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...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.展开更多
How managers’ knowledge and beliefs of human nature are formed and manifested has not been fully explored in the context of Chinese society going through rapid transition nowadays. And yet this could be the missing l...How managers’ knowledge and beliefs of human nature are formed and manifested has not been fully explored in the context of Chinese society going through rapid transition nowadays. And yet this could be the missing link in our discourse on Chinese managers. Based on a qualitative study conducted in Quanzhou, China, this study found certain assumptions of human nature that are deeply embedded in their managers’ intellectual framework, which in turn guide their managerial behaviours in diverse aspects of their work. Unless the managers are prepared to examine their own thoughts, especially those at the sub-conscious level, they would remain prisoners of their own thought, and all the efforts directed at transforming managers would be seriously compromised.展开更多
In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical...In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .展开更多
The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satis...The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes.展开更多
In this paper, let T be a bounded linear operator on a complex Hilbert H. We give and prove that every p-w-hyponormal operator has Bishop's property(β) and spectral properties; Quasi-similar p-w-hyponormal operat...In this paper, let T be a bounded linear operator on a complex Hilbert H. We give and prove that every p-w-hyponormal operator has Bishop's property(β) and spectral properties; Quasi-similar p-w-hyponormal operators have equal spectra and equal essential spectra. Finally, for p-w-hyponormal operators, we give a kind of proof of its normality by use of properties of partial isometry.展开更多
In this paper, both the roman domination number and the number of minimum roman dominating sets are found for any rectangular rook’s graph. In a similar fashion, the roman domination number and the number of minimum ...In this paper, both the roman domination number and the number of minimum roman dominating sets are found for any rectangular rook’s graph. In a similar fashion, the roman domination number and the number of minimum roman dominating sets are found on the square bishop’s graph for odd board sizes. Also found are the number of minimum total dominating sets associated with the light-colored squares when n?≡1(mod12)? (with n>1), and same for the dark-colored squares when n?≡7(mod12) .展开更多
In this paper we present a graphical method for decision of restitution coefficient based on ODE. To simulate and illustrate our proposed method and efficient characteristics that demonstrate for two colliding bodies ...In this paper we present a graphical method for decision of restitution coefficient based on ODE. To simulate and illustrate our proposed method and efficient characteristics that demonstrate for two colliding bodies we used MatLab. In simulation to approach to the real case we used an assumption of additional virtual body’s position and velocity for characterizing material of the body which is involved to express the restitution coefficient. The graphic animation program is developed based on ODE for the computer simulation of the proposed graphical method. Additionally, we determined this new characteristic for some sport game balls such as basketball, volleyball, etc.展开更多
文摘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.
文摘How managers’ knowledge and beliefs of human nature are formed and manifested has not been fully explored in the context of Chinese society going through rapid transition nowadays. And yet this could be the missing link in our discourse on Chinese managers. Based on a qualitative study conducted in Quanzhou, China, this study found certain assumptions of human nature that are deeply embedded in their managers’ intellectual framework, which in turn guide their managerial behaviours in diverse aspects of their work. Unless the managers are prepared to examine their own thoughts, especially those at the sub-conscious level, they would remain prisoners of their own thought, and all the efforts directed at transforming managers would be seriously compromised.
文摘In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .
基金the Henan Natural Science Foundation(072300410320)the Henan Education Department Foundational Study Foundation(200510460311)
文摘The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes.
基金Natural Science and Education Foundation of Henan Province(2007110016)
文摘In this paper, let T be a bounded linear operator on a complex Hilbert H. We give and prove that every p-w-hyponormal operator has Bishop's property(β) and spectral properties; Quasi-similar p-w-hyponormal operators have equal spectra and equal essential spectra. Finally, for p-w-hyponormal operators, we give a kind of proof of its normality by use of properties of partial isometry.
文摘In this paper, both the roman domination number and the number of minimum roman dominating sets are found for any rectangular rook’s graph. In a similar fashion, the roman domination number and the number of minimum roman dominating sets are found on the square bishop’s graph for odd board sizes. Also found are the number of minimum total dominating sets associated with the light-colored squares when n?≡1(mod12)? (with n>1), and same for the dark-colored squares when n?≡7(mod12) .
文摘In this paper we present a graphical method for decision of restitution coefficient based on ODE. To simulate and illustrate our proposed method and efficient characteristics that demonstrate for two colliding bodies we used MatLab. In simulation to approach to the real case we used an assumption of additional virtual body’s position and velocity for characterizing material of the body which is involved to express the restitution coefficient. The graphic animation program is developed based on ODE for the computer simulation of the proposed graphical method. Additionally, we determined this new characteristic for some sport game balls such as basketball, volleyball, etc.
