The research for the Intelligent Reflecting Surface(IRS)which has the advantages of cost and energy efficiency has been studied.Channel capacity can be effectively increased by appropriately setting the phase value of...The research for the Intelligent Reflecting Surface(IRS)which has the advantages of cost and energy efficiency has been studied.Channel capacity can be effectively increased by appropriately setting the phase value of IRS elements according to the channel conditions.However,the problem of obtaining an appropriate phase value of IRs is difficult to solve due to the non-convex problem.This paper proposes an iterative algorithm for the alternating optimal solution in the Single User Multiple-Input-Multiple-Output(SU-MIMO)systems.The proposed iterative algorithm finds an alternating optimal solution that is the phase value of IRS one by one.The results show that the proposed method has better performance than that of the randomized IRS systems.The number of iterations for maximizing the performance of the proposed algorithm depends on the channel state between the IRS and the receiver.展开更多
It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems kn...It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.展开更多
Sums of convergent series for any desired number of terms, which may be infinite, are estimated very accurately by establishing definite rational polynomials. For infinite number of terms the sum infinite is obtained ...Sums of convergent series for any desired number of terms, which may be infinite, are estimated very accurately by establishing definite rational polynomials. For infinite number of terms the sum infinite is obtained by taking the asymptotic limit of the rational polynomial. A rational function with second-degree polynomials both in the numerator and denominator is found to produce excellent results. Sums of series with different characteristics such as alternating signs are considered for testing the performance of the proposed approach.展开更多
In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,a...In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.展开更多
In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the sys...In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)). At last, we show that an operator space V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V = C.展开更多
基金supported by the MSIT(Ministry of Science and ICT),Korea,under the ITRC(Information Technology Research Center)support program(IITP-2022-2018-0-01423)supervised by the ITP(Institute for Information&Communications Technology Planning&Evaluation)supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2020R1A6A1A03038540).
文摘The research for the Intelligent Reflecting Surface(IRS)which has the advantages of cost and energy efficiency has been studied.Channel capacity can be effectively increased by appropriately setting the phase value of IRS elements according to the channel conditions.However,the problem of obtaining an appropriate phase value of IRs is difficult to solve due to the non-convex problem.This paper proposes an iterative algorithm for the alternating optimal solution in the Single User Multiple-Input-Multiple-Output(SU-MIMO)systems.The proposed iterative algorithm finds an alternating optimal solution that is the phase value of IRS one by one.The results show that the proposed method has better performance than that of the randomized IRS systems.The number of iterations for maximizing the performance of the proposed algorithm depends on the channel state between the IRS and the receiver.
文摘It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.
文摘Sums of convergent series for any desired number of terms, which may be infinite, are estimated very accurately by establishing definite rational polynomials. For infinite number of terms the sum infinite is obtained by taking the asymptotic limit of the rational polynomial. A rational function with second-degree polynomials both in the numerator and denominator is found to produce excellent results. Sums of series with different characteristics such as alternating signs are considered for testing the performance of the proposed approach.
文摘In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.
文摘In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)). At last, we show that an operator space V is finitely representable in {M<sub>n</sub>}<sub>n∈N</sub> in the system (Ⅱ<sub>1</sub>(⋅,⋅), π<sub>1</sub>(⋅)) if and only if V = C.