Superconductivity in small metallic grains is carefully checked as their size is decreased to a few nm when the average level spacing d could be compared with the bulk gapΔ.Using random matrix theory to the mean fiel...Superconductivity in small metallic grains is carefully checked as their size is decreased to a few nm when the average level spacing d could be compared with the bulk gapΔ.Using random matrix theory to the mean field,we find that the average theoretical values of the critical level spacing for both odd and even numbers of electrons and the transition temperature Tc in three Gauss ensembles are quite different for those from the model of uniformly spaced levels.For Sz=1/2,as grain size is reduced,the transition temperature or the granular gap decreases monotonously,and the relation 2△(0)/kB T_(c)≤3.53 always exists.展开更多
The elliptic loop equation of cosniic string is studied in the Minkowski space and during the radiation-dominated era in the Robertson-Walker universe.A remarkable fact about this equation is that a loop may never con...The elliptic loop equation of cosniic string is studied in the Minkowski space and during the radiation-dominated era in the Robertson-Walker universe.A remarkable fact about this equation is that a loop may never contract to one with a Schwarzschild radius,if it is sufficiently non-circular.展开更多
Let f(x)=x^2-x+p, where p is a positive integer. What number are p such that f(n)(1≤n<p) are all primes? We call it the problem of being always a prime. We already know that if p= 2, 3, 5, 11, 17 and 41, f(n) is a...Let f(x)=x^2-x+p, where p is a positive integer. What number are p such that f(n)(1≤n<p) are all primes? We call it the problem of being always a prime. We already know that if p= 2, 3, 5, 11, 17 and 41, f(n) is always a prime in (1)There are some results about how to determine that f(n) is always a prime in (2—4)In this paper we have proved that the展开更多
基金Supported in part by the Science and Technology Commission of Chongqing City under Grant No.97-4730 and Key Laboratory Fund of Jiangsu Province.
文摘Superconductivity in small metallic grains is carefully checked as their size is decreased to a few nm when the average level spacing d could be compared with the bulk gapΔ.Using random matrix theory to the mean field,we find that the average theoretical values of the critical level spacing for both odd and even numbers of electrons and the transition temperature Tc in three Gauss ensembles are quite different for those from the model of uniformly spaced levels.For Sz=1/2,as grain size is reduced,the transition temperature or the granular gap decreases monotonously,and the relation 2△(0)/kB T_(c)≤3.53 always exists.
文摘The elliptic loop equation of cosniic string is studied in the Minkowski space and during the radiation-dominated era in the Robertson-Walker universe.A remarkable fact about this equation is that a loop may never contract to one with a Schwarzschild radius,if it is sufficiently non-circular.
文摘Let f(x)=x^2-x+p, where p is a positive integer. What number are p such that f(n)(1≤n<p) are all primes? We call it the problem of being always a prime. We already know that if p= 2, 3, 5, 11, 17 and 41, f(n) is always a prime in (1)There are some results about how to determine that f(n) is always a prime in (2—4)In this paper we have proved that the
