Utilizing translation operators we get the powers sums on arithmetic progressions and the Bernoulli polynomials of order munder the form of differential operators acting on monomials. It follows that (d/dn-d/dz) appli...Utilizing translation operators we get the powers sums on arithmetic progressions and the Bernoulli polynomials of order munder the form of differential operators acting on monomials. It follows that (d/dn-d/dz) applied on a power sum has a meaning and is exactly equal to the Bernoulli polynomial of the same order. From this new property we get the formula giving powers sums in term of sums of successive derivatives of Bernoulli polynomial multiplied withprimitives of the same order of n. Then by changing the two arguments z,n into Z=z(z-1), λ where λ designed the 1st order power sums and proving that Bernoulli polynomials of odd order vanish for arguments equal to 0, 1/2, 1, we obtain easily the Faulhaber formula for powers sums in term of polynomials in λ having coefficients depending on Z. These coefficients are found to be derivatives of odd powers sums on integers expressed in Z. By the way we obtain the link between Faulhaber formulae for powers sums on integers and on arithmetic progressions. To complete the work we propose tables for calculating in easiest manners possibly the Bernoulli numbers, the Bernoulli polynomials, the powers sums and the Faulhaber formula for powers sums.展开更多
Utilizing the translation operator to represent Bernoulli polynomials and power sums as polynomials of Sheffer-type, we obtain concisely almost all their known properties as so as many new ones, especially new recursi...Utilizing the translation operator to represent Bernoulli polynomials and power sums as polynomials of Sheffer-type, we obtain concisely almost all their known properties as so as many new ones, especially new recursion relations for calculating Bernoulli polynomials and numbers, new formulae for obtaining power sums of entire and complex numbers. Then by the change of arguments from z into Z = z(z-1) and n into λ which is the 1<sup>st</sup> order power sum we obtain the Faulhaber formula for powers sums in term of polynomials in λ having coefficients depending on Z. Practically we give tables for calculating in easiest possible manners, the Bernoulli numbers, polynomials, the general powers sums.展开更多
The analytical calculation of the area moments of inertia used for special mechanical tests in materials science and further generalizations for moments of different orders and broader symmetry properties has led to a...The analytical calculation of the area moments of inertia used for special mechanical tests in materials science and further generalizations for moments of different orders and broader symmetry properties has led to a new type of trigonometric power sums. The corresponding generalized equations are presented, proven, and their characteristics discussed. Although the power sums have a basic form, their results have quite different properties, dependent on the values of the free parameters used. From these equations, a large variety of power reduction formulas can be derived. This is shown by some examples.展开更多
Let <em>p</em> be an odd prime, the harmonic congruence such as <img alt="" src="Edit_843b278d-d88a-45d3-a136-c30e6becf142.bmp" />, and many different variations and generalizatio...Let <em>p</em> be an odd prime, the harmonic congruence such as <img alt="" src="Edit_843b278d-d88a-45d3-a136-c30e6becf142.bmp" />, and many different variations and generalizations have been studied intensively. In this note, we consider the congruences involving the combination of alternating harmonic sums, <img alt="" src="Edit_e97d0c64-3683-4a75-9d26-4b371c2be41e.bmp" /> where P<em><sub>P </sub></em>denotes the set of positive integers which are prime to <em>p</em>. And we establish the combinational congruences involving alternating harmonic sums for positive integer <em>n</em>=3,4,5.展开更多
为了研究对任意素数模p的一类广义Kloosterman和的四次均值,利用初等与解析方法、Gauss和以及三角和的转换性质引入了当素数p≡1 mod 4时该均值的计算问题,并将该类均值转化为特征和的简易形式。从计算结果上对均值的估计具有充分性,从...为了研究对任意素数模p的一类广义Kloosterman和的四次均值,利用初等与解析方法、Gauss和以及三角和的转换性质引入了当素数p≡1 mod 4时该均值的计算问题,并将该类均值转化为特征和的简易形式。从计算结果上对均值的估计具有充分性,从计算方法上对广义Kloosterman和各种形式的四次均值研究具有重要的参考价值。此外,这也为指数和均值计算问题提供了一种新的转化思路与方法,必将对有关问题的进一步探索起到推动作用。展开更多
在基于非正交多址接入技术的多用户下行室内可见光通信(Visible light communication system based on non⁃orthogonal multiple access technology,VLC⁃NOMA)系统中,针对和速率与用户公平性冲突的问题,提出一种基于加权和速率最大化的...在基于非正交多址接入技术的多用户下行室内可见光通信(Visible light communication system based on non⁃orthogonal multiple access technology,VLC⁃NOMA)系统中,针对和速率与用户公平性冲突的问题,提出一种基于加权和速率最大化的迭代功率分配方案。该方案以最大化加权和速率为目标,可通过改变权重因子来调节用户公平性。由于目标问题属于非凸优化问题,通过辅助变量法和凸优化理论将该非凸问题转化为凹问题,再通过拉格朗日对偶法进行求解,并根据问题的解设计了一种迭代功率分配算法。对所提算法的收敛性、系统和速率以及用户公平性进行了仿真。结果表明,所提迭代功率分配算法具有良好的收敛性,相较于VLC⁃OMA系统,VLC⁃NOMA系统能够获得更好的和速率性能。通过调整权重因子,在牺牲较小系统和速率的情况下能够获得比现有功率分配方案更好的系统和速率与用户公平性。展开更多
5G通信基站通常配备光储,数量庞大、功耗可调,是一种优质的电力灵活性调节资源。提出了多类型光储式5G基站集群灵活性资源聚合方法以及参与电网调峰的协同调度策略。首先,分析休眠机制下多类型基站功耗可调特性与计及基站备用电量的储...5G通信基站通常配备光储,数量庞大、功耗可调,是一种优质的电力灵活性调节资源。提出了多类型光储式5G基站集群灵活性资源聚合方法以及参与电网调峰的协同调度策略。首先,分析休眠机制下多类型基站功耗可调特性与计及基站备用电量的储能调节能力。基于极限场景思想,构建了光储式5G基站的灵活性空间量化模型。在此基础上,利用闵可夫斯基和法刻画异构基站柔性资源的时空耦合能量轨迹,得到海量基站集群的灵活性资源聚合可调域。其次,建立了基站集群聚合资源参与电能量市场和辅助服务市场的协同调度优化模型,提出了基于交替方向乘子法(alternating direction method of multipliers, ADMM)的分层分布式基站集群协同优化调度策略,将大规模基站集群调度问题降维分解为统一协同调峰功率响应、聚合功率自治调度和基站集群功率分配3个子问题进行求解。通过算例对比分析可知,所提策略可降低通信基站69.86%的用能成本,为提升通信资源利用率和电力系统灵活调节能力提供了有效手段。展开更多
非正交多址接入(Non-Orthogonal Multiple Access,NOMA)技术与设备到设备(Device-to-Device,D2D)通信技术相结合在实现高效频谱利用率和大规模接入上有着突出的优势。针对现有的NOMA-D2D系统存在的信道分配模式单一和D2D组内功率分配难...非正交多址接入(Non-Orthogonal Multiple Access,NOMA)技术与设备到设备(Device-to-Device,D2D)通信技术相结合在实现高效频谱利用率和大规模接入上有着突出的优势。针对现有的NOMA-D2D系统存在的信道分配模式单一和D2D组内功率分配难以获得最优解的问题,构建了以D2D组和速率为优化目标的联合资源分配算法的方案:首先,在子信道分配上,将问题转换为双边匹配问题,提出了一种基于多对一场景下的D2D组信道分配算法;然后运用基于逐次凸逼近的凸差分(Difference of two Convex functions,DC)编程方法求出接近最优的功率分配值。仿真结果表明,提出的多对一场景下信道匹配算法在和速率上明显优于一对一场景下的信道匹配算法,提出的功率分配算法相比起对偶迭代算法更接近最优功率分配。展开更多
文摘Utilizing translation operators we get the powers sums on arithmetic progressions and the Bernoulli polynomials of order munder the form of differential operators acting on monomials. It follows that (d/dn-d/dz) applied on a power sum has a meaning and is exactly equal to the Bernoulli polynomial of the same order. From this new property we get the formula giving powers sums in term of sums of successive derivatives of Bernoulli polynomial multiplied withprimitives of the same order of n. Then by changing the two arguments z,n into Z=z(z-1), λ where λ designed the 1st order power sums and proving that Bernoulli polynomials of odd order vanish for arguments equal to 0, 1/2, 1, we obtain easily the Faulhaber formula for powers sums in term of polynomials in λ having coefficients depending on Z. These coefficients are found to be derivatives of odd powers sums on integers expressed in Z. By the way we obtain the link between Faulhaber formulae for powers sums on integers and on arithmetic progressions. To complete the work we propose tables for calculating in easiest manners possibly the Bernoulli numbers, the Bernoulli polynomials, the powers sums and the Faulhaber formula for powers sums.
文摘Utilizing the translation operator to represent Bernoulli polynomials and power sums as polynomials of Sheffer-type, we obtain concisely almost all their known properties as so as many new ones, especially new recursion relations for calculating Bernoulli polynomials and numbers, new formulae for obtaining power sums of entire and complex numbers. Then by the change of arguments from z into Z = z(z-1) and n into λ which is the 1<sup>st</sup> order power sum we obtain the Faulhaber formula for powers sums in term of polynomials in λ having coefficients depending on Z. Practically we give tables for calculating in easiest possible manners, the Bernoulli numbers, polynomials, the general powers sums.
文摘The analytical calculation of the area moments of inertia used for special mechanical tests in materials science and further generalizations for moments of different orders and broader symmetry properties has led to a new type of trigonometric power sums. The corresponding generalized equations are presented, proven, and their characteristics discussed. Although the power sums have a basic form, their results have quite different properties, dependent on the values of the free parameters used. From these equations, a large variety of power reduction formulas can be derived. This is shown by some examples.
文摘Let <em>p</em> be an odd prime, the harmonic congruence such as <img alt="" src="Edit_843b278d-d88a-45d3-a136-c30e6becf142.bmp" />, and many different variations and generalizations have been studied intensively. In this note, we consider the congruences involving the combination of alternating harmonic sums, <img alt="" src="Edit_e97d0c64-3683-4a75-9d26-4b371c2be41e.bmp" /> where P<em><sub>P </sub></em>denotes the set of positive integers which are prime to <em>p</em>. And we establish the combinational congruences involving alternating harmonic sums for positive integer <em>n</em>=3,4,5.
文摘为了研究对任意素数模p的一类广义Kloosterman和的四次均值,利用初等与解析方法、Gauss和以及三角和的转换性质引入了当素数p≡1 mod 4时该均值的计算问题,并将该类均值转化为特征和的简易形式。从计算结果上对均值的估计具有充分性,从计算方法上对广义Kloosterman和各种形式的四次均值研究具有重要的参考价值。此外,这也为指数和均值计算问题提供了一种新的转化思路与方法,必将对有关问题的进一步探索起到推动作用。
文摘在基于非正交多址接入技术的多用户下行室内可见光通信(Visible light communication system based on non⁃orthogonal multiple access technology,VLC⁃NOMA)系统中,针对和速率与用户公平性冲突的问题,提出一种基于加权和速率最大化的迭代功率分配方案。该方案以最大化加权和速率为目标,可通过改变权重因子来调节用户公平性。由于目标问题属于非凸优化问题,通过辅助变量法和凸优化理论将该非凸问题转化为凹问题,再通过拉格朗日对偶法进行求解,并根据问题的解设计了一种迭代功率分配算法。对所提算法的收敛性、系统和速率以及用户公平性进行了仿真。结果表明,所提迭代功率分配算法具有良好的收敛性,相较于VLC⁃OMA系统,VLC⁃NOMA系统能够获得更好的和速率性能。通过调整权重因子,在牺牲较小系统和速率的情况下能够获得比现有功率分配方案更好的系统和速率与用户公平性。
文摘5G通信基站通常配备光储,数量庞大、功耗可调,是一种优质的电力灵活性调节资源。提出了多类型光储式5G基站集群灵活性资源聚合方法以及参与电网调峰的协同调度策略。首先,分析休眠机制下多类型基站功耗可调特性与计及基站备用电量的储能调节能力。基于极限场景思想,构建了光储式5G基站的灵活性空间量化模型。在此基础上,利用闵可夫斯基和法刻画异构基站柔性资源的时空耦合能量轨迹,得到海量基站集群的灵活性资源聚合可调域。其次,建立了基站集群聚合资源参与电能量市场和辅助服务市场的协同调度优化模型,提出了基于交替方向乘子法(alternating direction method of multipliers, ADMM)的分层分布式基站集群协同优化调度策略,将大规模基站集群调度问题降维分解为统一协同调峰功率响应、聚合功率自治调度和基站集群功率分配3个子问题进行求解。通过算例对比分析可知,所提策略可降低通信基站69.86%的用能成本,为提升通信资源利用率和电力系统灵活调节能力提供了有效手段。
文摘非正交多址接入(Non-Orthogonal Multiple Access,NOMA)技术与设备到设备(Device-to-Device,D2D)通信技术相结合在实现高效频谱利用率和大规模接入上有着突出的优势。针对现有的NOMA-D2D系统存在的信道分配模式单一和D2D组内功率分配难以获得最优解的问题,构建了以D2D组和速率为优化目标的联合资源分配算法的方案:首先,在子信道分配上,将问题转换为双边匹配问题,提出了一种基于多对一场景下的D2D组信道分配算法;然后运用基于逐次凸逼近的凸差分(Difference of two Convex functions,DC)编程方法求出接近最优的功率分配值。仿真结果表明,提出的多对一场景下信道匹配算法在和速率上明显优于一对一场景下的信道匹配算法,提出的功率分配算法相比起对偶迭代算法更接近最优功率分配。
