In this paper, we study a certain partition function a（n） defined by ∑n≥0 a（n）qn ：= ∏n=1（1- qn）-1（1 -2n）-1. We prove that given a positive integer j 〉 1 and a prime m _〉 5, there are infinitely many cong...In this paper, we study a certain partition function a（n） defined by ∑n≥0 a（n）qn ：= ∏n=1（1- qn）-1（1 -2n）-1. We prove that given a positive integer j 〉 1 and a prime m _〉 5, there are infinitely many congruences of the type a（An ＋ B） ≡ 0 （rood m3）. This work is inspired by Ono＇s ground breaking result in the study of the distribution of the partition function p（n）.展开更多
The purpose of this paper is to introduce to you, the Western people, nowadays a “widely unknown” Japanese thermodynamicist by the name of Motoyosi Sugita and his study on the thermodynamics of transient phenomena a...The purpose of this paper is to introduce to you, the Western people, nowadays a “widely unknown” Japanese thermodynamicist by the name of Motoyosi Sugita and his study on the thermodynamics of transient phenomena and his theory of life. This is because although he was one of the top theoretical physicists in Japan before, during and after WWII and after WWII he promoted the establishment of the biophysical society of Japan as one of the founding members, he himself and his studies themselves have seemed to be totally forgotten nowadays in spite that his study was absolutely important for the study of life. Therefore, in this paper I would like to present what kind of person he was and what he studied in physics as a review on the physics work of Motoyosi Sugita for the first time. I will follow his past studies to introduce his ideas in theoretical physics as well as in biophysics as follows: He proposed the bright ideas such as the quasi-static change in the broad sense, the virtual heat, and the field of chemical potential etc. in order to establish his own theory of thermodynamics of transient phenomena, as the generalization of the Onsager-Prigogine’s theory of the irreversible processes. By the concept of the field of chemical potential that acquired the nonlinear transport, he was seemingly successful to exceed and go beyond the scope of Onsager and Prigogine. Once he established his thermodynamics, he explored the existence of the 4th law of thermodynamics for the foundation of theory of life. He applied it to broad categories of transient phenomena including life and life being such as the theory of metabolism. He regarded the 4th law of thermodynamics as the maximum principle in transient phenomena. He tried to prove it all life long. Since I have recently found that his maximum principle can be included in more general maximum principle, which was known as the Pontryagin’s maximum principle in the theory of optimal control, I would like to explain such theories produced by Motoyosi Sugita as detailed as possible. And also I have put short history of Motoyosi Sugita’s personal life in order for you to know him well. I hope that this article helps you to know this wonderful man and understand what he did in the past, which was totally forgotten in the world and even in Japan.展开更多
Based on the partition function in statistical thermodynamics, atomic partit ion parameter fi =lg[(ni－1)0.5·Ar,i] is introduced in this paper. The fi has demonstrated good unitarity for all the ground state ato ...Based on the partition function in statistical thermodynamics, atomic partit ion parameter fi =lg[(ni－1)0.5·Ar,i] is introduced in this paper. The fi has demonstrated good unitarity for all the ground state ato ms, and excellent correlativity with the standard entropies (,J·mol－1·K －1) of 70 cations in solid compounds: = －10.247＋27.508 fi , r=0.996. A satisfactory curve equation is developed as follows: =6.229＋13.257 fi1.5, r= 0.999. On the basis of adjacency matrices and fi , a novel partition connectivit y index is developed for the study on the standard entropies of 64 S block compo unds. The linear regression equation is set up by the least square method: =－3 9.416＋33.9610H, r=0.985. The binary linear equation among and 0H, nM (princip al quantum number of the ground state atoms for S block) is drawn up: =－21.591 ＋32.0720H－31.013nM－1, R=0.990. The calculated values of basically tally w ith the experiment values. fi and 0H demonstrate that the method possesses the a dvantage of easy computation and clear physical significance.展开更多
文摘In this paper, we study a certain partition function a（n） defined by ∑n≥0 a（n）qn ：= ∏n=1（1- qn）-1（1 -2n）-1. We prove that given a positive integer j 〉 1 and a prime m _〉 5, there are infinitely many congruences of the type a（An ＋ B） ≡ 0 （rood m3）. This work is inspired by Ono＇s ground breaking result in the study of the distribution of the partition function p（n）.
文摘The purpose of this paper is to introduce to you, the Western people, nowadays a “widely unknown” Japanese thermodynamicist by the name of Motoyosi Sugita and his study on the thermodynamics of transient phenomena and his theory of life. This is because although he was one of the top theoretical physicists in Japan before, during and after WWII and after WWII he promoted the establishment of the biophysical society of Japan as one of the founding members, he himself and his studies themselves have seemed to be totally forgotten nowadays in spite that his study was absolutely important for the study of life. Therefore, in this paper I would like to present what kind of person he was and what he studied in physics as a review on the physics work of Motoyosi Sugita for the first time. I will follow his past studies to introduce his ideas in theoretical physics as well as in biophysics as follows: He proposed the bright ideas such as the quasi-static change in the broad sense, the virtual heat, and the field of chemical potential etc. in order to establish his own theory of thermodynamics of transient phenomena, as the generalization of the Onsager-Prigogine’s theory of the irreversible processes. By the concept of the field of chemical potential that acquired the nonlinear transport, he was seemingly successful to exceed and go beyond the scope of Onsager and Prigogine. Once he established his thermodynamics, he explored the existence of the 4th law of thermodynamics for the foundation of theory of life. He applied it to broad categories of transient phenomena including life and life being such as the theory of metabolism. He regarded the 4th law of thermodynamics as the maximum principle in transient phenomena. He tried to prove it all life long. Since I have recently found that his maximum principle can be included in more general maximum principle, which was known as the Pontryagin’s maximum principle in the theory of optimal control, I would like to explain such theories produced by Motoyosi Sugita as detailed as possible. And also I have put short history of Motoyosi Sugita’s personal life in order for you to know him well. I hope that this article helps you to know this wonderful man and understand what he did in the past, which was totally forgotten in the world and even in Japan.
文摘Based on the partition function in statistical thermodynamics, atomic partit ion parameter fi =lg[(ni－1)0.5·Ar,i] is introduced in this paper. The fi has demonstrated good unitarity for all the ground state ato ms, and excellent correlativity with the standard entropies (,J·mol－1·K －1) of 70 cations in solid compounds: = －10.247＋27.508 fi , r=0.996. A satisfactory curve equation is developed as follows: =6.229＋13.257 fi1.5, r= 0.999. On the basis of adjacency matrices and fi , a novel partition connectivit y index is developed for the study on the standard entropies of 64 S block compo unds. The linear regression equation is set up by the least square method: =－3 9.416＋33.9610H, r=0.985. The binary linear equation among and 0H, nM (princip al quantum number of the ground state atoms for S block) is drawn up: =－21.591 ＋32.0720H－31.013nM－1, R=0.990. The calculated values of basically tally w ith the experiment values. fi and 0H demonstrate that the method possesses the a dvantage of easy computation and clear physical significance.
