Research on the Ideological and Political Construction of Mathematics Foundations of Information Security

Mathematics foundations of information security is a core course in the subject of information security.In view of the current national ideological and political conference in universities,finding a way to integrate this course with ideological and political education attracts a lot of attention from the education community.This paper makes an assay of the significance of the combination of mathematics foundations of information security course and ideological and political education,and introduces the teaching practice of mathematics foundations of information security course combined with ideological and political education.Through the combination of ideological and political education and curriculum content,cultivating all-round development of talents who study information security.

Higher Variations of the Monty Hall Problem (3.0, 4.0) and Empirical Definition of the Phenomenon of Mathematics, in Boole’s Footsteps, as Something the Brain Does

In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.

Mathematical Foundation of Visual Query Languageon Spatial Information

Visual Query Language on Spatial Information (SIVQL) is one kind of visual query language based on the extension of Query by Example (QBE). It is a visual operation based on graphics or media object, such as point, line and area elements. In this paper, the relation calculation and query function of SIVQL have been studied and discussed by using set theory and relation algebra. The theory foundation of SIVQL has been investigated by the mathematical method. Finally, its application examples are also given with the specific information system.

Mathematical Modeling of a Metabolic Network to Study the Impact of Food Contaminants on Genomic Methylation and DNA Instability

Environmental contamination of food is a worldwide public health problem. Folate mediated one- carbon metabolism plays an important role in epigenetic regulation of gene expression and mutagenesis. Many contaminants in food cause cancer through epigenetic mechanisms and/or DNA instability i.e. default methylation of uracil to thymine, subsequent to the decrease of 5-methylte- trahydrofolate (5 mTHF) pool in the one-carbon metabolism network. Evaluating consequences of an exposure to food contaminants based on systems biology approaches is a promising alternative field of investigation. This report presents a dynamic mathematical modeling for the study of the alteration in the one-carbon metabolism network by environmental factors. It provides a model for predicting “the impact of arbitrary contaminants that can induce the 5 mTHF deficiency. The model allows for a given experimental condition, the analysis of DNA methylation activity and dumping methylation in the de novo pathway of DNA synthesis.

To Comma or Not to Comma: The Mathematics of the Relative Clause, All Types, via Boole and Venn

The present paper is part of a large scale project in Intelligence Science. The nearterm aim of this project is the increased digitalization of the analysis of human intelligence in as far as intelligence is rational. The ultimate aim is to draw up a complete and definitive map of the totality of rational human intelligence or rational thought and language. As far as the mathematical component of this project is concerned, two contributions have appeared so far, the following: 1) “The Monty Hall Problem and beyond: Digital-Mathematical and Cognitive Analysis in Boole’s Algebra, Including an Extension and Generalization to Related Cases”, in Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154;2) “Higher Variations of the Monty Hall Problem (3.0, 4.0) and Empirical Definition of the Phenomenon of Mathematics, in Boole’s Footsteps, as Something the Brain Does”, in Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 2, No. 4 (July 2012), pp. 243-273, including an appendix by Richard D. Gill. The present paper pertains to the linguistics branch of the project. It is concerned with linguistic cognition. The focus of this paper is on a single phenomenon, the relative clause and all its possible types. The method of analyzing the structure of rational thought and language that is advanced in this paper and applied to the relative clause claims validity on the following three grounds. First, it is mathematical and digital in the strictest possible sense. Second, the empirical data to which this mathematical method is applied are fully accessible in language. After all, all that is essential to that structure must be exteriorized in sounds or written symbols for the structure to be transported from one brain to another and understood. The structure must somehow be encoded in its entirety in the airwaves or light beams that travel to a hearer’s ear or a reader’s eye. And these airwaves and light beams are accessible to observation. Third, general inspiration and encouragement can be drawn from the fact that it has already been long established that the brain teems with digital activity, including in the prefrontal cortex. In sum, there is every incentive for dissecting language in search of the digital structure of rational thought and its expression in language. The design of the present paper is to demonstrate that the structure can be found.

Teaching Reform of Mathematics Foundations of Information Security with Algorithm as the Core

In view of the problems existing in the teaching of Mathematics Foundations of Information Security,such as emphasizing theory but neglecting practice,combined with the concept of engineering education certification and emerging engineering education teaching reform,this paper combs the knowledge points and learning context of Mathematics Foundations of Information Security,puts forward a new teaching mode of Mathematics Foundations of Information Security with algorithm as the core,and gives the teaching content,organization form and assessment method.Thus,it improves the students’learning interest and practical ability,and improves the achievement of graduation requirements.

Hilbert's Second Problems and Uncertainty Computing, from HCP Logic's Point of View

Hilbert’s complete perfect (HCP) logic is introduced. The Gdel’s incompleteness theorem discloses the limit of logic.Huang’s universal consistent theorem and relative consistent theorem extends the limit of logic.The proofs of these theorems are in 2-valued logic but the completeness can be extended in the three-valued HCP logic. The author proposes HCP logic for the foundation of uncertainty computing as well.

GENERALIZATION OF THE METHOD OF FULL APPROXIMATION AND ITS APPLICATIONS

This paper presents a generalized form of the method of full approximation. By using the concept of asymptotic linearization and making the coordinate transformations including the nonlinear functionals of dependent variables, the original nonlinear problems are linearized and their higher-order solutions are given in terms of the first-term asymptotic solutions and corresponding transformations. The analysis of a model equation and some problems of weakly nonlinear oscillations and waves with the generalized method shows that it is effective and straightforward.

SOIL PILE INTERACTION UNDER STATIC, DYNAMIC AND CYCLIC LATERAL LOADS AND A PROPOSAL OF p-y CURVE FORMULA

In this paper, the studies on soil-pile interaction behaviors in saturated sands under static, dynamic and cyclic lateral loads by model testing are described. By comparing with the field test results for piles in soft sandy clay, a formula of p-y curves based on constitutive relationship of soils applicable for both sandy and soft clays is proposed. Good agreements are obtained in comparison with the field test results performed by other investigators abroad. A p-y hysteresis curve formula based on the modified Masing's doubling criterion is also proposed, and the results are in satisfactory agreement with field test results.

The Monty Hall Problem and beyond: Digital-Mathematical and Cognitive Analysis in Boole’s Algebra, Including an Extension and Generalization to Related Cases

The Monty Hall problem has received its fair share of attention in mathematics. Recently, an entire monograph has been devoted to its history. There has been a multiplicity of approaches to the problem. These approaches are not necessarily mutually exclusive. The design of the present paper is to add one more approach by analyzing the mathematical structure of the Monty Hall problem in digital terms. The structure of the problem is described as much as possible in the tradition and the spirit—and as much as possible by means of the algebraic conventions—of George Boole’s Investigation of the Laws of Thought (1854), the Magna Charta of the digital age, and of John Venn’s Symbolic Logic (second edition, 1894), which is squarely based on Boole’s Investigation and elucidates it in many ways. The focus is not only on the digital-mathematical structure itself but also on its relation to the presumed digital nature of cognition as expressed in rational thought and language. The digital approach is outlined in part 1. In part 2, the Monty Hall problem is analyzed digitally. To ensure the generality of the digital approach and demonstrate its reliability and productivity, the Monty Hall problem is extended and generalized in parts 3 and 4 to related cases in light of the axioms of probability theory. In the full mapping of the mathematical structure of the Monty Hall problem and any extensions thereof, a digital or non-quantitative skeleton is fleshed out by a quantitative component. The pertinent mathematical equations are developed and presented and illustrated by means of examples.

CO-SATISFIABLE AND CO-VALID OF TWO FIRST-ORDER LANGUAGES

In this paper,the authors point out and demonstrate the difference of theconcepts concerning co-satisfiable and co-valid between one first-order language andtwo first-order languages,and put forward the concepts about uniform co-identical truthand uniform co-satisfiability.Thus some theorems in the book“A Course inMathematical Logic”,written by J.L.Bell and M.Machover,are corrected.

REMARKS OF SOME PROBLEMS FOR RECTANGULAR THIN PLATES WITH FREE EDGES ON ELASTIC FOUNDATIONS

For the bending, stability and vibrations of rectangular thin plates with free edges on elastic foundations, in this paper we give a flexural function which exactly satisfies not only all the boundary conditions on free edges but also the conditions at free corner points. Applying energy variation principle, we give equations defining parameters in flexural function, stability equation, frequency equation, and general formulae of minimum critical force and minimum eigenfrequency as well.

Dynamic Analysis of Submarine Pipelines on an Elastic / Viscoelastic Foundation

This paper presents a new finite element method for solving static and dynamic problems in laying operation of pipelines. The effect of the viscoelastic soil behavior is considered by using the Pasternak foundation model. Some examples are also presented.

BENDING PROBLEMS OF RECTANGULAR REISSNER PLATE WITH FREE EDGES LAID ON TENSIONLESS WINKLER FOUNDATIONS

In this paper, an analytical method for solving the bending problems of rectangular Reissner plate with free edges under arbitrary loads laid on tensionless Winkler foundations is proposed. By assuming proper form of Fourier series with supplementary terms, which meet derivable conditions, for deflection and shear force functions, the basic differential equations with given boundary conditions can be transformed into a set of simple infinite algebraic equations. For common Winkler foundations, this set of equations can be solved directly and for tensionless Winkler foundations, it is a set of weak nonlinear algebraic equations, the solution of which can be obtained easily by using iterative procedures.

A Novel Design of Octal-Valued Logic Full Adder Using Light Color State Model

Due to the demand of high computational speed for processing big data that requires complex data manipulations in a timely manner,the need for extending classical logic to construct new multi-valued optical models becomes a challenging and promising research area.This paper establishes a novel octal-valued logic design model with new optical gates construction based on the hypothesis of Light Color State Model to provide an efficient solution to the limitations of computational processing inherent in the electronics computing.We provide new mathematical definitions for both of the binary OR function and the PLUS operation in multi valued logic that is used as the basis of novel construction for the optical full adder model.Four case studies were used to assure the validity of the proposed adder.These cases proved that the proposed optical 8-valued logic models provide significantly more information to be packed within a single bit and therefore the abilities of data representation and processing is increased.

Conceptions of Intuition in Poincar6＇s Philosophy of Mathematics

The aim of this paper is to contribute to the identification and characterization of the various types of intuition put forward by Poincar6, taking his texts as a laboratory for looking for what intuition might be. I will stress that these diverse conceptions are mainly formulated in the context of Poincar6＇s controversies in opposition to logicism, to formalism, and in the context of Poincar6＇s very peculiar conventionalism. I will try to demonstrate that, in each case, Poincar~ comes close to a specific tradition （Kant, of course, but also Leibniz and Peirce）.

Philosophical Analysis of the Concept of Reality in Bertrand Russell's Philosophy

The quest to understand and explain the ultimate nature of reality is a recurring problem in the history of Philosophy.All attempts to give credible answers by philosophers have led to so many divergent metaphysical and epistemological theories,some of which are not only opposing but also conflicting.Like Wittgenstein,Bertrand Russell believes that mathematical logic could reveal the basic structure of reality,a structure that is hidden beneath the cloak of ordinary language.By his new logic,he showed that the world is made up of simple or-atomic‖facts,which in turn are made up of particular objects.Atomic facts are complex,mind-independent features of reality.Both Russell and Wittgenstein held that the basic propositions of logic,which Wittgenstein called-elementary propositions‖refer to atomic facts.There is thus an immediate connection between formal languages,such as the logical system of Russell‘s Principia Mathematica(written with Alfred North Whitehead and published between 1910 and 1913),and the structure of the real world.Elementary propositions represent atomic facts,which are constituted by particular objects,which are the meaning of logically proper names.Russell differed from Wittgenstein in that he held that the meanings of proper names are-sense data‖,or immediate perceptual experiences,rather than particular objects.Thus,this study is geared to x-rays Russell‘s theory of reality in order to ascertain the tenability of his philosophy and its contemporary relevance.

A Mathematical Theory of Big Data

This article presents a cardinality approach to big data,a fuzzy logic-based approach to big data,a similarity-based approach to big data,and a logical approach to the marketing strategy of social networking services.All these together constitute a mathematical theory of big data.This article also examines databases with infinite attributes.The research results reveal that relativity and infinity are two characteristics of big data.The relativity of big data is based on the theory of fuzzy sets.The relativity of big data leads to the continuum from small data to big data,big data-driven small data analytics to become statistical significance.The infinity of big data is based on the calculus and cardinality theory.The infinity of big data leads to the infinite similarity of big data.The proposed theory in this article might facilitate the mathematical research and development of big data,big data analytics,big data computing,and data science with applications in intelligent business analytics and business intelligence.

A Study of the Popularity of Alice’s Adventures in Wonderland among Adults

A children’s book as Alice’s Adventures in Wonderland,it is incredibly popular among adults.Finding out why the book arouses adults’interest will enhance people’s understanding of it.This paper draws on the elements in the book which only adults could appreciate,and finds out that it requires A Priori knowledge,from mathematical analogies to logic,as well as A Posteriori knowledge,including the awareness of social hierarchy,to understand them,which leads to the book’s popularity among adults.

数学新课标总目标中基本概念的内在逻辑

《义务教育数学课程标准(2022年版)》总目标中的基本概念是“三会”导向的数学课程目标的主要构成。但因数量较多,渊源复杂,给基层教师理解“三会”导向的数学课程目标造成困扰。准确理解总目标中的基本概念,厘清隐含其中的逻辑关系,构建以基层教师教育经验为基石的数学课程目标整体逻辑框架,可以为基层教师理解和落实“三会”导向的数学课程目标提供经验支撑和方向引导,填补素养导向的数学课程目标与教师的教育经验之间的鸿沟。