scholarly journals Finite field and group algorithms for orthogonal sequence search

2021 ◽  
pp. 2-17
Author(s):  
Nikolay Balonin ◽  
Alexander Sergeev ◽  
Olga Sinitshina
Keyword(s):  
Finite Fields ◽  
Practical Importance ◽  
Video Data ◽  
Polynomial Equations ◽  
Ideal Object ◽  
Domestic Literature ◽  
Finite Dimensional ◽  
Sequence Search ◽  
Lack Of Information ◽  
First Time

Introduction: Hadamard matrices consisting of elements 1 and –1 are an ideal object for a visual application of finite dimensional mathematics operating with a finite number of addresses for –1 elements. The notation systems of abstract algebra methods, in contrast to the conventional matrix algebra, have been changing intensively, without being widely spread, leading to the necessity to revise and systematize the accumulated experience. Purpose: To describe the algorithms of finite fields and groups in a uniform notation in order to facilitate the perception of the extensive knowledge necessary for finding orthogonal and suborthogonal sequences. Results: Formulas have been proposed for calculating relatively unknown algorithms (or their versions) developed by Scarpis, Singer, Szekeres, Goethal — Seidel, and Noboru Ito, as well as polynomial equations used to prove the theorems about the existence of finite-dimensional solutions. This replenished the significant lack of information both in the domestic literature (most of these issues are published here for the first time) and abroad. Practical relevance: Orthogonal sequences and methods for their effective finding via the theory of finite fields and groups are of direct practical importance for noise-immune coding, compression and masking of video data.

scholarly journals A note on extensions of multilinear maps defined on multilinear varieties

2021 ◽  
pp. 1-26
Author(s):  
W. T. Gowers ◽  
L. Milićević
Keyword(s):  
Finite Fields ◽  
Vector Spaces ◽  
Restriction Map ◽  
Zero Set ◽  
Dimensional Vector ◽  
Prime Field ◽  
Finite Dimensional ◽  
Multilinear Maps ◽  
Multilinear Map

Abstract Let $G_1, \ldots , G_k$ be finite-dimensional vector spaces over a prime field $\mathbb {F}_p$ . A multilinear variety of codimension at most $d$ is a subset of $G_1 \times \cdots \times G_k$ defined as the zero set of $d$ forms, each of which is multilinear on some subset of the coordinates. A map $\phi$ defined on a multilinear variety $B$ is multilinear if for each coordinate $c$ and all choices of $x_i \in G_i$ , $i\not =c$ , the restriction map $y \mapsto \phi (x_1, \ldots , x_{c-1}, y, x_{c+1}, \ldots , x_k)$ is linear where defined. In this note, we show that a multilinear map defined on a multilinear variety of codimension at most $d$ coincides on a multilinear variety of codimension $O_{k}(d^{O_{k}(1)})$ with a multilinear map defined on the whole of $G_1\times \cdots \times G_k$ . Additionally, in the case of general finite fields, we deduce similar (but slightly weaker) results.

scholarly journals Atomic Latin Squares based on Cyclotomic Orthomorphisms

10.37236/1919 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Ian M. Wanless
Keyword(s):  
Finite Fields ◽  
Complete Graph ◽  
Prime Order ◽  
Automorphism Groups ◽  
Latin Square ◽  
Latin Squares ◽  
Established Method ◽  
Cyclic Groups ◽  
Complete Bipartite Graphs ◽  
First Time

Atomic latin squares have indivisible structure which mimics that of the cyclic groups of prime order. They are related to perfect $1$-factorisations of complete bipartite graphs. Only one example of an atomic latin square of a composite order (namely 27) was previously known. We show that this one example can be generated by an established method of constructing latin squares using cyclotomic orthomorphisms in finite fields. The same method is used in this paper to construct atomic latin squares of composite orders 25, 49, 121, 125, 289, 361, 625, 841, 1369, 1849, 2809, 4489, 24649 and 39601. It is also used to construct many new atomic latin squares of prime order and perfect $1$-factorisations of the complete graph $K_{q+1}$ for many prime powers $q$. As a result, existence of such a factorisation is shown for the first time for $q$ in $\big\{$529, 2809, 4489, 6889, 11449, 11881, 15625, 22201, 24389, 24649, 26569, 29929, 32041, 38809, 44521, 50653, 51529, 52441, 63001, 72361, 76729, 78125, 79507, 103823, 148877, 161051, 205379, 226981, 300763, 357911, 371293, 493039, 571787$\big\}$. We show that latin squares built by the 'orthomorphism method' have large automorphism groups and we discuss conditions under which different orthomorphisms produce isomorphic latin squares. We also introduce an invariant called the train of a latin square, which proves to be useful for distinguishing non-isomorphic examples.

scholarly journals First-principles study of the structural, optoelectronic and thermophysical properties of the π-SnSe for thermoelectric applications

2021 ◽  
Vol 12 ◽  
pp. 1101-1114
Author(s):  
Muhammad Atif Sattar ◽  
Najwa Al Bouzieh ◽  
Maamar Benkraouda ◽  
Noureddine Amrane
Keyword(s):  
Thermoelectric Properties ◽  
Density Functional ◽  
Practical Importance ◽  
Next Generation ◽  
Thermoelectric Devices ◽  
Functional Theory ◽  
Tin Selenide ◽  
Large Lattice ◽  
The Density Functional Theory ◽  
First Time

Tin selenide (SnSe) has thermoelectric (TE) and photovoltaic (PV) applications due to its exceptional advantages, such as the remarkable figure of merit (ZT ≈ 2.6 at 923 K) and excellent optoelectronic properties. In addition, SnSe is nontoxic, inexpensive, and relatively abundant. These aspects make SnSe of great practical importance for the next generation of thermoelectric devices. Here, we report structural, optoelectronic, thermodynamic, and thermoelectric properties of the recently experimentally identified binary phase of tin monoselenide (π-SnSe) by using the density functional theory (DFT). Our DFT calculations reveal that π-SnSe features an optical bandgap of 1.41 eV and has an exceptionally large lattice constant (12.2 Å, P213). We report several thermodynamic, optical, and thermoelectric properties of this π-SnSe phase for the first time. Our finding shows that the π-SnSe alloy is exceptionally promising for the next generation of photovoltaic and thermoelectric devices at room and high temperatures.

THE CONCEPT OF ENEMY: REPRESENTATION IN THE UKRAINIAN MILITARY DOCUMENTARIES

2021 ◽  
Author(s):  
Alina Chervinchuk
Keyword(s):  
Content Analysis ◽  
Emotional State ◽  
Descriptive Analysis ◽  
Practical Importance ◽  
Military Conflict ◽  
Scientific Methods ◽  
General Scientific ◽  
Creative Space ◽  
The Military ◽  
First Time

Research methodology. The following methods were used in this research: general scientific methods (descriptive, analysis, synthesis, comparison) and special (structural, hermeneutic, narrative, method of content analysis). We identified words related to the concept of the enemy and determined the context in which they are used by the authors of the collections Results. The formats of reflection of military reality in collections of military documentaries are investigated. It is emphasized that the authors-observers of events as professional communicators form a vision of events based on categories understandable to the audience – «own» and «others». Instead, the authors-participants go events have more creative space and pay more attention to their own emotional state and reflections. It is defined how the enemy is depicted and what place he occupies in the military reality represented by the authors. It is emphasized that the authors reflect the enemy in different ways. In particular, the authors-observers of the events tried to form a comprehensive vision of the events, and therefore paid much attention to the opposite side of the military conflict. Authors-participants of the events tend to show the enemy as a mass to be opposed. In such collections, the enemy is specified only in the presence of evidence confirming the presence of Russians or militants. Novelty. The research for the first time investigates the methods of representation of mi­litary activity in the collections of Ukrainian military documentaries. The article is devoted to the analysis of how the authors represent the enemy. Practical importance. The analysis of collections of military documentaries will allow to study the phenomenon of war and to trace the peculiarities of the authors’ representation of military reality.

Stochastic comparisons of random processes, with applications in reliability

1973 ◽  
Vol 10 (03) ◽  
pp. 572-585 ◽  
Author(s):  
Gordon Pledger ◽  
Frank Proschan
Keyword(s):  
Practical Importance ◽  
Random Processes ◽  
Stochastic Comparison ◽  
Random Vectors ◽  
Stochastic Comparisons ◽  
Usual Definition ◽  
Definition Of ◽  
First Time

The usual definition of stochastic comparison of random vectors is extended to stochastic comparison of random processes. Conditions are stated under which {X (t), t ≧ 0} stochastically larger than {Y (t), t ≧ 0} implies that for increasing functionals f. Applications are made to reliability problems, yielding stochastic comparisons for systems of independently operating machines assuming exponential failure and exponential repair. From these stochastic comparisons we may then deduce similar stochastic comparisons for functionals of practical importance in reliability applications, such as the total machine up-time, the first time that the number of functioning machines drops below a specified number, the total time during which at least a specified number of machines are functioning, etc.

scholarly journals Illuminating Insights into the Biodiversity of the Australian Psyllids (Hemiptera: Psylloidea) Collected Using Light Trapping

Insects ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 354
Author(s):  
Francesco Martoni ◽  
Gary S. Taylor ◽  
Mark J. Blacket
Keyword(s):  
Host Plants ◽  
Light Trapping ◽  
Light Sources ◽  
Undescribed Species ◽  
Biological Control Agents ◽  
Numerous Species ◽  
Lack Of Information ◽  
Species Of Conservation Concern ◽  
Conservation Concern ◽  
First Time

The superfamily Psylloidea includes numerous species which play a key role in Australian ecology and biodiversity, as well as pests and biological control agents, and sometimes threatened species of conservation concern. Different psyllid sampling and collection techniques are usually performed depending on the nature and aim of the study: from the beating and sweeping of psyllid host plants for conservation and biodiversity assessment, to suction and sticky traps in agriculture. Due to a general lack of information on its efficacy for psyllids, however, light trapping has not usually been employed. Here we present the results obtained trapping psyllids using different light sources and we discuss the strengths and weaknesses of this technique to assess psyllid biodiversity. In particular, we highlight the strength of using this methodology paired with DNA barcoding, to cast some light on psyllid biodiversity. The results obtained here suggest that the psyllid fauna of Australia is heavily understudied and the number of undescribed species might be many times higher than previously expected. Additionally, we report, for the first time, the species Trioza adventicia Tuthill 1952, and Cryptoneossa triangula Taylor 1990 in the state of Queensland.

scholarly journals A generalised quantifier theory of natural language in categorical compositional distributional semantics with bialgebras

2019 ◽  
Vol 29 (06) ◽  
pp. 783-809
Author(s):  
Jules Hedges ◽  
Mehrnoosh Sadrzadeh
Keyword(s):  
Natural Language ◽  
Vector Space ◽  
Generative Grammar ◽  
Distributional Semantics ◽  
Compositional Semantics ◽  
Finite Dimensional ◽  
Linear Maps ◽  
First Time ◽  
Quantifier Theory ◽  
Compositional Distributional Semantics

AbstractCategorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, and then instantiate the abstract setting to sets and relations and to finite-dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalised quantifiers. The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases and sentences compositionally in distributional semantics.

scholarly journals Primal Lower Nice Functions in Reflexive Smooth Banach Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2066
Author(s):  
Messaoud Bounkhel ◽  
Mostafa Bachar
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Space Setting ◽  
Nonlinear Anal ◽  
Finite Dimensional ◽  
In Trans ◽  
First Time ◽  
The Relationship ◽  
Primal Lower Nice Functions

In the present work, we extend, to the setting of reflexive smooth Banach spaces, the class of primal lower nice functions, which was proposed, for the first time, in finite dimensional spaces in [Nonlinear Anal. 1991, 17, 385–398] and enlarged to Hilbert spaces in [Trans. Am. Math. Soc. 1995, 347, 1269–1294]. Our principal target is to extend some existing characterisations of this class to our Banach space setting and to study the relationship between this concept and the generalised V-prox-regularity of the epigraphs in the sense proposed recently by the authors in [J. Math. Anal. Appl. 2019, 475, 699–29].

scholarly journals Finding roots in with the successive resultants algorithm

2014 ◽  
Vol 17 (A) ◽  
pp. 203-217 ◽  
Author(s):  
Christophe Petit
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Finite Fields ◽  
Coding Theory ◽  
Discrete Logarithm ◽  
Discrete Logarithm Problem ◽  
Polynomial Equations ◽  
Preliminary Results ◽  
Characteristic Case ◽  
Practical Security

AbstractThe problem of solving polynomial equations over finite fields has many applications in cryptography and coding theory. In this paper, we consider polynomial equations over a ‘large’ finite field with a ‘small’ characteristic. We introduce a new algorithm for solving this type of equations, called the successive resultants algorithm (SRA). SRA is radically different from previous algorithms for this problem, yet it is conceptually simple. A straightforward implementation using Magma was able to beat the built-in Roots function for some parameters. These preliminary results encourage a more detailed study of SRA and its applications. Moreover, we point out that an extension of SRA to the multivariate case would have an important impact on the practical security of the elliptic curve discrete logarithm problem in the small characteristic case.Supplementary materials are available with this article.

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