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1
Content available remote Stress controlled shape optimization of 2D elastic structures
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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.
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Content available remote A Petri Net Interpretation of Open Reconfigurable Systems
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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.
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Content available remote Topologies on the set of iterates of a holomorphic function in infinite dimensions
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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.
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Content available A Coherent Model of DCF Valuation
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Business valuation through DCF is recognized as one of the most popular valuation approaches. DCF valuation models, however, have become extremely complex. Modeling requires plenty of input data to be processed, the process is done in many stages, and the data obtained on each of the stages may be interrelated. The process then is not simply a chain of tasks. The modern models work via sophisticated mechanisms of loops being triggered whenever a new piece of information is revealed and the whole model needs updating. Technically speaking, in the spreadsheets environment, this may only be done with the use of iterations. The valuation model should also be subjected to the sensitivity analysis, which is able to quantify the impact of every single assumption made on the final company value. The analysis points out the set of critical assumptions, which have the major impact on the calculated company’s value. Apart from quantifying the impact of the assumptions, the analysis runs qualitative checks on the assumptions assessing the robustness of the arguments standing behind the critical factors for valuation. Consequently, the sensitivity analysis improves the objectivity of the model and mitigates the exposure for the possible results manipulation. The sensitivity analysis reveals its critical role in the valuation process and proves that it should be considered as the standard step in every DCF valuation.
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.
EN
Our aim is to study continuous solutions φ of the classical linear iterative equation φ(f(x,y)) = g(x,y)φ(x,y) + h(x,y), where the given function f is defined as a pair of means. We are interested in the case when f has no fixed points. In turns out that in such a case continuous solutions of (1) depend on an arbitrary function.
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Content available Optical feedback. I static effects
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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.
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Content available remote A new iterative method for solution of the dual problem of geometric programming
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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.
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.
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.
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Let ϕ be an arbitrary bijection of $ℝ_+$. We prove that if the two-place function $ϕ^{-1}[ϕ (s)+ϕ (t)]$ is subadditive in $ℝ^2_+$ then $ϕ $ must be a convex homeomorphism of $ℝ_+$. This is a partial converse of Mulholland's inequality. Some new properties of subadditive bijections of $ℝ_+$ are also given. We apply the above results to obtain several converses of Minkowski's inequality.
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.
13
Content available remote Two results on Jachymski-Schörder-Stein contractions
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We establish two fixed point theorems for certain mappings of contractive type.
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Content available remote X-minimal patterns and a generalization of Sharkovskiĭ's theorem
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We study the law of coexistence of different types of cycles for a continuous map of the interval. For this we introduce the notion of eccentricity of a pattern and characterize those patterns with a given eccentricity that are simplest from the point of view of the forcing relation. We call these patterns X-minimal. We obtain a generalization of Sharkovskiĭ's Theorem where the notion of period is replaced by the notion of eccentricity.
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.
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Content available remote Postbuckling of an Imperfect Plate Loaded in Compression
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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.
17
Content available remote A study of a meromorphic perturbation of the sine family
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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.
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.
PL
Jakość stanowi podstawowe kryterium satysfakcji użytkownika oprogramowania. Ze względu na złożony charakter tego pojęcia, kryteria akceptacji umożliwiają lepsze zrozumienie oczekiwanego poziomu jakości. Stąd też, dla projektów Agile, zaproponowano koncepcję wiodącej roli kryteriów akceptacji w zapewnianiu jakości tworzonego oprogramowania. Przedstawiono definicje tych kryteriów oraz sformułowano listę warunków ich poprawności. Najpierw podczas definiowania wysokopoziomowych, a także szczegółowych specyfikacji wymagań użytkownika, a następnie podczas kolejnych iteracji. Udział kryteriów akceptacji we wszystkich iteracjach projektu przedstawiono za pomocą schematu graficznego. Rozważono problem rosnących kosztów naprawy błędów ze względu na czas ich wykrycia. Proponuje się rozwiązanie tego problemu za pomocą kluczowej roli kryteriów akceptacji, wynikającej z zauważonych zmian w projektach Agile, a dotyczących sekwencji działań testowania i kodowania oraz wzmocnionej roli iteracji.
EN
Quality constitutes the basic criterion of end user satisfaction. For the reason of the complex nature of the concept of quality acceptance criteria allow for a better understanding of the expected level of quality. Therefore, for Agile projects, proposed the concept of a leading role to acceptance criteria in ensuring that software quality. There are the definitions of these criteria and formulated a list of conditions for their correctness. First, when is defined a high-level and detailed specification of the user requirements, and then in the next iterations. Participation of acceptance criteria in all iterations in a project using the graphical schema presented. A problem of the rising cost of repairing program faults due to the time of their detection. It is proposed to solve this problem by using the key role of acceptance criteria, resulting from the observed change in Agile projects, testing and coding sequence, and the enhanced role of the iteration.
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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.
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