Symbol alphabets from plabic graphs III: n = 9

Symbol alphabets of n-particle amplitudes in $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory are known to contain certain cluster variables of G(4, n) as well as certain algebraic functions of cluster variables. In this paper we solve the C Z = 0 matrix equations associated to several cells of the totally non-negative Grassmannian, combining methods of arXiv:2012.15812 for rational letters and arXiv:2007.00646 for algebraic letters. We identify sets of parameterizations of the top cell of G+(5, 9) for which the solutions produce all of (and only) the cluster variable letters of the 2-loop nine-particle NMHV amplitude, and identify plabic graphs from which all of its algebraic letters originate.

Definite Integral of Power and Algebraic Functions in terms of the Lerch Function

Bierens de haan (1867) evaluated a definite integral involving the cotangent function and this result was also listed in Gradshteyn and Ryzhik (2007). The objective of this present note is to use this integral along with Cauchy's integral formula to derive a definite logarithmic integral in terms of the Lerch function. We will use this integral formula to produce a table of known and new results in terms of special functions and thereby expanding the list of definite integrals in both text books.

Thermodynamic compatibility conditions of a new class of hysteretic materials

The thermodynamic compatibility defined by the Drucker postulate applied to a phenomenological hysteretic material, belonging to a recently formulated class, is hereby investigated. Such a constitutive model is defined by means of a set of algebraic functions so that it does not require any iterative procedure to compute the response and its tangent operator. In this sense, the model is particularly feasible for dynamic analysis of structures. Moreover, its peculiar formulation permits the computation of thermodynamic compatibility conditions in closed form. It will be shown that, in general, the fulfillment of the Drucker postulate for arbitrary displacement ranges requires strong limitations of the constitutive parameters. Nevertheless, it is possible to determine a displacement compatibility range for arbitrary sets of parameters so that the Drucker postulate is fulfilled as long as the displacement amplitude does not exceed the computed threshold. Numerical applications are provided to test the computed compatibility conditions.

Developing A Learning Media on Limit of Algebraic Functions by Using Google Forms

The objective of the research is to develop a valid and practical learning media using google forms for material on the limit of algebraic functions. The type of research is Research and Development (R & D) using the ADDIE model in the process of developing a learning media. The ADDIE model development procedure is Analysis, Design, Development, Implementation, and Evaluation in validation results of development research involved six students at SMAN 11 Pandeglang and six teachers who are media experts and material experts. The results of this study are (1) Produce mathematics learning media using google forms with good qualifications on the material limit of algebraic functions, (2) Media expert assessments of well-qualified learning media products, and (3) Average results of validation by students on media products with good qualifications. Keywords: learning media, e-learning, google forms, limits of algebraic functions.

IDENTIFICATION OF STUDENT ERRORS IN SOLVING DERIVATIVE PROBLEMS IN SMA NEGERI 3 PALANGKA RAYA

This study aims to find out: (1) students' mistakes in solving problems derived from algebraic functions, and (2) the causes of studenterrors. This research is qualitative descriptive research, conducted in October until November 2020. The subjects in this study were 37 students of grade XI MIPA 3 SMA Negeri 3 Palangka Raya. Next, 3 students are selected for the interview, to find out why the student made a mistake. The instrument in this study consists of 5 test questions in the form of descriptions used to determine the type of mistakes made by students. Based on the results of the study, the types of mistakes made by students solve the problem of AlgebraIc Function Derivatives are: errors in facts, concepts, operations and principles Factors that cause students to make mistakes in solving problems derived from algebraic functions based on aspects of errors in understanding facts, concepts, operations and principles that contain students' knowledge of materials that have been learned from simple to difficult then students' memories of the concept of limits, root concepts and concepts of inverse , lack of ability to understand students to the material that has been studied such as understanding the concept of limit, root concept and concept of inverse. lack of ability to decipher material or apply material that has been studied in new situations and concerns the use of rules or principles such as applying the concept of limit, root concept, inverse concept and operating numbers.

Identification of Student Errors in Solving Problems on the Limit of Algebra Functions in Class XI SMAN 4 Palangkaraya

This study aims to describe the mistakes of class XI students of SMA Negeri 4 Palangka Raya in solving the limit problem of algebraic functions and their causative factors. This research is a descriptive study with a qualitative approach. Data collection techniques are tests and interviews. The research instrument was a question sheet and interview guidelines. The questions used are in the form of a description consisting of 5 questions. Before being used, the questions were reviewed by 3 raters, namely 2 mathematics education lecturers and 1 mathematics teacher. From the results of the study it was concluded that all questions could be used. Checking the validity of the data was carried out by observing persistence and triangulation of sources. Then the collected data were analyzed using data analysis techniques proposed by Miles and Huberman, namely data reduction, data presentation, and drawing conclusions. The results showed that the errors made by students on the limit of algebraic functions were: (1) Conceptual errors: (a) errors in understanding the concept of limits which consist of formulas, theorems and definitions of limits. (b) the use of formulas, theorems and definitions of limits that are inconsistent with the conditions for the application of the formula; 2) Procedural errors: (a) errors in calculations, (b) inability to write work steps regularly. (c) errors in applying rules, principles or formulas. (d) the inability of students to manipulate algebraic forms based on applicable properties or principles. As for the factors causing students in this study in terms of internal factors of students.

DEFRAGMENTATION THINKING STRUCTURE TO OVERCOME ERRORS IN ADDRESSING MATHEMATICAL PROBLEM

This research is intended to describe students' procedural errors in solving problems derivative of algebraic functions and efforts to overcome these errors by using the defragmentation process. Error analysis is carried out based on the procedural error theory based on Elbrink which includes the following aspects of errors: 1) Mis-identification; 2) Mis-generalization; 3) Repair Theory; and 4) Overspecialization. The subjects in this study are students of class XII MIPA Islamic State Senior High School (MAN) 3 Tulungagung taken from snowball random sampling. In taking the subject, the researchers select one of the students who make procedural errors by considering the completeness of the students when solving the given problems based on the problem-solving phase according to Polya. Based on the results of this study, it is found that the procedural errors made by the students are repair theory errors and overspecialization. The defragmenting process to correct these errors is intended to provide dis-equilibration and scaffolding. The results after the defragmenting process are the students can correct their mistakes and the structure of their thinking.Keywords: Defragmenting structure thinking; derivative algebraic functions; problem solving; procedural errors. AbstrakPenelitian ini bertujuan untuk menggambarkan kesalahan prosedural siswa dalam menyelesaikan masalah turunan fungsi aljabar dan upaya untuk mengatasi kesalahan tersebut dengan menggunakan proses defragmenting. Analisis kesalahan dilakukan berdasarkan konsep teori kesalahan prosedural menurut Elbrink yang mencakup aspek kesalahan sebagai berikut: Mis-identificstion; 2) Mis-generalization; 3) Repair Theory; dan 4) Overspecialization. Subjek dalam penelitian ini adalah siswa kelas XII MIPA MAN 3 Tulungagung yang diambil secara snowball random sampling. Dalam pengambilan subjek dipilih salah satu siswa yang melakukan kesalahan prosedural dengan mempertimbangkan kelengkapan siswa ketika menyelesaikan masalah yang diberikan berdasarkan tahap pemecahan masalah menurut Polya. Dari hasil penelitian ini ditemukan bahwa kesalahan prosedural yang dilakukan siswa ialah kesalahan repair theory dan overspecialization. Proses defragmenting yang dilakukan untuk memperbaiki kesalahan tersebut ialah dengan memberikan dissequillibrasi dan scaffolding. Hasil yang diperoleh setelah proses defragmenting dilakukan ialah siswa mampu memperbaiki kesalahannya dan struktur berpikirnya.Kata kunci: Defragmenting struktur berpikir, kesalahan prosedural, pemecahan masalah, turunan fungsi aljabar.

Symbol alphabets from plabic graphs II: rational letters

Symbol alphabets of n-particle amplitudes in $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory are known to contain certain cluster variables of G(4, n) as well as certain algebraic functions of cluster variables. The first paper arXiv:2007.00646 in this series focused on n = 8 algebraic letters. In this paper we show that it is possible to obtain all rational symbol letters (in fact all cluster variables) by solving matrix equations of the form C Z = 0 if one allows C to be an arbitrary cluster parameterization of the top cell of G+(n−4, n).