Solutions For System Of Equations Research Articles

Разработка и применение программы для автоматического нахождения невязки при пространственном контроле режимной метеорологической информации

Objective: to develop and apply software for automatic finding of discrepancies in automated meteorological stations in order to identify dubious and unreliable data without direct manual control in Fortran using PostgreSQL programming language queries. Write a program block for processing data from the archive of the database of meteorological stations of the unified network. Having provided a connection, with the help of requests, to ensure the receipt of data of the averaged values of ten-minute meteorological reports according to a special processing technique. Create a subroutine for solving the equation by the least squares matrix method, compare it to check the results with the linear regression method in a third-party application. Ensure proper recording of data before sending them to the database, prepare the necessary table for correct demonstration of data and user convenience in their use. Formulate correct queries to send the results of finding the discrepancy to the database. Formulate queries to create the necessary table, formulate queries and identify conditions for the implementation of the program for its more “flexible”functioning, that is, the ability to process data and find a discrepancy in the case of non-daily operation of the program. Methods: the methodology is similar to the principles of recommendations for the analysis of the results of spatial monitoring of regime meteorological information of the Main Geophysical Observatory named after Voeikova A. I. Methods include the translation of coordinates into a Cartesian system and the implementation of the solution of equation systems by the least squares method. Results: a program has been created that can work without the participation of an operator, performing automatic startup, data processing and data recording for further storage. Practical importance: the program allows you to receive data quickly due to the fast processing speed without errors caused by the human factor.

Algorithms for Constructing Minimal Generating Set of Solutions for Systems of Linear Equations

Algorithms for Constructing Minimal Generating Set of Solutions for Systems of Linear Equations

A multivariate model of deep slurry infiltration in slurry shield tunneling

There are multiple factors that influence slurry infiltration processes, making it necessary to consider these factors when comprehensively analyze the process of deep slurry infiltration. Firstly, this paper proposes a theoretical model for multivariate deep slurry infiltration and introduces a control equation governing the variation of the slurry infiltration domain. This equation accurately reflects changes in the infiltration boundary during the slurry infiltration process and meticulously responds to variations in pore water pressure, slurry retention rate, and pressure conversion efficiency-critical factors in the slurry infiltration process. Then, the Lax method was used to solve the corresponding control equations of the model, realizing the effective solution of the implicit partial differential equation system. The computational results of the theoretical model were compared with the indoor test results. Finally, the validated model was used to analyze the deep slurry infiltration characteristics. The results indicate that the theoretical model can reasonably simulate the deep slurry infiltration process, and the use of dynamic computational domain to describe deep slurry infiltration process is more in line with engineering practice. Furthermore, this model has guiding significance for the division of deep slurry infiltration stage and slurry surface infiltration stage.

Effectiveness of matrix measure in finding periodic solutions for nonlinear systems of differential and integro-differential equations with delays

Effectiveness of matrix measure in finding periodic solutions for nonlinear systems of differential and integro-differential equations with delays

An investigation of the solutions for rational systems of difference equations of order two

An investigation of the solutions for rational systems of difference equations of order two

A novel method to study time fractional coupled systems of shallow water equations arising in ocean engineering

<abstract><p>This study investigates solutions for the time-fractional coupled system of the shallow-water equations. The shallow-water equations are employed for the purpose of elucidating the dynamics of water motion in oceanic or sea environments. Also, the aforementioned system characterizes a thin fluid layer that maintains a hydrostatic equilibrium while exhibiting uniform density. Shallow water flows have a vertical dimension that is considerably smaller in magnitude than the typical horizontal dimension. In the current work, we employ an innovative and effective technique, known as the natural transform decomposition method, to obtain the solutions for these fractional systems. The present methodology entails the utilization of both singular and non-singular kernels for the purpose of handling fractional derivatives. The Banach fixed point theorem is employed to demonstrate the uniqueness and convergence of the obtained solution. The outcomes obtained from the application of the suggested methodology are compared to the exact solution and the results of other numerical methods found in the literature, including the modified homotopy analysis transform method, the residual power series method and the new iterative method. The results obtained from the proposed methodology are presented through the use of tabular and graphical simulations. The current framework effectively captures the behavior exhibited by different fractional orders. The findings illustrate the efficacy of the proposed method.</p></abstract>

Multiplicity results of periodic solutions for a coupled system of wave equations

Multiplicity results of periodic solutions for a coupled system of wave equations

Characterizations of entire solutions for the system of Fermat-type binomial and trinomial shift equations in ℂ n#

Abstract In this article, we investigate the existence and the precise form of finite-order transcendental entire solutions of some system of Fermat-type quadratic binomial and trinomial shift equations in C n {{\mathbb{C}}}^{n} . Our results are the generalizations of the results of [H. Y. Xu, S. Y. Liu, and Q. P. Li, Entire solutions for several systems of nonlinear difference and partial differential-difference equations of Fermat-type, J. Math. Anal. Appl. 483 (2020), 123641, 1–22, DOI: https://doi.org/10.1016/j.jmaa.2019.123641.] and [H. Y. Xu and Y. Y. Jiang, Results on entire and meromorphic solutions for several systems of quadratic trinomial functional equations with two complex variables, RACSAM 116 (2022), 8, DOI: https://doi.org/10.1007/s13398-021-01154-9.] to a large extent. Most interestingly, as a consequence of our main result, we have shown that the system of quadratic trinomial shift equation has no solution when it reduces to a system of quadratic trinomial difference equation. In addition, some examples relevant to the content of the article have been exhibited.

Finding And Comparing Solutions For An Undetermined System Of Linear Equations Using Scilab: Minimum-Norm Solution And Consistency Analysi

Finding And Comparing Solutions For An Undetermined System Of Linear Equations Using Scilab: Minimum-Norm Solution And Consistency Analysi

Extension of the Optimal Auxiliary Function Method to Solve the System of a Fractional-Order Whitham–Broer–Kaup Equation

In this paper, we introduce and implement the optimal auxiliary function method to solve a system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial differential equations with broad applications in mathematical physics. This method provides a systematic and efficient approach to finding accurate solutions for complex systems of fractional-order equations. We give a full analysis using tables and figures to demonstrate the reliability and accuracy of our approach. We confirm the effectiveness of our suggested method in solving the considered equations using numerical simulations and comparisons, emphasizing its potential for applications in a variety of scientific and engineering areas.

Estimates of matrix solutions of operator equations with random parameters under uncertainties

We investigate problems of estimating solutions of linear operator equations with random parameters under conditions of uncertainty. We establish that the guaranteed rms estimates of the matrices are found as solutions of special optimization problems under certain observations of the system state. As the output signals of the system, we have observations that are described by linear functions from the solutions of such equations with random right-hand sides, which have unknown second moments. Under the condition that the observation second moments of the right-hand parts and errors belong to certain sets, it is proved that the guaranteed estimates are expressed through solutions of operator equation systems. When the linear operator is given by the scalar product of rectangular matrices, a quasi-minimax estimate and its error are constructed. It is shown that the quasi-minimax estimation error tends to zero when the number of observations tends to infinity. An example of calculating the guaranteed rms estimate of the matrix's trace, which is a solution of a matrix equation with a random parameter, is given.

Existence of mild solutions for a coupled system of fractional evolution equations via Mönch's fixed point theorem in Banach spaces

Existence of mild solutions for a coupled system of fractional evolution equations via Mönch's fixed point theorem in Banach spaces

A Hybrid Method for All Types of Solutions of the System of Cauchy-Type Singular Integral Equations of the First Kind

In this note, the hybrid method (combination of the homotopy perturbation method (HPM) and the Gauss elimination method (GEM)) is developed as a semi-analytical solution for the first kind system of Cauchy-type singular integral equations (CSIEs) with constant coefficients. Before applying the HPM, we have to first reduce the system of CSIEs into a triangle system of algebraic equations using GEM, which is then carried out using the HPM. Using the theory of the bounded, unbounded and semi-bounded solutions of CSIEs, we are able to find inverse operators for the system of CSIEs of the first kind. A stability analysis and convergent of the proposed method has been conducted in the weighted Lp space. Moreover, the proposed method is proven to be exact in the Holder class of functions for the system of characteristic SIEs for any type of initial guess. For each of the four cases, several examples are provided and examined to demonstrate the proposed method’s validity and accuracy. Obtained results are compared with the Chebyshev collocation method and modified HPM (MHPM). Example 3 reveals that the error term of the MHPM is slightly superior to that of the HPM. One of the features of the proposed method is that it can be solved as a complex-valued system of CSIEs. Numerical results revealed that the hybrid method dominates others.

Periodic Solutions for an Impulsive System of Fractional Order Integro-Differential Equations with Maxima

Periodic Solutions for an Impulsive System of Fractional Order Integro-Differential Equations with Maxima

Influence of strong solar proton events on propagation of radio signals in the VLF range in a high-latitude region

In this paper, we examine the features of RSDN-20 signal propagation in a high-latitude Earth–ionosphere waveguide during solar proton events, using computational experiment methods. We have analyzed two proton ground-level enhancement (GLE) events of December 13, 2006 (GLE70) and September 10, 2017 (GLE72). Electron density profiles were constructed using the Global Dynamic Model of Ionosphere (GDMI) and the RUSCOSMICS model, developed at PGI. We present estimated phase and amplitude changes in RSDN-20 signals during precipitation of high-energy protons in the high-latitude region of the Earth–ionosphere waveguide. From the results of computational experiments and the analysis of the electromagnetic signal attenuation based on analytical Maxwell’s equation system solution in magnetized ionospheric plasma, we have found a pattern in the signal attenuation frequency dependence associated simultaneously with the signal reflection height, electron density profiles, and the collision frequency of electrons with neutral particles and ions. We discuss limitations of the computational experiment method and compare simulation results with data from Lovozero and Tuloma observatories.

Влияние сильных солнечных протонных событий на распространение радиосигналов в диапазоне ОНЧ в области высоких широт

In this paper, we examine the features of RSDN-20 signal propagation in a high-latitude Earth–ionosphere waveguide during solar proton events, using computational experiment methods. We have analyzed two proton ground-level enhancement (GLE) events of December 13, 2006 (GLE70) and September 10, 2017 (GLE72). Electron density profiles were constructed using the Global Dynamic Model of Ionosphere (GDMI) and the RUSCOSMICS model, developed at PGI. We present estimated phase and amplitude changes in RSDN-20 signals during precipitation of high-energy protons in the high-latitude region of the Earth–ionosphere waveguide. From the results of computational experiments and the analysis of the electromagnetic signal attenuation based on analytical Maxwell’s equation system solution in magnetized ionospheric plasma, we have found a pattern in the signal attenuation frequency dependence associated simultaneously with the signal reflection height, electron density profiles, and the collision frequency of electrons with neutral particles and ions. We discuss limitations of the computational experiment method and compare simulation results with data from Lovozero and Tuloma observatories.

Stochastic finite volume method for uncertainty quantification of transient flow in gas pipeline networks

We develop a weakly intrusive framework to simulate the propagation of uncertainty in solutions of generic hyperbolic partial differential equation systems on graph-connected domains with nodal coupling and boundary conditions. The method is based on the Stochastic Finite Volume (SFV) approach, and can be applied for uncertainty quantification (UQ) of the dynamical state of fluid flow over actuated transport networks. The numerical scheme has specific advantages for modeling intertemporal uncertainty in time-varying boundary parameters, which cannot be characterized by strict upper and lower (interval) bounds. We describe the scheme for a single pipe, and then formulate the controlled junction Riemann problem (JRP) that enables the extension to general network structures. We demonstrate the method's capabilities and performance characteristics using a standard benchmark test network.

Existence of Solutions for a Coupled System of Nonlinear Implicit Differential Equations Involving $$\varrho $$-Fractional Derivative with Anti Periodic Boundary Conditions

Existence of Solutions for a Coupled System of Nonlinear Implicit Differential Equations Involving $$\varrho $$-Fractional Derivative with Anti Periodic Boundary Conditions

Analysis of Implicit Solutions for a Coupled System of Hybrid Fractional Order Differential Equations with Hybrid Integral Boundary Conditions in Banach Algebras

This paper investigates the existence and uniqueness of implicit solutions in a coupled symmetry system of hybrid fractional order differential equations, along with hybrid integral boundary conditions in Banach Algebras. The methodology centers on a hybrid fixed-point theorem that involves mixed Lipschitz and Carathéodory conditions, serving to establish the existence of solutions. Moreover, it derives sufficient conditions for solution uniqueness and establishes the Hyers–Ulam types of solution stability. This study contributes valuable insights into complex hybrid fractional order systems and their practical implications.

Results on Solutions for Several Systems of Partial Differential-Difference Equations with Two Complex Variables

This article is to describe the entire solutions of some partial differential-difference equations and systems. Some theorems about the forms of transcendental entire solutions with finite order for several high-order partial differential-difference equations (or systems) of the Fermat type with two complex variables are obtained. Moreover, some examples are provided to explain that our results are precise to some extent.