Reductibilities in intuitionistic topology

1968 ◽  
Vol 33 (3) ◽  
pp. 412-417 ◽  
Author(s):  
Dirk Van Dalen
Keyword(s):  
General Sense ◽  
Mathematical Objects ◽  
Definition Of ◽  
Intuitionistic Mathematics

In intuitionistic mathematics one distinguishes between sets with a constructive character and sets in a more general sense. The first kind consists of spreads and the latter of species. The definition of a spread utilizes so-called choice sequences (in [5] infinitely proceeding sequence or ips), i.e., sequences of well-determined mathematical objects which are chosen more or less freely. One can restrict the choices by some law, which, however, need not be predetermined (changing one's mind is allowed).

Remarks on some generalization of the notion of microscopic sets

2020 ◽  
Vol 70 (6) ◽  
pp. 1349-1356
Author(s):  
Aleksandra Karasińska
Keyword(s):  
General Sense ◽  
Equivalent Definition ◽  
Definition Of ◽  
Null Set

AbstractWe consider properties of defined earlier families of sets which are microscopic (small) in some sense. An equivalent definition of considered families is given, which is helpful in simplifying a proof of the fact that each Lebesgue null set belongs to one of these families. It is shown that families of sets microscopic in more general sense have properties analogous to the properties of the σ-ideal of classic microscopic sets.

scholarly journals Corrective Feedback and EFL Learning Style

2021 ◽  
Vol 2 (10) ◽  
pp. 47-54
Author(s):  
Steven Samie
Keyword(s):  
Learning Style ◽  
Corrective Feedback ◽  
General Sense ◽  
Definition Of ◽  
Efl Learning

The present study is an attempt to address an important issue for an instructor in the classroom. It begins with an account of how to provide Corrective Feedback (CF) for individuals so that they have the highest rate of uptake in the classroom, then it is followed by the definition of the concept in its general sense of the term. Next, the study has provided information on some of the previous studies along with the researcher’s insights on the issue. Finally, the essay concludes by explaining how this term project will help me change the instructor’s attitude in my future teaching in the classroom. Some suggestions for fellow instructors are provided to give them some food for thought.

scholarly journals Categories as Mathematical Models

2018 ◽  
Author(s):  
David I. Spivak
Keyword(s):  
Dynamical Systems ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Category Theory ◽  
Vector Spaces ◽  
Mathematical Objects ◽  
Working Definition ◽  
Modelling Framework ◽  
Categorical Models ◽  
Definition Of

Category theory is presented as a mathematical modelling framework that highlights the relationships between objects, rather than the objects in themselves. A working definition of model is given, and several examples of mathematical objects, such as vector spaces, groups, and dynamical systems, are considered as categorical models.

Exploded Points

1981 ◽  
Vol 36 (1) ◽  
pp. 72-75
Author(s):  
Okan Gurel
Keyword(s):  
Lorenz System ◽  
Stability Index ◽  
Mathematical Object ◽  
Recursive Formula ◽  
Functional Characteristics ◽  
Mathematical Objects ◽  
The Lorenz System ◽  
Definition Of

A new concept of a mathematical object of zero dimension, an exploded point, is introduced. The dimension used is defined on the basis of the functional characteristics of the system, thus it may be referred to as f-dimension. A stability index is also defined for the mathematical objects including exploded points, which can be related to the f-dimension. It is shown that the mathematical object exhibited by the Lorenz system after the second bifurcation is such a point. A recursive formula based on the definition of the exploded point

Collective Security

2014 ◽  
Author(s):  
Ademola Abass
Keyword(s):  
Cold War ◽  
United Nations ◽  
International Law ◽  
Collective Security ◽  
General Sense ◽  
Regional Organizations ◽  
The United Nations ◽  
Definition Of ◽  
The Cold War

The term collective security in a general sense is given many understandings both professional and nonprofessional. The phrase is sometimes used to describe the organization of security on a “collective” basis. Often, it is used to denote the “collective organization” of security. While neither of these uses is inherently wrong, neither succinctly captures what “collective security” implies when used by international lawyers. In international law, collective security is a term connoting something more dense and intricate, and much more slippery, than the above more straightforward expressions. The notion of collective security, its premise, and objectives are deeply contested by states and scholars. It is universally acknowledged that collective security is today organized under the United Nations; however, regional organizations, which used to focus primarily on economic matters, have attained greater prominence in collective security efforts especially since the end of the Cold War. This article examines the definition of collective security, its features and objectives, the actors that have the responsibility for operating it globally and regionally, its various manifestations, its limitations and, above all, its role in future.

An intuitionistic theory of types

1998 ◽  
Author(s):  
Per Martin-Löf
Keyword(s):  
Set Theory ◽  
Predicate Logic ◽  
Mathematical Object ◽  
Present Theory ◽  
Reflection Principle ◽  
Simple Type ◽  
Elimination Rule ◽  
Mathematical Objects ◽  
Special Cases ◽  
Intuitionistic Mathematics

The theory of types with which we shall be concerned is intended to be a full scale system for formalizing intuitionistic mathematics as developed, for example, in the book by Bishop 1967. The language of the theory is richer than the language of first order predicate logic. This makes it possible to strengthen the axioms for existence and disjunction. In the case of existence, the possibility of strengthening the usual elimination rule seems first to have been indicated by Howard 1969, whose proposed axioms are special cases of the existential elimination rule of the present theory. Furthermore, there is a reflection principle which links the generation of objects and types and plays somewhat the same role for the present theory as does the replacement axiom for Zermelo-Fraenkel set theory. An earlier, not yet conclusive, attempt at formulating a theory of this kind was made by Scott 1970. Also related, although less closely, are the type and logic free theories of constructions of Kreisel 1962 and 1965 and Goodman 1970. In its first version, the present theory was based on the strongly impredicative axiom that there is a type of all types whatsoever, which is at the same time a type and an object of that type. This axiom had to be abandoned, however, after it was shown to lead to a contradiction by Jean Yves Girard. I am very grateful to him for showing me his paradox. The change that it necessitated is so drastic that my theory no longer contains intuitionistic simple type theory as it originally did. Instead, its proof theoretic strength should be close to that of predicative analysis. Mathematical objects and their types. We shall think of mathematical objects or constructions. Every mathematical object is of a certain kind or type. Better, a mathematical object is always given together with its type, that is, it is not just an object, it is an object of a certain type.

scholarly journals New Bifurcation Critical Criterion of Flip-Neimark-Sacker Bifurcations for Two-Parameterized Family ofn-Dimensional Discrete Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Shengji Yao
Keyword(s):  
Jacobian Matrix ◽  
Polynomial Equation ◽  
Discrete Systems ◽  
Feasible Region ◽  
General Sense ◽  
Codimension Two ◽  
Parameterized Family ◽  
Critical Criterion ◽  
Definition Of ◽  
Codimension Two Bifurcation

A new bifurcation critical criterion of flip-Neimark-Sacker bifurcation is proposed for detecting or anticontrolling this type of codimension-two bifurcation of discrete systems in a general sense. The criterion is built on the properties of coefficients of characteristic equations instead of the properties of eigenvalues of Jacobian matrix of nonlinear system, which is formulated using a set of simple equalities and inequalities consisting of the coefficients of characteristic polynomial equation. The inequality conditions enable us to easily pick off the fake parameter domain whereas the equality conditions are used to accurately locate the critical bifurcation point. In particular, after the bifurcation parameter piont is determined, the inequality conditions can be used to figure out the feasible region of other system parameters. Thus, the criterion is suitable for two-parameterized family ofn-dimensional discrete systems. As compared with the classical critical criterion (or definition) of flip-Neimark-Sacker bifurcation stated in terms of the properties of eigenvalues, the proposed criterion is preferable in anticontrolling or detecting the existence of flip-Neimark-Sacker bifurcation in high-dimension nonlinear systems, due to its explicit parameter mechanism of the bifurcation.

COMPARING PEARSON, SPEARMAN AND HOEFFDING'S D MEASURE FOR GENE EXPRESSION ASSOCIATION ANALYSIS

2009 ◽  
Vol 07 (04) ◽  
pp. 663-684 ◽  
Author(s):  
ANDRÉ FUJITA ◽  
JOÃO RICARDO SATO ◽  
MARCOS ANGELO ALMEIDA DEMASI ◽  
MARI CLEIDE SOGAYAR ◽  
CARLOS EDUARDO FERREIRA ◽  
...  
Keyword(s):  
Gene Expression ◽  
Regulatory Networks ◽  
Dna Microarrays ◽  
Expression Profiles ◽  
Gene Expression Profiles ◽  
Expression Data ◽  
General Sense ◽  
Nonlinear Associations ◽  
Definition Of ◽  
Spearman’S Correlation

DNA microarrays have become a powerful tool to describe gene expression profiles associated with different cellular states, various phenotypes and responses to drugs and other extra- or intra-cellular perturbations. In order to cluster co-expressed genes and/or to construct regulatory networks, definition of distance or similarity between measured gene expression data is usually required, the most common choices being Pearson's and Spearman's correlations. Here, we evaluate these two methods and also compare them with a third one, namely Hoeffding's D measure, which is used to infer nonlinear and non-monotonic associations, i.e. independence in a general sense. By comparing three different variable association approaches, namely Pearson's correlation, Spearman's correlation and Hoeffding's D measure, we aimed at assessing the most approppriate one for each purpose. Using simulations, we demonstrate that the Hoeffding's D measure outperforms Pearson's and Spearman's approaches in identifying nonlinear associations. Our results demonstrate that Hoeffding's D measure is less sensitive to outliers and is a more powerful tool to identify nonlinear and non-monotonic associations. We have also applied Hoeffding's D measure in order to identify new putative genes associated with tp53. Therefore, we propose the Hoeffding's D measure to identify nonlinear associations between gene expression profiles.

scholarly journals Regarding the Problem of Defining the Concept of «Administrative and Legal Provision of Citizens’ Rights»

2020 ◽  
Vol 9 (26) ◽  
pp. 473-478
Author(s):  
Hanna Ivanova ◽  
Vasyl Felyk ◽  
Iryna Shopina ◽  
Konstantin Bieliakov
Keyword(s):  
Law Enforcement ◽  
Civil Rights ◽  
Scientific Literature ◽  
The State ◽  
Modern World ◽  
Structural Components ◽  
General Sense ◽  
Legal Provision ◽  
Legitimate Interests ◽  
Definition Of

The purpose authors of this article aim to analyze the scientific literature on understanding the concept of “administrative and legal provision of civil rights”, its structural components and on this basis to offer our own view in regard to this administrative and legal category. To achieve this goal, such methods of scientific knowledge were used as: formal-logical; comparative analysis; logical and legal. Different scientific approaches and concepts to defining the notion of citizens’ rights have been analyzed in the article. On this basis the understanding of the category of “administrative and legal provision of citizens’ rights” has been improved. It includes two interrelated components – “administrative and legal” and “provision”. It has been determined that the term provision in the general sense means the creation of conditions, security, protection of something from danger. The rights of citizens as a subject matter of administrative provision have been analyzed. The features of human and civil rights have been outlined. It has been stated that human and civil rights, freedoms and legitimate interests in the modern world must be both declared in regulatory acts, and must be really guaranteed and secured by the state. It has been emphasized that officials of the state authorities, including law enforcement system, play a crucial role in the development of interaction between society, government and citizens. The main directions of ensuring the rights, freedoms and legitimate interests of citizens by the norms of administrative legislation, as well as the mechanism of their implementation have been determined. The authors have offered own definition of the concept of “administrative and legal provision of citizens’ rights”.

scholarly journals The Concept of Ontological Security in International Political Discourse

2020 ◽  
Vol 12 (6) ◽  
pp. 129-149
Author(s):  
A. V. Khudaykulova ◽  
N. Y. Neklyudov
Keyword(s):  
The State ◽  
Ir Theory ◽  
Ontological Security ◽  
Environment Change ◽  
Security Dilemma ◽  
General Sense ◽  
The Subject ◽  
Definition Of ◽  
State Projects

The article studies “ontological” security concept. In a general sense the term depicts expectations of a state about its stable and predictable relations with counterparts. With the term gaining theoretical sway in constructivism since the 21st century, we argue, that it still lacks instrumental definition with fixed assumptions and variables. The analysis of ontological security is conducted in twofold manner. First, we overview the broad range of interpretations, demonstrate the absence of an instrumental definition of the concept and suggest some parameters of such a definition. Secondly, we study the ways how a state can gain ontological security. Three options of achieving ontological security are being presented: adaptation (assuming the role of ‘another’ from the external environment); change of rules (imposing its own role on the subject with whom the interaction occurs); and the breach of relations. At all these stages, the state tries either to adopt the norms and practices by which it interacts with the environment, or to redefine its position in ongoing relations with counterparties. We conclude by presenting a sought definition of the term and by arguing that the concept enhances the constructivist contribution to the IR theory since it allows to define the logic of states’ behavior in international arena. Thus, states seek to be socialized into an intersubjective reality and to define norms, practices and status through forging common and communicative knowledge with ‘other’. Otherwise, the state’s behavior could be irrational. Theory emphasizes the need to avoid situations of the ontological security dilemma: the state projects its own, mostly protective reality, which, however, does not provide it with ontological security from the counterparty and could potentially push for further escalation of crisis interactions.Authors declare the absence of conflict of interests.

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