowych statków morskich wynikającą z założeń projektowych armatora. Ewaluację procesu zilustrowano na przykładzie optymalizacji lokalnej jednowymiarowego problemu projektowego śruby napędowej, układu ruchowego jednostki typu Ro-Pax.

7

Structure-preserving numerical scheme for a generalized area-preserving crystalline curvature flow

Ishiwata T., Yazaki S.

Computer Methods in Materials Science

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2017

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Vol. 17, No. 2

122--135

EN

The presented numerical scheme preserves variational structure of a generalized area-preserving crystalline curvature flow. The scheme is based on an iteration and a projection method. Several numerical examples will verify that the enclosed area is preserved in numerical computation with high accuracy in the sense of double precision. Numerical computations realize theoretical convexification results starting from almost convex polygon, and are extended to a general setting starting from nonconvex polygon.

PL

Przedstawiony schemat numeryczny zachowuje zmienną strukturę uogólnionego krystalicznego ruchu krzywizny zachowującego stałą powierzchnię ograniczoną tą krzywizną. Schemat wykorzystuje metody iteracyjną i rzutowania. Szereg numerycz¬nych przykładów potwierdza, że w czasie obliczeń numerycznych niezmienność otoczonej powierzchni jest zachowana z dokładnością podwójnej precyzji. Numeryczne obliczenia potwierdzają teoretyczne wyniki uwypuklenia zaczynając od prawie wypukłego wielokąta i są rozszerzone dla ogólnego układu zaczynając od wklęsłego wielokąta.

8

Postbuckling of an Imperfect Plate Loaded in Compression

Havran J., Psotny M.

Mechanics and Mechanical Engineering

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2016

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Vol. 20, nr 2

143--149

EN

The stability analysis of a plate loaded in compression is presented. The non–linear FEM equations are derived from the minimum total potential energy principle. The peculiarities of the effects of the initial imperfections are investigated using the user computer code. Special attention is paid to the influence of imperfections on the post– critical buckling mode. The FEM computer program using a 48 DOF element has been used for analysis. FEM model consists of 4x4 finite elements. Full Newton-Raphson procedure has been applied.

9

Analysis for quasi-stationary electromagnetic field with ferromagnetic objects present within

Apanasewicz S., Pawłowski S., Plewako J.

Przegląd Elektrotechniczny

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2013

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R. 89, nr 12

169-172

EN

A method for calculating a distribution for a quasi-stationary electromagnetic field in the systems containing ferromagnetic objects of nonlinear properties is proposed. An iterative version of fundamental solutions method was applied in the presented research. Numerical tests performed on a simple, model system successfully proved the procedure to be correct and convergent. The report continues our research aimed at developing a method competitive to widely applied domain methods such as FEM, or FDM.

PL

W prezentowanej pracy zaproponowano metodę obliczania rozkładu quasi-stacjonarnego pola elektromagnetycznego w układach zawierających ciała ferromagnetyczne o nieliniowych właściwościach, wykorzystującej iteracyjną wersję metody rozwiązań fundamentalnych. Na prostym układzie modelowym przeprowadzono testy numeryczne wykazujące poprawność I zbieżność opisanej procedury. Praca jest kontynuacją badań zmierzających do opracowania metody konkurencyjnej wobec powszechnie stosowanych metod obszarowych (MES, MRS).

10

A Petri Net Interpretation of Open Reconfigurable Systems

Peschanski F., Klaudel H., Devillers R.

Fundamenta Informaticae

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2013

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Vol. 122, nr 1-2

85--117

EN

We present a Petri net interpretation of the pi-graphs - a graphical variant of the picalculus where recursion and replication are replaced by iteration. The concise and syntax-driven translation can be used to reason in Petri net terms about open reconfigurable systems. We demonstrate that the pi-graphs and their translated high-level Petri nets agree at the semantic level. In consequence, existing results on pi-graphs naturally extend to the translated Petri nets, most notably a guarantee of finiteness by construction.

11

Fundamental solutions method applied to non-linear, three-dimensional problems in electromagnetism

Pawłowski S., Plewako J.

Przegląd Elektrotechniczny

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2012

|

R. 88, nr 12b

93-96

EN

The method for solving non-linear 3D magnetostatics problems is presented in the paper. It is based on the iterative version of the fundamental solutions method. A dozen of numerical tests performed on a simple model system provided grounds to evaluate the method as effective and correct.

PL

W pracy zaprezentowano metodę rozwiązywania nieliniowych 3D zagadnień magnetostatyki opartą na iteracyjnej wersji metody rozwiązań fundamentalnych. Na prostym przykładzie modelowym przeprowadzono szereg testów numerycznych, które wstępnie pozwalają ocenić ją jako poprawną i skuteczną. (Zastosowanie metody rozwiązań fundamentalnych w nieliniowych trójwymiarowych zagadnieniach elektromagnetyzmu).

12

Akceleracja obliczeń komputerowych za pomocą układów graficznych z wykorzystaniem technologii CUDA

Stefanowicz Ł., Wiśniewski R., Wiśniewska M.

Pomiary Automatyka Kontrola

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2011

|

R. 57, nr 8

954-956

PL

W artykule zaprezentowano możliwość zastosowania układów graficznych celem przyspieszenia obliczeń komputerowych. Przedstawiono technologię oraz architekturę CUDA firmy nVidia, a także podstawowe rozszerzenia względem standardów języka C. W referacie omówiono autorskie algorytmy testowe oraz metodykę badań, które przeprowadzono w celu określenia skuteczności akceleracji obliczeń komputerowych z wykorzystaniem procesorów graficznych GPU w porównaniu do rozwiązań tradycyjnych, opartych o CPU.

EN

The paper deals with application of the graphic processor units (GPUs) to acceleration of computer operations and computations. The traditional computation methods are based on the Central Processor Unit (CPU), which ought to handle all computer operations and tasks. Such a solution is especially not effective in case of distributed systems where some sub-tasks can be performed in parallel. Many parallel threads can accelerate computing, which results in a shorter execution time. In the paper a new CUDA technology and architecture is shown. The presented idea of CUDA technology bases on application of the GPU processors to compu-tation to achieve better performance in comparison with the traditional methods, where CPUs are used. The GPU processors may perform multi-thread calculation. Therefore, especially in case of tasks where concurrency can be applied, CUDA may highly speed-up the computation process. The effectiveness of CUDA technology was verified experimentally. To perform investigations and experiments, the own test modules were used. The library of benchmarks consists of various algorithms, from simple iteration scripts to video processing methods. The results obtained from calculations performed via CPU and via GPU are compared and discussed.

13

Existence and uniqueness theorem for a hammerstein nonlinear integral equation

Khachatryan A. Kh., Khachatryan Kh. A.

Opuscula Mathematica

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2011

|

Vol. 31, no. 3

393-398

EN

The existence of a solution, as well as some properties of the obtained solution for a Hammerstein type nonlinear integral equation have been investigated. For a certain class of functions the uniqueness theorem has also been proved.

14

K3M: A universal algorithm for image skeletonization and a review of thinning techniques

Saeed K., Tabędzki M., Rybnik M., Adamski M.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 2

317-335

EN

This paper aims at three aspects closely related to each other: first, it presents the state of the art in the area of thinning methodologies, by giving descriptions of general ideas of the most significant algorithms with a comparison between them. Secondly, it proposes a new thinning algorithm that presents interesting properties in terms of processing quality and algorithm clarity, enriched with examples. Thirdly, the work considers parallelization issues for intrinsically sequential algorithms of thinning. The main advantage of the suggested algorithm is its universality, which makes it useful and versatile for a variety of applications.

15

Two results on Jachymski-Schörder-Stein contractions

Reich S., Zaslavski A. J.

Bulletin of the Polish Academy of Sciences. Mathematics

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2008

|

Vol. 56, no 1

53-58

EN

We establish two fixed point theorems for certain mappings of contractive type.

16

A new iterative method for solution of the dual problem of geometric programming

Yatsko A., Sudakov R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2007

|

Vol. 12

115-120

EN

In this article a new method of optimal solution of the dual problem is proposed. This method is based on Newton's attraction theorem. An estimate of iteration convergence is given. The method uses some new procedure of correction of the current iteration. It is shown that the method uses matrix operations at each step of calculations and has a quadric speed of the convergence.

17

Asymptotic behavior of inexact orbits for a class of operators in complete metric spaces

Butnariu D., Reich S., Zaslavski A. J.

Journal of Applied Analysis

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2007

|

Vol. 13, nr 1

1-11

EN

We exhibit a class of nonlinear operators with the property that their iterates converge to their unique fixed points even when com- putational errors are present. We also showthat most (in the sense of the Baire category) elements in an appropriate complete metric space of operators do, in fact, possess this property.

18

Stress controlled shape optimization of 2D elastic structures

Gutkowski W, Zawidzka J., Zawidzki J.

Engineering Transactions

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2004

|

Vol. 52, iss.1-2

23-35

EN

A simple and effective method of stress-controlled shape optimization of 2D linear elastic structures is presented. The main elements of the method are: adaptive FE grids fitting well to the structure shape at each iteration step of the proposed simple optimization algorithm and the concept of stress level factor, controlling directly the design variables being the gird parameters.Several examples of beam-type and plate-type 2D structures are investigated. A few iterations only are needed in order to reach a nearly optimal solution.

19

Aproksymacja skończonego układu punktów płaszczyzny figurą będącą sumą punktu i prostej

Korczak A.

Badania Operacyjne i Decyzje

|

2004

|

nr 2

37-50

PL

Przedstawiono nową metodę aproksymacji skończonego układu punktów płaszczyzny, zawierającego punkty "odstające" od układu. Dotychczas proponowane metody eliminowały te punkty, a pozostały układ aproksymowały prostą. W opisanej metodzie nie odrzuca się żadnego punktu. Jako krzywą aproksymującą przyjęto figurę będącą sumą punktu i prostej i wyznaczono jej parametry. Otrzymana w ten sposób prosta - nazwana odporną prostą regresji - jest uniezależniona od "odstających" punktów, które opisuje wyznaczony punkt. Metodę zilustrowano przykładami.

EN

Approximation of the plane point finite system is not only a theoretical problem. It exists also in engineering and economy. The points on the plane are the result of investigation and experience. So, it is highly probable to obtain results - point that are :not congruent" with the others. Sometimes it happens just accidentally, it may, however, be also the evidence of some anomalies. In this article, we consider a finite plane points the system dispersed along the straight line, including the points "not congruent" with the system. While seeking the regression curve describing a given plane point system, we often ask ourselves to that extent the curve course is influence by those "not congruent" points. The method proposed previously assumed that the curve course is not influenced by those substantially by those "not congruent" points and approximation the whole system by straight line or eliminated those points and the remaining system was approximated by the straight line. In the method described below no points is rejected. As an approximating curve there was assumed a figure being the sum of point and straight lines, and afterwards its parameter were determined. The straight line obtained in this way - called the resistant regression line - does not depend on the "not congruent" points described by the point determined. The method is illustrated by examples calculating each time - for comparison - the residstant regression straight line and regression straight line.

20

Rigidity of tame rational functions

Przytycki F., Urbański M.

Bulletin of the Polish Academy of Sciences. Mathematics

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1999

|

Vol. 47, no 2

163-181

EN

We introduce and establish some basic properties of the tame rational functions. The class of these functions contains all the rational functions with no recurrent critical points in their Julia sets. For tame non-exceptional functions we prove that the Lipschitz conjugacy, the same spectra of moduli of derivatives at periodic orbits and conformal conjugavcy are mutually equivalent. We prove also the following rigidity result: If h is a Borel measurable invertible map which conjugates two tame functions f and g a.e. and if h transports conformal measure m[sub f] to a measure equivalent to m[sub g] then h extends from a set of full measure m[sub f] to a conformal homeomorphism of neighbourhoods of respective Julia sets. This extends D. Sullivan's rigidity theorem for holomorphic expanding repellers. We provide also a few lines proof of E. Prado's theorem that two generalized polinomial-like maps at zero Teichmueller's distance are holomorphically conjugate.