脉冲时滞细胞神经网络的周期解的存在性

利用重合度理论中的延拓定理和微分不等式技巧,给出了具有状态依赖时滞和分布时滞的脉冲细胞神经网络的周期解的存在性的充分条件.     

一类具阶段结构的Leslie系统正周期解的存在性

考虑一类具有阶段结构和Holling-TannerⅡ类功能反应的Leslie周期系统,利用重合度理论得到该系统正周期解存在的充分条件.     

一类具脉冲效应和单调功能反应的时滞捕食系统的正周期解

利用重合度理论中的延拓定理,获得了一类具有脉冲效应和单调功能反应的时滞捕食系统正周期解存在性的充分条件.最后,通过列举三个例子表示我们等待结果的有效性.     

Coincidence Imaging and interference with coherent Gaussian beams

we present a theoretical study of coincidence imaging and interference with coherent Gaussian beams. The equations for the coincidence image formation and interference fringes are derived, from which it is clear that the imaging is due to the corresponding focusing in the two paths. The quality and visibility of the images and fringes can be high simultaneously. The nature of the coincidence imaging and interference between quantum entangled photon pairs and coherent Gaussian beams are different. The coincidence image with coherent Gaussian beams is due to intensity-intensity correspondence, a classical nature, while that with entangled photon pairs is due to the amplitude correlation a quantum nature. Selected from Acta Sinica Quantum Optica, 2005, 11(4)(in Chinese)     

共振条件下积分边值问题解的存在性

运用Mawhin重合度理论建立了二阶Stieltjes积分边值问题解的存在性定理,其所得结果推广了多点边值问题已有的一些结论。     

时间测度上一类种群动力系统的周期解

在时间测度上研究一类具有时滞和Beddington-DeAngelis功能性反应的n种群食物链系统.利用Mawhin重合度理论建立了这一类系统的正周期解存在的充分性条件,从而使这一类系统的连续时间和离散时间情形即微分方程和差分方程得到了统一研究.     

Coincidences of projections and linear n-valued maps of tori

We prove that the Nielsen fixed point number N(φ) of an n-valued map φ:X?X of a compact connected triangulated orientable q-manifold without boundary is equal to the Nielsen coincidence number of the projections of the graph of φ, a subset of X×X, to the two factors. For certain q×q integer matrices A, there exist “linear” n-valued maps Φn,A,σ:Tq?Tq of q-tori that generalize the single-valued maps fA:Tq→Tq induced by the linear transformations TA:Rq→Rq defined by TA(v)=Av. By calculating the Nielsen coincidence number of the projections of its graph, we calculate N(Φn,A,σ) for a large class of linear n-valued maps.     

“Can you help me count these pennies?”: Surfacing preschoolers’ understandings of counting

ABSTRACT

Capturing the breadth and variety of children’s understanding is critical if studies of children’s mathematical thinking are to inform policy and practice in early childhood education. This article presents an investigation of young children’s counting. Detailed coding and analyses of assessment interviews with 476 preschoolers revealed understandings that would be overlooked by solely assessing the accuracy of their responses. In particular, many children demonstrated understandings of counting principles on a challenging task that were not captured by other, simpler tasks. We conclude that common approaches to capturing young children’s mathematical understanding are likely underestimating their capabilities. This study contributes to researchers’ understanding of what making sense of counting looks and sounds like for preschool age children (3–5 years), the development and relations among counting principles (one-to-one, cardinal, and patterns of the number sequence), and the affordances of challenging, open-ended tasks. We close by considering the implications of recognizing and building from what children know and can do for researchers, practitioners, and policymakers.     

A good foundation for number learning for five-year-olds? An evaluation of the English Early Learning ‘Numbers’ Goal in the light of research

This article sets out to evaluate the English Early Years Foundation Stage Goal for Numbers, in relation to research evidence. The Goal, which sets out to provide ‘a good foundation in mathematics’, has greater breadth of content and higher levels of difficulty than previous versions. Research suggests that the additional expectations are unachievable by the majority of rising fives, but that a more effective foundation to ensure progress and prevent later difficulties would prioritise number sense with numbers to 10, including subitising, numeral comprehension, relative number size, one more/less than and part–whole relationships.     

Random Coincidence Point Theorem in Fréchet Spaces with Applications

Abstract

We proved a random coincidence point theorem for a pair of commuting random operators in the setup of Fréchet spaces. As applications, we obtained random fixed point and best approximation results for *-nonexpansive multivalued maps. Our results are generalizations or stochastic versions of the corresponding results of Shahzad and Latif [Shahzad, N.; Latif, A. A random coincidence point theorem. J. Math. Anal. Appl. 2000, 245, 633–638], Khan and Hussain [Khan, A.R.; Hussain, N. Best approximation and fixed point results. Indian J. Pure Appl. Math. 2000, 31 (8), 983–987], Tan and Yaun [Tan, K.K.; Yaun, X.Z. Random fixed point theorems and approximation. Stoch. Anal. Appl. 1997, 15 (1), 103–123] and Xu [Xu, H.K. On weakly nonexpansive and *-nonexpansive multivalued mappings. Math. Japon. 1991, 36 (3), 441–445].