scholarly journals Two-Body Elliptic Model in Proper Variables: Lie Algebraic Forms and Their Discretizations

2000 ◽  
pp. 473-484
Author(s):  
Alexander Turbiner
Keyword(s):  
Elliptic Model ◽  
Algebraic Forms

Several classes of permutation trinomials from Niho exponents over finite fields of characteristic 3

2019 ◽  
Vol 18 (04) ◽  
pp. 1950069
Author(s):  
Qian Liu ◽  
Yujuan Sun
Keyword(s):  
Positive Integer ◽  
Finite Field ◽  
Coding Theory ◽  
Permutation Polynomials ◽  
Combinatorial Designs ◽  
Dickson Polynomial ◽  
Niho Exponents ◽  
Characteristic 3 ◽  
Permutation Trinomials ◽  
Algebraic Forms

Permutation polynomials have important applications in cryptography, coding theory, combinatorial designs, and other areas of mathematics and engineering. Finding new classes of permutation polynomials is therefore an interesting subject of study. Permutation trinomials attract people’s interest due to their simple algebraic forms and additional extraordinary properties. In this paper, based on a seventh-degree and a fifth-degree Dickson polynomial over the finite field [Formula: see text], two conjectures on permutation trinomials over [Formula: see text] presented recently by Li–Qu–Li–Fu are partially settled, where [Formula: see text] is a positive integer.

scholarly journals Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space

2018 ◽  
Vol 92 ◽  
pp. 49-53 ◽  
Author(s):  
L.A. Khajiyeva ◽  
D.A. Prikazchikov ◽  
L.A. Prikazchikova
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Elastic Half Space ◽  
Elliptic Model

Defragmenting structures of students’ translational thinking in solving mathematical modeling problems based on CRA framework

2020 ◽  
Vol 13 (2) ◽  
pp. 130-151
Author(s):  
Kadek Adi Wibawa ◽  
I Putu Ade Andre Payadnya ◽  
I Made Dharma Atmaja ◽  
Marius Derick Simons
Keyword(s):  
Mathematical Modeling ◽  
Problem Solving ◽  
Undergraduate Students ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Graph Representations ◽  
Symbolic Representations ◽  
Mathematics Educators ◽  
Three Stages ◽  
Algebraic Forms

 [English]: The fragmentation of thinking structure is a failed construction existing in students’ memory due to disconnections on what they have learned. It makes students undergo difficulties and errors in solving mathematical modeling problems. There is a need to prevent permanent fragmentations. The problem-solving involving modeling problems requires translational thinking, changing from source representations to targeted representations. This research aimed to formulate undergraduate students’ effort in restructuring their fragmented translational thinking (defragmentation of translational thinking structure). The defragmentation was mapped through the CRA framework (checking, repairing, ascertaining). The subjects were three of eighty-five 4th and 6th-semester students. Data were analyzed through three stages; categorization, reduction, and conclusion. The analysis resulted in three types of defragmentation of translational thinking structure: from verbal representations to graph representations, from graph representations to symbolic representations (algebraic forms), and from the graph and symbolic representations to mathematical models. The finding shows that it is essential for mathematics educators to allow students to manage their thinking structures while experiencing difficulties and errors in mathematical problem-solving. Keywords: Thinking structure, Fragmentation, Defragmentation, Translational thinking, CRA framework  [Bahasa]: Fragmentasi struktur berpikir merupakan kegagalan konstruksi yang terjadi di dalam memori akibat dari konsep-konsep yang dipelajari tidak terkoneksi dengan baik. Hal ini membuat mahasiswa sering mengalami kesulitan dan kesalahan dalam memecahkan masalah pemodelan matematika. Untuk itu, perlu dilakukan upaya agar tidak terjadi fragmentasi struktur berpikir yang permanen. Dalam memecahkan masalah pemodelan matematika, mahasiswa perlu melakukan berpikir translasi, yaitu mengubah representasi sumber menjadi representasi yang ditargetkan. Penelitian ini bertujuan untuk merumuskan upaya mahasiswa dalam melakukan penataan fragmentasi struktur berpikir translasi yang terjadi (defragmentasi struktur berpikir translasi) dalam memecahkan masalah pemodelan matematika. Defragmentasi yang dilakukan mahasiswa dipetakan melalui kerangka CRA (checking, repairing, dan ascertaining). Subjek penelitian adalah mahasiswa semester 4 dan 6 yang terdiri dari 3 orang dipilih dari 85 mahasiswa. Analisis data dilakukan melalui tiga tahap, yaitu pengategorian data, reduksi data, dan penarikan kesimpulan. Penelitian ini menemukan tiga jenis defragmentasi struktur berpikir translasi: defragmentasi dari representasi verbal ke grafik, dari representasi grafik ke simbol (bentuk aljabar), dan representasi grafik dan simbol (bentuk aljabar) ke model matematika. Penelitian ini menunjukkan pentingnya pengajar matematika memberikan kesempatan kepada mahasiswa dalam menata struktur berpikirnya ketika mengalami kesulitan dan kesalahan dalam memecahkan masalah matematika. Kata kunci: Struktur berpikir, Fragmentasi, Defragmentasi, Berpikir translasi, Kerangka CRA

APPLICATIONS INVOLVING ALGEBRAIC FORMS

Symmetry ◽  
1963 ◽  
pp. 140-165
Author(s):  
R. McWEENY
Keyword(s):  
Algebraic Forms

scholarly journals ANALISIS PERCOBAAN FAKTORIAL UNTUK MELIHAT PENGARUH PENGGUNAAN ALAT PERAGA BLOK ALJABAR TERHADAP PRESTASI BELAJAR ALJABAR SISWA

2013 ◽  
Vol 2 (2) ◽  
pp. 1
Author(s):  
NI PUTU AYU MIRAH MARIATI ◽  
NI LUH PUTU SUCIPTAWATI ◽  
KARTIKA SARI
Keyword(s):  
Academic Achievement ◽  
Experimental Design ◽  
Block Design ◽  
Student Academic Achievement ◽  
Visual Aids ◽  
Geometry Model ◽  
Randomized Block Design ◽  
Algebraic Forms ◽  
Block Algebra ◽  
Better Than

The experimental design was applied in research in many different fields of science, such as in education, as used in this study. Block algebra visual aids is a visual aids in the form of the geometry model used to concretize understanding the variables and constants in the algebra which is an abstract concept. This visual aids are used as a basis for factoring algebraic forms. In connection with this, the aims of this research is to determine the effect of the application of algebra block in student academic achievement in class VII in the field of algebra in schools categorized as private, SSN (Sekolah Standar Nasional) and the previously categorized RSBI (Rintisan Sekolah Bertaraf Internasional). The method of analysis used in this study was two-factor experimental design in a randomized block design. The results showed that the academic achievement of students in the field of algebra after learning with block algebra visual aids obtained better than the academic achievement of students who received learning without using block algebra visual aids. Moreover, it also shows that the categories of schools have a significant effect on student achievement.

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