We prove the explicit formula for the hyperbolic scattering determinant in the case of a general subgroup F of PSL （2, R）. The class of test functions involved （not necessarily odd nor continuous） is much broader ...We prove the explicit formula for the hyperbolic scattering determinant in the case of a general subgroup F of PSL （2, R）. The class of test functions involved （not necessarily odd nor continuous） is much broader than that previously known. As an application of the technique, a new representation of the Millson-Shintani zeta function is obtained.展开更多
A spectral interpretation for the poles and zeros of the L-function of algebraic number fields is given by Meyer. As Meyer works with Schwartz spaces which are not Hilbert spaces, the information on the location of ze...A spectral interpretation for the poles and zeros of the L-function of algebraic number fields is given by Meyer. As Meyer works with Schwartz spaces which are not Hilbert spaces, the information on the location of zeros of the L-function is lost. In 1999, A. Connes gave a spectral interpretation for the critical zeros the Riemann zeta function. He works with Hilbert spaces. In this paper, we show that a variant of Connes’ trace formula is essentially equal to the explicit formula of A. Weil.展开更多
In this paper, two recurrence formulas for radial average values of N-dimensional hydrogen atom are derived. Explicit expressions for <n rJ N-2 |r s|n rJ N-2 > are given for 3≥s≥-6. These results can be applie...In this paper, two recurrence formulas for radial average values of N-dimensional hydrogen atom are derived. Explicit expressions for <n rJ N-2 |r s|n rJ N-2 > are given for 3≥s≥-6. These results can be applied to discuss average value of centrifugal potential energy and other physical quantities. The relevant results of the usual hydrogen atom are contained in more general conclusion of this paper as special cases.展开更多
This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is ...This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is an autoregressive model of order p,representing a time series with dependencies on its p previous values.Additionally,the study evaluates the accuracy of both explicit and numerical integral equation(NIE)solutions for AR(p)using the TEWMA control chart,focusing on the absolute percentage relative error.The results indicate that the explicit and approximate solutions are in close agreement.Furthermore,the study investigates the performance of exponentially weighted moving average(EWMA)and TEWMA control charts in detecting changes in the process,using the relative mean index(RMI)as a measure.The findings demonstrate that the TEWMA control chart outperforms the EWMA control chart in detecting process changes,especially when the value ofλis sufficiently large.In addition,an analysis using historical data from the SET index between January 2024 and May 2024 and historical data of global annual plastic production,the results of both data sets also emphasize the superior performance of the TEWMA control chart.展开更多
In the data encryption standard （DES） algorithm, there exist several bit-switching functions, including permutations, expansion, and permuted choices. They are generally presented in the form of matrixes and realize...In the data encryption standard （DES） algorithm, there exist several bit-switching functions, including permutations, expansion, and permuted choices. They are generally presented in the form of matrixes and realized by using table look-up technique in the implementation of the cryptosystem. This paper presents explicit formulas for the initial permutation IP, its inverse IP-1 , the expansion function E, and the permuted choice PC_1. It also gives the program realizations of these functions in C＋＋ applying these formulas. With the advantage of the omission of the storage space for these matrixes and the tedious inputs of tables in the implementations of DES, our experimental results shows that the explicit formulas are useful in some situations, such as wireless sensor networks where the memory capacity is limited, especially when the size of file for encrypting is not too large, preferably smaller than 256KB.展开更多
In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models...In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with Mbeing a positive integer for regular grids are discussed and illustrated by constructing the second order （M= 1） and the fourth order （M = 2） recursion formulas.展开更多
In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform ...In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order （M=1） recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.展开更多
文摘We prove the explicit formula for the hyperbolic scattering determinant in the case of a general subgroup F of PSL （2, R）. The class of test functions involved （not necessarily odd nor continuous） is much broader than that previously known. As an application of the technique, a new representation of the Millson-Shintani zeta function is obtained.
文摘A spectral interpretation for the poles and zeros of the L-function of algebraic number fields is given by Meyer. As Meyer works with Schwartz spaces which are not Hilbert spaces, the information on the location of zeros of the L-function is lost. In 1999, A. Connes gave a spectral interpretation for the critical zeros the Riemann zeta function. He works with Hilbert spaces. In this paper, we show that a variant of Connes’ trace formula is essentially equal to the explicit formula of A. Weil.
文摘In this paper, two recurrence formulas for radial average values of N-dimensional hydrogen atom are derived. Explicit expressions for <n rJ N-2 |r s|n rJ N-2 > are given for 3≥s≥-6. These results can be applied to discuss average value of centrifugal potential energy and other physical quantities. The relevant results of the usual hydrogen atom are contained in more general conclusion of this paper as special cases.
基金the National Science,Research and Innovation Fund(NSRF)King Mongkuts University of Technology North Bangkok under contract no.KMUTNB-FF-68-B-08.
文摘This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is an autoregressive model of order p,representing a time series with dependencies on its p previous values.Additionally,the study evaluates the accuracy of both explicit and numerical integral equation(NIE)solutions for AR(p)using the TEWMA control chart,focusing on the absolute percentage relative error.The results indicate that the explicit and approximate solutions are in close agreement.Furthermore,the study investigates the performance of exponentially weighted moving average(EWMA)and TEWMA control charts in detecting changes in the process,using the relative mean index(RMI)as a measure.The findings demonstrate that the TEWMA control chart outperforms the EWMA control chart in detecting process changes,especially when the value ofλis sufficiently large.In addition,an analysis using historical data from the SET index between January 2024 and May 2024 and historical data of global annual plastic production,the results of both data sets also emphasize the superior performance of the TEWMA control chart.
基金Supported by the National Natural Science Foundation of China (61272045)Natural Science Foundation of Outstanding Youth Team Project of Zhejiang Province (R1090138)Project of the State Key Laboratory of Information Security (Institute of Information Engineering, Chinese Academy of Sciences, Beijing)
文摘In the data encryption standard （DES） algorithm, there exist several bit-switching functions, including permutations, expansion, and permuted choices. They are generally presented in the form of matrixes and realized by using table look-up technique in the implementation of the cryptosystem. This paper presents explicit formulas for the initial permutation IP, its inverse IP-1 , the expansion function E, and the permuted choice PC_1. It also gives the program realizations of these functions in C＋＋ applying these formulas. With the advantage of the omission of the storage space for these matrixes and the tedious inputs of tables in the implementations of DES, our experimental results shows that the explicit formulas are useful in some situations, such as wireless sensor networks where the memory capacity is limited, especially when the size of file for encrypting is not too large, preferably smaller than 256KB.
文摘In this paper, we obtain an explicit formula of general solution for a class of the homogeneous recurrence of variable coefficients with two indices.
基金National Basic Research Program of China Under Grant No. 2007CB714200National Natural Science Foundation of China Under Grant No. 90715038
文摘In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with Mbeing a positive integer for regular grids are discussed and illustrated by constructing the second order （M= 1） and the fourth order （M = 2） recursion formulas.
基金China Postdoctoral Science Foundation Under Grant No.20100480321National Basic Research Program of China Under Grant No. 2007CB714200
文摘In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order （M=1） recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.
