The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler...The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.展开更多
This paper gives a new generalization of higher order Daehee and Bernoulli numbers and polynomials. We define the multiparameter higher order Daehee numbers and polynomials of the first and second kind. Moreover, we d...This paper gives a new generalization of higher order Daehee and Bernoulli numbers and polynomials. We define the multiparameter higher order Daehee numbers and polynomials of the first and second kind. Moreover, we derive some new results for these numbers and polynomials. The relations between these numbers and Stirling and Bernoulli numbers are obtained. Furthermore, some interesting special cases of the generalized higher order Daehee and Bernoulli numbers and polynomials are deduced.展开更多
With respect to the decision making problems where a lot of fuzzy and grey information always exists in the real-life decision making information system methods as fuzzy mathematics, it is difficult for such uncertain...With respect to the decision making problems where a lot of fuzzy and grey information always exists in the real-life decision making information system methods as fuzzy mathematics, it is difficult for such uncertainty probability, and interval numbers to deal with. To this end, based on the thought and method of grey numbers, grey degrees and interval numbers, the concept of dominance grey degree is defined. And then a method of ranking interval grey numbers based on the dominance grey degree is proposed. After discussing the relevant properties, the paper finally uses an example to demonstrate the effectiveness and applicability of the model. The result shows that the proposed model can more accurately describe uncertainty decision making problems, and realize the total ordering process for multiple-attribute decision-making problems.展开更多
In this paper, the definitons of both higher-order multivariable Euler's numbersand polynomial. higher-order multivariable Bernoulli's numbers and polynomial aregiven and some of their important properties...In this paper, the definitons of both higher-order multivariable Euler's numbersand polynomial. higher-order multivariable Bernoulli's numbers and polynomial aregiven and some of their important properties are expounded. As a result, themathematical relationship between higher-order multivariable Euler's polynomial(numbers) and higher-order higher -order Bernoulli's polynomial (numbers) are thusobtained.展开更多
By virtue of the Weyl ordering method,we find a new formalism of optical field operator expansion in number state representation.Miscellaneous optical fields＇（coherent state,squeezed field,Wigner operator,etc.） new...By virtue of the Weyl ordering method,we find a new formalism of optical field operator expansion in number state representation.Miscellaneous optical fields＇（coherent state,squeezed field,Wigner operator,etc.） new expansions are therefore exhibited.Some new generating functions of special polynomials are derived herewith.展开更多
In this paper, we consider the Cauchy numbers and polynomials of order k and give some relation between Cauchy polynomials of order k and special polynomials by using generating functions and the Riordan matrix method...In this paper, we consider the Cauchy numbers and polynomials of order k and give some relation between Cauchy polynomials of order k and special polynomials by using generating functions and the Riordan matrix methods. In addition, we establish some new equalities and relations involving high-order Cauchy numbers and polynomials, high-order Daehee numbers and polynomials, the generalized Bell polynomials, the Bernoulli numbers and polynomials, high-order Changhee polynomials, high-order Changhee-Genocchi polynomials, the combinatorial numbers, Lah numbers and Stirling numbers, etc.展开更多
One of the limitations of using OFDM technique is its higher PAPR in the time domain signal. The higher PAPR OFDM signal would cause the fatal degradation of BER performance and undesirable spectrum regrowth in the no...One of the limitations of using OFDM technique is its higher PAPR in the time domain signal. The higher PAPR OFDM signal would cause the fatal degradation of BER performance and undesirable spectrum regrowth in the nonlinear channel. One of the promising PAPR reduction methods for OFDM signal is the Partial Transmit Sequence (PTS) method which can achieve better PAPR performance with reasonable computation complexity. However the PTS method is required to inform the phase coefficients of PTS as the side information to the receiver for the correct demodulation of data information through the data or separate channels. To simplify the transceiver of OFDM system with the PTS method, the phase coefficients of PTS are usually embedded in the data information. However since the phase coefficients of PTS are obtained after the PTS processing only for the data information at each OFDM symbol, it is hard to embed the phase coefficients of PTS in the data information separately without degradation of PAPR performance. To solve this problem, this paper proposes a new PAPR reduction method based on the packet-switched transmission systems in which all the clusters within the certain number of OFDM symbols have the sequential cluster ID numbers embedded in the header of each cluster. The salient features of the proposed method are to reduce the PAPR performance by re-ordering of clusters (ROC) in the frequency domain at the transmitter and to reconstruct the original ordering of clusters by using the cluster ID number demodulated from each cluster at the receiver. This paper also proposes a reduction technique of computation complexity for the proposed ROC method by using the feature of IFFT processing. This paper presents various computer simulation results to verify the effectiveness of the proposed ROC method with the reduction technique of computation complexity.展开更多
基金Supported by the NNSF of China(10001016) SF for the Prominent Youth of Henan Province
文摘The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.
文摘This paper gives a new generalization of higher order Daehee and Bernoulli numbers and polynomials. We define the multiparameter higher order Daehee numbers and polynomials of the first and second kind. Moreover, we derive some new results for these numbers and polynomials. The relations between these numbers and Stirling and Bernoulli numbers are obtained. Furthermore, some interesting special cases of the generalized higher order Daehee and Bernoulli numbers and polynomials are deduced.
基金supported by the National Natural Science Foundation of China(7117310471171113+8 种基金70901041712712267130107571301064)the Humanities and Social Sciences of Education Ministry(12YJC630262)the Jiangsu Province University Philosophy and Social Sciences for Key Research Program(2012ZDIXM030)the Jiangsu Innovation Program for Graduate Education and the Fundamental Research Funds for the Central Universities(CXLX12 0175)the Nanjing University of Aeronautics and Astronautics(NUAA)Innovation and Excellence Program for PHD Dissertation(BCXJ12-12)NUAA Program for I-U-R(NC2012006)
文摘With respect to the decision making problems where a lot of fuzzy and grey information always exists in the real-life decision making information system methods as fuzzy mathematics, it is difficult for such uncertainty probability, and interval numbers to deal with. To this end, based on the thought and method of grey numbers, grey degrees and interval numbers, the concept of dominance grey degree is defined. And then a method of ranking interval grey numbers based on the dominance grey degree is proposed. After discussing the relevant properties, the paper finally uses an example to demonstrate the effectiveness and applicability of the model. The result shows that the proposed model can more accurately describe uncertainty decision making problems, and realize the total ordering process for multiple-attribute decision-making problems.
文摘In this paper, the definitons of both higher-order multivariable Euler's numbersand polynomial. higher-order multivariable Bernoulli's numbers and polynomial aregiven and some of their important properties are expounded. As a result, themathematical relationship between higher-order multivariable Euler's polynomial(numbers) and higher-order higher -order Bernoulli's polynomial (numbers) are thusobtained.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10975125 and 11175113)
文摘By virtue of the Weyl ordering method,we find a new formalism of optical field operator expansion in number state representation.Miscellaneous optical fields＇（coherent state,squeezed field,Wigner operator,etc.） new expansions are therefore exhibited.Some new generating functions of special polynomials are derived herewith.
文摘In this paper, we consider the Cauchy numbers and polynomials of order k and give some relation between Cauchy polynomials of order k and special polynomials by using generating functions and the Riordan matrix methods. In addition, we establish some new equalities and relations involving high-order Cauchy numbers and polynomials, high-order Daehee numbers and polynomials, the generalized Bell polynomials, the Bernoulli numbers and polynomials, high-order Changhee polynomials, high-order Changhee-Genocchi polynomials, the combinatorial numbers, Lah numbers and Stirling numbers, etc.
文摘One of the limitations of using OFDM technique is its higher PAPR in the time domain signal. The higher PAPR OFDM signal would cause the fatal degradation of BER performance and undesirable spectrum regrowth in the nonlinear channel. One of the promising PAPR reduction methods for OFDM signal is the Partial Transmit Sequence (PTS) method which can achieve better PAPR performance with reasonable computation complexity. However the PTS method is required to inform the phase coefficients of PTS as the side information to the receiver for the correct demodulation of data information through the data or separate channels. To simplify the transceiver of OFDM system with the PTS method, the phase coefficients of PTS are usually embedded in the data information. However since the phase coefficients of PTS are obtained after the PTS processing only for the data information at each OFDM symbol, it is hard to embed the phase coefficients of PTS in the data information separately without degradation of PAPR performance. To solve this problem, this paper proposes a new PAPR reduction method based on the packet-switched transmission systems in which all the clusters within the certain number of OFDM symbols have the sequential cluster ID numbers embedded in the header of each cluster. The salient features of the proposed method are to reduce the PAPR performance by re-ordering of clusters (ROC) in the frequency domain at the transmitter and to reconstruct the original ordering of clusters by using the cluster ID number demodulated from each cluster at the receiver. This paper also proposes a reduction technique of computation complexity for the proposed ROC method by using the feature of IFFT processing. This paper presents various computer simulation results to verify the effectiveness of the proposed ROC method with the reduction technique of computation complexity.
