APPLICATIONS INVOLVING ALGEBRAIC FORMS

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

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

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.

Algebraic Algorithm for the Kinematic Analysis of Slider-Crank/Rocker Mechanisms

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Giorgio Figliolini ◽  
Marco Conte ◽  
Pierluigi Rea
Keyword(s):  
Kinematic Analysis ◽  
Algebraic Curves ◽  
Algebraic Form ◽  
Complex Algebra ◽  
Geometric Invariants ◽  
Matlab Code ◽  
Algebraic Forms ◽  
Implicit And Explicit ◽  
First Time

This paper deals with the formulation and validation of a comprehensive algebraic algorithm for the kinematic analysis of slider-crank/rocker mechanisms, which is based on the use of geometric loci, as the fixed and moving centrodes, along with their evolutes, the cubic of stationary curvature and the inflection circle. In particular, both centrodes are formulated in implicit and explicit algebraic forms by using the complex algebra. Moreover, the algebraic curves representing the moving centrodes are recognized and proven to be Jeřábek’s curves for the first time. Then, the cubic of stationary curvature along with the inflection circle are expressed in algebraic form by using the instantaneous geometric invariants. Finally, the proposed algorithm has been implemented in a MATLAB code and significant numerical and graphical results are shown, along with the particular cases in which these geometric loci degenerate in lines and circles or give cycloidal positions.

Algebraic Algorithm for the Kinematic Analysis of Slider-Crank/Rocker Mechanisms

2010 ◽  
Author(s):  
Giorgio Figliolini ◽  
Marco Conte ◽  
Pierluigi Rea
Keyword(s):  
Kinematic Analysis ◽  
Algebraic Curves ◽  
Algebraic Form ◽  
Complex Algebra ◽  
Geometric Invariants ◽  
Matlab Code ◽  
Algebraic Forms ◽  
Implicit And Explicit ◽  
First Time

This paper deals with the formulation of an algebraic algorithm for the kinematic analysis of slider-crank/rocker mechanisms, which is based on the use of geometric loci, as the fixed and moving centrodes, the cubic of stationary curvature and the inflection circle. In particular, both centrodes are formulated in implicit and explicit algebraic forms by using the complex algebra. Moreover, the algebraic curves representing the moving centrodes are also recognized and proven to be Jerˇa´bek’s curves for the first time. Then, the cubic of stationary curvature along with the inflection circle are expressed in algebraic form by using the geometric invariants. Finally, the proposed algorithm has been implemented in a Matlab code and interesting numerical and graphical results are shown along with some particular cases in which the geometric loci degenerate in lines and circles.

scholarly journals A Concise Analysis of Certain Algebraic Forms

1941 ◽  
Vol 12 (1) ◽  
pp. 77-83
Author(s):  
Franklin E. Satterthwaite
Keyword(s):  
Algebraic Forms

Global General Relativity

1979 ◽  
Vol 368 (1732) ◽  
pp. 19-21
Keyword(s):  
General Relativity ◽  
High Speed ◽  
Equations Of State ◽  
Perturbation Expansion ◽  
Theoretical Work ◽  
Field Equations ◽  
Gravitational Fields ◽  
Highly Nonlinear ◽  
Mathematical Techniques ◽  
Algebraic Forms

Much of the theoretical work that has been carried out in General Relativity, particularly in the earlier years of the subject, has been concerned with finding explicit solutions of Einstein’s field equations, either in the vacuum case or, with suitable equations of state, when matter is present. These have been very useful in giving us some sort of feeling for the nature of more general ‘ physically reasonable ’ solutions, but they can, at best, only be rough approximations to such solutions. Exact solutions must, owing to the limitations of human energy and ingenuity, and to the complexity of Einstein’s equations, involve a number of simplifying assumptions, such as special symmetries or particular algebraic forms for the metric or curvature. Sometimes it is legitimate to regard such a special solution as the first term in some perturbation expansion towards something more realistic. But in the highly nonlinear situations of strong gravitational fields, such as in gravitational collapse to a black hole, or perhaps also in cosmology, it is often not clear when the results of such perturbation calculations (themselves often very complicated) can be trusted. High-speed computers can come to our aid (Smarr 1979, this symposium), of course, and can often give important insights in particular situations. But complementary to these are the global qualitative mathematical techniques that have been introduced into relativity over the past several years (Hawking & Ellis 1973; Penrose 1972).

Algebra. A Text-book of Determinants, Matrices, and Algebraic Forms.

1942 ◽  
Vol 49 (1) ◽  
pp. 51
Author(s):  
R. F. Rinehart ◽  
W. L. Ferrar
Keyword(s):  
Text Book ◽  
Algebraic Forms

scholarly journals SECONDARY SCHOOL STUDENTS’ ERROR OF TERM OF ALGEBRAIC FORMS BASED ON MATHEMATICAL COMMUNICATION

2020 ◽  
Vol 9 (2) ◽  
pp. 252
Author(s):  
Yus Mochamad Cholily ◽  
Tika Rifky Kamil ◽  
Putri Ayu Kusgiarohmah
Keyword(s):  
Secondary School ◽  
Secondary School Students ◽  
School Students ◽  
Mathematical Communication ◽  
Algebraic Forms ◽  
And Algebra

The purpose of this study is to describe students’ error on (1) the ability to understand the term of algebraic forms, and (2) the ability to communicate the term of algebraic forms into words and verbal forms. This is a case study. The study shows that: (1) the ability to understand the term of algebraic forms are low because of misunderstanding the slight differences between exponent and algebra itself, and (2) the ability to communicate the term of algebraic forms into words and verbal forms are challenging for them especially when they do not really understand the concepts.

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