A model for particles based on preons in chiral, vector and tensor/graviton supermultiplets of unbroken global supersymmetry is engineered. The framework of the model is little string theory. Phenomenological predicti...A model for particles based on preons in chiral, vector and tensor/graviton supermultiplets of unbroken global supersymmetry is engineered. The framework of the model is little string theory. Phenomenological predictions are discussed.展开更多
Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposi...Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1- cosγ) is a rational square, and it has elements of order three iff the cubic (2cosγ)x3-3x2+1=0 has a rational solution 0<x<1. This shows that the set of values ofγ for which Hr has two-torsion is dense in [0, π], and similarly for three-torsion. We also show that there is at most one copy of either Z2 or Z3 in Hr. Finally, we give some examples of higher order torsion elements in Hr.展开更多
An optimal Monte Carlo renormalization group method is applied to 3-state Potts model on 3-dimensional random triangle lattice.The scaling exponent v of the first order phase transition of this model has been obtained...An optimal Monte Carlo renormalization group method is applied to 3-state Potts model on 3-dimensional random triangle lattice.The scaling exponent v of the first order phase transition of this model has been obtained.In the disorder phase v=0.369(±0.044),y_(T)=1/ν=2.71(±0.32),in the order phase ν=0.393(±0.048),y_(T)=2.54(±0.31).They approximate to the prediction of the scaling theory.展开更多
Though with different times and backgrounds,these three masterpieces-"The Egg","The Secret Life of Walter Mitty"and"Shiloh"all humorously characterize the same type protagonist-the"l...Though with different times and backgrounds,these three masterpieces-"The Egg","The Secret Life of Walter Mitty"and"Shiloh"all humorously characterize the same type protagonist-the"little man".Penetrating the humorous characterization,the three works on the one hand present the rational question of the mainstream society and the serious critique of the dominant forces,on the other hand,they also offer the humanistic affirm and concern of the marginalized little man.Thus,bundle these three master pieces together,this paper makes an effort to analyze the humorous characterization of the little man;the comic gender relationships so as to figure out the coherent thematic significance as well as the philosophical seriousness of humor in these three masterpieces.展开更多
Important changes have taken place in the study of Chinese literary anthropology since 21st century. Chinese literary anthropologists make every effort to explore and construct one theoretical system which is suitable...Important changes have taken place in the study of Chinese literary anthropology since 21st century. Chinese literary anthropologists make every effort to explore and construct one theoretical system which is suitable for China＇s local culture consciousness. Its development context is clear： from literary text to culture text, and from the mythological outlook of literary standard to the mythological outlook driven by faith. We need rely on quadruple-evidence approaches which are integrated with multidisciplinary knowledge to reconstruct Chinese culture of the great tradition and little tradition theory from the new perspective of mythistory, to elaborate N-level coding theory, and to explore the faith in jade myth as the potential driving force of the beginning of civilization. By combing the complete symbolic process from the faith in jade myth to Chinese civilization core values, we wish to seek out the deep cultural genes among Chinese civilization identities ultimately.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
文摘A model for particles based on preons in chiral, vector and tensor/graviton supermultiplets of unbroken global supersymmetry is engineered. The framework of the model is little string theory. Phenomenological predictions are discussed.
文摘Let 0<γ<π be a fixed pythagorean angle. We study the abelian group Hr of primitive integral triangles (a,b,c) for which the angle opposite side c is γ. Addition in Hr is defined by adding the angles β opposite side b and modding out by π-γ. The only Hr for which the structure is known is Hπ/2, which is free abelian. We prove that for generalγ, Hr has an element of order two iff 2(1- cosγ) is a rational square, and it has elements of order three iff the cubic (2cosγ)x3-3x2+1=0 has a rational solution 0<x<1. This shows that the set of values ofγ for which Hr has two-torsion is dense in [0, π], and similarly for three-torsion. We also show that there is at most one copy of either Z2 or Z3 in Hr. Finally, we give some examples of higher order torsion elements in Hr.
基金Supported by Funds of Institute of Theoretical Physics,Academia Sinica.
文摘An optimal Monte Carlo renormalization group method is applied to 3-state Potts model on 3-dimensional random triangle lattice.The scaling exponent v of the first order phase transition of this model has been obtained.In the disorder phase v=0.369(±0.044),y_(T)=1/ν=2.71(±0.32),in the order phase ν=0.393(±0.048),y_(T)=2.54(±0.31).They approximate to the prediction of the scaling theory.
文摘Though with different times and backgrounds,these three masterpieces-"The Egg","The Secret Life of Walter Mitty"and"Shiloh"all humorously characterize the same type protagonist-the"little man".Penetrating the humorous characterization,the three works on the one hand present the rational question of the mainstream society and the serious critique of the dominant forces,on the other hand,they also offer the humanistic affirm and concern of the marginalized little man.Thus,bundle these three master pieces together,this paper makes an effort to analyze the humorous characterization of the little man;the comic gender relationships so as to figure out the coherent thematic significance as well as the philosophical seriousness of humor in these three masterpieces.
文摘Important changes have taken place in the study of Chinese literary anthropology since 21st century. Chinese literary anthropologists make every effort to explore and construct one theoretical system which is suitable for China＇s local culture consciousness. Its development context is clear： from literary text to culture text, and from the mythological outlook of literary standard to the mythological outlook driven by faith. We need rely on quadruple-evidence approaches which are integrated with multidisciplinary knowledge to reconstruct Chinese culture of the great tradition and little tradition theory from the new perspective of mythistory, to elaborate N-level coding theory, and to explore the faith in jade myth as the potential driving force of the beginning of civilization. By combing the complete symbolic process from the faith in jade myth to Chinese civilization core values, we wish to seek out the deep cultural genes among Chinese civilization identities ultimately.
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. .
