A Novel Multivariable MGM (1, m) Direct Prediction Model and Its Optimization

With regard to the traditional MGM (1, m) model having jumping error in solving process, an MGM (1, m) direct prediction model (denoted as DMGM (1, m) model) is proposed and its solution method is put forward at first. Second, considering the inherent time development trend of system behavior sequence is ignored in the DMGM (1, m) model, the DMGM (1, m) model is optimized by introducing a time polynomial term, and the optimized model can be abbreviated as TPDMGM (1, m, φ ) model. Subsequently, it is theoretically proved that the TPDMGM (1, m, φ ) model can achieve mutual transformation with the traditional MGM (1, m) model and the DMGM (1, m) model by adjusting the parameter values. Finally, two case studies about predicting the deformation of foundation pit and Henan’s vehicle ownership have been carried out to validate the effectiveness of proposed models. Meanwhile, the MGM (1, m) model and Verhulst model are established for comparison. Results show that the modeling performance of four models from superior to inferior is ranked as TPDMGM (1, m, φ ) model, DMGM (1, m) model, MGM (1, m) model, and Verhulst model, which on the one hand testifies the correctness of defect analysis of the MGM (1, m) model and on the other hand verifies that the TPDMGM (1, m, φ ) model has advantages in predicting the system variables with mutual relation, mutual restriction, and time development trend characteristic.

A new grey quadratic polynomial model and its application in the COVID-19 in China

This paper develops a new grey prediction model with quadratic polynomial term. Analytical expressions of the time response function and the restored values of the new model are derived by using grey model technique and mathematical tools. With observations of the confirmed cases, the death cases and the recovered cases from COVID-19 in China at the early stage, the proposed forecasting model is developed. The computational results demonstrate that the new model has higher precision than the other existing prediction models, which show the grey model has high accuracy in the forecasting of COVID-19.

Approximate Solutions of the Space-Fractional Diffusion Equations with Additive Noise

In this article we take into account a class of stochastic space diffusion equations with polynomials forced by additive noise. We derive rigorously limiting equations which de…ne the critical dynamics. Also, we approximate solutions of stochastic fractional space di¤usion equations with polynomial term by limiting equations, which are ordinary di¤er-ential equations. Moreover, we address the e¤ect of the noise on the solution’s stabilization. Finally, we apply our results to Fisher’s equation and Ginzburg–Landau models.

A New Approach in Event Studies: Time Varied Analysis

This study proposes a modified market model of event study that takes into account the asynchronous behavior between individual stocks and the stock market by using an added Chebyshev polynomial term. The proposed model takes into account both the macro market performance and the micro individual stock behavior and is empirically tested. The empirical analysis results demonstrate that the proposed model improves the explanatory power of the model as well as the heteroskedasticity. More importantly, its performance is almost independent of the choice of the events and stocks.

A Note on Estimation of Multi-Sigmoidal Gompertz Functions with Random Noise

The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is introduced whose mean function is a curve of this type, concretely a transformation of the well-known Gompertz model after introducing in its expression a polynomial term. The maximum likelihood estimation of the parameters of the model is studied, and various criteria are provided for the selection of the degree of the polynomial when real situations are addressed. Finally, some simulated examples are presented.

Control of Cascaded H-Bridge Multilevel Inverter Based on Optimum Regulation of Switching Angles, and the FPGA Implementation

A new concept in control of cascaded H-Bridge multi-level inverters is proposed in this paper. According to this concept, switching angles are considered to be independent from the fundamental voltage. A polynomial term is presented to show the relation between switching angles and DC voltages. Based on this concept, Total Harmonic Distortion (THD) calculations are updated and proved to be independent from the fundamental voltage. Thus, once calculated for minimum THD, the switching pattern can be used for any required level of output voltage. To examine the effectiveness of the proposed method, it is applied in control of an eleven level inverter. The simulation results are demonstrated and verified through experiments with a setup controlled by Xilinx SPARTAN3 family FPGA (XC3S400-PQG208).

k-Hypergeometric Series Solutions to One Type of Non-Homogeneous k-Hypergeometric Equations

In this paper, we expound on the hypergeometric series solutions for the second-order non-homogeneous k-hypergeometric differential equation with the polynomial term. The general solutions of this equation are obtained in the form of k-hypergeometric series based on the Frobenius method. Lastly, we employ the result of the theorem to find the solutions of several non-homogeneous k-hypergeometric differential equations.

EXACT ASYMPTOTICS OF SAMPLE-MEAN-RELATED RARE-EVENT PROBABILITIES

Relying only on the classical Bahadur–Rao approximation for large deviations (LDs) of univariate sample means, we derive strong LD approximations for probabilities involving two sets of sample means. The main result concerns the exact asymptotics (asn→∞) of$$ {\open P}\left({\max_{i\in\{1,\ldots,d_x\}}\bar X_{i,n} \les \min_{i\in\{1,\ldots,d_y\}}\bar Y_{i,n}}\right),$$with the${\bar X}_{i,n}{\rm s}$(${\bar Y}_{i,n}{\rm s}$, respectively) denotingdx(dy) independent copies of sample means associated with the random variableX(Y). Assuming${\open E}X \gt {\open E}Y$, this is a rare event probability that vanishes essentially exponentially, but with an additional polynomial term. We also point out how the probability of interest can be estimated using importance sampling in a logarithmically efficient way. To demonstrate the usefulness of the result, we show how it can be applied to compare the order statistics of the sample means of the two populations. This has various applications, for instance in queuing or packing problems.