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This paper attempts to establish the general formula for computing the inverse of grey matrix, and the results are applied to solve grey linear programming. The inverse of a grey matrix and grey linear programming plays an important role in establishing a grey computational system.

Starting from the fact that missing information often appears in complex systems, and therefore that true values of elements are uncertain when the authors construct a matrix, as well as calculate its inverse. However, the authors can get their ranges, which are called the number-covered sets, by using grey computational rules. How to get the matrix-covered set of inverse grey matrix became a typical approach. In this paper, grey linear programming was explained in detail, for the point of grey meaning and the methodology to calculate the inverse grey matrix can successfully solve grey linear programming.

The results show that the ranges of grey value of inverse grey matrix and grey linear programming can be obtained by using the computational rules.

Because the matrix and the linear programming have been widely used in many fields such as system controlling, economic analysis and social management, and the missing information is a general phenomenon for complex systems, grey matrix and grey linear programming may have great potential application in real world. The methodology realizes the feasibility to control the complex system under uncertain situations.

The paper successfully obtained the ranges of uncertain inverse matrix and linear programming by using grey system theory, when the elements of matrix and the coefficients of linear programming are intervals and the results enrich the contents of grey mathematics.

During the grave war years the greater part of the burden of factory and field work lay on the shoulders of women and young workers. Thousands of young people were compelled to leave school so as to take the places at the bench and lathe of their fathers and brothers who left for the front. Therefore, every young person who did not finish his education on account of the war, must now fill up the gap.

The purpose of this research is to propose a new choice of nonnegative parameter t in Dai–Liao conjugate gradient method.

Conjugate gradient algorithms are used to solve both constrained monotone and general systems of nonlinear equations. This is made possible by combining the conjugate gradient method with the Newton method approach via acceleration parameter in order to present a derivative-free method.

A conjugate gradient method is presented by proposing a new Dai–Liao nonnegative parameter. Furthermore the proposed method is successfully applied to handle the application in motion control of the two joint planar robotic manipulators.

The proposed algorithm is a new approach that will not either submitted or publish somewhere.

To suggest a polynomial complexity method for determining the range of real eigenvalues in the case of the generalized eigenvalue problem when the elements of the matrices involved are independent intervals.

The basic approach is to make use of approximate interval solutions as regards the right and left eigenvectors of the eigenproblem considered, the so‐called outer solutions, in order to determine the range.

First, a new method for computing the outer solutions has been suggested. The main result of the paper, however, is the development of a simple method for determining the range of the real eigenvalues. Unlike the known general‐purpose methods that have exponential complexity, the present range determination method is much simpler as its complexity is only polynomial.

The method is applicable if certain sufficient conditions reported in the paper are satisfied (an incomplete quadratic system is to have a positive solution and the signs of the outer solutions should satisfy a complete or partial invariance).

The method guarantees reliable numerical results when the original eigenproblems contain interval uncertainties as is, strictly speaking, most often the case in practice.

To the best of the author's knowledge, the present paper suggests, for the first time, a simple method of polynomial complexity for solving the problem considered which is inherently a NP‐hard problem (of exponential complexity).

This work presents a new two-step iterative technique for solving absolute value equations. The developed technique is valuable and effective for solving the absolute value equation. Various examples are given to demonstrate the accuracy and efficacy of the suggested technique.

In this paper, we present a new two-step iterative technique for solving absolute value equations. This technique is very straightforward, and due to the simplicity of this approach, it can be used to solve large systems with great effectiveness. Moreover, under certain assumptions, we examine the convergence of the proposed method using various theorems. Numerical outcomes are conducted to present the feasibility of the proposed technique.

This paper gives numerical experiments on how to solve a system of absolute value equations.

Nowadays, two-step approaches are very popular for solving equations (1). For solving AVEs, Liu in Shams (2021), Ning and Zhou (2015) demonstrated two-step iterative approaches. Moosaei et al. (2015) introduced a novel approach that utilizes a generalized Newton’s approach and Simpson’s rule to solve AVEs. Zainali and Lotfi (2018) presented a two-step Newton technique for AVEs that converges linearly. Feng and Liu (2016) have proposed minimization approaches for AVEs and presented their convergence under specific circumstances. Khan et al. (2023), suggested a nonlinear CSCS-like technique and a Picard-CSCS approach. Based on the benefits and drawbacks of the previously mentioned methods, we will provide a two-step iterative approach to efficiently solve equation (1). The numerical results show that our proposed technique converges rapidly and provides a more accurate solution.

Previous RMIL versions of the conjugate gradient method proposed in literature exhibit sufficient descent with Wolfe line search conditions, yet their global convergence depends on certain restrictions. To alleviate these assumptions, a hybrid conjugate gradient method is proposed based on the conjugacy condition.

The conjugate gradient (CG) method strategically alternates between RMIL and KMD CG methods by using a convex combination of the two schemes, mitigating their respective weaknesses. The theoretical analysis of the hybrid method, conducted without line search consideration, demonstrates its sufficient descent property. This theoretical understanding of sufficient descent enables the removal of restrictions previously imposed on versions of the RMIL CG method for global convergence result.

Numerical experiments conducted using a hybrid strategy that combines the RMIL and KMD CG methods demonstrate superior performance compared to each method used individually and even outperform some recent versions of the RMIL method. Furthermore, when applied to solve an image reconstruction model, the method exhibits reliable results.

The strategy used to demonstrate the sufficient descent property and convergence result of RMIL CG without line search consideration through hybrid techniques has not been previously explored in literature. Additionally, the two CG schemes involved in the combination exhibit similar sufficient descent structures based on the assumption regarding the norm of the search direction.

The purpose of this paper is to present the results in the area of modern computer‐aided control system design tools relating to system identification.

The finite‐frequency identification method was designed for the needs of active identification. The test signal represents the sum of harmonics with automatically tuned (self‐tuned) amplitudes and frequencies where the number of harmonics does not exceed the state space dimension of the plant. The self‐tuning of amplitudes is carried out to satisfy those requirements on the bounds of the input and output which hold true in the absence of a test signal.

In this paper, the software implementation of finite‐frequency identification method in the system GAMMA is considered. GAMMA is the two‐level computer‐aided design (CAD) tool for identification and controllers algorithms synthesis for linear plants.

The system GAMMA is the complete and really working system.

A new structure of the CAD tool for engineers‐developers of control systems is proposed and its program implementation is described. The new variant of finite‐frequency identification method with self‐tuning of identification parameters (test signal and identification time) is considered.

This paper aims to provide a method for obtaining physically sound temperature fields to be used in geophysical inversions in the presence of immersed essential conditions.

The method produces a thermal field in agreement with a given location of the interface between the Lithosphere and Asthenosphere. It leverages the known location of the interface to enforce the location of a given isotherm while relaxing other constraints known with less precision. The method splits the domain: in the Lithosphere the solution is immediately obtained by standard procedures, while in the Asthenosphere a minimization problem is solved to fulfill continuity of temperatures (strongly imposed) and fluxes at the interface (weakly imposed).

The numerical methodology, based on the relaxation of the bottom fluxes, correctly recovers the thermal field in the complete domain. To obtain bottom fluxes following geophysical expected values, a constrained minimization strategy is required. The sensitivity of the method could be improved by relaxing other quantities such as lateral fluxes or mantle velocities.

A statement of the energy balance problem in terms of a known immersed condition is presented. A novel numerical procedure based on a domain-splitting strategy allows the solution of the problem. The procedure is tailored to be used within geophysical inversions and provides physically sound solutions.

A 2D numerical simulation using a finite element technique is presented for computing spreading resistance of a semiconductor buried ridge stripe laser. The simplified physical model is analyzed from the functional analysis point of view and a proof of existence and uniqueness of the nonlinear partial differential equations obtained from this simplified model is given. The discrete associated nonlinear problem is solved on triangular finite elements using conjugate gradient algorithms. Some results are presented for a specific semiconductor laser

Biotechnology is closely associated to microfluidics. During the last decade, designs of microfluidic devices such as geometries and scales have been modified and improved according to the applications for better performance. Numerous sensor technologies existing in the industry has potential use for clinical applications. Fabrication techniques of microfluidics initially rooted from the electromechanical systems (EMS) technology.

In this review, we emphasized on the most available manufacture approaches to fabricate microchannels, their applications and the properties which make them unique components in biological studies.

Major fundamental and technological advances demonstrate the enhancing of capabilities and improving the reliability of biosensors based on microfluidic. Several researchers have been reported verity of methods to fabricate different devices based on EMS technology due to the electroconductivity properties and their small size of them. Therefore, controlled fabrication method of MEMS plays an important role to design and fabricate a highly selective detection of medical devices in a variety of biological fluids. Stable, tight and reliable monitoring devices for biological components still remains a massive challenge and several studies focused on MEMS to fabricate simple and easy monitoring devices.

This paper is not submitted or under review in any other journal.