Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived ...Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.展开更多
In this paper, we consider the application of the equation of non-classical mathematical physics to magneto-hydrodynamic equilibrium (in the case of a mixed magnetic field) for magnetic stars. First, we give the neces...In this paper, we consider the application of the equation of non-classical mathematical physics to magneto-hydrodynamic equilibrium (in the case of a mixed magnetic field) for magnetic stars. First, we give the necessary concepts about the equation of non-classical mathematical physics and the possibility of their applicability to astrophysical problems. The conditions of magneto-hydrodynamic equilibrium are determinate, and self-consistence provides the means to derive the corresponding partial differential equations describing this equilibrium in a magnetosphere magnetic star. Namely, this process is to the non-classical equations of mathematical physics in cases of types. Keldysh-Tricomi, a common case equation of non-classical type, is at first introduced by the author. Using the two main physical efficiencies of MHD. A mathematical model of a poloidal-toroidal mixed magnetic field for magnetic stars is constructed, and this model is classified with respect to degenerating case equations. According to Hopf’s theorem, Maxwell’s equation and the magnetic force balance equation constructed equilibrium conditions of the poloidal-toroidal of the magnetic field for a magnetic star. At the same time, the taken example, which is the self-consistency of this model by observation dates, is investigated. At first, in an application, the method of straight lines for recurrent formulas of calculation of magnetic flux and stream functions is used. The physical means, the corresponding singular point of the sonic line, cutoff, and resonance phenomena are considered. In this case, a general solution equation is found, which is interpreted by this phenomenon as a cutoff, resonance. Finally, this obtained solution gives the conditions of magneto-hydrodynamic equilibrium on the magnetosphere of magnetic stars. Methodology and obtained equations are new approaches that are at first considered.展开更多
As a fundamental course in science and engineering education at universities,advanced mathematics plays an irreplaceable role in cultivating students’logical thinking,scientific spirit,and comprehensive qualities.Int...As a fundamental course in science and engineering education at universities,advanced mathematics plays an irreplaceable role in cultivating students’logical thinking,scientific spirit,and comprehensive qualities.Integrating ideological and political education into advanced mathematics teaching is not only an inevitable requirement for achieving the goal of“three-dimensional and holistic education”but also a crucial path for promoting students’comprehensive development.This article delves into the necessary logic,practical possibilities,and real-world challenges of ideological and political education in advanced mathematics courses,systematically analyzing the implementation pathways and illustrating practical approaches through specific cases.Meanwhile,to address issues such as insufficient teacher capability,lagging resource development,disconnected instructional design,and inadequate evaluation mechanisms encountered during implementation,this article proposes practical improvement strategies.It aims to provide theoretical insights and practical guidance for the further advancement of ideological and political education in advanced mathematics courses.展开更多
Logicians have worked with so many different logical systems that it is not possible even to esti-mate the number. Of these, many are best seen as extensions of classical logic, including both thoseof interest to math...Logicians have worked with so many different logical systems that it is not possible even to esti-mate the number. Of these, many are best seen as extensions of classical logic, including both thoseof interest to mathematics and those of interest to philosophy and computer science. (Henceforth Iwill use the term "intelligent systems theory" for the common ground of philosophical logic and展开更多
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 approach...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.展开更多
Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous...Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.展开更多
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 i...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.展开更多
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....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.展开更多
In primary school teaching, each subject focuses on the ability of training are different, and in primary school mathematics teaching activities, the cultivation of logical thinking ability is particularly important. ...In primary school teaching, each subject focuses on the ability of training are different, and in primary school mathematics teaching activities, the cultivation of logical thinking ability is particularly important. Mathematics is a subject with strong logic. Mathematics teaching is the process of cultivating students' logical thinking. It runs through every grade in primary school, every class hour, every link and teaching content runs through the whole process of teaching activities. Therefore, this paper analyzes the necessity of cultivating logical thinking in primary school mathematics teaching and discusses the cultivation strategies for the reference of teachers.展开更多
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 i...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.展开更多
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 bec...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.展开更多
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 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.展开更多
Hilbert’s complete perfect (HCP) logic is introduced. The Gdel’s incompleteness theorem discloses the limit of logic.Huang’s universal consistent theorem and relative consistent theorem extends the limit of logic...Hilbert’s complete perfect (HCP) logic is introduced. The Gdel’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.展开更多
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 ...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）.展开更多
The method presented in this work is based on the fundamental concepts of Paraconsistent Annotated Logic with annotation of 2 values (PAL2v). The PAL2v is a non-classic Logics which admits contradiction and in this pa...The method presented in this work is based on the fundamental concepts of Paraconsistent Annotated Logic with annotation of 2 values (PAL2v). The PAL2v is a non-classic Logics which admits contradiction and in this paper we perform a study using mathematical interpretation in its representative lattice. This studies result in algorithms and equations give an effective treatment on signals of information that represent situations found in uncertainty knowledge database. From the obtained equations, algorithms are elaborated to be utilized in computation models of the uncertainty treatment Systems. We presented some results that were obtained of analyses done with one of the algorithms that compose the paraconsistent analyzing system of logical signals with the PAL2v Logic. The paraconsistent reasoning system built according to the PAL2v methodology notions reveals itself to be more efficient than the traditional ones, because it gets to offer an appropriate treatment to contradictory information.展开更多
文摘Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler’s equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic assumptions can be derived using the conservation and balance laws of classical or non-classical continuum mechanics. The mathematical models based on Kirchhoff hypothesis (classical plate theory, CPT) and first order shear deformation theory (FSDT) that are representative of most mathematical models for plates/shells are investigated in this paper for their thermodynamic consistency. This is followed by the details of a general and higher order thermodynamically consistent plate/shell thermoelastic mathematical model that is free of a priori consideration of kinematic assumptions and remains valid for very thin as well as thick plates/shells with comprehensive nonlinear constitutive theories based on integrity. Model problem studies are presented for small deformation behavior of linear elastic plates in the absence of thermal effects and the results are compared with CPT and FSDT mathematical models.
文摘In this paper, we consider the application of the equation of non-classical mathematical physics to magneto-hydrodynamic equilibrium (in the case of a mixed magnetic field) for magnetic stars. First, we give the necessary concepts about the equation of non-classical mathematical physics and the possibility of their applicability to astrophysical problems. The conditions of magneto-hydrodynamic equilibrium are determinate, and self-consistence provides the means to derive the corresponding partial differential equations describing this equilibrium in a magnetosphere magnetic star. Namely, this process is to the non-classical equations of mathematical physics in cases of types. Keldysh-Tricomi, a common case equation of non-classical type, is at first introduced by the author. Using the two main physical efficiencies of MHD. A mathematical model of a poloidal-toroidal mixed magnetic field for magnetic stars is constructed, and this model is classified with respect to degenerating case equations. According to Hopf’s theorem, Maxwell’s equation and the magnetic force balance equation constructed equilibrium conditions of the poloidal-toroidal of the magnetic field for a magnetic star. At the same time, the taken example, which is the self-consistency of this model by observation dates, is investigated. At first, in an application, the method of straight lines for recurrent formulas of calculation of magnetic flux and stream functions is used. The physical means, the corresponding singular point of the sonic line, cutoff, and resonance phenomena are considered. In this case, a general solution equation is found, which is interpreted by this phenomenon as a cutoff, resonance. Finally, this obtained solution gives the conditions of magneto-hydrodynamic equilibrium on the magnetosphere of magnetic stars. Methodology and obtained equations are new approaches that are at first considered.
文摘As a fundamental course in science and engineering education at universities,advanced mathematics plays an irreplaceable role in cultivating students’logical thinking,scientific spirit,and comprehensive qualities.Integrating ideological and political education into advanced mathematics teaching is not only an inevitable requirement for achieving the goal of“three-dimensional and holistic education”but also a crucial path for promoting students’comprehensive development.This article delves into the necessary logic,practical possibilities,and real-world challenges of ideological and political education in advanced mathematics courses,systematically analyzing the implementation pathways and illustrating practical approaches through specific cases.Meanwhile,to address issues such as insufficient teacher capability,lagging resource development,disconnected instructional design,and inadequate evaluation mechanisms encountered during implementation,this article proposes practical improvement strategies.It aims to provide theoretical insights and practical guidance for the further advancement of ideological and political education in advanced mathematics courses.
文摘Logicians have worked with so many different logical systems that it is not possible even to esti-mate the number. Of these, many are best seen as extensions of classical logic, including both thoseof interest to mathematics and those of interest to philosophy and computer science. (Henceforth Iwill use the term "intelligent systems theory" for the common ground of philosophical logic and
文摘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.
文摘Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.
文摘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.
文摘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.
文摘In primary school teaching, each subject focuses on the ability of training are different, and in primary school mathematics teaching activities, the cultivation of logical thinking ability is particularly important. Mathematics is a subject with strong logic. Mathematics teaching is the process of cultivating students' logical thinking. It runs through every grade in primary school, every class hour, every link and teaching content runs through the whole process of teaching activities. Therefore, this paper analyzes the necessity of cultivating logical thinking in primary school mathematics teaching and discusses the cultivation strategies for the reference of teachers.
文摘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.
文摘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.
文摘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.
文摘Hilbert’s complete perfect (HCP) logic is introduced. The Gdel’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.
文摘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）.
文摘The method presented in this work is based on the fundamental concepts of Paraconsistent Annotated Logic with annotation of 2 values (PAL2v). The PAL2v is a non-classic Logics which admits contradiction and in this paper we perform a study using mathematical interpretation in its representative lattice. This studies result in algorithms and equations give an effective treatment on signals of information that represent situations found in uncertainty knowledge database. From the obtained equations, algorithms are elaborated to be utilized in computation models of the uncertainty treatment Systems. We presented some results that were obtained of analyses done with one of the algorithms that compose the paraconsistent analyzing system of logical signals with the PAL2v Logic. The paraconsistent reasoning system built according to the PAL2v methodology notions reveals itself to be more efficient than the traditional ones, because it gets to offer an appropriate treatment to contradictory information.
