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1
Content available Multiple solutions of boundary value problems on time scales for φ-laplacian operator
Amster Pablo, Kuna Mariel Paula, Santos Dionicio Pastor
Opuscula Mathematica
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2020
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Vol. 40, no. 4
405--425
EN
We establish the existence and multiplicity of solutions for some boundary value problems on time scales with a y-Laplacian operator. For this purpose, we employ the concept of lower and upper solutions and the Leray-Schauder degree. The results extend and improve known results for analogous problems with discrete p-Laplacian as well as those for boundary value problems on time scales.
2
Content available remote Approaches to the determination of the working area of parallel robots and the analysis of their geometric characteristics
Malyshev Dmitry, Rybak Larisa, Posypkin Mikhail, Usov Alexander
Engineering Transactions
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2019
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Vol. 67, iss. 3
333--345
EN
The article presents and experimentally confirms two approaches to the problem of determining the working area of parallel robots using the example of a planar robot DexTAR with two degrees of freedom. The proposed approaches are based on the use of constraint equations of coordinates. In the first approach, the original kinematic equations of coordinates in the six-dimensional space (two coordinates describing the position of the output link and four coordinates – the rotation angles of the rods) followed by projecting the solution onto the two-dimensional plane is used. In the second approach, the system of constraint equations is reduced to a system of inequalities describing the coordinates of the output link of the robot, which are solved in a two-dimensional Euclidean space. The results of the computational experiments are given. As an algorithmic basis of the proposed approaches, the method of non-uniform coverings is used, which obtains the external and internal approximation of the solution set of equality/inequality systems with a given accuracy. The approximation is a set of boxes. It is shown that in the first approach, it is more efficient to apply interval estimates that coincide with the extremes of the function on the box, and in the second approach, grid approximation performs better due to multiple occurrences of variables in inequalities.
3
Content available Multiplicity results for perturbed fourth-order Kirchhoff-type problems
Tavani M. R. H., Afrouzi G. A., Heidarkhani S.
Opuscula Mathematica
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2017
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Vol. 37, no. 5
755--772
EN
In this paper, we investigate the existence of three generalized solutions for fourth-order Kirchhoff-type problems with a perturbed nonlinear term depending on two real parameters. Our approach is based on variational methods.
4
Content available remote Regularising Ill-posed Discrete Optimisation: Quests with P Systems
Nicolescu R., Gimel’farb G., Morris J., Delmas P., Gong R.
Fundamenta Informaticae
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2014
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Vol. 131, nr 3-4
465--483
EN
We propose a novel approach to justify and guide regularisation of an ill-posed one-dimensional global optimisation with multiple solutions using a massively parallel (P system) model of the solution space. Classical optimisation assumes a well-posed problem with a stable unique solution. Most of important practical problems are ill posed due to an unstable or non-unique global optimum and are regularised to get a unique best-suited solution. Whilst regularisation theory exists largely for unstable unique solutions, its recommendations are often routinely applied to inverse optical problems with essentially non-unique solutions, e.g. computer stereo vision or image segmentation, typically formulated in terms of global energy minimisation. In these cases the recommended regularisation becomes purely heuristic and does not guarantee a unique solution. As a result, classical optimisation algorithms: dynamic programming (DP) and belief propagation (BP) – meet with difficulties. Our recent concurrent propagation (CP), leaning upon the P systems paradigm, extends DP and BP to always detect whether the problem is ill posed or not and store in the ill-posed case an entire space of solutions that yield the same global optimum. This suggests a radically new path to proper regularisation: select the best-suited unique solution by exploring statistical and structural features of this space. We propose a P systems based implementation of CP and set out as a case study an application of CP to the image matching problem in stereo vision.
5
Content available Multiple solutions for systems of multi-point boundary value problems
Graef J. R., Heidarkhani S., Kong L.
Opuscula Mathematica
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2013
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Vol. 33, no. 2
293--306
EN
In this paper, we establish the existence of at least three solutions of the multi-point boundary value system [formula]. The approaches used are based on variational methods and critical point theory.
6
Content available remote A Novel RNA Genetic Algorithm for the Parameter Estimation of the Ordinary Differential Equations with Multiple Solutions
Si X. Y., Fang G. H., Yang F., Guo W., Wang T., Si X. H.
Przegląd Elektrotechniczny
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2012
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R. 88, nr 9b
118-120
EN
In fluid mechanics, to obtain the multiple solutions in ordinary differential equations is always a concerned and difficult problem. In this paper, a novel RNA genetic algorithm (NRNA-GA) inspired by RNA molecular structure and operators is proposed to solve the parameter estimation problems of the multiple solutions in fluid mechanics. This algorithm has improved greatly in precision and the success rate. Multiple solutions can be found through changing accuracy and search coverage and multi-iterations of computer. At last, parameter estimation of the ordinary differential equations with multiple solutions is calculated. We found that the result has great accuracy and this method is practical.
PL
W artykule zaproponowano nowy algorytm genetyczny NRNA-GA inspirowany strukturą molekularną RNA przeznaczony do rozwiązywania równań z wieloma rozwiązaniami w mechanice cieczy.
7
Content available remote Analysis of CMOS circuits having multiple DC operating points
Hałgas M., Tadeusiewicz M.
Przegląd Elektrotechniczny
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2011
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R. 87, nr 5
40-42
EN
This paper is devoted to the analysis of the circuits containing short-channel MOS transistors, having multiple DC solutions (operating points). The transistors are characterized by the PSP model, the most advanced surface-potential-based compact MOSFET model, selected (since December 2005) as standard for the new generation of integrated circuits. This paper offers an algorithm enabling us to find multiple DC solutions and trace multivalued input-output characteristics of integrated circuits using the latest PSP 103.1.1 MOSFET model. The main idea of the algorithm is based on a single-valued driving point characteristic, called a test characteristic and the section-wise piecewise-linear approximations. The approach proposed in this paper is illustrated via a numerical example.
PL
Praca dotyczy analizy układów zawierających tranzystory MOS z krótkim kanałem, mających wiele rozwiązań DC. Tranzystory są opisane za pomocą modelu PSP, najbardziej zaawansowanego, opartego na koncepcji potencjału powierzchniowego modelu MOSFET, uznanego w 2005 roku za standardowy w zastosowaniu do nowej generacji układów scalonych. W pracy zaproponowano algorytm obliczania wielokrotnych rozwiązań DC oraz wyznaczania wielowartościowych charakterystyk typu wejście-wyjście układów scalonych, z użyciem najnowszej wersji PSP 103.1.1 modelu MOSFET. W algorytmie wykorzystano pewne jedno-wartościowe charakterystyki wejściowe, zwane charakterystykami testowymi oraz uogólnioną odcinkowo-liniową aproksymację. Dla ilustracji podano przykład liczbowy.
8
Content available remote Contraction and elimination methods for finding multiple DC solutions of bipolar circuits
Tadeusiewicz M., Hałgas S.
Przegląd Elektrotechniczny
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2010
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R. 86, nr 1
11-13
EN
The paper is focused on the analysis of diode-transistor circuits having multiple DC solutions and brings two methods enabling us to find the solutions, without any piecewise-linear approximations. The first method is a modification of an earlier developed method, whereas the other is new and based on an original idea. Both the methods are implemented in an algorithm that guarantees finding all the DC solutions. Numerical experiments show that the proposed approach is efficient, the analysis is improved and the computation process is speeded up.
PL
Artykuł dotyczy analizy układów diodowo-tranzystorowych o wielu rozwiązaniach stałoprądowych. Zaproponowano dwie metody umożliwiające wyznaczanie tych rozwiązań bez konieczności stosowania aproksymacji odcinkowo-liniowej. Metody te zaimplementowano w postaci algorytmu gwarantującego znalezienie wszystkich rozwiązań DC. Eksperymenty numeryczne potwierdziły efektywność zaproponowanego podejścia.
9
Content available Some Contraction Methods for Locating and Finding All the DC Operating Points of Diode-Transistor Circuits
Tadeusiewicz M., Hałgas S.
International Journal of Electronics and Telecommunications
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2010
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Vol. 56, No. 4
331-338
EN
The paper is focused on the analysis of diodetransistor circuits having multiple DC solutions (operating points) and brings two methods enabling us to find all the solutions. The first method contracts and eliminates some hyperrectangular regions where the solutions are sought. It is based on the idea of framing of the nonlinear functions appearing in the mathematical description of the circuit by linear ones and exploits the Woodbury formula in matrix theory. The other method finds quickly and easily preliminary bounds on the location of all the solutions. The method employs some monotonic functions and generates convergent sequences leading to a shrinked hyperrectangle that contains all the solutions. Both the proposed methods are rigorously proved. They constitute the core of an algorithm which efficiently finds all the DC operating points of diode-transistor circuits. It is illustrated via numerical examples.
10
Content available remote Analiza układów nieliniowych o wielu rozwiązaniach DC
Tadeusiewicz M., Hałgas S.
Przegląd Elektrotechniczny
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2009
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R. 85, nr 11
149-152
PL
Praca dotyczy analizy nieliniowych układów analogowych o wielu punktach równowagi (rozwiązaniach DC). Przedstawiono prostą metodę pozwalającą wyznaczyć niektóre z tych rozwiązań, opartą na idei charakterystyk testowych. Zdefiniowano cztery rodzaje charakterystyk testowych. Zaproponowano wykorzystanie tej metody w algorytmie gwarantującym znalezienie wszystkich rozwiązań DC oraz zamieszczono przykład liczbowy potwierdzający skuteczność tego rodzaju podejścia.
EN
The paper deals with nonlinear circuits having multiple equilibrium points (DC solutions). A simple method enabling us to find some of the multiple DC solutions is developed. It is based on the idea of test characteristics. Four types of the characteristics have been defined. The proposed method can be combined with an algorithm that guarantees finding all the solutions. A numerical example given in the paper shows that the proposed approach is efficient.
11
Finding all the DC solutions of circuits containing diodes and bipolar transistors
Tadeusiewicz M., Hałgas S.
Elektronika : konstrukcje, technologie, zastosowania
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2009
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Vol. 50, nr 12
39-42
EN
The paper deals with diode-transistor circuits having multiple DC solutions and offers two contraction and elimination methods enabling us to find all the DC solutions. They can be directly used to the circuits with constant parameters, when the chip is at fixed temperature, or merged into an earlier developed algorithm enabling us to analyze circuits with the thermal constraint. Numerical experiments show that the proposed approach is efficient and improves the analysis of transistor circuits having multiple DC solutions. It is illustrated via a numerical example.
PL
Praca dotyczy analizy układów diodowo-tranzystorowych o wielu punktach równowagi. Zaproponowano w niej dwie metody zawężania i eliminacji umożliwiające opracowanie algorytmu wyznaczania wszystkich rozwiązań stałoprądowych. Metody te mogą być użyte bezpośrednio do analizy układów o stałych parametrach, rozpatrywanych w ustalonej temperaturze lub wprowadzone, jako procedury, do wcześniej opracowanego algorytmu wyznaczania wszystkich rozwiązań DC z uwzględnieniem zjawiska samonagrzewania chipu. Przykłady numeryczne pokazały, że zaproponowane podejście jest skuteczne i usprawnia analizę układów tranzystorowych o wielu rozwiązaniach DC. Jeden z przykładów zamieszczono w pracy.
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