Subitising activity relative to units construction: a case study

Subitising, a quick apprehension of the numerosity of a small set of items, has been found to change from an individual's reliance on perceptual to conceptual processes. In this study, we utilised a constructivist teaching experiment methodology to investigate how the subitising activity of one preschool student, Amy, related to her construction of prenumerical units. Subitising and counting tasks were designed to assess and perturb Amy's thinking relative to her construction of units, and to observe changes in Amy's activity associated with the different tasks. Findings indicate that as Amy's subitising activity changed from perceptual to conceptual, she constructed subitised motor units and subitised figurative units. Implications of this study suggest that the construction of subitised units may support young children's later development of arithmetic units.     

模糊数关于紧承下方图度量的线性性质

证明了紧承下方图度量不是平移不变的.对紧承下方图度量的代数运算的连续性进行了讨论.证明了关于紧承下方图度量,模糊数空间只能是嵌入到拓扑向量空间当中,但不嵌入赋范线性空间当中.并与关于上确界度量的结果进行了比较.最后,给出了一个紧承下方图度量的下界.     

Chapter 3 Translation invariance in data envelopment analysis: A generalization

In this paper, we undertake a revision and a generalization of the results contained in the only paper so far published on the matter of translation invariance by allowing inputs and outputs to take not only zero but negative values. This broadens the field of application of the DEA methodology.     

Another proof of Bianchi's identity in arbitrary bundles

In this paper we relate the group of automorphisms of a principal fibre bundle with the (second) Bianchi identity generalizing a result of Kazdan.During the preparation of this paper the author was supported by a fellowship of theGraduiertenkolleg Geometrie und Mathematische Physik at the Ruhr-Universität Bochum.     

Scaling laws for plasma transport due toη i-driven turbulence

The scale invariance technique has been employed to discuss theη _i-driven turbulent transport under a new fluid model developed by Kimet al [1]. Our analysis reveals that the finite Larmour radius effect plays a decisive role to determine the scaling behaviour of the energy transport under the new fluid model. However, the overall scaling of the transport coefficient remains unchanged as compared to that derived by Connor [2] under the traditional fluid model. The approximations considered by Connor [2] are qualified with additional requirements within the new fluid approach. In the dissipative case, which has not been discussed earlier, additional constraints on the power scaling laws of the transport properties are imposed due to the dissipative mechanisms in the basic governing equations.     

Hölderian Invariance Principle for Triangular Arrays of Random Variables

In this paper, we extend the Hölderian invariance principle of Lamperti [6] to the case of partial-sum processes based on a triangular array of row-wise independent random variables. As an application, we obtain necessary and sufficient conditions for the almost sure (resp. in probability) weak Hölder convergence of partial-sum processes based on bootstrapped samples.     

Is Empty Spacetime a Physical Thing?

This article deals with empty spacetime and the question of its physical reality. By “empty spacetime” we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric objects—themselves intrinsic to the concept of field—might be observable through some physical test. By taking quantum-mechanical notions into account, we challenge the negative conclusion drawn from the diffeomorphism invariance postulate of general relativity, and we propose new foundational ideas regarding the possible observation—as well as conceptual overthrow—of this geometric ether.     

Estimates in the invariance principle in terms of truncated power moments

We obtain estimates for the distributions of errors which arise in approximation of a random polygonal line by a Wiener process on the same probability space. The polygonal line is constructed on the whole axis for sums of independent nonidentically distributed random variables and the distance between it and the Wiener process is taken to be the uniform distance with an increasing weight. All estimates depend explicitly on truncated power moments of the random variables which is an advantage over the earlier estimates of Komlos, Major, and Tusnady where this dependence was implicit.     

A natural value unit—Econophysics as arbiter between finance and economics

Foreign exchange markets show that currency units (= accounting or nominal price units) are variables. Technical and economic progress evidences that the consumer baskets (= purchasing power units or real price units) are also variables. In contrast, all physical measurement units are constants and either defined in the SI (=metric) convention or based upon natural constants (= “natural” or Planck units). Econophysics can identify a constant natural value scale or value unit (natural numeraire) based upon Planck energy. In honor of the economist L. Walras, this “Planck value” could be called Walras (Wal), thereby using the SI naming convention. One Wal can be shown to have a physiological and an economic interpretation in that it is equal to the annual minimal real cost of physiological life of a reference person at minimal activity. The price of one Wal in terms of any currency can be estimated by hedonic regression techniques used in inflation measurement (axiometry). This pilot research uses official disaggregated Swiss Producer and Consumer Price Index (PPI and CPI) data and estimates the hedonic Walras price (HWP), quoted in Swiss francs in 2003, and its inverse, the physical purchasing power (PhPP) of the Swiss franc in 2003.