scholarly journals Characteristic of Rings. Prime Fields

2015 ◽  
Vol 23 (4) ◽  
pp. 333-349 ◽  
Author(s):  
Christoph Schwarzweller ◽  
Artur Korniłowicz
Keyword(s):  
Rational Numbers ◽  
Basic Properties ◽  
Prime Fields

Summary The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over rationals are computed.

scholarly journals On the geometry of multisymplectic manifolds

1999 ◽  
Vol 66 (3) ◽  
pp. 303-330 ◽  
Author(s):  
F. Cantrijn ◽  
A. Ibort ◽  
M. De León
Keyword(s):  
Differential Form ◽  
Structure Theorem ◽  
General Structure ◽  
Linear Case ◽  
Characteristic Distribution ◽  
Basic Properties ◽  
Lagrangian Fibration ◽  
Zero Characteristic

AbstractA multisymplectic structure on a manifold is defined by a closed differential form with zero characteristic distribution. Starting from the linear case, some of the basic properties of multisymplectic structures are described. Various examples of multisymplectic manifolds are considered, and special attention is paid to the canonical multisymplectic structure living on a bundle of exterior k-forms on a manifold. For a class of multisymplectic manifolds admitting a ‘Lagrangian’ fibration, a general structure theorem is given which, in particular, leads to a classification of these manifolds in terms of a prescribed family of cohomology classes.

scholarly journals Modern Classification of the Properties of Papillary Patterns of Human Hands and Feet for the Solution of Identification and Non-Identification Problems in Forensic Expert Activities

2021 ◽  
Vol 18 (4) ◽  
pp. 445-459
Author(s):  
V. I. Balko
Keyword(s):  
Body Fat ◽  
Human Body ◽  
Identification Problems ◽  
Basic Properties ◽  
Modern Classification ◽  
Definition Of ◽  
Hands And Feet ◽  
First Time ◽  
Papillary Pattern

The relevance and novelty of the topic of the article is connected with the fact that for the first time the improved classification of the properties of human papillary patterns and their displays and the dynamic trend of expanding the legal base of fingerprint registration in the world are considered. The goal is to systematize the properties of human papillary patterns and their representations. General scientific and special methods were used. The analysis of the literature and the author's practice allow us to identify and consider the following properties of papillary patterns and their mappings, which were divided into three groups for cognitive purposes: their own properties, the properties of mappings, and the properties of the fat-rich substance of the human papillary pattern and its trace. For the first time, the properties of the poly-fat substance of the human papillary pattern and its trace are presented, which is important in view of the trend in the development of complex fingerprint examination. For the first time, the first and second groups are conditionally divided into four subgroups: for solving identification, diagnostic, classification and situational problems. For the first time, the third group is further conditionally divided into four subgroups: according to the interaction of the human body fat with the carrier object; according to the isolation of the human body fat trace; according to the dynamics of the preservation and contrast of the display of the fat-free substance of the human papillary pattern. On the other hand, the properties of papillary patterns themselves are divided into basic properties and properties for solving identification and non-identification problems, respectively. The author's definition of the following concepts is presented: "basic properties of human papillary patterns" and "properties of human papillary patterns", "basic properties of human papillary patterns mappings" and "properties of human papillary patterns mappings", "basic properties of human papillary matter" and "properties of human papillary matter", "basic properties of human papillary matter" and" properties of human papillary matter". This provides an opportunity for specialists and teachers to improve their cognitive and practical activities, and for those responsible and competent for the organization of examinations to consider creating a center for comprehensive fingerprint examination.

scholarly journals Maximal Chow constant and cohomologically constant fibrations

2020 ◽  
pp. 2050075
Author(s):  
Kristin DeVleming ◽  
David Stapleton
Keyword(s):  
Chow Groups ◽  
Generic Fiber ◽  
Basic Properties ◽  
Rationally Connected

Motivated by the study of rationally connected fibrations, we study different notions of birationally simple fibrations. Our main result is the construction of maximal Chow constant and cohomologically constant fibrations. This paper is largely self-contained and we prove a number of basic properties of these fibrations. One application is to the classification of “rationalizations of singularities of cones.” We also consider consequences for the Chow groups of the generic fiber of a Chow constant fibration.

scholarly journals Optimal factorizations of rational numbers using factorization trees

2015 ◽  
Vol 11 (03) ◽  
pp. 739-769 ◽  
Author(s):  
Charles L. Samuels ◽  
Tanner J. Strunk
Keyword(s):  
Data Structure ◽  
Recent Work ◽  
Efficient Method ◽  
Algebraic Number ◽  
Single Point ◽  
Rational Numbers ◽  
Basic Properties ◽  
Tree Data ◽  
Metric Mahler Measure ◽  
Tree Data Structure

Let mt(α) denote the t-metric Mahler measure of the algebraic number α. Recent work of the first author established that the infimum in mt(α) is attained by a single point [Formula: see text] for all sufficiently large t. Nevertheless, no efficient method for locating [Formula: see text] is known. In this paper, we define a new tree data structure, called a factorization tree, which enables us to find [Formula: see text] when α ∈ ℚ. We establish several basic properties of factorization trees, and use these properties to locate [Formula: see text] in previously unknown cases.

scholarly journals INNOVATIONS OF JURISPRUDENCE AND LEGALITY IN THE SPHERE OF TRANSPORT AND TRANSPORT TECHNOLOGIES

2021 ◽  
Author(s):  
Оleksandr A. Kyrychenko ◽  
◽  
Julia О. Lantsedova ◽  
Tuntula Оleksandra S ◽  
Keyword(s):  
Deviant Behavior ◽  
Basic Properties ◽  
Legal Force

The monograph draws attention to the innovative nature, functions and system of anti-offenses bodies in ensuring the legality in the field of transport and transport technologies. The basic properties of deviant behavior of individuals and the powers of anti-tortists to overcome it are described. An innovative species division of legal facts, offenses and juridical liability in the context of ensuring legality in the field of transport and transport technologies is proposed. An innovative understanding of the reliability of information and their sources as a basis for juridical and other competence in this area is revealed. The basic values of law and the tasks of jurisprudence and other doctrinal basis of the innovative nature of the transport branch of law and code are considered. The essence of the ratio of legal acts in the field of transport and transport technologies by legal force is clarified. The essence of the nature and bases of the transport branch of law according to the innovative classification of juridical sciences on the basis of their basic hypertasks is revealed. An innovative eleven-level procedure for transporting basic and related juridical and other education by carriers is outlined. It can be useful for anyone interested in innovations in jurisprudence and legality in the field of transport and transport technologies.

An Artist's Works through the Eyes of a Physicist: Graphic Illustration of Particle Symmetries

Leonardo ◽  
2006 ◽  
Vol 39 (1) ◽  
pp. 51-57 ◽  
Author(s):  
György Darvas ◽  
Tamás F. Farkas
Keyword(s):  
Physical Properties ◽  
Internal Structure ◽  
General Public ◽  
Graphical Representation ◽  
Basic Properties ◽  
Graphic Artist ◽  
Subatomic Particles ◽  
Graphic Illustration ◽  
Physical Objects

The paper presents remarks by a physicist and a graphic artist on an artwork series produced by the artist. They associate the colors and twists represented in these graphics with the properties of subatomic particles—their structures and connections. The authors use graphical representation to visualize the inner structure of atoms, the classification of quarks and the metaphorical names of abstract physical properties. No textbooks that make visible these basic properties by means of art are currently available. Artistic visualization brings these “mysterious” physical objects closer to the understanding of students and the general public and leaves physicists better able to discover new secrets of the internal structure of quarks and their properties.

scholarly journals Automatic Sets of Rational Numbers

2015 ◽  
Vol 26 (03) ◽  
pp. 343-365 ◽  
Author(s):  
Eric Rowland ◽  
Jeffrey Shallit
Keyword(s):  
Rational Numbers ◽  
Closure Properties ◽  
Basic Properties

The notion of a [Formula: see text]-automatic set of integers is well-studied. We develop a new notion — the [Formula: see text]-automatic set of rational numbers — and prove basic properties of these sets, including closure properties and decidability.

scholarly journals Tracking the seasons: the internal calendars of vertebrates

2007 ◽  
Vol 363 (1490) ◽  
pp. 341-361 ◽  
Author(s):  
Matthew J Paul ◽  
Irving Zucker ◽  
William J Schwartz
Keyword(s):  
Environmental Cues ◽  
Basic Properties ◽  
Physiological Adaptations ◽  
Biological Substrates

Animals have evolved many season-specific behavioural and physiological adaptations that allow them to both cope with and exploit the cyclic annual environment. Two classes of endogenous annual timekeeping mechanisms enable animals to track, anticipate and prepare for the seasons: a timer that measures an interval of several months and a clock that oscillates with a period of approximately a year. Here, we discuss the basic properties and biological substrates of these timekeeping mechanisms, as well as their reliance on, and encoding of environmental cues to accurately time seasonal events. While the separate classification of interval timers and circannual clocks has elucidated important differences in their underlying properties, comparative physiological investigations, especially those regarding seasonal prolactin secretions, hint at the possibility of common substrates.

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