Optimal control of delay systems via block pulse functions

The concept of coefficient shift matrix is introduced to represent delay variables in block pulse series. The optimal control of a linear delay system with quadratic performance index is then studied via block pulse functions, which convert the problems into the minimization of a quadratic form with linear algebraic equation constraints. The solution of the two-point boundary-value problem with both delay and advanced arguments is circumvented. The control variable obtained is piecewise constant.     

Wiener–Itô Theorem in Terms of Wick Tensors

Wick tensors are used to describe homogeneous chaos and to define multiple Wiener integrals. The Wiener–Itô decomposition is expressed by the formula $$\varphi (x) = \sum\limits_{n = 0}^\infty {\frac{1}{{n!}}\int_B {[D^n (\mu \varphi )(0)]^ \sim}} (x + iy,...,x + iy)d\mu (y)$$ . We use this formula to interpret Hida's original idea of generalized multiple Wiener integrals as generalized functions acting on the space of test functions.     

A remark on the two dimensional water wave problem with surface tension

We consider the motion of a two-dimensional interface between air (above) and an irrotational, incompressible, inviscid, infinitely deep water (below), with surface tension present. We propose a new way to reduce the original problem into an equivalent quasilinear system which is related to the interface's tangent angle and a quantity related to the difference of tangential velocities of the interface in the Lagrangian and the arc-length coordinates. The new way is relatively simple because it involves only taking differentiation and the real and the imaginary parts. Then if assuming that waves are periodic, we establish a priori energy inequality.     

Max-min of polynomials and exponential diophantine equations

In this paper we study the maximum-minimum value of polynomials over the integer ring Z. In particular, we prove the following: Let F(x,y) be a polynomial over Z. Then, maxx∈Z(T)miny∈Z|F(x,y)|=o(T1/2) as T→∞ if and only if there is a positive integer B such that maxx∈Zminy∈Z|F(x,y)|?B. We then apply these results to exponential diophantine equations and obtain that: Let f(x,y), g(x,y) and G(x,y) be polynomials over Q, G(x,y)∈(Q[x,y]−Q[x])∪Q, and b a positive integer. For every α in Z, there is a y in Z such that f(α,y)+g(α,y)bG(α,y)=0 if and only if for every integer α there exists an h(x)∈Q[x] such that f(x,h(x))+g(x,h(x))bG(x,h(x))≡0, and h(α)∈Z.     

A Simple Approach for Multi‐fidelity Experimentation Applied to Financial Engineering

In practical applications, information about the accuracy or ‘fidelity’ of alternative surrogate systems may be ambiguous and difficult to determine. To address this problem, we propose to treat surrogate system fidelity level as a categorical factor in optimal response surface design. To design the associated experiments, we apply the Expected Integrated Mean Squared Error optimal design criterion, which takes into account both variance and bias errors. The performance of the proposed design was compared using three test cases to four types of alternatives using the Empirical Integrated Squared Error. Because of its ability to foster relatively accurate predictions, the proposed design is recommended in fidelity experimental design, particularly when the experimenters lack sufficient information about the fidelity levels of surrogate systems. The method was applied to the case of intraday trading optimization in which data were collected from the Taiwan Futures Exchange. We also calculated the implied volatility from the Merton's Jump‐diffusion model via the fast Fourier transform algorithm with three different models of varying fidelity levels. Copyright © 2014 John Wiley & Sons, Ltd.     

Exact stability regions for quartic polynomials

Given an arbitrary real quartic polynomial, we find the exact region containing the coefficients of the polynomial such that all roots have absolute values less than 1.     

Secondary Options and Post‐secondary Expectations: Standards‐based Mathematics Programs and Student Achievement on College Mathematics Placement Exams

Research on student achievement within the University of Chicago School Mathematics Project (UCSMP) and Core‐Plus Mathematics Project (CPMP) at the secondary level is beginning to accumulate, however, much less is known about how prepared these students are for post‐secondary education. Therefore this study involving students within one tracked school district used multiple linear regression to examine the role of differential experience within two secondary Standards‐based mathematics programs, gender, and prior mathematics achievement on college algebra and calculus readiness placement test scores. Results show that there are no significant differences between students who had completed three and four years of the CPMP curriculum. UCSMP students with four or five years of experience significantly outperformed CPMP students on both assessments. Prior achievement was a significant predictor of student achievement on both examinations. Male students outperformed female students on the algebra placement exam. Students who had studied from both CPMP and UCSMP significantly outperformed students who had studied from CPMP for four years on the calculus readiness examination.     

Hybrid evolutionary algorithms in a SVR traffic flow forecasting model

Accurate urban traffic flow forecasting is critical to intelligent transportation system developments and implementations, thus, it has been one of the most important issues in the research on road traffic congestion. Due to complex nonlinear data pattern of the urban traffic flow, there are many kinds of traffic flow forecasting techniques in literature, thus, it is difficult to make a general conclusion which forecasting technique is superior to others. Recently, the support vector regression model (SVR) has been widely used to solve nonlinear regression and time series problems. This investigation presents a SVR traffic flow forecasting model which employs the hybrid genetic algorithm-simulated annealing algorithm (GA-SA) to determine its suitable parameter combination. Additionally, a numerical example of traffic flow data from northern Taiwan is used to elucidate the forecasting performance of the proposed SVRGA-SA model. The forecasting results indicate that the proposed model yields more accurate forecasting results than the seasonal autoregressive integrated moving average (SARIMA), back-propagation neural network (BPNN), Holt-Winters (HW) and seasonal Holt-Winters (SHW) models. Therefore, the SVRGA-SA model is a promising alternative for forecasting traffic flow.     

On the origin of the ferromagnetism in Zn0.8Mn0.2O having a higher Curie temperature than Zn0.8Co0.2O

Zn_0.8Co_0.2O and Zn_0.8Mn_0.2O films were deposited on substrates by a sol–gel technique. X-ray diffraction, field-emission scanning electron microscopy, photoluminescence, and ferromagnetism measurements were used to characterize these dilute magnetic semiconductors. It is shown that the ferromagnetic properties might be related to the formation of acceptor-like defects in the Zn_0.8Co_0.2O and Zn_0.8Mn_0.2O films. It is found that ferromagnetic Zn_0.8Mn_0.2O has a higher Curie temperature than Zn_0.8Co_0.2O. In addition, the higher ratio of grain-boundary area to grain volume of Zn_0.8Mn_0.2O than Zn_0.8Co_0.2O indicates that grain boundaries and related acceptors are the intrinsic origin for ferromagnetism.     

Crystal structure,thermal expansion and magnetic properties of Nd2Cu0.8Ge3 compound

A new ternary intermetallic compound, Nd₂Cu_0.8Ge₃, was synthesized and its crystal structure was determined by Rietveld refinement of X-ray powder diffraction data. The Nd₂Cu_0.8Ge₃ compound crystallizes in space group I4₁/amd (No. 141), with a tetragonal a-ThSi₂ structure type, and a=0.41783(2) nm, c=1.43689(9) nm, Z=2 and D_calc=7.466 g/cm³. Using the high temperature powder X-ray diffraction (HTXRD) technique, the lattice thermal expansion behavior of the compound was investigated in the temperature range of 298–648 K, and the result shows that its unit-cell parameters increased anisotropically when temperature increased. The magnetic susceptibility measured in the temperature range of 5–300 K indicated antiferromagnetic order of Nd₂Cu_0.8Ge₃ at low temperatures, and the magnetic susceptibility can be well described over the range of 50–300 K using Curie–Weiss law. The calculated effective magnetic moment (μ_eff) is 3.53 μ_B and dominated by the contribution of the Nd³⁺ ions.