Approximation of Linear Sets in the Plane

2019 ◽  
Vol 7 (3) ◽  
pp. 60-69 ◽  
Author(s):  
В. Юрков ◽  
V. Yurkov
Keyword(s):  
Finite Number ◽  
Continuous Family ◽  
Point Sets ◽  
Multiple Points ◽  
Linear Set ◽  
Linear Sets ◽  
The Best Approximation ◽  
Special Factor ◽  
Almost All ◽  
The Given

A few general lines in the ordinary Euclidean plane are said to be line generators of a plane linear set. To be able to say that every line of the set belongs to one-parametrical line set we have to find their envelope. We thus create a pencil of lines. In this article it will be shown that there are a finite number of pencils in one linear set. To find a pencil of lines the linear parametrical approximation is applied. Almost all of problems concerning the parametrical approximation of figure sets are well known and deeply developed for any point sets. The problem of approximation for non-point sets is an actual one. The aim of this paper is to give a path to parametrical approximation of linear sets defined in plane. The sets are discrete and consist of finite number of lines without any order. Each line of the set is given as y = ax + b. Parametrical approximation means a transformation the discrete set of lines into completely continuous family of lines. There are some problems. 1. The problem of order. It is necessary to represent the chaotic set of lines as well-ordered one. The problem is solved by means of directed circuits. Any of chaotic sets has a finite number of directed circuits. To create an order means to find all directed circuits in the given set. 2. The problem of choice. In order to find the best approximation, for example, the simplest one it is necessary to choose the simplest circuit. Some criteria of the choice are discussed in the paper. 3. Interpolation the set of line factors. A direct approach would simply construct an interpolation for all line factors. But this can lead to undesirable oscillations of the line family. To eliminate the oscillations the special factor interpolation are suggested. There are linear sets having one or several multiple points, one or several multiple lines and various combinations of multiple points and lines. Some theorems applied to these cases are formulated in the paper.

scholarly journals Translation Hyperovals and $\mathbb{F}_2$-Linear Sets of Pseudoregulus Type

10.37236/8818 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Jozefien D'haeseleer ◽  
Geertrui Van de Voorde
Keyword(s):  
Finite Fields ◽  
Point Sets ◽  
Linear Set ◽  
Linear Sets ◽  
Even Order ◽  
Translation Ovals

In this paper, we study translation hyperovals in PG(2,qk). The main result of this paper characterises the point sets defined by translation hyperovals in the André/Bruck-Bose representation. We show that the affine point sets of translation hyperovals in PG(2,qk) are precisely those that have a scattered F2-linear set of pseudoregulus type in PG(2k−1,q) as set of directions. This correspondence is used to generalise the results of Barwick and Jackson who provided a characterisation for translation hyperovals in PG(2,q2), see [S.G. Barwick, Wen-Ai Jackson, A characterization of translation ovals in finite even order planes. Finite fields Appl. 33 (2015), 37--52.].

Deskripsi Kesulitan Belajar Siswa Berdasarkan Karakteristik Lerner dalam Menyelesaikan Soal Geometri

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Nazom Murio ◽  
Roseli Theis
Keyword(s):  
Qualitative Research ◽  
Visual Perception ◽  
Learning Difficulties ◽  
Research Subjects ◽  
Visual Objects ◽  
Almost All ◽  
Personality Classification ◽  
The Given ◽  
Classification Test ◽  
Descriptive Qualitative

Geometri adalah bagian matematika yang sangat dekat dari siswa, karena hampir semua objek visual yang ada di sekitar siswa adalah objek geometri, tetapi tidak semua siswa menyukai pembelajaran yang menyertakan gambar, sehingga memungkinkan siswa mengalami kesulitan dalam belajar geometri. Tujuan dari penelitian ini adalah untuk menggambarkan kesulitan belajar siswa berdasarkan karakteristik Lerner dalam menyelesaikan pertanyaan geometri. Jenis penelitian ini adalah penelitian deskriptif kualitatif. Subjek penelitian adalah siswa dengan kepribadian wali yang mengalami kesulitan belajar di kelas IX A SMP N 30 Muaro Jambi. Instrumen yang digunakan dalam penelitian ini adalah penulis sendiri, lembar tes klasifikasi kepribadian, lembar tes kesulitan belajar, dan pedoman wawancara. Hasil penelitian menunjukkan siswa dengan kepribadian wali yang mengalami kesulitan belajar, 100% mengalami kelainan persepsi visual, di mana siswa mengalami kesulitan dalam menentukan seperti apa bangun datar pada masalah tersebut. 60% mengalami kesulitan mengenali dan memahami simbol, di mana siswa melihat simbol "//" sebagai simbol untuk kesesuaian. Serta 40% mengalami kesulitan dalam bahasa dan membaca, di mana siswa kesulitan dalam memahami pertanyaan yang diberikan.   Geometry is a very close mathematical part of the student, because almost all visual objects that exist around the students are objects of geometry, but not all students like learning that includes images, thus allowing students to have difficulty in learning geometry. The purpose of this research is to describe students' learning difficulties based on Lerner's characteristic in solving the geometry question. This type of research is descriptive qualitative research. Research subjects were students with guardian personality who had difficulty studying in class IX A SMP N 30 Muaro Jambi. Instruments used in this study are the authors themselves, personality classification test sheets, learning difficulties test sheets, and interview guidelines. The results showed students with guardian personality who experienced learning difficulties, 100% experienced visual perception abnormalities, where students have difficulty in determining what kind of flat wake on the matter. 60% have difficulty recognizing and understanding symbols, where students see the symbol "//" as a symbol for conformity. As well as 40% have difficulty in language and reading, where students difficulty in understanding the given question.

Be Careful, if You Learn Geography for 8th Grade with „Ucha.se“

2021 ◽  
Vol 30 (1) ◽  
pp. 37-53
Author(s):  
Ivan Drenovski ◽  
Keyword(s):  
Test Items ◽  
Educational Site ◽  
8Th Grade ◽  
Basic Concepts ◽  
Almost All ◽  
The Given

The article analyses the content of the video lessons and corresponding to them test items in Geography and Economics for 8 th grade, available for a fee, on the educational site "Ucha.se". The studied curriculum is related to the introduction of basic concepts and explanations of key processes studied by geology, geophysics, astronomy, geochemistry, geomorphology, meteorology, climatology, hydrology, biology and other sciences. There are serious lapses in the scientific reliability and correctness of the given statements in almost all lessons. Examples of factual errors, incorrectly asked questions, inaccurate images and pseudo-scientific simplifications are pointed.

scholarly journals Cryptosystem using double vertex graph

2020 ◽  
Vol 13 (44) ◽  
pp. 4483-4489
Author(s):  
C Beaula ◽  
Keyword(s):  
Graph Theory ◽  
Secure Communication ◽  
System Method ◽  
Encryption And Decryption ◽  
Vertex Graph ◽  
Private And Public ◽  
Almost All ◽  
Encryption Method ◽  
The Given ◽  
Edge Labeling

Background/Objective: The Coronavirus Covid-19 has affected almost all the countries and millions of people got infected and more deaths have been reported everywhere. The uncertainty and fear created by the pandemic can be used by hackers to steal the data from both private and public systems. Hence, there is an urgent need to improve the security of the systems. This can be done only by building a strong cryptosystem. So many researchers started embedding different topics of mathematics like algebra, number theory, and so on in cryptography to keep the system, safe and secure. In this study, a cryptosystem using graph theory has been attempted, to strengthen the security of the system. Method: A new graph is constructed from the given graph, known as a double vertex graph. The edge labeling of this double vertex graph is used in encryption and decryption. Findings: A new cryptosystem using the amalgamation of the path, its double vertex graph and edge labeling has been proposed. From the double vertex graph of a path, we have given a method to find the original path. To hack such an encrypted key, the knowledge of graph theory is important, which makes the system stronger. Applications:The one-word encryption method will be useful in every security system that needs a password for secure communication or storage or authentication. Keywords: Double vertex graphs; path; adjacency matrix; encryption; cryptography

scholarly journals Hermite–Hadamard-Type Inequalities for Product of Functions by Using Convex Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Tariq Nawaz ◽  
M. Asif Memon ◽  
Kavikumar Jacob
Keyword(s):  
Convex Function ◽  
Finite Number ◽  
Convex Functions ◽  
The Many ◽  
The Given

One of the many techniques to obtain a new convex function from the given functions is to calculate the product of these functions by imposing certain conditions on the functions. In general, the product of two or finite number of convex function needs not to be convex and, therefore, leads us to the study of product of these functions. In this paper, we reframe the idea of product of functions in the setting of generalized convex function to establish Hermite–Hadamard-type inequalities for these functions. We have analyzed different cases of double and triple integrals to derive some new results. The presented results can be viewed as the refinement and improvement of previously known results.

A Context-Aware Model of Trust for Facilitating Secure Ad Hoc Collaborations

2010 ◽  
pp. 250-281 ◽  
Author(s):  
Indrajit Ray ◽  
Indrakshi Ray ◽  
Sudip Chakraborty
Keyword(s):  
Incomplete Information ◽  
Ad Hoc ◽  
Sensitive Information ◽  
Trust Value ◽  
Trust Relationships ◽  
The Face ◽  
Trust Models ◽  
Almost All ◽  
Ad Hoc Collaborations ◽  
The Given

Ad hoc collaborations often necessitate impromptu sharing of sensitive information or resources between member organizations. Each member of resulting collaboration needs to carefully assess and tradeoff the requirements of protecting its own sensitive information against the requirements of sharing some or all of them. The challenge is that no policies have been previously arrived at for such secure sharing (since the collaboration has been formed in an ad hoc manner). Thus, it needs to be done based on an evaluation of the trustworthiness of the recipient of the information or resources. In this chapter, the authors discuss some previously proposed trust models to determine if they can be effectively used to compute trustworthiness for such sharing purposes in ad hoc collaborations. Unfortunately, none of these models appear to be completely satisfactory. Almost all of them fail to satisfy one or more of the following requirements: (i) well defined techniques and procedures to evaluate and/or measure trust relationships, (ii) techniques to compare and compose trust values which are needed in the formation of collaborations, and (iii) techniques to evaluate trust in the face of incomplete information. This prompts the authors to propose a new vector (we use the term “vector” loosely; vector in this work means a tuple) model of trust that is suitable for reasoning about the trustworthiness of systems built from the integration of multiple subsystems, such as ad hoc collaborations. They identify three parameters on which trust depends and formulate how to evaluate trust relationships. The trust relationship between a truster and a trustee is associated with a context and depends on the experience, knowledge, and recommendation that the truster has with respect to the trustee in the given context. The authors show how their model can measure trust in a given context. Sometimes enough information is not available about a given context to calculate the trust value. Towards this end the authors show how the relationships between different contexts can be captured using a context graph. Formalizing the relationships between contexts allows us to extrapolate values from related contexts to approximate a trust value of an entity even when all the information needed to calculate the trust value is not available. Finally, the authors develop formalisms to compare two trust relationships and to compose two or more of the same – features that are invaluable in ad hoc collaborations.

scholarly journals Performance and Statistical Analysis of Stream ciphers in GSM Communications

2020 ◽  
Vol 16 (1) ◽  
pp. 11-18 ◽  
Author(s):  
Nagendar Yerukala ◽  
V Kamakshi Prasad ◽  
Allam Apparao
Keyword(s):  
Statistical Analysis ◽  
Stream Cipher ◽  
Statistical Tests ◽  
Stream Ciphers ◽  
Test Suite ◽  
Secret Key ◽  
Initial State ◽  
Detailed Statistical Analysis ◽  
Almost All ◽  
The Given

For a stream cipher to be secure, the keystream generated by it should be uniformly random with parameter 1/2.Statistical tests check whether the given sequence follow a certain probability distribution. In this paper, we perform a detailed statistical analysis of various stream ciphers used in GSM 2G,3G, 4G and 5G communications. The sequences output by these ciphers are checked for randomness using the statistical tests defined by the NIST Test Suite. It should also be not possible to derive any information about secret key and the initial state ofthe cipher from the keystream. Therefore, additional statisticaltests based on properties like Correlation between Keystreamand Key, and Correlation between Keystream and IV are also performed. Performance analysis of the ciphers also has been done and the results tabulated. Almost all the ciphers pass thetests in the NIST test suite with 99% confidence level. For A5/3stream cipher, the correlation between the keystream and key is high and correlation between the keystream and IV is low when compared to other ciphers in the A5 family.

Generic Partial Two-Point Sets Are Extendable

1999 ◽  
Vol 42 (1) ◽  
pp. 46-51 ◽  
Author(s):  
Jan J. Dijkstra
Keyword(s):  
Point Sets ◽  
Martin's Axiom ◽  
Martin’S Axiom ◽  
Almost All

AbstractIt is shown that under ZFC almost all planar compacta that meet every line in at most two points are subsets of sets that meet every line in exactly two points. This result was previously obtained by the author jointly with K. Kunen and J. vanMill under the assumption that Martin’s Axiom is valid.

The Floodlight Problem

1997 ◽  
Vol 07 (01n02) ◽  
pp. 153-163 ◽  
Author(s):  
Prosenjit Bose ◽  
Leonidas Guibas ◽  
Anna Lubiw ◽  
Mark Overmars ◽  
Diane Souvaine ◽  
...  
Keyword(s):  
Fixed Points ◽  
Point Sets ◽  
Entire Plane ◽  
The Given

Given three angles summing to 2π, given n points in the plane and a tripartition k1 + k2 + k3 = n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge contains ki of the points. This new result on dissecting point sets is used to prove that lights of specified angles not exceeding π can be placed at n fixed points in the plane to illuminate the entire plane if and only if the angles sum to at least 2π. We give O(n log n) algorithms for both these problems.

scholarly journals A proof of Aronhold's theorem upon quartic curves

1940 ◽  
Vol 6 (3) ◽  
pp. 190-191
Author(s):  
H. W. Richmond
Keyword(s):  
Finite Number ◽  
Simple Proof ◽  
Plane Curves ◽  
Cubic Surface ◽  
Quartic Curves ◽  
Order Four ◽  
The Given

It is to be expected that a finite number of plane curves of order four should have seven given lines as bitangents, because the number of conditions imposed is equal to the number of effective free constants in the equation of such a curve, viz., 14. Aronhold made the interesting discovery that one curve could be determined in which no three of the given lines have their six points of contact on a conic. The method, due to Geiser, of obtaining the bitangents as projections of the lines of a cubic surface leads to a simple proof of the existence of this quartic.

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