光谱辐射照度量值复现中计算大口径固定点黑体拐点温度的新方法

我国光谱辐射照度基准量值复现的理论基础是普朗克定律,它揭示了波长、温度和光谱辐射照度之间存在着精确的定量关系。采用比较法、通过卤钨灯来进行光谱辐射照度量值的保存与传递。其中,黑体的温度测量在量值复现中是最主要的不确定来源。以往都是采用变温黑体作为量值复现的辐射源,其温度通过高温计溯源至温标固定点黑体。为满足我国对地观测、气象遥感、应对气候变化、海洋水色等领域对光谱辐射照度高精度的测量需求,中国计量科学研究院NIM建立了一套14 mm大口径钨碳-碳WC-C高温固定点黑体系统,作为基准辐射源直接复现光谱辐射照度量值,进一步缩短了量值溯源链,减少了温度测量误差。实验中高温计用来测量黑体的相对温度,采用固定点熔化温坪曲线的拐点POI值校准后得到温度绝对值。因此拐点POI的合理评估计算就十分重要。与小口径WC-C固定点黑体不同,大口径固定点的熔化温坪曲线的持续时间更长,但温度起伏也更大,因此广泛用于小口径固定点的传统拐点POI算法不再适用。提出了一种可筛选多次拟合法,用于计算大口径固定点黑体的拐点温度。采用3 mm小口径WC-C和Re-C固定点对新方法的有效性进行验证,结果表明新方法与三种传统方法的平均值的最大偏差为-0.007和-0.001 K,在500 nm引入的光谱辐射照度测量误差分别为0.002 2%和0.000 3%。进一步采用14 mm大口径WC-C大口径固定点对新方法的稳健性进行验证。分析比较了筛选条件、数据平滑处理、拟合范围对拐点POI计算结果的影响,新方法和三种传统POI计算方法的最大影响量分别为0.001和0.633 K,在500 nm引入的光谱辐射照度不确定度分别为0.000 3%和0.20%。所提出的新方法能够有效减小外界因素引入的温度误差,进一步提升光谱辐射照度量值的复现准确度,更适用于大口径高温固定点黑体拐点温度的计算。     

Fuzzy stability of quadratic-cubic functional equations

In this paper, the direct method and the fixed point alternative method are implemented to give Hyers-Ulam-Rassias stability of the functional equation

Approximation of Nearest Common Fixed Point of Nonexpansive Mappings in Hilbert Spaces

The purpose of this paper is to study the convergence problem of the iteration scheme xn＋l = λn＋1y ＋ （1 - λn＋1）Tn＋1xn for a family of infinitely many nonexpansive mappings T1, T2,... in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve some recent results.     

Generalized I-Contractions and Pointwise R-Subweakly Commuting Maps

The existence of common fixed points and invariant approximations for pointwise R- subweakly commuting and compatible maps is established. Our results unify and generalize various known results to a more general class of noncommuting mappings.     

CONVERGENT AND DIVERGENT SOLUTIONS OF TWO-DIMENSIONAL NONLINEAR DIFFERENCE SYSTEM

In this paper, we are concerned with the existence of convergent or divergent solutions of two-dimensional nonlinear difference system of the form (?)xn+1=anxn+bnf(yn), yn=cnyn-1+dng(xn). We classify their solutions according to asymptotic behavior and give some sufficient and necessary conditions for the existence of solutions of such classes by using the method of the fixed point theorem. We also give an example and show how the results can he applied to certain difference systems.     

Multiple positive solutions for a class of nonlinear four-point boundary value problem with <Emphasis Type="Italic">p</Emphasis>-Laplacian

This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：
{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1,
αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,
where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.     

Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings

In this work we prove a new strong convergence result of the regularized successive approximation method given by yn＋1 = qnz0 ＋ （1 - qn）T^nyn, n = 1, 2,…,where lim n→∞ qn = 0 and ∞∑n=1 qn=∞ for T a total asymptotically nonexpansive mapping, i.e., T is such that
││T^n x - T^n y││ ≤ x - y ││ ＋ kn^（1）φ（││x - y││） ＋ kn^（2）,where kn^1 and kn^2 are real null convergent sequences and φ：R^＋→R^＋ is continuous such that φ（0）=0 and limt→∞φ（t）/t≤ C for a certain constant C 〉 0.
Among other features, our results essentially generalize existing results on strong convergence for T nonexpansive and asymptotically nonexpansive. The convergence and stability analysis is given for both self- and nonself-mappings.     

TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem: -u′′(t) = λf(t, u(t)) for all t ∈ (0, 1) subjecting to u(0) = 0 and αu(η) = u(1), where η∈ (0, 1), α∈ [0, 1), and λ is a positive parameter. The nonlinear term f(t, u) is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ* ∈ (0, +∞], such that the above problem has at least two positive solutions for any λ∈ (0, λ*) under certain conditions on the nonlinear term f.     

Solutions to BSDEs driven by both standard and fractional Brownian motions

The backward stochastic differential equations driven by both standard and fractional Brownian motions (or, in short, SFBSDE) are studied. A Wick-Itô stochastic integral for a fractional Brownian motion is adopted. The fractional Itô formula for the standard and fractional Brownian motions is provided. Introducing the concept of the quasi-conditional expectation, we study some its properties. Using the quasi-conditional expectation, we also discuss the existence and uniqueness of solutions to general SFBSDEs, where a fixed point principle is employed. Moreover, solutions to linear SFBSDEs are investigated. Finally, an explicit solution to a class of linear SFBSDEs is found.     

FIXED POINTS AND STABILITY FOR QUARTIC MAPPINGS IN β-NORMED LEFT BANACH MODULES ON BANACH ALGEBRAS

The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.