ANALISIS GAYA BELAJAR VISUAL DITINJAU DARI KEMAMPUAN PEMECAHAN MASALAH SISTEM PERSAMAAN LINEAR DUA VARIABEL

This review means to depict the investigation of visual learning styles as far as critical thinking capacity of understudies' two-variable direct condition framework at MTS Negeri 3 Mempawah. The examination strategy utilized is enlightening subjective as contextual analyses. The subjects in this study were class VIII students at MTS Negeri 3 Mempawah. The number of students who were used as research subjects were 38 students who had studied the material for a two-variable system of linear equations. In this study, six students were selected consisting of two students who had SPLDV Problem Solving Ability in terms of high, medium, low learning styles. The object of this exploration is Visual Learning Style as far as Critical thinking Capacity. In light of the aftereffects of information examination, meetings and conversation, it can be concluded that Analysis of Visual Learning Styles Judging from the SPLDV Problem-Solving Ability of MT.S Negeri 3 Mempawah Students" shows that students' problem-solving abilities are relatively balanced with learning styles. As a rule, understudies who have high numerical critical thinking capacities have great visual learning styles, understudies with moderate critical thinking capacities have great visual learning styles, understudies with low numerical critical thinking capacities have great visual learning styles.

Some new semiring structures

In this paper, we introduce some new semiring structures by considering the prime factors, sum of divisors and the number of relatively prime positive divisors of a pair of non-negative integers and solve a variety of system of linear equations over one of these semirings. We then discuss the properties of these structures and how they compare with classical algebra. The paper is concluded by providing a key-exchange scheme using one of the newly discovered semirings.

Rasch model item response theory (IRT) to analyze the quality of mathematics final semester exam test on system of linear equations in two variables (SLETV)

A high-quality test has a balanced level of difficulty and can be completed by the respondent with their level of abilities. This study analyzed the test instrument used to measure students' mathematics abilities in the semester final exam on System of Linear Equations in Two-Variables. The purposive sampling technique was applied to select the respondent students (N=195). The test items were twenty multiple-choice questions. The researchers performed the data analysis using Rasch model Item Response Theory (IRT) approach with the QUEST program. The analysis revealed that the twenty items’ validity matched the Rasch model with a range of INFIT MNSQ values between 0.89 – 1.17. Items on the final semester exam can be used based on the estimated OUTFIT t-value less than equal to 2.00. The OUTFIT t analysis obtained nineteen qualified items and one unqualified item.

On $m$-th roots of nilpotent matrices

A new necessary and sufficient condition for the existence of an $m$-th root of a nilpotent matrix in terms of the multiplicities of Jordan blocks is obtained and expressed as a system of linear equations with nonnegative integer entries which is suitable for computer programming. Thus, computation of the Jordan form of the $m$-th power of a nilpotent matrix is reduced to a single matrix multiplication; conversely, the existence of an $m$-th root of a nilpotent matrix is reduced to the existence of a nonnegative integer solution to the corresponding system of linear equations. Further, an erroneous result in the literature on the total number of Jordan blocks of a nilpotent matrix having an $m$-th root is corrected and generalized. Moreover, for a singular matrix having an $m$-th root with a pair of nilpotent Jordan blocks of sizes $s$ and $l$, a new $m$-th root is constructed by replacing that pair by another one of sizes $s+i$ and $l-i$, for special $s,l,i$. This method applies to solutions of a system of linear equations having a special matrix of coefficients. In addition, for a matrix $A$ over an arbitrary field that is a sum of two commuting matrices, several results for the existence of $m$-th roots of $A^k$ are obtained.

Generalisation of the Frobenius Formula in the Theory of Block Operators on Normed Spaces

The efficient construction and employment of block operators are vital for contemporary computing, playing an essential role in various applications. In this paper, we prove a generalisation of the Frobenius formula in the setting of the theory of block operators on normed spaces. A system of linear equations with the block operator acting in Banach spaces is considered. Existence theorems are proved, and asymptotic approximations of solutions in regular and irregular cases are constructed. In the latter case, the solution is constructed in the form of a Laurent series. The theoretical approach is illustrated with an example, the construction of solutions for a block equation leading to a method of solving some linear integrodifferential system.

Algorithm to construct integro splines

We study some properties of integro splines. Using these properties, we design an algorithm to construct splines \(S_{m+1}(x)\) of neighbouring degrees to the given spline \(S_{m}(x)\) with degree \(m\). A local integro-sextic spline is constructed with the proposed algorithm. The local integro splines work efficiently, that is, they have low computational complexity, and they are effective for use in real time. The construction of nonlocal integro splines usually leads to solving a system of linear equations with band matrices, which yields high computational costs. doi:10.1017/S1446181121000316

Interval Approach to Magnetotelluric Data Processing

The article presents a new approach to estimate the frequency characteristics of the impedance tensor for processing magnetotelluric data. The approach is based on the applying of interval analysis methods when solving a system of linear equations. As a reference method, to compare with, a combined robust algorithm is used (with discarding data by the coherence criterion, median estimating, and weighting least squares method). This algorithm is compared with the results of the proposed interval computational algorithm that is based on the method of J. Rohn, implemented in the intvalpy Python library. Computational experiments on the data processing were performed using natural magnetotelluric field data. The interval approach can be successfully applied to the processing of magnetotelluric data.

A new method for obtaining a Born cross section using visible cross section data from e+e− colliders

In this paper, we propose a new method for obtaining a Born cross section using visible cross section data. It is assumed that the initial state radiation is taken into account in a visible cross section, while in a Born cross section this effect is ommited. Since the equation that connects Born and visible cross sections is an integral equation of the first kind, the problem of finding its numerical solution is ill-posed. Various regularization-based approaches are often used to solve ill-posed problems, since direct methods usually do not lead to an acceptable result. However, in this paper it is shown that a direct method can be successfully used to numerically solve the considered equation under the condition of a small beam energy spread and uncertainty. This naive method is based on finding a numerical solution to the integral equation by reducing it to a system of linear equations. The naive method works well because the kernel of the integral operator is a rapidly decreasing function of the variable x. This property of the kernel leads to the fact that the condition number of the matrix of the system of linear equations is of the order of unity, which makes it possible to neglect the ill-posedness of the problem when the above condition is satisfied. The advantages of the naive method are its model independence and the possibility of obtaining the covariance matrix of a Born cross section in a simple way.It should be noted that there are already a number of methods for obtaining a Born cross section using visible cross section data, which are commonly used in e+e− experiments. However, at least some of these methods have various disadvantages, such as model dependence and relative complexity of obtaining a Born cross section covariance matrix. It should be noted that this paper focuses on the naive method, while conventional methods are hardly covered. The paper also discusses solving the problem using the Tikhonov regularization, so that the reader can better understand the difference between regularized and non-regularized solutions. However, it should be noted that, in contrast to the naive method, regularization methods can hardly be used for precise obtaining of a Born cross section. The reason is that the regularized solution is biased and the covariance matrix of this solution do not represent the correct covariance matrix of a Born cross section.