568 results
Search Results
152. Qualitative properties of nonlinear parabolic operators II: the case of PDE systems.
- Author
-
Csóka, József, Faragó, István, Horváth, Róbert, Karátson, János, and Korotov, Sergey
- Subjects
- *
NONLINEAR operators , *PARABOLIC operators , *PARTIAL differential equations , *CONTINUATION methods , *MAXIMA & minima - Abstract
Abstract The solution of a parabolic problem is expected to reproduce the basic qualitative properties of the original phenomenon, such as nonnegativity/nonpositivity preservation, maximum/minimum principles and maximum norm contractivity, without which the model might lead to unrealistic quantities in conflict with physical reality. This paper presents characterizations of qualitative properties for a general class of nonlinear parabolic systems. This is a continuation of the authors' research, published in a previous paper in this journal on scalar equations. Cooperativity of the systems plays an essential role in most of the results. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
153. General framework to construct local-energy solutions of nonlinear diffusion equations for growing initial data.
- Author
-
Akagi, Goro, Ishige, Kazuhiro, and Sato, Ryuichi
- Subjects
- *
BURGERS' equation , *ELLIPTIC operators , *NONLINEAR operators , *HEAT equation , *MONOTONE operators , *POROUS materials , *ELLIPTIC equations , *SCHRODINGER operator , *MONOTONIC functions - Abstract
This paper presents an integrated framework to construct local-energy solutions to fairly general nonlinear diffusion equations for initial data growing at infinity under suitable assumptions on local-energy estimates for approximate solutions. A delicate issue for constructing local-energy solutions resides in the identification of weak limits of nonlinear terms for approximate solutions in a limiting procedure. Indeed, such an identification process often needs the maximal monotonicity of nonlinear elliptic operators (involved in the doubly-nonlinear equations) as well as uniform estimates for approximate solutions; however, even the monotonicity is violated due to a localization of the equations, which is also necessary to derive local-energy estimates for approximate solutions. In the present paper, such an inconsistency is systematically overcome by reducing the original equation to a localized one, where a (no longer monotone) localized elliptic operator is decomposed into the sum of a maximal monotone operator and a perturbation, and by integrating all the other relevant processes. Furthermore, the general framework developed in the present paper is also applied to the Finsler porous medium and fast diffusion equations , which are variants of the classical PME and FDE and also classified as a doubly-nonlinear equation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
154. ANALYTICAL METHODS FOR NON-LINEAR FRACTIONAL KOLMOGOROV-PETROVSKII-PISKUNOV EQUATION Soliton Solution and Operator Solution.
- Author
-
XU, Bo, ZHANG, Yufeng, and ZHANG, Sheng
- Subjects
- *
NONLINEAR equations , *NONLINEAR operators , *EQUATIONS - Abstract
Kolmogorov-Petrovskii-Piskunov equation can be regarded as a generalized form of the Fitzhugh-Nagumo, Fisher and Huxley equations which have many applications in physics, chemistry and biology. In this paper, two fractional extended versions of the non-linear Kolmogorov-Petrovskii-Piskunov equation are solved by analytical methods. Firstly, a new and more general fractional derivative is defined and some properties of it are given. Secondly, a solution in the form of operator representation of the non-linear Kolmogorov-Petrovskii- Piskunov equation with the defined fractional derivative is obtained. Finally, some exact solutions including kink-soliton solution and other solutions of the non-linear Kolmogorov-Petrovskii-Piskunov equation with Khalil et al.'s fractional derivative and variable coefficients are obtained. It is shown that the fractional- order affects the propagation velocity of the obtained kink-soliton solution. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
155. Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations.
- Author
-
Meinlschmidt, Hannes and Rehberg, Joachim
- Subjects
- *
EQUATIONS , *SEMICONDUCTORS , *DIFFERENTIAL operators , *NONLINEAR equations , *PARABOLIC operators , *NONLINEAR analysis , *NONLINEAR operators - Abstract
In this paper we present a general extrapolated elliptic regularity result for second order differential operators in divergence form on fractional Sobolev-type spaces of negative order X D s − 1 , q (Ω) for s > 0 small, including mixed boundary conditions and with a fully nonsmooth geometry of Ω and the Dirichlet boundary part D. We expect the result to find applications in the analysis of nonlinear parabolic equations, in particular for quasilinear problems or when treating coupled systems of equations. To demonstrate the usefulness of our result, we give a new proof of local-in-time existence and uniqueness for the van Roosbroeck system for semiconductor devices which is much simpler than already established proofs. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
156. A Continuous Nonlinear Fractional-Order PI Controller for Primary Frequency Control Application.
- Author
-
Elyaalaoui, Kamal, Labbadi, Moussa, Ouassaid, Mohammed, and Cherkaoui, Mohamed
- Subjects
- *
NONLINEAR operators , *OPERATOR functions , *NONLINEAR control theory , *WIND power plants , *NONLINEAR functions , *BALANCE of power , *INDUCTION generators - Abstract
In this paper, a nonlinear fractional-order PI (NL-FO-PI) controller is proposed for primary frequency control (PFC) of a wind farm based on the squirrel cage induction generator. The new structure composites a fractional-order operator and nonlinear function to achieve better control performance for the PFC system. The benchmarking process is demonstrated by investigating the performance of fractional-order PI (FO-PI) and nonlinear PI (NL-PI) controllers. Initially, the controller is applied to a single-area power system for design and stability study and then extended to the two-area interconnected wind farm to validate the applicability in the more realistic power system. The proposed control method ensures the balance of power and keeps the system frequency within a suitable range. The simulation results demonstrate that the proposed NL-FO-PI controller provides less percentage overshoot, settling time, rise time, and peak time than other controllers. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
157. Integral matching-based nonlinear grey Bernoulli model for forecasting the coal consumption in China.
- Author
-
Yang, Lu and Xie, Naiming
- Subjects
- *
MONTE Carlo method , *FORECASTING , *PARAMETER estimation , *NONLINEAR operators , *INTEGRALS - Abstract
Nonlinear grey Bernoulli model, abbreviated as NGBM model, has been validly used in real applications due to its high accuracy in nonlinear time series forecasting. However, there remain technical challenges to explain the mechanism of the accumulative sum operator in nonlinear grey modelling process and estimate structural parameters independent from the initial values. This paper aims to reconstruct the modelling process of the NGBM model so as to explain the modelling mechanism better by utilizing the integral matching approach, which consists of an integral formula and the numerical discretization-based least squares. First, the integral formula is employed to investigate the accumulative sum operator and further reconstruct the NGBM model to a generalized form, referred as to INGBM model. Then, a novel parameter estimation strategy, estimating structure parameters and initial values simultaneously, is developed by utilizing the numerical discretization-based least squares approach. Next, Monte Carlo simulation studies are designed to evaluate the finite sample performance of both models. Comparisons show that the INGBM model outperforms to the original one in terms of parameter estimation accuracy, forecasting accuracy and robustness to noise. Finally, we apply the INGBM model at a coal consumption in China study to further illustrate the usefulness of this model. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
158. Attractivity and Global Attractivity for System of Fractional Functional and Nonlinear Fractional q-Differential Equations.
- Author
-
Samei, M. E., Ranjbar, G. K., and Susahab, D. Nazari
- Subjects
- *
FRACTIONAL calculus , *FRACTIONAL differential equations , *CAPUTO fractional derivatives , *FIXED point theory , *NONLINEAR operators - Abstract
In the current work, we present some innovative solutions for the attractivity of fractional functional q-differential equations involving Caputo fractional q-derivative in a k-dimensional system, by using some fixed point principle and the standard Schauder's fixed point theorem. Likewise, we look into the global attractivity of fractional q-differential equations involving classical Riemann-Liouville fractional q-derivative in a k-dimensional system, by employing the famous fixed point theorem of Krasnoselskii. Also, we must note that, this paper is mainly on the analysis of the model, with numerics used only to verify the analysis for checking the attractivity and global attractivity of solutions in the system. Lastly, we give two examples to illustrate our main results. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
159. Planktons discrete -time dynamical systems.
- Author
-
Rozikov, U. A., Shoyimardonov, S. K., and Varro, R.
- Subjects
- *
DYNAMICAL systems , *NONLINEAR operators , *DISCRETE-time systems , *VOLTERRA operators , *PLANKTON , *ZOOPLANKTON , *MARINE zooplankton - Abstract
In this paper, we initiate the study of a discrete-time dynamical system modeling a trophic network connecting three types of plankton (phytoplankton, zooplankton, mixoplankton) and bacteria. The nonlinear operator V associated with this dynamical system is of type 4-Volterra quadratic stochastic operator with twelve parameters. We give conditions on the parameters under which this operator maps the five-dimensional standard simplex to itself and we find its fixed points. Moreover, we study the limit points of trajectories for this operator. For each situations we give some biological interpretations. [ABSTRACT FROM AUTHOR]
- Published
- 2021
160. A dynamical system approach to a class of radial weighted fully nonlinear equations.
- Author
-
Maia, Liliane, Nornberg, Gabrielle, and Pacella, Filomena
- Subjects
- *
NONLINEAR equations , *DYNAMICAL systems , *EXTREMAL problems (Mathematics) , *QUADRATIC differentials , *CRITICAL exponents , *ENERGY consumption , *NONLINEAR operators - Abstract
In this paper we study existence, nonexistence and classification of radial positive solutions of some weighted fully nonlinear equations involving Pucci extremal operators. Our results are entirely based on the analysis of the dynamics induced by an autonomous quadratic system which is obtained after a suitable transformation. This method allows to treat both regular and singular solutions in a unified way, without using energy arguments. In particular we recover known results on regular solutions for the fully nonlinear non weighted problem by alternative proofs. We also slightly improve the classification of the solutions for the extremal operator M −. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
161. Existence Results for a Class of p(x)-Kirchhoff Problems.
- Author
-
Allaoui, Mostafa
- Subjects
- *
SOBOLEV spaces , *ELLIPTIC operators , *NONLINEAR operators , *EQUATIONS , *EXPONENTS - Abstract
This paper is concerned with the existence of solutions to a class of p(x)-Kirchhoff-type equations with Robin boundary data as follows: − M ∫ Ω 1 p (x) ∇ u p (x) d x + ∫ ∂ Ω β (x) p (x) ∇ u p (x) d σ div( ∇ u p(x)-2 ∇ u)=f(x,u)in Ω , ∇ u p (x) − 2 ∂ u ∂ v + β (x) u p (x) − 2 u = 0 on ∂ Ω , Where β ∈ L ∞ (∂ Ω) and f : Ω × ℝ → ℝ satisfies Carathéodory condition. By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish conditions for the existence of weak solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
162. Horizontal Newton operators and high-order Minkowski formula.
- Author
-
Guidi, Chiara and Martino, Vittorio
- Subjects
- *
NONLINEAR operators - Abstract
In this paper, we study the horizontal Newton transformations, which are nonlinear operators related to the natural splitting of the second fundamental form for hypersurfaces in a complex space form. These operators allow to prove the classical Minkowski formulas in the case of real space forms: unlike the real case, the horizontal ones are not divergence-free. Here, we consider the highest order of nonlinearity and we will show how a Minkowski-type formula can be obtained in this case. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
163. Semilocal Convergence of a Newton-Secant Solver for Equations with a Decomposition of Operator.
- Author
-
Argyros, Ioannis K., Shakhno, Stepan, and Yarmola, Halyna
- Subjects
- *
OPERATOR equations , *NEWTON-Raphson method , *NONLINEAR operators , *LINEAR operators , *CLASSICAL conditioning , *INFORMATION needs - Abstract
We provide the semilocal convergence analysis of the Newton-Secant solver with a decomposition of a nonlinear operator under classical Lipschitz conditions for the first order Fréchet derivative and divided differences. We have weakened the sufficient convergence criteria, and obtained tighter error estimates. We give numerical experiments that confirm theoretical results. The same technique without additional conditions can be used to extend the applicability of other iterative solvers using inverses of linear operators. The novelty of the paper is that the improved results are obtained using parameters which are special cases of the ones in earlier works. Therefore, no additional information is needed to establish these advantages. [ABSTRACT FROM AUTHOR]
- Published
- 2021
164. Infinite dimensional orthogonality preserving nonlinear Markov operators.
- Author
-
Mukhamedov, Farrukh and Fadillah Embong, Ahmad
- Subjects
- *
MARKOV operators , *NONLINEAR operators - Abstract
In the present paper, we study infinite dimensional orthogonality preserving the second-order nonlinear Markov operators. It is proved that subjectivity of the second-order nonlinear Markov operators is equivalent to the orthogonality preserves in the class of π-Volterra operators. Moreover, a full description of such kind of operators has been found in terms of heredity coefficients. Besides, we are able to represent these operators their canonical forms. Furthermore, some properties of orthogonality preserving the second-order nonlinear operators and their fixed points are studied. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
165. Numerical solution of nonlinear weakly singular Volterra integral equations of the first kind: An hp-version collocation approach.
- Author
-
Dehbozorgi, Raziyeh and Nedaiasl, Khadijeh
- Subjects
- *
VOLTERRA equations , *COLLOCATION methods , *JACOBI polynomials , *NONLINEAR integral equations , *SINGULAR integrals , *JACOBI method , *NONLINEAR operators , *INTEGRAL equations - Abstract
This paper is concerned with the numerical solution for a class of nonlinear weakly singular Volterra integral equation of the first kind. The existence and uniqueness issue of this nonlinear Volterra integral equations is studied completely. An hp -version collocation method in conjunction with Jacobi polynomials is introduced so as an appropriate numerical solution to be found. We analyze it properly and find an error estimation in L 2 -norm. The efficiency of the method is illustrated by some numerical experiments. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
166. Existence of an approximate solution for a class of fractional multi-point boundary value problems with the derivative term.
- Author
-
Sang, Yanbin and He, Luxuan
- Subjects
- *
BOUNDARY value problems , *NONLINEAR operators , *MONOTONE operators - Abstract
In this paper, we consider a class of fractional boundary value problems with the derivative term and nonlinear operator term. By establishing new mixed monotone fixed point theorems, we prove these problems to have a unique solution, and we construct the corresponding iterative sequences to approximate the unique solution. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
167. Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold.
- Author
-
Gasiński, Leszek and Winkert, Patrick
- Subjects
- *
NONLINEAR equations , *ELLIPTIC equations , *NONLINEAR operators - Abstract
In this paper we study quasilinear elliptic equations driven by the so-called double phase operator and with a nonlinear boundary condition. Due to the lack of regularity, we prove the existence of multiple solutions by applying the Nehari manifold method along with truncation and comparison techniques and critical point theory. In addition, we can also determine the sign of the solutions (one positive, one negative, one nodal). Moreover, as a result of independent interest, we prove for a general class of such problems the boundedness of weak solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
168. A metamorphic positivity-preserving conservative formulation applied to the solution of general anisotropic diffusion problems in distorted 2-D grids.
- Author
-
Magalhães, Emerson W. D., Souza, Márcio R. A., and Gomes, Igor F.
- Subjects
- *
NONLINEAR operators , *ELLIPTIC operators , *LINEAR operators , *ELLIPTIC equations - Abstract
Numerical schemes which employ linear operator to discretize elliptic equation in arbitrary meshes are not capable to guarantee the positivity of the solutions when tensors with higher anisotropic ratio are considered. In this paper, we propose an alternative framework strategy which preserves the positivity of the solutions. The so-called Metamorphic method initially employs a linear operator in the discretization procedure and since the positivity of the solution is not satisfied in some cell of the mesh, the method suffers metamorphosis and uses a non-linear operator to recompute the solution only in those "problematic" control volumes. This strategy reduces the number of iterations when compared to conventional non-linear formulations. Besides, for some cases where the positivity is satisfied throughout the domain, the iterative procedure becomes unnecessary. The performance of our proposition is evaluated by solving a steady-state diffusion benchmark problem with distorted mesh where we observe the gain in accuracy of the solution. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
169. Modeling ICRH and ICRH-NBI synergy in high power JET scenarios using European transport simulator (ETS).
- Author
-
Huynh, P., Lerche, E. A., Van Eester, D., Bilato, R., Varje, J., Johnson, T., Sauter, O., Villard, L., Ferreira, J., Bonoli, Paul, Pinsker, Robert, and Wang, Xiaojie
- Subjects
- *
FOKKER-Planck equation , *PLASMA flow , *NONLINEAR operators , *WAVE equation , *FORECASTING - Abstract
The European Integrated Modelling effort (EU-IM) provides the European Transport Simulator (ETS) [1] which was designed to simulate arbitrary tokamak plasma discharges. Two new 1D Fokker-Planck solvers have recently been implemented within ETS: StixRedist [3] and FoPla [4]. To ensure the CPU time remains acceptable, the latter was parallelized with a generic and easy to implement method. In this paper, it will be shown how these modules were integrated in the ETS workflow in particular a first approach adopted to reach a consistency between wave and Fokker-Planck equation resolution. Also, the Verification and Validation efforts will be discussed. JET shots were analyzed and the ETS predictions were cross-checked against earlier validated codes external to the EU-IM effort, TRANSP [5] in particular, as well as against experimental neutron yield data. A good agreement was obtained, both when comparing the predictions with other codes for cases within their reach (minority or beam populations) and with experimental neutron yield data. Simulations illustrating the exploitation of the nonlinear collision operator when solving a set of coupled Fokker-Planck equations for cases when majority species play a key role will be also shown. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
170. Convergence Results for Elliptic Variational-Hemivariational Inequalities.
- Author
-
Cai, Dong-ling, Sofonea, Mircea, and Xiao, Yi-bin
- Subjects
- *
NONLINEAR operators , *BANACH spaces , *MATHEMATICAL models - Abstract
We consider an elliptic variational-hemivariational inequality 𝓟 in a reflexive Banach space, governed by a set of constraints K, a nonlinear operator A, and an element f. We associate to this inequality a sequence {𝓟n} of variational-hemivariational inequalities such that, for each n ∈ ℕ, inequality 𝓟n is obtained by perturbing the data K and A and, moreover, it contains an additional term governed by a small parameter εn. The unique solvability of 𝓟 and, for each n ∈ ℕ, the solvability of its perturbed version 𝓟n, are guaranteed by an existence and uniqueness result obtained in literature. Denote by u the solution of Problem 𝓟 and, for each n ∈ ℕ, let un be a solution of Problem 𝓟n. The main result of this paper states the strong convergence of un → u in X, as n → ∞. We show that the main result extends a number of results previously obtained in the study of Problem 𝓟. Finally, we illustrate the use of our abstract results in the study of a mathematical model which describes the contact of an elastic body with a rigid-deformable foundation and provide the corresponding mechanical interpretations. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
171. Approximation of modified Favard Szasz-Mirakyan operators of maximum-product type.
- Author
-
Baruğ, Fahri and Serenbay, Sevilay Kirci
- Subjects
- *
POSITIVE operators , *NONLINEAR operators - Abstract
Nonlinear positive operators by means of maximum and product were introduced by B. Bede. In this paper, we introduce nonlinear maximum-product type modified Favard Szasz-Mirakyan operators. Our main purpose is to give a theorem on the rate of convergence. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
172. Positive kernels, fixed points, and integral equations.
- Author
-
Burton, Theodore A. and Purnaras, Ioannis K.
- Subjects
- *
INTEGRAL equations , *KERNEL (Mathematics) , *FIXED point theory , *NONLINEAR operators , *INTEGRO-differential equations - Abstract
There is substantial literature going back to 1965 showing boundedness properties of solutions of the integro-differential equation ... when A is a positive kernel and h is a continuous function using ... In that study there emerges the pair: Integro-differential equation and Supremum norm. In this paper we study qualitative properties of solutions of integral equations using the same inequality and obtain results on Lp solutions. That is, there occurs the pair: Integral equations and Lp norm. The paper also offers many examples showing how to use the Lp idea effectively. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
173. Comments on some fixed point theorems in metric spaces.
- Author
-
BERINDE, VASILE
- Subjects
- *
FIXED point theory , *METRIC spaces , *BANACH spaces , *NONLINEAR operators , *NUMERICAL analysis - Abstract
In a recent paper [Pata, V., A fixed point theorem in metric spaces, J. Fixed Point Theory Appl., 10 (2011), No. 2, 299–305], the author stated and proved a fixed point theorem that is intended to generalize the well known Banach's contraction mapping principle. In this note we show that the main result in the above paper does not hold at least in two extremal cases for the parameter #949; involved in the contraction condition used there. We also present some illustrative examples and related results. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
174. A Class of New General Iteration Approximation of Common Fixed Points for Total Asymptotically Nonexpansive Mappings in Hyperbolic Spaces.
- Author
-
Ting-jian Xiong and Heng-you Lan
- Subjects
- *
APPROXIMATION theory , *FUNCTIONAL analysis , *MATHEMATICAL functions , *HYPERBOLIC spaces , *NONLINEAR operators - Abstract
In this paper, we introduce and study a class of new general iteration processes for two finite families of total asymptotically nonexpansive mappings in hyperbolic spaces, which includes asymptotically nonexpansive mapping, (generalized) nonexpansive mapping of all normed linear spaces, Hadamard manifolds and CAT(0) spaces as special cases. Some important related properties to the new general iterative processes are also given and analyzed, and Δ-convergence and strong convergence of the iteration in hyperbolic spaces are proved. Furthermore, some meaningful illustrations for clarifying our results and two open questions are proposed. The results presented in this paper extend and improve the corresponding results announced in the current literature. [ABSTRACT FROM AUTHOR]
- Published
- 2017
175. Signal denoising based on empirical mode decomposition.
- Author
-
Klionskiy, Dmitry, Kupriyanov, Mikhail, and Kaplun, Dmitry
- Subjects
- *
SIGNAL denoising , *HILBERT-Huang transform , *THRESHOLDING algorithms , *CONFIDENCE intervals , *NONLINEAR operators - Abstract
The present paper discusses the empirical mode decomposition technique relative to signal denoising, which is often included in signal preprocessing. We provide some basics of the empirical mode decomposition and introduce intrinsic mode functions with the corresponding illustrations. The problem of denoising is described in the paper and we illustrate denoising using soft and hard thresholding with the empirical mode decomposition. Furthermore, we introduce a new approach to signal denoising in the case of heteroscedastic noise using a classification statistics. Our denoising procedure is shown for a harmonic signal and a smooth curve corrupted with white Gaussian heteroscedastic noise. We conclude that empirical mode decomposition is an efficient tool for signal denoising in the case of homoscedastic and heteroscedastic noise. Finally, we also provide some information about denoising applications in vibrational signal analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
176. EXISTENCE AND STABILITY RESULTS FOR COINCIDENCE POINTS OF NONLINEAR CONTRACTIONS.
- Author
-
Choudhury, Binayak S., Metiya, Nikhilesh, and Kundu, Sunirmal Kundu
- Subjects
- *
NONLINEAR operators , *MATHEMATICAL mappings - Abstract
In this paper we define-admissibility of multi-valued mapping with respect to a single-valued mapping and use this concept to establish a coincidence point theorem for pairs of nonlinear multi-valued and single-valued mappings under the assumption of an inequality with rational terms. We illustrate the result with an example. In the second part of the paper we prove the stability of the coincidence point sets associated with the pairs of mappings in our coincidence point theorem. For that purpose we define the corresponding stability concepts of coincidence points. The results are primarily in the domain of nonlinear set-valued analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
177. Global Bifurcation of Stationary Solutions for a Volume-Filling Chemotaxis Model with Logistic Growth.
- Author
-
Dong, Yaying and Li, Shanbing
- Subjects
- *
CHEMOTAXIS , *FREDHOLM operators , *NEUMANN boundary conditions , *HOPF bifurcations , *COMPACT operators , *NONLINEAR operators - Abstract
In this paper, we show how the global bifurcation theory for nonlinear Fredholm operators (Theorem 4.3 of [Shi & Wang, 2009]) and for compact operators (Theorem 1.3 of [Rabinowitz, 1971]) can be used in the study of the nonconstant stationary solutions for a volume-filling chemotaxis model with logistic growth under Neumann boundary conditions. Our results show that infinitely many local branches of nonconstant solutions bifurcate from the positive constant solution (u c , α β u c) at χ = χ ¯ k . Moreover, for each k ≥ 1 , we prove that each Γ k can be extended into a global curve, and the projection of the bifurcation curve Γ k onto the χ -axis contains ( χ ¯ k , ∞). [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
178. Solvability of nonlinear integral equations and surjectivity of nonlinear Markov operators.
- Author
-
Mukhamedov, Farrukh, Khakimov, Otabek, and Embong, Ahmad Fadillah
- Subjects
- *
MARKOV operators , *NONLINEAR operators , *HAMMERSTEIN equations , *INTEGRAL equations , *POLYNOMIAL operators , *NONLINEAR integral equations - Abstract
In the present paper, we consider integral equations, which are associated with nonlinear Markov operators acting on an infinite‐dimensional space. The solvability of these equations is examined by investigating nonlinear Markov operators. Notions of orthogonal preserving and surjective nonlinear Markov operators defined on infinite dimension are introduced, and their relations are studied, which will be used to prove the main results. We show that orthogonal preserving nonlinear Markov operators are not necessarily satisfied surjective property (unlike finite case). Thus, sufficient conditions for the operators to be surjective are described. Using these notions and results, we prove the solvability of Hammerstein equations in terms of surjective nonlinear Markov operators. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
179. Solutions for a Singular Hadamard-Type Fractional Differential Equation by the Spectral Construct Analysis.
- Author
-
Zhang, Xinguang, Yu, Lixin, Jiang, Jiqiang, Wu, Yonghong, and Cui, Yujun
- Subjects
- *
FRACTIONAL differential equations , *LINEAR operators , *NONLINEAR operators , *LINEAR statistical models - Abstract
In this paper, we consider the existence of positive solutions for a Hadamard-type fractional differential equation with singular nonlinearity. By using the spectral construct analysis for the corresponding linear operator and calculating the fixed point index of the nonlinear operator, the criteria of the existence of positive solutions for equation considered are established. The interesting point is that the nonlinear term possesses singularity at the time and space variables. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
180. Some exact solutions and infinite conservation laws of an extended KdV integrable system.
- Author
-
Lu, Huanhuan, Zhang, Yufeng, and Mei, Jianqin
- Subjects
- *
CONSERVATION laws (Physics) , *SELFADJOINT operators , *CONSERVATION laws (Mathematics) , *NONLINEAR operators , *EXERCISE , *SYMMETRY - Abstract
In this paper, we investigate some symmetries and Lie-group transformations of an integrable system by using the symmetry analysis method. It follows that the resulting similarity solutions are obtained by applying the characteristic equations of the symmetries. By applying the software Maple,we work out some exact solutions of the generalized KdV system, including the rational solutions, the periodic solutions, the dark soliton solutions, and so on. Finally, we make use of the self-adjoint operators to investigate the nonlinear self-adjointness and the conservation laws of the generalized KdV integrable system. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
181. Common Solution for Nonlinear Operators in Banach Spaces.
- Author
-
EKUMA-OKEREKE, Enyinnaya and OKORO, Felix Moibi
- Subjects
- *
BANACH spaces , *MONOTONE operators , *NONLINEAR operators - Abstract
This paper formulates a hybrid approximation process involving inertial component and demonstrates a convergence results for it. The formulated scheme converges faster and finds a common solution for some nonlinear operators in Banach spaces. The method of our proof and results obtained is well involved and significant. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
182. Finite dimensional estimation algebras with state dimension 3 and rank 2, Mitter conjecture.
- Author
-
Shi, Ji and Yau, Stephen S. T.
- Subjects
- *
FUNCTION algebras , *ALGEBRA , *PARTIAL differential operators , *SYSTEMS theory , *PARTIAL differential equations , *NONLINEAR operators - Abstract
In this paper, we study the structure of finite dimensional estimation algebras with state dimension 3 and rank 2 arising from a nonlinear filtering system by using the theories of the Euler operator and under-determined partial differential equations. It is proved that if the estimation algebra contains a degree two polynomial, then the Wong Ω-matrix must be a constant matrix. Moreover, all functions in the estimation algebra must be linear functions. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
183. Asymptotic properties of singular solutions in degenerate parabolic equation with boundary flux.
- Author
-
Liu, Bingchen and Dong, Mengzhen
- Subjects
- *
BLOWING up (Algebraic geometry) , *DEGENERATE parabolic equations , *NONLINEAR operators , *FLUX (Energy) - Abstract
This paper deals with blow-up and quenching solutions of degenerate parabolic problem involving m-Laplacian operator and nonlinear boundary flux. The blow-up and quenching criteria are classified under the conditions on the initial data but with less conditions on the relationship among the exponents, respectively. Moreover, asymptotic properties including singular rates, set and time estimates are determined for the blow-up solutions and the quenching solutions, respectively. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
184. Some Fixed Point Results for Perov-Ćirić-Prešić Type F-Contractions with Application.
- Author
-
Gholidahneh, Abdolsattar, Sedghi, Shaban, and Parvaneh, Vahid
- Subjects
- *
METRIC spaces , *NONLINEAR operators , *NONLINEAR systems - Abstract
Ćirić and Prešić developed the concept of Prešić contraction to Ćirić-Prešić type contractive mappings in the background of a metric space. On the other hand, Altun and Olgun introduced Perov type F-contractions. In this paper, we extend the concept of Ćirić-Prešić contractions to Perov-Ćirić-Prešić type F-contractions. Our results modify some known ones in the literature. To support our main result, an example and an application to nonlinear operator systems are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
185. Some Fixed Point Results for Perov-Ćirić-Prešić Type F-Contractions with Application.
- Author
-
Gholidahaneh, Abdolsatar, Sedghi, Shaban, and Parvaneh, Vahid
- Subjects
- *
METRIC spaces , *NONLINEAR operators , *NONLINEAR systems - Abstract
Ćirić and Prešić developed the concept of Prešić contraction to Ćirić-Prešić type contractive mappings in the background of a metric space. On the other hand, Altun and Olgun introduced Perov type F-contractions. In this paper, we extend the concept of Ćirić-Prešić contractions to Perov-Ćirić-Prešić type F-contractions. Our results modify some known ones in the literature. To support our main result, an example and an application to nonlinear operator systems are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
186. On the strong maximum principle.
- Author
-
Mohammed, Ahmed and Vitolo, Antonio
- Subjects
- *
MAXIMUM principles (Mathematics) , *NONLINEAR operators , *ELLIPTIC operators , *NONLINEAR equations , *ELLIPTIC equations , *VISCOSITY solutions , *EQUATIONS - Abstract
In this paper we study the strong maximum principle for equations of the form F [ u ] = H (u , | D u |) where F is either a fully nonlinear elliptic operator or is the p-Laplace operator. We give sufficient conditions on H to ensure that the strong maximum principle (SMP) holds. The condition is also necessary for SMP to hold for the the equation F [ u ] = g (| D u |). [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
187. Convergence analysis of an optimally accurate frozen multi-level projected steepest descent iteration for solving inverse problems.
- Author
-
Mittal, Gaurav and Kumar Giri, Ankik
- Subjects
- *
PROBLEM solving , *NONLINEAR operators , *STABILITY constants , *CONVEX sets , *FAMILY stability - Abstract
In this paper, we introduce a novel projected steepest descent iterative method with frozen derivative. The classical projected steepest descent iterative method involves the computation of derivative of the nonlinear operator at each iterate. The method of this paper requires the computation of derivative of the nonlinear operator only at an initial point. We exhibit the convergence analysis of our method by assuming the conditional stability of the inverse problem on a convex and compact set. Further, by assuming the conditional stability on a nested family of convex and compact subsets, we develop a multi-level method. In order to enhance the accuracy of approximation between neighboring levels, we couple it with the growth of stability constants. This along with a suitable discrepancy criterion ensures that the algorithm proceeds from level to level and terminates within finite steps. Finally, we discuss an inverse problem on which our methods are applicable. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
188. Solutions of Nonlinear Operator Equations by Viscosity Iterative Methods.
- Author
-
Aibinu, Mathew, Thakur, Surendra, and Moyo, Sibusiso
- Subjects
- *
OPERATOR equations , *NONLINEAR equations , *INTEGRAL equations , *FREDHOLM equations , *ALGORITHMS , *NONLINEAR operators , *ITERATIVE methods (Mathematics) - Abstract
Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our technique is indispensable in terms of explicitly clarifying the associated concepts and analysis. The scheme is effective for obtaining the solutions of various nonlinear operator equations as it involves the generalized contraction. The results are applied to obtain a fixed point of λ -strictly pseudocontractive mappings, solution of α -inverse-strongly monotone mappings, and solution of integral equations of Fredholm type. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
189. Krylov Subspace Method for Nonlinear Dynamical Systems with Random Noise.
- Author
-
Yuka Hashimoto, Isao Ishikawa, Masahiro Ikeda, Yoichi Matsuo, and Yoshinobu Kawahara
- Subjects
- *
RANDOM dynamical systems , *KRYLOV subspace , *NONLINEAR operators , *RANDOM noise theory , *NONLINEAR dynamical systems , *NONLINEAR analysis , *NONLINEAR systems - Abstract
Operator-theoretic analysis of nonlinear dynamical systems has attracted much attention in a variety of engineering and scientific fields, endowed with practical estimation methods using data such as dynamic mode decomposition. In this paper, we address a lifted representation of nonlinear dynamical systems with random noise based on transfer operators, and develop a novel Krylov subspace method for estimating the operators using finite data, with consideration of the unboundedness of operators. For this purpose, we first consider Perron-Frobenius operators with kernel-mean embeddings for such systems. We then extend the Arnoldi method, which is the most classical type of Kryov subspace methods, so that it can be applied to the current case. Meanwhile, the Arnoldi method requires the assumption that the operator is bounded, which is not necessarily satisfied for transfer operators on nonlinear systems. We accordingly develop the shift-invert Arnoldi method for Perron-Frobenius operators to avoid this problem. Also, we describe an approach of evaluating predictive accuracy by estimated operators on the basis of the maximum mean discrepancy, which is applicable, for example, to anomaly detection in complex systems. The empirical performance of our methods is investigated using synthetic and real-world healthcare data. [ABSTRACT FROM AUTHOR]
- Published
- 2020
190. A revisit on Landweber iteration.
- Author
-
Real, Rommel and Jin, Qinian
- Subjects
- *
INVERSE problems , *BANACH spaces , *NONLINEAR operators , *NONLINEAR equations , *DISCREPANCY theorem , *REFLEXIVITY - Abstract
In this paper we revisit the discrepancy principle for Landweber iteration for solving linear as well as nonlinear inverse problems in Banach spaces and prove a new convergence result which requires neither the Gâteaux differentiability of the forward operator nor the reflexivity of the image space. Therefore, we expand the applied range of the discrepancy principle for Landweber iteration to cover non-smooth ill-posed inverse problems and to handle the situation that the data is contaminated by various types of noise. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
191. Boundedness of multi-parameter pseudo-differential operators on multi-parameter local Hardy spaces.
- Author
-
Chen, Jiao, Ding, Wei, and Lu, Guozhen
- Subjects
- *
PSEUDODIFFERENTIAL operators , *HARDY spaces , *SINGULAR integrals , *NONLINEAR operators , *GEOMETRIC analysis , *HARMONIC analysis (Mathematics) , *INTEGRAL operators - Abstract
After the celebrated work of L. Hörmander on the one-parameter pseudo-differential operators, the applications of pseudo-differential operators have played an important role in partial differential equations, geometric analysis, harmonic analysis, theory of several complex variables and other branches of modern analysis. For instance, they are used to construct parametrices and establish the regularity of solutions to PDEs such as the ∂ ¯ {\overline{\partial}} problem. The study of Fourier multipliers, pseudo-differential operators and Fourier integral operators has stimulated further such applications. It is well known that the one-parameter pseudo-differential operators are L p (ℝ n) {L^{p}({\mathbb{R}^{n}})} bounded for 1 < p < ∞ {1
- Published
- 2020
- Full Text
- View/download PDF
192. Self‐adaptive fractional‐order LQ‐PID voltage controller for robust disturbance compensation in DC‐DC buck converters.
- Author
-
Saleem, Omer, Awan, Fahim Gohar, Mahmood‐ul‐Hasan, Khalid, and Ahmad, Muaaz
- Subjects
- *
ADAPTIVE control systems , *NONLINEAR operators , *PID controllers , *PUBLIC transit , *ROBUST control , *GAUSSIAN function , *INTEGRAL operators , *PARTICLE swarm optimization - Abstract
This paper presents a state‐dependent self‐tuning fractional control strategy for a DC‐DC buck converter in order to enhance its output voltage regulation and disturbance attenuation capability. The proposed control scheme primarily employs a ubiquitous proportional‐integral‐derivative (PID) controller, where gains are optimally selected using a linear‐quadratic state‐space tuning approach. The optimal PID controller is then augmented with fractional‐order integral and derivative operators in order to improve the controller's degrees‐of‐freedom as well as the system's overall time‐domain performance. The fractional controller's robustness against bounded exogenous disturbances, contributed by the input fluctuations and load‐step transients, is further enhanced by adaptively modulating the fractional‐orders of the integro‐differential operators as a smooth nonlinear function of controlled‐variable's error‐dynamics. An online dynamic adjustment law, comprising of a zero‐mean Gaussian function of error and its derivative, is used to individually update the two fractional orders after every sampling interval. The error derivative is evaluated by measuring the output capacitor's current in order to compensate the noise injected by parasitic impedance. The other controller parameters are tuned via particle‐swarm‐optimization algorithm. The proposed self‐adaptive control strategy renders rapid transits, minimum transient recovery time, and minimal fluctuations around steady state in the response. Its efficacy is validated through hardware in‐the‐loop experiments conducted on a buck converter prototype. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
193. Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method.
- Author
-
Daoues, Adel, Hammami, Amani, and Saoudi, Kamel
- Subjects
- *
LAPLACIAN operator , *CRITICAL exponents , *NONLINEAR operators , *SMOOTHNESS of functions , *EXPONENTS - Abstract
In this paper we investigate the following nonlocal problem with singular term and critical Hardy-Sobolev exponent (P) (− Δ) s u = λ u γ + | u | 2 α ∗ − 2 u | x | α in Ω , u > --> 0 in Ω , u = 0 in R N ∖ Ω , $$\begin{array}{} ({\rm P}) \left\{ \begin{array}{ll} (-\Delta)^s u = \displaystyle{\frac{\lambda}{u^\gamma}+\frac{|u|^{2_\alpha^*-2}u}{|x|^\alpha}} \ \ \text{ in } \ \ \Omega, \\ u >0 \ \ \text{ in } \ \ \Omega, \quad u = 0 \ \ \text{ in } \ \ \mathbb{R}^{N}\setminus \Omega, \end{array} \right. \end{array}$$ where Ω ⊂ ℝN is an open bounded domain with Lipschitz boundary, 0 < s < 1, λ > 0 is a parameter, 0 < α < 2s < N, 0 < γ < 1 < 2 < 2 s ∗ $\begin{array}{} \displaystyle 2_s^* \end{array}$ , where 2 s ∗ = 2 N N − 2 s and 2 α ∗ = 2 (N − α) N − 2 s $\begin{array}{} \displaystyle 2_s^* = \frac{2N}{N-2s} ~\text{and}~ 2_\alpha^* = \frac{2(N-\alpha)}{N-2s} \end{array}$ are the fractional critical Sobolev and Hardy Sobolev exponents respectively. The fractional Laplacian (–Δ)s with s ∈ (0, 1) is the nonlinear nonlocal operator defined on smooth functions by (− Δ) s u (x) = − 1 2 ∫ R N u (x + y) + u (x − y) − 2 u (x) | y | N + 2 s d y , for all x ∈ R N. $$\begin{array}{} \displaystyle (-\Delta)^s u(x)=-\frac{1}{2} \displaystyle\int_{\mathbb{R}^N} \frac{u(x+y)+u(x-y)-2u(x)}{|y|^{N+2s}}{\rm d }y, \;\; \text{ for all }\, x \in \mathbb{R}^N. \end{array}$$ By combining variational and approximation methods, we provide the existence of two positive solutions to the problem (P). [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
194. Workload-driven coordination between virtual machine allocation and task scheduling.
- Author
-
Xiao, Zheng, Wang, Bangyong, Li, Xing, and Du, Jiayi
- Subjects
- *
SERVICE level agreements , *MARKOV processes , *GENETIC algorithms , *REACTION time , *NONLINEAR operators , *GREEDY algorithms , *TASKS - Abstract
The current task scheduling is separated from the virtual machine (VM) allocation, which, to some extent, wastes resources or degrades application performance. The scheduling algorithm influences the demand of VMs in terms of service-level agreement, while the number of VMs determines the performance of task scheduling. Workload plays an indispensable role in both dynamic VM allocation and task scheduling. To address this problem, we coordinate task scheduling and VM allocation based on workload characteristics. Workload is empirically time-varying and stochastic. We demonstrate that the acquired workload data set has Markov property which can be modeled as a Markov chain. Then, three workload characteristic operators are extracted: persistence, recurrence and entropy, which quantify the relative stability, burstiness, and unpredictability of the workload, respectively. Experiments indicate that the persistence and recurrence of workloads has a direct bearing on the average response time and resource utilization of the system. A nonlinear model between the load characteristic operators and the number of VMs is established. In order to test the performance of the collaborative framework, we design a scheduling algorithm based on genetic algorithm (GA), which takes the estimated number of VMs as input and the task completion time as the optimization target. Simulation experiments have been performed on the CloudSim platform, testifying that the estimated average absolute VMs error is only 2.6%. The GA-based task scheduling algorithm could improve resource utilization and reduce task completion time compared with the first come first serve and greedy algorithm. The proposed coordination mechanism in this paper has proved able to find the optimal match and reduce the resource cost by utilizing the interaction between VM allocation and task scheduling. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
195. Global boundedness of weak solutions for a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and rotation.
- Author
-
Wang, Wei
- Subjects
- *
DIFFUSION , *ROTATIONAL motion , *SMOOTHNESS of functions , *GLOBAL analysis (Mathematics) , *NONLINEAR systems , *NONLINEAR operators - Abstract
This paper deals with the chemotaxis-Stokes system with nonlinear diffusion and rotation: n t + u ⋅ ∇ n = Δ n m − ∇ ⋅ (n S (x , n , c) ⋅ ∇ c) , c t + u ⋅ ∇ c = Δ c − n c , u t + ∇ P = Δ u + n ∇ ϕ + f (x , t) and ∇ ⋅ u = 0 , in a bounded domain Ω ⊂ R 3 , where m > 0 , and ϕ : Ω ¯ → R , f : Ω ¯ × [ 0 , ∞) → R 3 and S : Ω ¯ × [ 0 , ∞) 2 → R 3 × 3 are given sufficiently smooth functions such that f is bounded in Ω × (0 , ∞) and S satisfies | S (x , n , c) | ≤ S 0 (c) (1 + n) − α for all (x , n , c) ∈ Ω ¯ × [ 0 , ∞) 2 with α > 0 and some nondecreasing function S 0 : [ 0 , ∞) → [ 0 , ∞). It is shown that if m + α > 10 9 and m + 5 4 α > 9 8 , then for any reasonably smooth initial data, the corresponding Neumann-Neumann-Dirichlet initial-boundary problem possesses a globally bounded weak solution. This extends the previous global boundedness result for m > 9 8 and α = 0 [43] , and improves that for m ≥ 1 and m + α > 7 6 [34] , or for m + α > 7 6 in the associated fluid-free system [31]. Our proof consists at its core in using, inter alia , the maximal Sobolev regularity theory to elaborately derive some spatio-temporal estimates for the signal and the fluid equations so as to decouple the system. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
196. Toward a variational assimilation of polarimetric radar observations in a convective-scale numerical weather prediction (NWP) model.
- Author
-
Thomas, Guillaume, Mahfouf, Jean-François, and Montmerle, Thibaut
- Subjects
- *
NUMERICAL weather forecasting , *RADAR meteorology , *FINITE difference method , *JACOBIAN matrices , *GAUSSIAN distribution , *NONLINEAR operators - Abstract
This paper presents the potential of nonlinear and linear versions of an observation operator for simulating polarimetric variables observed by weather radars. These variables, deduced from the horizontally and vertically polarized backscattered radiations, give information about the shape, the phase and the distributions of hydrometeors. Different studies in observation space are presented as a first step toward their inclusion in a variational data assimilation context, which is not treated here. Input variables are prognostic variables forecasted by the AROME-France numerical weather prediction (NWP) model at convective scale, including liquid and solid hydrometeor contents. A nonlinear observation operator, based on the T-matrix method, allows us to simulate the horizontal and the vertical reflectivities (ZHH and ZVV), the differential reflectivity ZDR , the specific differential phase KDP and the co-polar correlation coefficient ρHV. To assess the uncertainty of such simulations, perturbations have been applied to input parameters of the operator, such as dielectric constant, shape and orientation of the scatterers. Statistics of innovations, defined by the difference between simulated and observed values, are then performed. After some specific filtering procedures, shapes close to a Gaussian distribution have been found for both reflectivities and for ZDR , contrary to KDP and ρHV. A linearized version of this observation operator has been obtained by its Jacobian matrix estimated with the finite difference method. This step allows us to study the sensitivity of polarimetric variables to hydrometeor content perturbations, in the model geometry as well as in the radar one. The polarimetric variables ZHH and ZDR appear to be good candidates for hydrometeor initialization, while KDP seems to be useful only for rain contents. Due to the weak sensitivity of ρHV , its use in data assimilation is expected to be very challenging. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
197. Langevin equation in terms of conformable differential operators.
- Author
-
AHMAD, Bashir, AGARWAL, Ravi P., ALGHANMI, Madeaha, and ALSAEDI, Ahmed
- Subjects
- *
DIFFERENTIAL operators , *LANGEVIN equations , *NONLINEAR equations , *FUNCTIONAL analysis , *NONLINEAR operators - Abstract
In this paper, we establish sufficient criteria for the existence of solutions for a new kind of nonlinear Langevin equation involving conformable differential operators of different orders and equipped with integral boundary conditions. We apply the modern tools of functional analysis to derive the desired results for the problem at hand. Examples are constructed for the illustration of the obtained results. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
198. Operator-based nonlinear free vibration control of a flexible plate with sudden perturbations.
- Author
-
Jin, Guang and Deng, Mingcong
- Subjects
- *
PIEZOELECTRIC actuators , *FREE vibration , *NONLINEAR operators , *STABILITY of nonlinear systems , *NONLINEAR analysis , *ACTIVE noise & vibration control , *DYNAMIC models - Abstract
In this paper, a new nonlinear vibration control scheme using piezoelectric actuator is proposed for a flexible plate with a free vibration and sudden perturbations. First, the effect of hysteresis nonlinearity from the piezoelectric actuator is considered by Prandtl-Ishlinskii (P-I) hysteresis model. Simultaneously, a dynamic model of the flexible plate with piezoelectric actuator is considered. Then, based on the dynamic model of the flexible plate, operator-based controllers are designed to guarantee the robust stability of the nonlinear control system. In addition, for ensuring the desired vibration control performance of the flexible plate with a free vibration and sudden perturbations, operator-based compensation method is given by the proposed design scheme. In the designed compensator, the desired compensation performances of tracking and of perturbations are obtained by increasing the number of designed n-times feedback loops. Finally, both of numerical simulation and experimental result are shown to verify the effectiveness of the proposed design scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
199. Comparison of Contraction Coefficients for f-Divergences.
- Author
-
Makur, A. and Zheng, L.
- Subjects
- *
STOCHASTIC matrices , *NONLINEAR operators , *GAUSSIAN distribution , *ELECTRONIC data processing - Abstract
Contraction coefficients are distribution dependent constants that are used to sharpen standard data processing inequalities for f-divergences (or relative f-entropies) and produce so-called "strong" data processing inequalities. For any bivariate joint distribution, i.e., any probability vector and stochastic matrix pair, it is known that contraction coefficients for f-divergences are upper bounded by unity and lower bounded by the contraction coefficient for χ2-divergence. In this paper, we elucidate that the upper bound is achieved when the joint distribution is decomposable, and the lower bound can be achieved by driving the input f-divergences of the contraction coefficients to zero. Then, we establish a linear upper bound on the contraction coefficients of joint distributions for a certain class of f-divergences using the contraction coefficient for χ2-divergence, and refine this upper bound for the salient special case of Kullback-Leibler (KL) divergence. Furthermore, we present an alternative proof of the fact that the contraction coefficients for KL and χ2-divergences are equal for bivariate Gaussian distributions (where the former coefficient may impose a bounded second moment constraint). Finally, we generalize the well-known result that contraction coefficients of stochastic matrices (after extremizing over all possible probability vectors) for all nonlinear operator convex f-divergences are equal. In particular, we prove that the so-called "less noisy" preorder over stochastic matrices can be equivalently characterized by any nonlinear operator convex f-divergence. As an application of this characterization, we also derive a generalization of Samorodnitsky's strong data processing inequality. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
200. hp-version collocation method for a class of nonlinear Volterra integral equations of the first kind.
- Author
-
Nedaiasl, Khadijeh, Dehbozorgi, Raziyeh, and Maleknejad, Khosrow
- Subjects
- *
NONLINEAR integral equations , *COLLOCATION methods , *INTEGRAL equations , *VOLTERRA equations , *NONLINEAR operators , *ERROR analysis in mathematics - Abstract
In this paper, we present a collocation method for nonlinear Volterra integral equation of the first kind. This method benefits from the idea of hp -version projection methods. We provide an approximation based on the Legendre polynomial interpolation. The convergence of the proposed method is completely studied and an error estimate under the L 2 -norm is provided. Finally, several numerical experiments are presented in order to verify the obtained theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.