Acknowledging User Requirements for Accuracy in Computational Chemistry Benchmarks

Computational chemistry has become an important complement to experimental measurements. In order to choose among the multitude of the existing approximations, it is common to use benchmark data sets, and to issue recommendations based on numbers such as mean absolute errors. We argue, using as an example bandgaps calculated with density functional approximations, that a more careful study of the benchmark data is needed, stressing that the user's requirements play a role in the choice of an appropriate method. We also appeal to those who measure data capable of being used as a reference, to publish error estimates. We show how the latter can affect the judgment of approximations used in computational chemistry.     

Entanglement propagation and typicality of measurements in the quantum Kac ring

We study the time evolution of entanglement in a new quantum version of the Kac ring, where two spin chains become dynamically entangled by quantum gates, which are used instead of the classical markers. The features of the entanglement evolution are best understood by using knowledge about the behavior of an ensemble of classical Kac rings. For instance, the recurrence time of the quantum many-body system is twice the length of the chain and “thermalization” only occurs on time scales much smaller than the dimension of the Hilbert space. The model thus elucidates the relation between the results of measurements in quantum and classical systems: While in classical systems repeated measurements are performed over an ensemble of systems, the corresponding result is obtained by measuring the same quantum system prepared in an appropriate superposition repeatedly.     

Examination of the dynamic software-supported learning environment in data analysis

The Fatih Project in Turkey has improved software in mathematics teaching such as data analysis software. As a result, the need to inquire into the efficiency of computer-supported learning environments has emerged. This study aims to examine the effect of dynamic data analysis software-supported learning environments on secondary school students’ achievement and attitude. The research method employs a quasi-experimental design with a pre-test, post-test control group. Basic topics related to data analysis were introduced through dynamic statistics software in the experimental group while the students were taught with the help of smart boards, course books and exercises in the control group. Data were collected with an achievement test, attitude scale and semi-structured interviews. Also, interviews were conducted with four students from the experimental group in order to get more detailed information from students. The data gained in the study were analysed both quantitatively and qualitatively. The findings revealed that statistics teaching through statistics software is more efficient than the one with the traditional method on achievement and attitudes. In accordance with this result, it is suggested that computer-supported statistics software should be used in statistics teaching.     

A continuous-state polynomial branching process

A continuous-state polynomial branching process is constructed as the pathwise unique solution of a stochastic integral equation with absorbing boundary condition. The process can also be obtained from a spectrally positive Lévy process through Lamperti type transformations. The extinction and explosion probabilities and the mean extinction and explosion times are computed explicitly. Some of those are also new for the classical linear branching process. We present necessary and sufficient conditions for the process to extinguish or explode in finite times. In the critical or subcritical case, we give a construction of the process coming down from infinity. Finally, it is shown that the continuous-state polynomial branching process arises naturally as the rescaled limit of a sequence of discrete-state processes.     

基于极值理论高龄死亡率模型的比较研究

基于极值理论模型,对中国与日本高龄人口死亡率进行拟合和预测,克服了其他死亡率参数外推模型的主观性.在极值理论高龄死亡率模型的基础上使用加权最小二乘法,通过反复试验方式选择最优门限年龄和模型参数估计值,并且预测中国与日本人口最高年龄以及最高年龄区间估计.此研究为我国经验生命表的编制工作提供借鉴.     

超辐射中的亚泊松光子统计

本文利用推广的Jaynes-Cummings模型描述N个二能级原子的超辐射,得到了辐射场的二阶关联函数的一般表达式。并进而用于缓变耦合情况,着重研究了共振情况下由超泊松光场演化成亚泊松光场的初始条件。作为例子,讨论了推广相干态及压缩相干态的演化条件。最后提出了利用相干态光场观察亚泊松光子统计的实验建议。     

Incomplete Dirichlet integrals with applications to ordered uniform spacings

Sobel, Uppuluri, and Frankowski, (Selected Tables in Math. Statistics, Vol. IV. Amer. Math. Soc., Providence, R. I., 1977) consider an incomplete Dirichlet integral of type I with several interesting applications connected with the multinomial distribution and provide tables of this integral along with other useful tables. Two incomplete Dirichlet integrals are discussed here along with some useful recurrence relations, providing simple methods of deriving the distribution theory of ordered uniform spacings.     

Patterns and estimation of the entropies of formation of fluorine containing aqueous anions

Entropies of formation ( of aqueous fluorine containing anions were shown to follow different entropic patterns than those of oxygen or hydrogen containing anions. Approaches to estimation of the entropies of formation of these anions are based on “simple” entropic patterns, where simple means the use of parameters derived only from the stoichiometry of these species, which are investigated, discussed and commented upon. This article is dedicated to Professor Neil Bartlett, fellow fluorinophile and friend, on the occasion of his 75th birthday.     

Generating and improving orthogonal designs by using mixed integer programming

Analysts faced with conducting experiments involving quantitative factors have a variety of potential designs in their portfolio. However, in many experimental settings involving discrete-valued factors (particularly if the factors do not all have the same number of levels), none of these designs are suitable.In this paper, we present a mixed integer programming (MIP) method that is suitable for constructing orthogonal designs, or improving existing orthogonal arrays, for experiments involving quantitative factors with limited numbers of levels of interest. Our formulation makes use of a novel linearization of the correlation calculation.The orthogonal designs we construct do not satisfy the definition of an orthogonal array, so we do not advocate their use for qualitative factors. However, they do allow analysts to study, without sacrificing balance or orthogonality, a greater number of quantitative factors than it is possible to do with orthogonal arrays which have the same number of runs.