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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 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.
3
Content available remote Postbuckling of an Imperfect Plate Loaded in Compression
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.
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).
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).
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.
7
EN
In this paper, we establish some fixed point theorems for Noor iterations associated with Zamfirescu mappings in uniformly convex Banach spaces and deduce similar other results on Mann and Ishikawa iterations as special cases. Our results improve a multitude of recent results in the fixed point theory especially the result of Ciric [5].
EN
The article contains an effective and easily realized multilevel turbocoding scheme based on two-dimensional linear iterative codes with diagonal paritet checks.
PL
. Artykuł opisuje skuteczna I prosta realizację wielopoziomowego kodowania wykorzystującego dwuwymiarową liniową iterację kodu ze sprawdzanie parzystości diagonalnej.
9
Content available remote Two results on Jachymski-Schörder-Stein contractions
EN
We establish two fixed point theorems for certain mappings of contractive type.
10
Content available remote A new iterative method for solution of the dual problem of geometric programming
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.
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.
12
Content available remote Stress controlled shape optimization of 2D elastic structures
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.
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.
14
Content available remote Stability of anew iteration method for strongly pseudocontractive mappings
EN
In this note we prove that a recently introduced iteration procedure is almost stable with respect to strong pseudocontractions in real uniformly Banach spaces.
EN
Let K be a closed convex cone with the nonempty interior in a real Banach space and cc(K) denote the family of all nonempty convex compact subsets of K. If {Ff : t ≥ 0} is a concave iteration semigroup of continuous linear set-valued functions Ft : K → cc(K) with F°(x) = {x} for x ∈ K, then DtFt(x) = Ft (G(x)) for x ∈ K and t ≥ 0, where DtFt(x) denotes the Hukuhara derivative of Ft(x) with respect to t and (wzór) for x ∈ K.
16
Content available remote Rigidity of tame rational functions
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.
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