scholarly journals ON THE AREA OF THE FUNDAMENTAL REGION OF A BINARY FORM ASSOCIATED WITH ALGEBRAIC TRIGONOMETRIC QUANTITIES

Mathematika ◽  
2021 ◽  
Vol 67 (2) ◽  
pp. 532-551
Author(s):  
Anton Mosunov
Keyword(s):  
Binary Form ◽  
Fundamental Region

Non-standard methods for converting numbers from one number system to another

2020 ◽  
Vol 1 (9) ◽  
pp. 28-30
Author(s):  
D. M. Zlatopolski
Keyword(s):  
Binary System ◽  
Maximum Degree ◽  
Number System ◽  
Binary Form ◽  
Binary Number ◽  
Standard Methods ◽  
Optimal Variant ◽  
Decimal System ◽  
Large Numbers ◽  
Independent Work

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.

Discrete fundamental region and its asymptotics

1992 ◽  
Vol 32 (1) ◽  
pp. 129-134
Author(s):  
A. I. Vinogradov
Keyword(s):  
Fundamental Region

Vertex Subgroups of Irreducible Representations of Solvable Groups

1971 ◽  
Vol 23 (1) ◽  
pp. 12-21
Author(s):  
J. Malzan
Keyword(s):  
Vector Space ◽  
Unit Sphere ◽  
Convex Subset ◽  
Orthogonal Group ◽  
Solvable Groups ◽  
Fundamental Region ◽  
Irreducible Representations ◽  
Theoretical Problem ◽  
Real Vector ◽  
The Real

If ρ(G) is a finite, real, orthogonal group of matrices acting on the real vector space V, then there is defined [5], by the action of ρ(G), a convex subset of the unit sphere in V called a fundamental region. When the unit sphere is covered by the images under ρ(G) of a fundamental region, we obtain a semi-regular figure.The group-theoretical problem in this kind of geometry is to find when the fundamental region is unique. In this paper we examine the subgroups, ρ(H), of ρ(G) with a view of finding what subspace, W of V consists of vectors held fixed by all the matrices of ρ(H). Any such subspace lies between two copies of a fundamental region and so contributes to a boundary of both. If enough of these boundaries might be found, the fundamental region would be completely described.

scholarly journals Natural Language Processing by Enhanced Honey Encryption Technique

2019 ◽  
Vol 8 (12S) ◽  
pp. 159-163
Keyword(s):  
Natural Language Processing ◽  
Natural Language ◽  
Language Processing ◽  
Cyber Attacks ◽  
Binary Form ◽  
Brute Force ◽  
Natural Languages ◽  
Cipher Text ◽  
The Right ◽  
Binary Strings

Traditional encryption systems and techniques have always been vulnerable to brute force cyber-attacks. This is due to bytes encoding of characters utf8 also known as ASCII characters. Therefore, an opponent who intercepts a cipher text and attempts to decrypt the signal by applying brute force with a faulty pass key can detect some of the decrypted signals by employing a mixture of symbols that are not uniformly dispersed and contain no meaningful significance. Honey encoding technique is suggested to curb this classical authentication weakness by developing cipher-texts that provide correct and evenly dispersed but untrue plaintexts after decryption with a false key. This technique is only suitable for passkeys and PINs. Its adjustment in order to promote the encoding of the texts of natural languages such as electronic mails, records generated by man, still remained an open-end drawback. Prevailing proposed schemes to expand the encryption of natural language messages schedule exposes fragments of the plaintext embedded with coded data, thus they are more prone to cipher text attacks. In this paper, amending honey encoded system is proposed to promote natural language message encryption. The main aim was to create a framework that would encrypt a signal fully in binary form. As an end result, most binary strings semantically generate the right texts to trick an opponent who tries to decipher an error key in the cipher text. The security of the suggested system is assessed..

scholarly journals Hyperbolization of Euclidean Ornaments

10.37236/78 ◽  
2009 ◽  
Vol 16 (2) ◽  
Author(s):  
Martin von Gagern ◽  
Jürgen Richter-Gebert
Keyword(s):  
Differential Geometry ◽  
Pattern Recognition ◽  
Hyperbolic Plane ◽  
Discrete Differential Geometry ◽  
Fundamental Region ◽  
Symmetry Groups ◽  
Symmetry Detection ◽  
Conformal Deformation ◽  
Optimal Resolution ◽  
Wallpaper Groups

In this article we outline a method that automatically transforms an Euclidean ornament into a hyperbolic one. The necessary steps are pattern recognition, symmetry detection, extraction of a Euclidean fundamental region, conformal deformation to a hyperbolic fundamental region and tessellation of the hyperbolic plane with this patch. Each of these steps has its own mathematical subtleties that are discussed in this article. In particular, it is discussed which hyperbolic symmetry groups are suitable generalizations of Euclidean wallpaper groups. Furthermore it is shown how one can take advantage of methods from discrete differential geometry in order to perform the conformal deformation of the fundamental region. Finally it is demonstrated how a reverse pixel lookup strategy can be used to obtain hyperbolic images with optimal resolution.

On Convex Fundamental Regions for a Lattice

1961 ◽  
Vol 13 ◽  
pp. 177-178 ◽  
Author(s):  
A. M. Macbeath
Keyword(s):  
Lebesgue Measure ◽  
Convex Set ◽  
Fundamental Region ◽  
Linearly Independent ◽  
Whole Space ◽  
Closed Convex Set ◽  
Set Of Points

Let ∧ be a lattice in Euclidean n-space, that is, ∧ is a set of points ε1a1+ … + εnanwherea1… ,anare linearly independent vectors and the ε run over all integers. Letμdenote the Lebesgue measure. A closed convex setFis called afundamental regionfor ∧ if the setsF+x (x∈∧) cover the whole space without overlapping; that is, ifF0is the interior ofF,and 0 ≠x∈ ∧, thenF0∩(F0+x) =ϕ.

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