The Historical Logic on the Basic Theory of Physics—A Summary on the Cosmic Continuum Theory

Any scientific system has a unified basic theory. But physics has no unified basic theory in the modern sense. Classical mechanics, relativity and quantum mechanics have their own basic concepts, categories and principles, so none of them can be regarded as true basic theories of physics. Cosmic Continuum Theory holds that the continuity and discreteness of the universe are fundamental issues related to the unification of physics. Because the contradiction between quantum non-locality and local reality is the fundamental obstacle to the unification of physics, while locality and non-locality correspond to the continuity and discreteness of physical reality respectively. The cosmic continuum theory introduces mathematical continuum and axiomatic ideas to reconstruct the basic theory of physics, and by the correspondence of existence and its dimensions to achieve the unification of the essence of physical reality, by introducing the cosmic continuum hypothesis to achieve the unification of the continuity and discreteness of physical reality, by introducing axiomatic methods to achieve formal unification of the foundations on physics. From the perspective of Cosmic Continuum, classical mechanics, relativity and quantum mechanics are no longer the basic theories of physics, but three branch theories of physics that are respectively applicable to macroscopic, cosmoscopic and microcosmic systems.

New Hybrid AD Methodology for Minimizing the Total Amount of Information Content:A Case Study of Rehabilitation Robot Design

Converting customer needs into specific forms and providing consumers with services are crucial in product design.Currently,conversion is no longer difficult due to the development of modern technology,and various measures can be applied for product realization,thus increasing the complexity of analysis and evaluation in the design process.The focus of the design process has thus shifted from problem solving to minimizing the total amount of information content.This paper presents a New Hybrid Axiomatic Design(AD)Methodology based on iteratively matching and merging design parameters that meet the independence axiom and attribute constraints by applying trimming technology,the ideal final results,and technology evolution theory.The proposed method minimizes the total amount of information content and improves the design quality.Finally,a case study of a rehabilitation robot design for hemiplegic patients is presented.The results indicate that the iterative matching and merging of related attributes can minimize the total amount of information content,reduce the cost,and improve design efficiency.Additionally,evolutionary technology prediction can ensure product novelty and improve market competitiveness.The methodology provides an excellent way to design a new(or improved)product.

Formal Inferring the Law of Conservation of Energy from Assuming A-Priori-ness of Knowledge in a Formal Axiomatic Epistemology System Sigma

The research purpose is invention (construction) of a formal logical inference of the Law of Conservation of Energy within a logically formalized axiomatic epistemology-and-axiology theory Sigma from a precisely defined assumption of a-priori-ness of knowledge. For realizing this aim, the following work has been done: 1) a two-valued algebraic system of formal axiology has been defined precisely and applied to proper-philosophy of physics, namely, to an almost unknown (not-recognized) formal-axiological aspect of the physical law of conservation of energy;2) the formal axiomatic epistemology-and-axiology theory Sigma has been defined precisely and applied to proper-physics for realizing the above-indicated purpose. Thus, a discrete mathematical model of relationship between philosophy of physics and universal epistemology united with formal axiology has been constructed. Results: 1) By accurate computing relevant compositions of evaluation-functions within the discrete mathematical model, it is demonstrated that a formal-axiological analog of the great conservation law of proper physics is a formal-axiological law of two-valued algebra of metaphysics. (A precise algorithmic definition of the unhabitual (not-well-known) notion “formal-axiological law of algebra of metaphysics” is given.) 2) The hitherto never published significantly new nontrivial scientific result of investigation presented in this article is a formal logical inference of the law of conservation of energy within the formal axiomatic theory Sigma from conjunction of the formal-axiological analog of the law of conservation of energy and the assumption of a-priori-ness of knowledge.

Formally Deriving the Third Newton’s Law from a Pair of Nontrivial Assumptions in a Formal Axiomatic Theory “Sigma-V”

The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism;hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.

An Axionatics of Geomechanics

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Axiomatic Differential Geometry III-3-Its Landscape-Chapter 3: The Old Kingdom of Differential Geometers

The principal objective of this paper is to study the relationship between the old kingdom of differential geometry (the category of smooth manifolds) and its new kingdom (the category of functors on the category of Weil algebras to some smooth category). It is shown that the canonical embedding of the old kingdom into the new kingdom preserves Weil functors.

New Discovery on Planck Units and Physical Dimension in Cosmic Continuum Theory

In 1899, Max Planck integrated the Planck constant h with the gravitational constant G and the speed of light c, discovered a set of physical constants, and created Planck Units System. Since 20th century, the development of physics made the gravitational constant, the speed of light, and the Planck constant the most important fundamental constants of physics representing classical theory, relativity, and quantum theory, respectively. Now, the Planck Units have been given new physical meanings, revealing the mysteries of many physical boundaries. However, more than 100 years have passed, Planck Units System not only failed to get rid of the incompatibility between the basic theories of physics, but also cannot surpass the limitations of existing physics theories. In Cosmic Continuum Theory, physical dimensions can be transformed under the principle of equivalence. Planck units system not only integrates into the axiom system of Cosmic Continuum Theory, but also establishes a benchmark for the unity of physical dimensions. The introduction of the abstract physical dimensions “JX” and “XJ” makes the physical dimension of existence quantity and dimension quantity unified respectively.

A Davidsonian Truth-theoretic Semantics Treatment of an EkeGusii Proverb

The paper examines some doctrines of the Davidsonian Programme of truth conditional Semantics that relates truth to meaning using Tarski’s T-Convention,in relation to its efficacy in a semantic valuation of the EkeGusii proverb:Nda’indongi ereta morogi ereta moibi which exemplifies a kind of complex sentence that a given system of Semantics is meant to account for.The coverage of Davidsonian truth-conditional notion of T-convention and that of compositionality are considered to have only a partial reach in accounting for the meaning of the proverb by not incorporating pragmatic aspects.The failure of T-convention is not alleviated by the adoption of radical interpretation as posited by Davidson but is extended to consider aspects of pragmatic enrichment and dynamic Semantics.

Semantic model and optimization of creative processes at mathematical knowledge formation

The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.

The General Compromise Value for Cooperative Games With Transferable Utility

The authors introduce the general compromise value for cooperative games with transferable utility.With respect to a set of potential payoffs of which the maximal and minimal potential payoff vectors are regarded as the upper and lower bounds for players,the unique pre-imputation lying on the straight line segment with these two vectors as the extreme points is defined as the general compromise value.Potential-consistency and maximal proportional property are introduced to characterize the general compromise value.

Location optimization of multiple distribution centers under fuzzy environment

Locating distribution centers optimally is a crucial and systematic task for decision-makers.Optimally located distribution centers can significantly improve the logistics system's efficiency and reduce its operational costs.However,it is not an easy task to optimize distribution center locations and previous studies focused primarily on location optimization of a single distribution center.With growing logistics demands,multiple distribution centers become necessary to meet customers' requirements,but few studies have tackled the multiple distribution center locations(MDCLs) problem.This paper presents a comprehensive algorithm to address the MDCLs problem.Fuzzy integration and clustering approach using the improved axiomatic fuzzy set(AFS) theory is developed for location clustering based on multiple hierarchical evaluation criteria.Then,technique for order preference by similarity to ideal solution(TOPSIS) is applied for evaluating and selecting the best candidate for each cluster.Sensitivity analysis is also conducted to assess the influence of each criterion in the location planning decision procedure.Results from a case study in Guiyang,China,reveals that the proposed approach developed in this study outperforms other similar algorithms for MDCLs selection.This new method may easily be extended to address location planning of other types of facilities,including hospitals,fire stations and schools.

Deriving invariant checkers for critical infrastructure using axiomatic design principles

Cyber-physical systems(CPSs)in critical infrastructure face serious threats of attack,motivating research into a wide variety of defence mechanisms such as those that monitor for violations of invariants,i.e.logical properties over sensor and actuator states that should always be true.Many approaches for identifying invariants attempt to do so automatically,typically using data logs,but these can miss valid system properties if relevant behaviours are not well-represented in the data.Furthermore,as the CPS is already built,resolving any design flaws or weak points identified through this process is costly.In this paper,we propose a systematic method for deriving invariants from an analysis of a CPS design,based on principles of the axiomatic design methodology from design science.Our method iteratively decomposes a high-level CPS design to identify sets of dependent design parameters(i.e.sensors and actuators),allowing for invariants and invariant checkers to be derived in parallel to the implementation of the system.We apply our method to the designs of two CPS testbeds,SWaT and WADI,deriving a suite of invariant checkers that are able to detect a variety of single-and multi-stage attacks without any false positives.Finally,we reflect on the strengths and weaknesses of our approach,how it can be complemented by other defence mechanisms,and how it could help engineers to identify and resolve weak points in a design before the controllers of a CPS are implemented.

Optimal utility allocations under multicriteria situation

By considering the maximal-utilities among operational strategies(or decisions)vectors,we introduce three utility allocations under multicriteria situation.In order to present the rationalities for these allocations,we propose several reductions to offer some axiomatic results.