Applying Hybrid ARIMA-SGARCH in Algorithmic Investment Strategies on S&P500 Index

This research aims to compare the performance of ARIMA as a linear model with that of the combination of ARIMA and GARCH family models to forecast S&P500 log returns in order to construct algorithmic investment strategies on this index. We used the data collected from Yahoo Finance with daily frequency for the period from 1 January 2000 to 31 December 2019. By using a rolling window approach, we compared ARIMA with the hybrid models to examine whether hybrid ARIMA-SGARCH and ARIMA-EGARCH can really reflect the specific time-series characteristics and have better predictive power than the simple ARIMA model. In order to assess the precision and quality of these models in forecasting, we compared their equity lines, their forecasting error metrics (MAE, MAPE, RMSE, MAPE), and their performance metrics (annualized return compounded, annualized standard deviation, maximum drawdown, information ratio, and adjusted information ratio). The main contribution of this research is to show that the hybrid models outperform ARIMA and the benchmark (Buy&Hold strategy on S&P500 index) over the long term. These results are not sensitive to varying window sizes, the type of distribution, and the type of the GARCH model.     

The interior proximal extragradient method for solving equilibrium problems

In this article we present a new and efficient method for solving equilibrium problems on polyhedra. The method is based on an interior-quadratic proximal term which replaces the usual quadratic proximal term. This leads to an interior proximal type algorithm. Each iteration consists in a prediction step followed by a correction step as in the extragradient method. In a first algorithm each of these steps is obtained by solving an unconstrained minimization problem, while in a second algorithm the correction step is replaced by an Armijo-backtracking linesearch followed by an hyperplane projection step. We prove that our algorithms are convergent under mild assumptions: pseudomonotonicity for the two algorithms and a Lipschitz property for the first one. Finally we present some numerical experiments to illustrate the behavior of the proposed algorithms.     

Photonic crystal beam splitters

In this work, the beam splitter with two input ports and two output ports in two-dimensional photonic crystals is studied through the finite-difference time-domain method. The beam splitter consists of two orthogonally cross line defects. The diameter of the two diagonal air holes at the intersection of the two line defects was modified. The input light can be identically divided into the two output ports. The beam splitters can be applied in the photonic crystal Mach-Zehnder interferometers or photonic crystal optical switches.     

Effects of surfactants on properties of polymer-coated magnetic nanoparticles for drug delivery application

The objective of this research was to compare the effects of two different surfactants on the physicochemical properties of thermo-responsive poly(N-isopropylacrylamide-acrylamide-allylamine) (PNIPAAm-AAm-AH)-coated magnetic nanoparticles (MNPs). Sodium dodecyl sulfate (SDS) as a commonly used surfactant in nanoparticle formulation process and Pluronic F127 as an FDA approved material were used as surfactants to synthesize PNIPAAm-AAm-AH-coated MNPs (PMNPs). The properties of PMNPs synthesized using SDS (PMNPs-SDS) and PF127 (PMNPs-PF127) were compared in terms of size, polydispersity, surface charge, drug loading efficiency, drug release profile, biocompatibility, cellular uptake, and ligand conjugation efficiency. These nanoparticles had a stable core–shell structure with about a 100-nm diameter and were superparamagnetic in behavior with no difference in the magnetic properties in both types of nanoparticles. In vitro cell studies showed that PMNPs-PF127 were more cytocompatible and taken up more by prostate cancer cells than that of PMNPs-SDS. Cells internalized with these nanoparticles generated a dark negative contrast in agarose phantoms for magnetic resonance imaging. Furthermore, a higher doxorubicin release at 40 °C was observed from PMNPs-PF127, and the released drugs were pharmacologically active in killing cancer cells. Finally, surfactant type did not affect the conjugation efficiency to the nanoparticles when folic acid was used as a targeting ligand model. These results indicate that PF127 might be a better surfactant to form polymer-coated magnetic nanoparticles for targeted and controlled drug delivery.     

On a backward problem for fractional diffusion equation with Riemann-Liouville derivative

In the present paper, we study the initial inverse problem (backward problem) for a two-dimensional fractional differential equation with Riemann-Liouville derivative. Our model is considered in the random noise of the given data. We show that our problem is not well-posed in the sense of Hadamard. A truncated method is used to construct an approximate function for the solution (called the regularized solution). Furthermore, the error estimate of the regularized solution in L² and H^τ norms is considered and illustrated by numerical example.     

Cs(6D5/2)+H2→CsH[ X1Σ+(v,J)]+H转动分辨总截面的测量

利用泵浦-检测方法,在样品池条件下,研究了Cs(6D5/2)与H2反应碰撞传能过程。利用激光感应荧光（LIF）光谱技术,确定了CsH[X1Σ+(v,J)]振转能级上的布居分布,转动态分布与热统计分布基本一致.Cs激发态原子密度由激光能量吸收得到.记录A1Σ+(v',J+1)→X1Σ+(v,J)的时间分辨荧光,从荧光强度的对数值给出的直线斜率确定(v',J+1)→(v,J)的自然辐射率,结合(v,J)→(v',J+1)吸收系数的测量,得到反应生成物CsH[X1Σ+(v,J)]态的分子密度.由速率方程分析,给出反应截面(v,J),对J求和,得到(v)[10-16cm2单位]分别为（0.64±0.19）（v=0）和（0.58±0.17）（v=1）.     

New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained.     

强外加电场与大调制度下光折变动力学光栅形成研究

强外加电场与大调制度在光折变效应的研究中已经得到了广泛应用。采用PDECOL算法,严格求解光折变带输运方程,得到外加电场时不同调制度下光折变晶体中随时间变化的空间电荷场、载流子浓度,并讨论了外加电场对它们的影响。通过将物质方程与耦合波方程联立数值求解,可得到光折变光栅形成过程中两波耦合增益系数以及光束条纹相位的变化。模拟结果表明,在强外加电场作用下,两束记录光之间的光强与相位耦合都得到了增强,而原有的解析式忽视了强外加电场与大调制度对空间电荷场相位耦合的影响,此时不再适用。同时发现折射率光栅与记录光束条纹均发生弯曲,并不再保持平行。     

双中心全息记录的矢量分析与记录方向优化

对描述双掺杂晶体非挥发性全息记录动力学过程的Kukhtarev方程进行了矢量分析,分析中考虑了体光生伏特效应和外加电场的作用。在小信号近似的基础上给出了双中心全息记录中记录与固定阶段空间电荷场的矢量解析解。在综合考虑空间电荷场的各向异性以及晶体有效电光系数的各向异性后,给出了双中心全息记录的优化记录方向。结果表明,对(Fe,Mn)∶LiNbO3晶体633nm寻常光记录,优化记录方向主要由有效电光系数决定,光栅波矢与光轴夹角为22°,方位角为30°;对(Fe,Mn)∶LiNbO3晶体633nm非寻常光记录,优化记录方向主要由固定空间电荷场决定,光栅波矢与光轴夹角为44°,方位角为90°。