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1
Content available remote A Dai-Liao-type projection method for monotone nonlinear equations and signal processing
Ibrahim Abdulkarim Hassan, Kumam Poom, Abubakar Auwal Bala, Abdullahi Muhammad Sirajo, Mohammad Hassan
Demonstratio Mathematica
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2022
|
Vol. 55, nr 1
978--1013
EN
In this article, inspired by the projection technique of Solodov and Svaiter, we exploit the simple structure, low memory requirement, and good convergence properties of the mixed conjugate gradient method of Stanimirović et al. [New hybrid conjugate gradient and broyden-fletcher-goldfarbshanno conjugate gradient methods, J. Optim. Theory Appl. 178 (2018), no. 3, 860–884] for unconstrained optimization problems to solve convex constrained monotone nonlinear equations. The proposed method does not require Jacobian information. Under monotonicity and Lipschitz continuity assumptions, the global convergence properties of the proposed method are established. Computational experiments indicate that the proposed method is computationally efficient. Furthermore, the proposed method is applied to solve the ℓ1 -norm regularized problems to decode sparse signals and images in compressive sensing.
2
Content available remote Hasimoto surfaces for two classes of curve evolution in Minkowski 3-space
Gürbüz Nevin, Yoon Dae Won
Demonstratio Mathematica
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2020
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Vol. 53, nr 1
277--284
EN
In this work, we study Hasimoto surfaces for the second and third classes of curve evolution corresponding to a Frenet frame in Minkowski 3-space. Later, we derive two formulas for the differentials of the second and third Hasimoto-like transformations associated with the repulsive-type nonlinear Schrödinger equation.
3
Content available Applications of python programs in solving of equations based on selected numerical methods
Ziółkowski M., Stępień L., Stępień M. R., Gola A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2017
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Vol. 22
31--45
EN
In this paper we present the mathematical background of the four most used numerical methods of solving equations and few examples of Python applications that find the approximations of the roots of the given equations. We also compare the exact and approximate solutions of polynomial equations of third degree. Exact solutions are obtained with usage of Cardano formulae by the help of Mathematica environment, the approximate ones – based on the selected numerical methods by the help of applications written in Python language.
4
Content available Fourth order nonlinear evolution equation for interfacial gravity waves in the presence of air flowing over water and a basic current shear
Majumder D. P., Dhar A. K.
International Journal of Applied Mechanics and Engineering
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2015
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Vol. 20, no. 3
517--530
EN
A fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves as first pointed out by Dysthe (1979) is derived for gravity waves propagating at the interface of two superposed fluids of infinite depth in the presence of air flowing over water and a basic current shear. A stability analysis is then made for a uniform Stokes gravity wave train. Graphs are plotted for the maximum growth rate of instability and for wave number at marginal stability against wave steepness for different values of air flow velocity and basic current shears. Significant deviations are noticed from the results obtained from the third order evolution equation, which is the nonlinear Schrödinger equation.
5
Content available Effect of capillarity on fourth order nonlinear evolution equation for two Stokes wave trains in deep water in the presence of air flowing over water
Dhar A. K., Mondal J.
International Journal of Applied Mechanics and Engineering
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2015
|
Vol. 20, no. 2
267--282
EN
Fourth order nonlinear evolution equations, which are a good starting point for the study of nonlinear water waves, are derived for deep water surface capillary gravity waves in the presence of second waves in which air is blowing over water. Here it is assumed that the space variation of the amplitude takes place only in a direction along which the group velocity projection of the two waves overlap. A stability analysis is made for a uniform wave train in the presence of a second wave train. Graphs are plotted for the maximum growth rate of instability wave number at marginal stability and wave number separation of fastest growing sideband component against wave steepness. Significant improvements are noticed from the results obtained from the two coupled third order nonlinear Schrödinger equations.
6
Zastosowanie obliczeń ewolucyjnych w zagadnieniach związanych z analizą sieci hydraulicznych
Handzel Z., Gajer M., Jamróz D.
Elektronika : konstrukcje, technologie, zastosowania
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2015
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Vol. 56, nr 1
56-58
PL
W artykule zaproponowano wykorzystanie algorytmów ewolucyjnych w celu przeprowadzania analizy oczkowych sieci hydraulicznych. Zadaniem algorytmu ewolucyjnego jest wyznaczenie wartości przepływów w poszczególnych gałęziach arbitralnie zadanej sieci hydraulicznej. W artykule zaproponowano sposób kodowania rozwiązań na materiale genetycznym ewoluujących osobników oraz zdefiniowano postać funkcji dopasowania pozwalającej na ocenę rozwiązań odnajdowanych w toku procesów ewolucyjnych.
EN
In the paper we propose to use evolutionary algorithms for the purpose of analysis of hydraulic networks. The aim of evolutionary algorithm is to determine the values of flow in the branches of arbitrarily given hydraulic network. In the paper we propose the way of coding of solutions on genetic material of evolving individuals and we define the fitness function to evaluate solutions found during the process of evolution.
7
Content available remote Numeryczne modelowanie indukcyjnych nadprzewodnikowych ograniczników prądu zwarciowego
Łanczont M.
Przegląd Elektrotechniczny
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2014
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R. 90, nr 2
65--67
PL
Artykuł opisuje projekt obwodowego modelu numerycznego indukcyjnego nadprzewodnikowego ogranicznika prądu. Przedstawiono założenia modelu matematycznego, charakterystykę modelowanego obiektu oraz wyniki symulacji.
EN
This paper describes project the peripheral numerical model of induction superconducting fault current limiter. The assumptions of a mathematical model, characteristics of a modeled device and the simulation results where presented.
8
Content available remote Leader Glowworm Swarm Optimization Algorithm for Solving Nonlinear Equations Systems
Zhou Y., Liu J., Zhao G.
Przegląd Elektrotechniczny
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2012
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R. 88, nr 1b
101-106
EN
This paper presents a leader glowworm swarm optimization algorithm (LGSO) for solving nonlinear equations systems. Since glowworm swarm optimization algorithm has bad optimized ability at high dimension, proposing glowworm swarm optimization algorithm with leader mechanism to strengthen the global optimization ability. Through various types nonlinear equations testing, experiment results show that the proposed algorithm has strong global searching capability and quickly finding the solutions of the equations, thus obviously improving the optimization global ability.
PL
Zaprezentowano optymalizacyjny algorytm mrówkowy “świetlikowy” do rozwiązywania system równań nieliniowych. Ponieważ algorytm ten ma słabe możliwości optymalizacyjne przy dużych rozmiarach wprowadzono wspomagający mechanizm prowadzący „leader”.
9
Content available remote Analytical solution of forced-convective boundary-layer flow over a flat plate
Mirgolbabaei H., Barari A., Ibsen L. B., Esfahani M. G.
Archives of Civil and Mechanical Engineering
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2010
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Vol. 10, no 2
43-51
EN
In this letter, the problem of forced convection heat transfer over a horizontal flat plate is investigated by employing the Adomian Decomposition Method (ADM). The series solution of the nonlinear differential equations governing on the problem is developed. Comparison between results obtained and those of numerical solution shows excellent agreement, illustrating the effectiveness of the method. The solution obtained by ADM gives an explicit expression of temperature distribution and velocity distribution over a flat plate.
PL
W artykule przedstawiono zastosowanie metody dekompozycji Adomiana do wymuszonego, konwekcyjnie przepływu ciepła w poziomej, płaskiej płycie. Rozwiązania nieliniowych równań różniczkowych opisujących zagadnienie poszukiwana w postaci szeregów Adomiana. Z porównania otrzymanych wyników z wynikami innych metod numerycznych wynika doskonała ich zgodność, która potwierdza skuteczność zastosowanej metody. Otrzymane rozwiązanie pozwoliło jednoznacznie wyznaczyć rozkład i prędkości mian temperatury w analizowanej płycie.
10
Content available remote Stability analysis from fourth order evolution equation for deep water capillary-gravity waves in the presence of air flowing over water
Majumder D. P., Dhar A. K.
International Journal of Applied Mechanics and Engineering
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2009
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Vol. 14, no 2
433-442
EN
Fourth order nonlinear evolution equations, which are a good starting point for the study of nonlinear water waves as first pointed out by Dysthe (1979) and later elaborated by Janssen (1983), are derived for deep water capillary-gravity waves in the presence of air flowing over water. Stability analysis is then made for a uniform Stokes capillary gravity wave train. Graphs are plotted for the maximum growth rate of instability, the frequency at marginal stability and the frequency separation for fastest growing side-band component as a function of wave steepness. Significant deviations are noticed from the results obtained from the third-order evolution equation, which is the nonlinear Schrödinger equation.
11
Content available remote A shock problem involving a nonlinear viscoelastic bar associated with a nonlinear boundary condition
Long N., Giai V., Truong L.
Demonstratio Mathematica
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2008
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Vol. 41, nr 1
85-108
EN
We study the initial-boundary value problem for a nonlinear wave equation given by [...] where p > 2, q > l, K, lambda are given constants and uo, u1, F are given functions, the unknown function u(x,t) and the unknown boundary value P (t) satisfy the following nonlinear integral equation [...] where K1, alpha, beta are given constants and g, k arę given functions. In Part 1 we prove a theorem of existence and uniqueness of a weak solution (u, P) of problem (1), (2). The proof is based on the Faedo-Galerkin method associated with a priori estimates, weak convergence and compactness techniques. In Part 3 we obtain an asymptotic expansion of the solution (u, P) of the problem (1), (2) up to order N+1 in three small parameters K, lambda, K1.
12
Content available remote On existence of solutions to nonlinear equations with degenerate mappings
Prusińska A., Tret'yakov A.
Journal of Mathematics and Applications
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2006
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Vol. 28
101-111
EN
The paper presents recent advances in p-regularity theory. The main result of this theory gives a detailed description of the structure of the zero set of an irregular nonlinear mapping. We illustrate the theory with an application to the problem of existence of the solutions to the nonlinear equations with singular mappings.
13
Content available remote Ishikawa iterative sequence with errors for k-subaccetive operators in arbitrary Banach spaces
Li Y.
Demonstratio Mathematica
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2006
|
Vol. 39, nr 1
161-168
EN
In this paper, the iterative solution is studied for equation x+Tx =f with a Lipschitz K-subaccetive operator in arbitrary Banach spaces, some previously results are generalized.
14
Content available remote Stability of iterative procedures for multivalued maps in metric spaces
Singh S., Bhatnagar C., Mishra S.
Demonstratio Mathematica
|
2005
|
Vol. 38, nr 4
905-916
EN
Let (X,d) be a metric space and T a self-map of X. Let Xn+i = f(T,Xn) denote some iterative procedure. Let {xn} be convergent to a fixed point u of T and {yn} be an arbitrary sequence in X. Set En=d[yn+i, f(T, yn)], n = 0,1,2,..., then the iterative procedure f(T,Xn) is T-stable provided that limEn = 0 implies that limnyn = u. This definition has been extended by Singh and Chadha [34] to discuss the problem of stability for multivalued operators on metric spaces. The purpose of this paper is to present a fixed point theorem for generalized multivalued contractions on a setting more general than metric spaces. The same is utilized to discuss the problem of stability of iterative procedures in multivalued analysis. Some special cases due to Stefan Czerwik and others are discussed as special cases.
15
Zastosowanie metody elementów skończonych w nieliniowych zagadnieniach przepływu masy
Bożenko B.
Zeszyty Naukowe. Matematyka / Politechnika Opolska
|
1999
|
z. 15
5-11
PL
W pracy podano schemat oparty na metodzie elementów skończonych rozwiązywania pewnego nieliniowego równania, opisującego pole koncentracji cząsteczek domieszki w ośrodku ciągłym z uwzględnieniem kombinacji dyfuzji i konwekcji.
EN
In the paper on the basis of the finite element method the technique of solving non-linear equation for convection diffusion is presented.
16
Content available remote Solution of nonlinear polyparabolic problem for the three-dimensional time-spatial cylinder with boundary conditions of Riquier type
Koroński J.
Opuscula Mathematica
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1998
|
Vol. 18,
33-41
EN
In this paper we shall construct the solution to the nonlinear polyparabolic problem for the cylindrical domain with limit conditions of Riquer type. To construct the solution we shall apply the convenient heat polyparabolic potentials with unknown densities and polyparabolic thermal potential compatible with the source function. We reduce the considered problem to a system of the nonlinear integro-differential equations examined on the base of the well-known Banach's fixed point theorem.
PL
Celem pracy jest dowód twierdzenia o istnieniu i o jednoznaczności rozwiązania nieliniowego równania poliparabolicznego Pmu(x, t) = ƒ(x, t, u(x, t), Pu(x, t), P2u(x, t),..., Pm-1(x, t)), gdzie x = (x1,x2), P = Δ- Dt,, Δ= D2/x1 + D2/x2, Pm = P(Pm-1) i 1 < m ∈ N jest ustaloną liczbą. Rozwiązanie powyższego równania jest konstruowane w obszarze D = {(x,t) : x ∈ D1,t ∈ (0,T)}, D1 = {(x,0 ): /x/ < R} i spełnia następujące warunki początkowe Piu(x,0) = ƒi(x), x ∈ D1, i = 0,1,...,m-1, m ∈ N i warunki brzegowe Piu(x, t) = hi(x, t), (x, t) ∈ S = {(x, t) : x ∈ B{D1) x (0,T)}, B(D1) = {{x,0) : /x/=R}, i = 0,1,2,...,m - 1, m ∈ N Funkcje ƒ ,ƒi, hi, i = 0,1,2,..., m-1, m ∈ N są dane. Powyższy problem początkowo-brzegowy jest zredukowany do nieliniowego układu równań różniczkowo-całkowych, który jest rozwiązany na bazie dobrze znanego twierdzenia Banacha o punkcie stałym.
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