基于一般学习效应下的单机排序问题

近来具有学习效应的机器排序问题收到广泛的关注.对于机器排序中工件的实际加工来说,与工件加工位置有关的学习模型更具有现实性.本文研究了工件加工位置和与已经加工过的工件之和有关的一般学习效应模型.首先证明文献中与位置和已经加工过的工件加工时间之和有关的学习模型是本模型的特殊情形.其次对于单机排序问题我们提出一般解法.     

Hydrothermal synthesis and characterization of a new three-dimensional hybrid zinc phosphate [Zn2(HPO4)2(4,4′-bipy)]·3H2O with neutral porous framework

Employing 4,4′-bipyridine as a bridged ligand, a new three-dimensional (3-D) hybrid zinc phosphate [Zn₂(HPO₄)₂(4,4′-bipy)]·3H₂O has been prepared under hydrothermal conditions and characterized by single crystal X-ray diffraction. This compound crystallizes in the monoclinic space group C2/c, with cell parameters, , , , β=90.21(3)°, and Z=4. The connectivity of the ZnO₃N and HPO₄ tetrahedra results in a 2-D neutral layer that with interesting 4,8² net along the bc plane. Furthermore, the 4,4′-bipyridine molecule links the 4,8² net into a 3-D structure. The water molecules sit in the middle of the channels and interact with the framework via hydrogen bonds. The compound exhibits intense photoluminescence at room temperature.     

New organically templated gallium oxalate-phosphate structures based on Ga4(PO4)4(C2O4) building unit

Five organic-inorganic hybrid gallium oxalate-phosphates, [Ga₂(PO₄)₂(H₂O)(C₂O₄)_0.5](C₃N₂H₁₂)_0.5(H₂O) (1), [Ga₂(PO₄)₂(C₂O₄)_0.5](C₂N₂H₁₀)_0.5(H₂O) (2), [Ga₂(PO₄)₂(C₂O₄)_0.5](C₃N₂H₁₂)_0.5 (3), [Ga₂(PO₄)₂(H₂PO₄)_0.5(C₂O₄)_0.5](C₄N₃H₁₆)_0.5 (H₂O)_1.5 (4) and [Ga_2.5(PO₄)_2.5(H₂O)_1.5(C₂O₄)_0.5](C₄N₃H₁₅)_0.5 (5), have been synthesized by using 1,3-diaminopropane, ethylenediamine and diethylene triamine as structure-directing agents under hydrothermal condition. The structures of 1-5 are based on Ga₄(PO₄)₄(C₂O₄) building unit made up from Ga₂O₈(C₂O₄) oxalate-bridging dimer and alternating PO₄ and GaO₄ tetrahedral units. Compound 1 is layered structure where the building units link together in the same orientation. Corner sharing of these similar layers result in three-dimensional (3-D) structure 2. However, in compound 3, the building units arrange in a wave-like way to generate two types of eight member ring (8MR) channels. Both 4 and 5 contain the layers where the building units have an opposite orientation. Those layers are linked by H₂PO₄ group and Ga(PO₄)(H₂O)₃ cluster, respectively, to form 3-D frameworks with 12MR large pore channels. Compounds 2-5 exhibit intersecting 3-D channels where the protoned amines are located.     

[Ni(C6N2H14)2][Zn4(H2O)(HPO3)5]: A new open-framework zinc phosphite with intersecting 8-, 12- and 16-ring channels

A new three-dimensional (3-D) zinc phosphite with Zn/P ratio of 4/5, [Ni(C₆N₂H₁₄)₂][Zn₄(H₂O)(HPO₃)₅] (1), has been prepared by using self-assembled nickel complexes as the structure-directing agents. Its structure is built up from strict alternation of ZnO₄ tetrahedra and HPO₃ pseudo-pyramids, resulting in an open framework with multi-directional intersecting 8-, 12- and 16-ring channels. The unique nickel complexes Ni(DACH)₂ (DACH=1,2-diaminocyclohexane) only involving the cis-DACH acting as ligands are self-assembled under hydrothermal conditions, and act as the structure-directing agents (SDAs) to direct the formation of compound 1. Nickel complexes reside in the channels in a manner that the hydrophobic ends of the cis-DACH molecules exclusively protrude into the 16-ring pores and the amino groups closely interact with the charged inorganic framework through weak H-bonds. The interesting arrangements of nickel complexes imply a feasible approach to the design and synthesis of extra-large pore materials.     

Nonlinear approximation using Gaussian kernels

It is well known that nonlinear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently by DeVore and Ron (in press) [2] for homogeneous radial basis function (surface spline) approximations. However, no such results are known for the Gaussian function, the preferred kernel in machine learning and several engineering problems. We introduce and analyze in this paper a new algorithm for approximating functions using translates of Gaussian functions with varying tension parameters. At heart it employs the strategy for nonlinear approximation of DeVore-Ron, but it selects kernels by a method that is not straightforward. The crux of the difficulty lies in the necessity to vary the tension parameter in the Gaussian function spatially according to local information about the approximand: error analysis of Gaussian approximation schemes with varying tension are, by and large, an elusive target for approximators. We show that our algorithm is suitably optimal in the sense that it provides approximation rates similar to other established nonlinear methodologies like spline and wavelet approximations. As expected and desired, the approximation rates can be as high as needed and are essentially saturated only by the smoothness of the approximand.     

A multilevel image thresholding using the honey bee mating optimization

Image thresholding is an important technique for image processing and pattern recognition. Many thresholding techniques have been proposed in the literature. Among them, the maximum entropy thresholding (MET) has been widely applied. In this paper, a new multilevel MET algorithm based on the technology of the honey bee mating optimization (HBMO) is proposed. This proposed method is called the maximum entropy based honey bee mating optimization thresholding (MEHBMOT) method. Three different methods such as the particle swarm optimization (PSO), the hybrid cooperative-comprehensive learning based PSO algorithm (HCOCLPSO) and the Fast Otsu’s method are also implemented for comparison with the results of the proposed method. The experimental results manifest that the proposed MEHBMOT algorithm can search for multiple thresholds which are very close to the optimal ones examined by the exhaustive search method. In comparison with the other three thresholding methods, the segmentation results using the MEHBMOT algorithm is the best and its computation time is relatively low. Furthermore, the convergence of the MEHBMOT algorithm can rapidly achieve and the results validate that the proposed MEHBMOT algorithm is efficient.     

Parameter estimation of delay dynamical system from a scalar time series under external noise

We introduce an adaptive learning rules for estimating all unknown parameters of delay dynamical system using a scalar time series. Sufficient condition for synchronization is derived using Krasovskii-Lyapunov theory. This scheme is highly applicable in secure communication since multiple messages can be transmitted through multiple parameter modulations. One of the advantage of this method is that parameter estimation is also possible even when only one time series of the transmitter is available. We present numerical examples for Mackey-Glass system with periodic delay time which are used to illustrate the validity of this scheme. The corresponding numerical results and the effect of external noise are also studied.     

The development of instructional guidelines for elementary mathematical writing

Mathematical writing recently has been defined as writing to reason and communicate mathematically. But mathematics instructional resources lack guidance for teachers as to how to implement such writing. The purpose of this paper is to describe how methods of design-based research were used to develop an instructional resource when one does not currently exist. Thirty-four participants—including teachers, mathematics coaches, mathematics curriculum developers, literacy coaches, a mathematician, and academics in elementary mathematics education, mathematics education, writing education, and science education—participated in a multi-step process to recommend, revise, and confirm instructional guidelines for elementary mathematical writing. The development process began with thirty-two recommendations from science writing and language arts writing. Through multiple cycles of feedback, five instructional guidelines and related considerations and techniques for implementation of elementary mathematical writing emerged.     

Analysis of proportional reasoning and misconceptions among students with mathematical learning disabilities

We investigated not only the effects of schema-based instruction (SBI) on the mathematical outcomes of seventh-grade students with mathematical learning disabilities (MLD), but also extended prior work to analyze students’ written explanations on open-ended items involving ratio and proportion situations—ratio, proportion, and percent of change problems— to understand the ability to reason about proportions and identify misconceptions. The sample of 338 students with MLD [scored below the 25th percentile on a proportional problem solving (PPS) pretest] was taken from Jitendra, Harwell, Im, et al. (2019), which randomly assigned classrooms to either the SBI or control condition. Students with MLD in SBI classrooms outperformed their counterparts in control classrooms on proportional problem solving and general mathematics problem solving. Similar results, favoring the SBI condition, were found on the open-ended items; however, overall mean scores across pretest, posttest, and delayed posttest were low. Findings provide evidence for the limited understanding of fractional representations of ratios and highlight students’ persistent use of numerical and additive reasoning in explaining their low performance on the open-ended items.