基于三阶和四阶龙格库塔法的GM(1,1)模型优化及应用

为提高GM(1,1)模型的预测精度,提出了应用三阶和四阶龙格库塔法对GM(1,1)模型的建模过程进行优化.给出了优化模型,并讨论了两种优化模型中发展系数的变化对其精度的影响.实例表明,基于三阶和四阶龙格库塔法所建立的GM(1,1)模型,可以有效地提高模型的预测精度和适用性.     

基于复化Simpson公式的GM(1,1)模型背景值优化

针对传统灰色模型GM(1,1)存在的模型精度不高的问题,提出了复化Simpson公式结合动态序列模型的联合方法.给定误差限,利用给出的计算背景值算法,对GM(1,1)模型的背景值进行优化.实例表明,基于复化Simpson公式的背景值优化算法所建立的GM(1,1)模型,可以有效地提高模型的预测精度和适用性.     

优化灰导数白化值的无偏灰色GM(1,1)模型

通过优化灰导数白化值 ,建立了无偏的 GM(1,1)模型 ,给出了估计模型参数的方法 ,证明了无偏GM(1,1)模型具有白指数律重合性 ,提出了新的预测公式 .实例分析表明 ,新方法提高了模型的精度 ,扩大了模型的适用范围 .     

灰色预测模型的优化及应用

针对GM(1,1)模型在不同初始条件下预测精度不同的问题,在同一准则下,给出了两种不同初始条件下GM(1,1)优化模型的预测公式.在此基础上,证明出在同一准则下两种优化模型的模拟预测值相等,且都能获得较高的模拟预测精度.最后选取2006-2011年河南省城镇居民人均收入实际值为依据,建立GM(1,1)优化模型,并预测出2012、2013年河南省城镇居民人均收入,为相关决策部门提供了理论依据.     

改进灰导数的GM(1,1)幂模型

为了提高灰色GM(1,1)幂模型的拟合精度,讨论了灰色GM(1,1)幂模型灰导数的白化问题.以白化微分方程为基础,利用梯形公式白化灰导数,得到了改进的GM(1,1)幂模型.实例分析结果表明改进的GM(1,1)幂模型具有更高的预测和拟合精度.     

基于改进的GM(1,1)-BP组合模型的人口预测研究

准确地预测人口总量发展趋势,对我国社会稳定发展具有重要意义.通过分析GM(1,1)模型背景值的构造理论,利用Newton插值公式和线性分段函数优化GM(1,1)模型的背景值,得到新的GM(1,1)模型,并结合BP神经网络模型,再利用遗传算法优化GM(1,1)-BP组合模型的权重系数,并将组合模型应用到新疆人口预测中.最后,分别应用不同的模型,以及改进的GM(1,1)-BP组合模型进行计算和平均相对误差对比,结果表明,改进的GM(1,1)-BP组合模型有效地提高了预测精度.     

基于机场货运预测的GM(1,1)建模过程问题分析

运用灰色系统GM(1,1)模型进行预测时,模拟精度和预测精度是关注的焦点.对原始数据构造缓冲算子和进行完整的前期检验,运用等维灰数递补的动态建模方法,针对误差建立残差修正模型,都可以提高预测的可信度.通过归纳建模各阶段可能出现的典型问题以及解决方法,以期对建立优化模型有所帮助.最后建立GM(1,1)模型预测天津滨海机场货邮吞吐量.     

新息累积非等间距GM(1,1)模型研究

为提高非等间距GM(1,1)模型的模拟效果和预测精度,在传统的累积非等间距GM(1,1)模型中结合了新息思想,对新息累积非等间距GM(1,1)模型的初始条件进行改进,并对参数的有效区间进行了讨论.仿真实例表明了改进后模型的有效性和高效性.     

GM(1,1)模型灰色作用量的优化

通过把GM(1,1)模型中的灰色作用量b改进为动态的b_1+b_2k,从而构建了对灰色作用量优化的GM(1,1)模型.通过实例的验证以及与GM(1,1)模型对比,发现优化的GM(1,1)模型的模拟精度和预测精度均较高.     

基于粒子群优化的分数阶PFGM(1,1)模型在建筑物沉降预测中的应用

针对传统的灰色预测模型对建筑物沉降预测精度不高、拟合数据较差的问题,在传统的GM(1,1)模型基础上提出了分数阶建模的思想,采用粒子群优化算法求解最优分数阶次,建立基于粒子群优化的分数阶PFGM(1,1)模型.实例计算表明,分数阶FGM(1,1)模型可以提高建筑物沉降的预测精度,通过粒子群优化算法选取最优阶次可以进一步提高预测精度和误差检验等级.由此可见,基于粒子群优化的分数阶PFGM(1,1)模型对建筑物的沉降控制有着重要的指导作用.     

An automatic multistep method for solving stiff initial value problems

A multistep method with matricial coefficients is developed. It can be used to solve stiff initial value problems of the form y′ = Ay + g(x, y). This method bears the nature of the classical Adams—Bashforth—Moulton PC formula and can be shown to be consistent, convergent and A-stable. A careful reformulation of this method legitimatizes the implementation of this algorithm in a variable-step variable-order fashion. Numerical test results from a PECE mode of this method show its possible advantages.     

New Families in the Stable Homotopy of Spheres Revisited

This paper constructs a new family in the stable homotopy of spheres π _{t −6} S represented by h _n g ₀γ₃∈E ^{6 t} ₂ in the Adams spectral sequence which revisits the b _{n −1} g ₀γ₃-elements ∈π _{t −7} S constructed in [3], where t = 2p ⁿ (p− 1) + 6(p ² + p + 1)(p− 1) and p≥ 7 is a prime, n≥ 4. Received October 7, 1998, Revised May 8, 2000, Accepted August 8, 2000.     

Adams operations on higherK-theory

We construct Adams operations on higher algebraicK-groups induced by operations such as symmetric powers on any suitable exact category, by constructing an explicit map of spaces, combinatorially defined. The map uses theS-construction of Waldhausen, and deloops (once) earlier constructions of the map.Supported by NSF grant DMS 90-02715     

A conjecture of M. J. Taylor concerning determinantal congruences

Let G be a finite group. The class group of the group ring of G is a quotient of the idèlic homomorphisms of R(G) by the global functions and the determinantal functions. Using Explicit Brauer Induction, we prove Adams operations, applied to determinantal functions, satisfy some congruences which were conjectured by M. J. Taylor. As an application, we construct some new maps defined on the class group.In memory of J. Frank Adams (1930–1989)Research partially supported by NSERC Grant # 0GP0042580.     

球面稳定同伦群中第三周期γ类非平凡新元素

本文研究了球面稳定同伦群的问题.以Adams谱序列中的第二非平凡微分为几何输入,给出了球面稳定同伦群中h₀g_n（n > 3）的收敛性.同时,由Yoneda乘积的知识,发掘了球面稳定同伦群中的一个非平凡新元素.非平凡元素的范围将被我们的结果进一步扩大.     

Geometric realization of Adams maps

Let G/P be a homogenous space with G a compact connected Lie group and P a connected subgroup of G of equal rank. As the rational cohomology ring of G/P is concentrated in even dimensions, for an integer k we can define the Adams map of type k to be l _k : H*(G/P, ℚ) → H*(G/P, ℚ), l _k (u) = k ⁱ u, u ∈ H ²ⁱ (G/P, ℚ). We show that if k is prime to the order of the Weyl group of G, then l _k can be induced by a self map of G/P. We also obtain results which imply the condition that k is prime to the order of the Weyl group of G is necessary.     

Extremal Functions for Adams Inequalities in Dimension Four

Let $\Omega\subset \mathbb{R}^4$ be a smooth bounded domain, $W_0^{2,2}(\Omega)$ be the usual Sobolev space. For any positive integer $\ell$, $\lambda_{\ell}(\Omega)$ is the $\ell$-th eigenvalue of the bi-Laplacian operator. Define $E_{\ell}=E_{\lambda_1(\Omega)}\oplus E_{\lambda_2(\Omega)}\oplus\cdots\oplus E_{\lambda_{\ell}(\Omega)}$, where $E_{\lambda_i(\Omega)}$ is eigenfunction space associated with $\lambda_i(\Omega)$. $E^{\bot}_{\ell}$ denotes the orthogonal complement of $E_\ell$ in $W_0^{2,2}(\Omega)$. For $0\leq\alpha<\lambda_{\ell+1}(\Omega)$, we define a norm by $\|u\|_{2,\alpha}^{2}=\|\Delta u\|^2_2-\alpha \|u\|^2_2$ for $u\in E^\bot_{\ell}$. In this paper, using the blow-up analysis, we prove the following Adams inequalities$$\sup_{u\in E_{\ell}^{\bot},\,\| u\|_{2,\alpha}\leq 1}\int_{\Omega}e^{32\pi^2u^2}{\rm d}x<+\infty;$$moreover, the above supremum can be attained by a function $u_0\in E_{\ell}^{\bot}\cap C^4(\overline{\Omega})$ with $\|u_0\|_{2,\alpha}=1$. This result extends that of Yang (J. Differential Equations, 2015), and complements that of Lu and Yang (Adv. Math. 2009) and Nguyen (arXiv: 1701.08249, 2017).     

A Potential Theoretic Inequality

In this paper is proved a weighted inequality for Riesz potential similar to the classical one by D. Adams. Here the gain of integrability is not always algebraic, as in the classical case, but depends on the growth properties of a certain function measuring some local potential of the weight.     

The convergence of\tilde a_s^{(n)} h_0 h_k

It is proved that (i) for survives to E∞; (ii) for survives to E∞. Project supported by the Doctoral Program Foundation of China.     

A delay differential equation solver based on the parallel Adams algorithms

IntroductionWith the rapid development of science and technology, a lot of delay-dynamic systems invarious fields of natural and social science have arisentl]. The presented delay systems are oftenof both multiparameter and largescale, that is, so-called large systems. Considering scientificcomputation and real-time simulation, the classical serial algorithmsIZ--4] have not fulfilled therequirements for solying this kind of systems. So, it becomes quite emergent to construct thefast algorithm…