Solutions For System Of Equations Research Articles

Systems of Stieltjes Differential Equations with Several Derivators

We set up the basic theory of existence and uniqueness of solutions for systems of differential equations with usual derivatives replaced by Stieltjes derivatives. In this occasion, we are concerned about those systems where each component has a different derivator. We also show the interest of these systems of equations with a population model.

Multiple positive solutions for a coupled system of nonlinear impulsive fractional differential equations with parameters

We consider the multiplicity of positive solutions (PSs) for a coupled system involving nonlinear impulsive fractional differential equations with parameters. By employing the classical Guo–Krasnosel’skii fixed point theorem, some sufficient criteria for the existence of multiple PSs in terms of different values of parameters are derived. As an application, an example is given to illustrate the theoretical results.

Approximate Solution for Nonlinear System of Integro-Differential Equations of Volterra Type with Boundary Conditions

Approximate Solution for Nonlinear System of Integro-Differential Equations of Volterra Type with Boundary Conditions

Global solutions for a path-dependent hybrid system of differential equations under parabolic signal

In this paper we propose local and global existence results for the solution of systems characterized by the coupling of ODEs and PDEs. The coexistence of distinct mathematical formalisms represents the main feature of hybrid approaches, in which the dynamics of interacting agents are driven by second-order ODEs, while reaction–diffusion equations are used to model the time evolution of a signal influencing them. We first present an existence result of the solution, locally in time. In particular, we generalize the framework of recent works, presented in the literature with a modeling and numerical approach, which have not been investigated from an analytical point of view so far. Then, the previous result is extended in order to obtain a global solution.

СТОХАСТИЧЕСКАЯ МОДЕЛЬ ПРОЦЕССА РАЗДЕЛЕНИЯ СЛОЖНЫХ ГЕТЕРОГЕННЫХ ДИСПЕРСНЫХ СИСТЕМ В ЦЕНТРИФУГАХ С РАДИАЛЬНО-ОСЕВЫМ ПОТОКОМ

The article describes separation processes in apparatus with complex hydrodynamic conditions. The new approach to the theoretical study consists in taking into account the action of the centrifugal field and the field of random forces, as it was implemented earlier for the simplest structures, but also in a detailed examination of the radial and axial flows. The movement of particles is investigated in the cramped conditions of precipitation during their interaction with each other. The processes of separation in centrifugal devices of various types have been identified, subject to stochasticity, constrained movement of a set of real particles and the possibility of their dispersion and coagulation. The combined deterministic and stochastic effects on the dispersed phase in a centrifugal field are described by means of a differential equation, the solution of which makes it possible to calculate the fractional and total centrifugation efficiency with high accuracy. A semi-analytical method has been developed and implemented for one-and two-dimensional stochastic models for the approximate solution of non-stationary centrifugal boundary value problems. Compared to difference schemes Faedo-Galerkin method gives the solution of equation systems with a smaller number of unknowns defined in all values of the arguments. The use of the method is possible only in the case of homogeneous boundary conditions and is limited by the possibility of selecting a complete system of functions that would satisfy them. The proposed approach to identification of refining fuels and lubricants is preferable since it fully reflects the essence of the processes occurring in centrifuges with a radial-axial flow. Generalization of stochastic effects on centrifugation, taking into account the hydrodynamic features of the flow of shared media in a centrifugal field, allows calculating all indicators of cleaning fuels and oils from mechanical impurities without model experiments, predicting the total and fractional efficiency of fuel oil filters and oil filters of the internal combustion engines. The developed identification method of separating complex dispersed systems is aimed at the synthesis of systems and devices for oil purification and fuel oil preparation of increased efficiency with predetermined parameters of purification quality in operating conditions.

Smooth solutions to mixed-order fractional differential systems with applications to stability analysis

Conditions for existence, uniqueness and smoothness of solutions for systems of fractional differential equations of Caputo and/or Riemann-Liouville type having all of them in general and not of the same derivation order are established in this paper. It includes mixed-order, multi-order or non-commensurate fractional systems. The smooth property is shown to be relevant for drawing consequences on the global behavior of solutions for such systems. In particular, we obtain sufficient conditions for global boundedness of solutions to mixed-order nonlinear systems and asymptotic stability of nonlinear fractional systems using backstepping control.

Existence of Positive Solutions for a Coupled System of Kirchhoff Type Equations with Sobolev Critical Exponent

Existence of Positive Solutions for a Coupled System of Kirchhoff Type Equations with Sobolev Critical Exponent

The Existence and Growth of Solutions for Several Systems of Complex Nonlinear Difference Equations

This article is devoted to investigate some properties of solutions for several systems of complex differential-q-difference equations. Some results about the existence and the estimate for the growth of solutions for a series of systems of q-difference–differential equations are obtained. Moreover, it is a very satisfactory fact that some examples are given to illustrate the existence of solutions for such systems in each case of some results.

Infinitely many sign-changing solutions for system of p-Laplace equations in [formula omitted

In this paper we consider the system of p-Laplacian equations in RN−Δpuj+μj(x)|uj|p−2uj=∑i=1kβij|ui|q|uj|q−2ujin RN,uj(x)→0as |x|→∞,j=1,…,k,where 1<p<N, max{2,p}<2q<p∗=NpN−p,βij are constants, i,j=1,…,k,βjj>0,j=1,2,…,k,βij≤0,i≠j,i,j=1,…,k; μj,j=1,…,k are the potential functions and satisfy suitable decay assumptions. The existence of infinitely many sign-changing solutions is proved by the truncation method and by the concentration-compactness analysis on the approximating solutions.

Exact solutions of fractional partial differential equation systems with conformable derivative

Main goal of this paper is to have the new exact solutions of some fractional partial differential equation systems (FPDES) in conformable sense. The definition of conformable fractional derivative (CFD) is similar to the limit based definition of known derivative. This derivative obeys both rules which other popular derivatives do not satisfy such as derivative of the quotient of two functions, the derivative product of two functions, chain rule and etc. By using conformable derivative it is seen that the solution procedure for (PDES) is simpler and more efficient.

On three-wave interaction Schrödinger systems with quadratic nonlinearities: Global well-posedness and standing waves

Reported here are results concerning the global well-posedness in the energy space and existence and stability of standing-wave solutions for 1-dimensional three-component systems of nonlinear Schrodinger equations with quadratic nonlinearities. For two particular systems we are interested in, the global well-posedness is established in view of the a priori bounds for the local solutions. The standing waves are explicitly obtained and their spectral stability is studied in the context of Hamiltonian systems. For more general Hamiltonian systems, the existence of standing waves is accomplished with a variational approach based on the Mountain Pass Theorem. Uniqueness results are also provided in some very particular cases.

Existence of tripled fixed points and solution of functional integral equations through a measure of noncompactness

In this paper, we propose fixed point results through the notion of a measure of noncompactness and give a generalization of a Darbo’s fixed point theorem. We also prove some new tripled fixed point results via a measure of noncompactness for a more general class of functions. Our results generalize and extend some comparable results in the literature. Further, we apply the obtained fixed point theorems to prove the existence of solutions for a general system of non-linear functional integral equations. In the end, an example is given to illustrate the validity of our results.

LOCAL BIFURCATION OF CRITICAL PERIODS IN QUADRATIC-LIKE CUBIC SYSTEMS

In this paper, we investigate quadratic-like cubic systems having a center at $ O $ for the local bifurcation of critical periods. We provide an inductive algorithm to compute polynomials of periodic coefficients, find structures of solutions for systems of algebraic equations corresponding to weak centers of finite order, and derive conditions on parameters under which the considered equilibrium is a weak center of order $ k $, $ k = 0,1,2,3,4 $. Furthermore, we show that with appropriate perturbations, at most four critical periods bifurcate from the weak center of finite order, and we give conditions under which exactly $ k $ critical periods bifurcate from the center $ O $ for each integer $ k = 1,2,3,4 $.

Устойчивость решений систем линейных разностных уравнений Ито с запаздыванием относительно начальных данных

Устойчивость решений систем линейных разностных уравнений Ито с запаздыванием относительно начальных данных

PERIODICITY AND SOLUTIONS OF SOME RATIONAL DIFFERENCE EQUATIONS SYSTEMS

In this paper we are interested in a technique for solving some nonlinear rational systems of difference equations of third order, in three-dimensional case. Moreover, we study the periodicity of solutions for such systems. Finally, some numerical examples are presented.

ZAKI+: A Machine Learning Based Process Mapping Tool for SpMV Computations on Distributed Memory Architectures

Smart cities and other cyber-physical systems (CPSs) rely on various scientific, engineering, business, and social applications that provide timely intelligence for their design, operations, and management. Many of these scientific and analytics applications require the solution of sparse linear equation systems, where sparse matrix-vector (SpMV) product is a key computing operation. Several factors determine the performance of parallel SpMV computations, including matrix characteristics, storage formats, and the rising complexity and heterogeneity of computer systems. There is a pressing need for new ways of exploiting parallelism, and mapping data and applications to the computing resources. We propose here ZAKI+, a data-driven machine-learning approach, allowing users to automatically, effortlessly, and speedily obtain the best configuration (the data distribution, the optimal number of processes, and mapping strategy) and performance for the execution of the parallel SpMV computations on distributed memory machines. We train and test the tool using three machine learning methods-decision trees, random forest, and Xtreme boosting-and nearly 2000 real-world matrices obtained from 45 application domains, including computer vision and robotics. ZAKI+ provides optimal process mapping and outperforms the MPI default mapping policy by a factor of 4.24. This is the first work where the sparsity structure of matrices has been exploited to predict the optimal mapping of processes and data in distributed-memory environments by using different base and ensemble machine learning methods. Various CPSs comprise compute-intensive machine learning applications, such as the SpMV, and hence, the process and data mapping contributions of this paper would be of paramount impact for the CPSs.

An improved adaptive decomposition method for forest parameters estimation using polarimetric SAR interferometry image

ABSTRACT Forest parameters estimation using polarimetric synthetic aperture radar interferometry (PolInSAR) images is one of the greatest interests in remote sensing applications. Applying the model-based decomposition concept to PolInSAR data opened a new way for forest parameters estimation. However, the method tends to underestimate the forest height due to reflection symmetry assumption and required the numerical solution of nonlinear equation system. In order to overcome these limitations, an improved adaptive decomposition technique with PolInSAR data is proposed. In this approach, an accurate topographical phase and asymmetry volume scattering model are applied to the model-based decomposition technique for polarimetric SAR interferometry image. The accurate topographical phase is first estimated and then used as the initial input parameter to our numerical method. This approach is not only avoiding large error generated by the constant topographical phase in fluctuating forest areas but also improve the accuracy of forest height estimation and the magnitude associated with each mechanism. The performance of proposed method is demonstrated with simulated data from PolSARproSim software and SIR-C/X-SAR spaceborne PolInSAR images over the Tien-Shan areas, China. Experimental results indicate that forest parameters could be effectively extracted by proposed method.

Nonlinear multivariable tracking control: application to an ethanol process

In this paper, a controller based on linear algebra for a fed-batch ethanol production process is proposed. It involves finding feed rate profiles (control actions obtained as a linear equations system solution) in order to make the system follow predefined concentration profiles. A Monte Carlo experiment is used for controller tuning. Moreover, several tests (adding parametric uncertainty, perturbations in the control action and in the initial conditions) are carried out so as to evaluate the controller performance. A comparison with other controller is made and the demonstration of the error convergence is included.

Nonlinear multivariable tracking control: application to an ethanol process

In this paper, a controller based on linear algebra for a fed-batch ethanol production process is proposed. It involves finding feed rate profiles (control actions obtained as a linear equations system solution) in order to make the system follow predefined concentration profiles. A Monte Carlo experiment is used for controller tuning. Moreover, several tests (adding parametric uncertainty, perturbations in the control action and in the initial conditions) are carried out so as to evaluate the controller performance. A comparison with other controller is made and the demonstration of the error convergence is included.

Solitary Wave and other Solutions of Nonlinear Space-Time Fractional Differential Equation Systems

In this study, we have successfully found some travelling wave solutions of the variant Boussinesq system and fractional system of two-dimensional Burgers' equations of fractional order by using the -expansion method. These exact solutions contain hyperbolic, trigonometric and rational function solutions. The fractional complex transform is generally used to convert a partial fractional differential equation (FDEs) with modified Riemann-Liouville derivative into ordinary differential equation. We showed that the considered transform and method are very reliable, efficient and powerful in solving wide classes of other nonlinear fractional order equations and systems.