Application of Elzaki Transform Method to Market Volatility Using the Black-Scholes Model

Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.

Research on the Digital Transformation of English Teaching in Vocational Education

With the advancement of technology,exploring the impact of digital transformation on vocational education English teaching has become crucial.This study aims to investigate the effectiveness of digital transformation in English teaching in vocational education in China by exploring students’and teachers’attitudes,views,and experiences on the use of digital technology in English teaching.This study employed a mixed method of qualitative and quantitative analysis.The research results indicate that digital transformation has had a positive impact on vocational education English teaching,as it enhances the teaching process,promotes communication and collaboration,and increases students’enthusiasm and participation.However,implementing digital transformation in vocational education English teaching also poses challenges,including a lack of resources,infrastructure,and training.This study provides an in-depth understanding of the advantages and challenges of digital transformation in vocational education English teaching and proposes strategies to improve the implementation of digital technology in this context.

Improved calibration method for displacement transformation coefficient in optical and visual measurements

Optical and visual measurement technology is used widely in fields that involve geometric measurements,and among such technology are laser and vision-based displacement measuring modules(LVDMMs).The displacement transformation coefficient(DTC)of an LVDMM changes with the coordinates in the camera image coordinate system during the displacement measuring process,and these changes affect the displacement measurement accuracy of LVDMMs in the full field of view(FFOV).To give LVDMMs higher accuracy in the FFOV and make them adaptable to widely varying measurement demands,a new calibration method is proposed to improve the displacement measurement accuracy of LVDMMs in the FFOV.First,an image coordinate system,a pixel measurement coordinate system,and a displacement measurement coordinate system are established on the laser receiving screen of the LVDMM.In addition,marker spots in the FFOV are selected,and the DTCs at the marker spots are obtained from calibration experiments.Also,a fitting method based on locally weighted scatterplot smoothing(LOWESS)is selected,and with this fitting method the distribution functions of the DTCs in the FFOV are obtained based on the DTCs at the marker spots.Finally,the calibrated distribution functions of the DTCs are applied to the LVDMM,and experiments conducted to verify the displacement measurement accuracies are reported.The results show that the FFOV measurement accuracies for horizontal and vertical displacements are better than±15μm and±19μm,respectively,and that for oblique displacement is better than±24μm.Compared with the traditional calibration method,the displacement measurement error in the FFOV is now 90%smaller.This research on an improved calibration method has certain significance for improving the measurement accuracy of LVDMMs in the FFOV,and it provides a new method and idea for other vision-based fields in which camera parameters must be calibrated.

基于残差U-Net和自注意力Transformer编码器的磁场预测方法

利用有限元方法对几何结构复杂的电机和变压器进行磁场分析,存在仿真时间长且无法复用的问题。因此,该文提出一种基于残差U-Net和自注意力Transformer编码器的磁场预测方法。首先建立永磁同步电机(PMSM)和非晶合金变压器(AMT)有限元模型,得到深度学习训练所需的数据集;然后将Transformer模块与U-Net模型结合,并引入短残差机制建立ResUnet-Transformer模型,通过预测图像的像素实现磁场预测;最后通过Targeted Dropout算法和动态学习率调整策略对模型进行优化,解决拟合问题并提高预测精度。计算实例证明,ResUnet-Transformer模型在PMSM和AMT数据集上测试集的平均绝对百分比误差(MAPE)均小于1%,且仅需500组样本。该文提出的磁场预测方法能减少实际工况和多工况下精细模拟和拓扑优化的时间和资源消耗,亦是虚拟传感器乃至数字孪生的关键实现方法之一。

Differential transformation method for studying flow and heat transfer due to stretching sheet embedded in porous medium with variable thickness, variable thermal conductivity,and thermal radiation

This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations （PDEs） are transformed into a system of coupled non-linear ordinary differential equations （ODEs） with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method （DTM）. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.

NONLINEAR TIME TRANSFORMATION METHOD FOR STRONG NONLINEAR OSCILLATION SYSTEMS

In this paper,a nonlinear time transformation method is presented for the analysis of strong nonlinear oscillation systems.This method can be used to study the limit cycle behavior of the autonomous systems and to analyze the forced vibration of a strong nonlinear system.

Analysis and Numerical Computations of the Multi-Dimensional,Time-Fractional Model of Navier-Stokes Equation with a New Integral Transformation

The analytical solution of the multi-dimensional,time-fractional model of Navier-Stokes equation using the triple and quadruple Elzaki transformdecompositionmethod is presented in this article.The aforesaidmodel is analyzed by employing Caputo fractional derivative.We deliberated three stimulating examples that correspond to the triple and quadruple Elzaki transform decomposition methods,respectively.The findings illustrate that the established approaches are extremely helpful in obtaining exact and approximate solutions to the problems.The exact and estimated solutions are delineated via numerical simulation.The proposed analysis indicates that the projected configuration is extremely meticulous,highly efficient,and precise in understanding the behavior of complex evolutionary problems of both fractional and integer order that classify affiliated scientific fields and technology.

On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods

Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analyticalmeans.Thus,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real domain.In this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main steps.First,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo sense.Secondly,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace space.Then the solution of the transformed equation is obtained in Laplace domain.Finally,the solution is converted into the real domain using numerical inversion of Laplace transform.Three inversion methods are evaluated in this paper,and their convergence is also discussed.Three test problems are used to validate the inversion methods.We demonstrate our results with the help of tables and figures.The obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.

On Time Fractional Partial Differential Equations and Their Solution by Certain Formable Transform Decomposition Method

This paper aims to investigate a new efficient method for solving time fractional partial differential equations.In this orientation,a reliable formable transform decomposition method has been designed and developed,which is a novel combination of the formable integral transform and the decomposition method.Basically,certain accurate solutions for time-fractional partial differential equations have been presented.Themethod under concern demandsmore simple calculations and fewer efforts compared to the existingmethods.Besides,the posed formable transformdecompositionmethod has been utilized to yield a series solution for given fractional partial differential equations.Moreover,several interesting formulas relevant to the formable integral transform are applied to fractional operators which are performed as an excellent application to the existing theory.Furthermore,the formable transform decomposition method has been employed for finding a series solution to a time-fractional Klein-Gordon equation.Over and above,some numerical simulations are also provided to ensure reliability and accuracy of the new approach.

Synthesis and Structure Transformation of Orthorhombic LiMnO2 Cathode Materials by Sol-gel Method

Orthorhombic LiMnO2 cathode materials were synthesized successfully at lower temperature by sol-gel method. When LiMnO2 precursor prepared by sol-gel method was fired in air, the product was a mixture of spinel structure LiMn2O4 and rock-salt structure Li2MnO3, whereas in argon single-phase orthorhombic LiMnO2 could obtain at the range of 750℃ to 920℃. The substitution of Mn by Zn2+ or Co3+ in LiMnO2 led to the structure of LiMnO2 transiting to Qα-LiFeO2. The results of electrochemical cycles indicated that the discharged capacity of orthorhombic-LiMnO2 was smaller at the initial stages, then gradually increased with the increasing of cycle number, finally the capacity stabilized to certain value after about 10th cycles. This phenomenon reveals that there is an activation process for orthorhombic LiMnO2 cathode materials during electrochemical cycles, which is a phase transition process from orthorhombic LiMnO2 to tetragonal spinel Li2Mn2O4. The capacity of orthorhombic LiMnO2 synthesized at lower temperature is larger than that synthesized at high temperature.

The Natural Transform Decomposition Method for Solving Fractional Klein-Gordon Equation

In this paper, a coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Klein-Gordan equation. The (NTDM), is introduced to derive the approximate solutions in series form for this equation. Solutions have been drawn for several values of the time power. To identify the strength of the method, three examples are presented.

A three-dimensional transient electromagnetic data inversion method based on a time–frequency transformation

Herein,a three-dimensional(3D)inversion method in the frequency domain based on a time–frequency transformation was developed to improve the efficiency of the 3D inversion of transient electromagnetic(TEM)data.The Fourier transform related to the electromagnetic response in the frequency and time domains becomes a sine or cosine transform under the excitation of downward-step current.We established a transformation matrix based on the digital fi ltering calculation for the sine transform,and then the frequency domain projection of the TEM data was determined from the linear transformation system using the smoothing constrained least squares inversion method,in which only the imaginary part was used to maintain the TEM data transformation equivalence in the bidirectional projection.Thus,the time-domain TEM inversion problem was indirectly and effectively solved in the frequency domain.In the 3D inversion of the transformed frequency-domain data,the limited-memory Broyden–Fletcher–Goldfarb–Shannoquasi–Newton(L-BFGS)method was used and modifi ed with a restart strategy to adjust the regularization parameter when the algorithm tended to a local minimum.Synthetic data tests showed that our domain transformation method can stably project the TEM data into the frequency domain with very high accuracy;furthe rmore,the 3D inversion of the transformed frequency-domain data is stable,can be used to recover the real resistivity model with an acceptable effi ciency.

Leaching and Transformation of Nitrogen Fertilizers in Soil After Application of N with Irrigation: A Soil Column Method

A soil column method was used to compare the effect of drip fertigation (the application of fertilizer through drip irrigation systems, DFI) on the leaching loss and transformation of urea-N in soil with that of surface fertilization combined with flood irrigation (SFI), and to study the leaching loss and transformation of three kinds of nitrogen fertilizers (nitrate fertilizer, ammonium fertilizer, and urea fertilizer) in two contrasting soils after the fertigation. In comparison to SFI, DFI decreased leaching loss of urea-N from the soil and increased the mineral N (NH4+-N + NO3- -N) in the soil. The N leached from a clay loam soil ranged from 5.7% to 9.6% of the total N added as fertilizer, whereas for a sandy loam soil they ranged between 16.2% and 30.4%. Leaching losses of mineral N were higher when nitrate fertilizer was used compared to urea or ammonium fertilizer. Compared to the control (without urea addition), on the first day when soils were fertigated with urea, there were increases in NH4+-N in the soils. This confirmed the rapid hydrolysis of urea in soil during fertigation. NH4+-N in soils reached a peak about 5 days after fertigation, and due to nitrification it began to decrease at day 10. After applying NH4+-N fertilizer and urea and during the incubation period, the mineral nitrogen in the soil decreased. This may be related to the occurrence of NH4+-N fixation or volatilization in the soil during the fertigation process.

集成卷积神经网络和视觉Transformer的隧道掌子面岩性判识研究

为研究综合高效的隧道掌子面岩性智能分类方法,首先,通过收集高铁沿线施工隧道高清掌子面照片、地质素描图及工程地质说明,筛选并统计出灰岩、泥岩、砂岩、玄武岩4种岩性,在此基础上,采用图像增强扩充样本数量并构建岩性样本集;然后,基于上述样本集分别构建ResNet50V2岩性分类迁移模型及VIT岩性分类模型,对比二者岩性分类效果,并采用Stacking方法集成2种模型的分类特点;最后,通过对比3种元学习器(逻辑回归、支持向量机、决策树)对2种模型的集成融合效果来选取最适用的元学习器。结果表明:采用逻辑回归集成ResNet50V2及VIT所构建的集成模型对岩性的分类效果最好,能充分融合掌子面岩性的全、局部特征来进行分类,模型准确率达到93.8%。

基于CNN-Swin Transformer Network的LPI雷达信号识别

针对在低信噪比(SNR)条件下,低截获概率雷达信号调制方式识别准确率低的问题,提出一种基于Transformer和卷积神经网络(CNN)的雷达信号识别方法。首先,引入Swin Transformer模型并在模型前端设计CNN特征提取层构建了CNN+Swin Transformer网络(CSTN),然后利用时频分析获取雷达信号的时频特征,对图像进行预处理后输入CSTN模型进行训练,由网络的底部到顶部不断提取图像更丰富的语义信息,最后通过Softmax分类器对六类不同调制方式信号进行分类识别。仿真实验表明:在SNR为-18 dB时,该方法对六类典型雷达信号的平均识别率达到了94.26%,证明了所提方法的可行性。

Measurement Method of Graviton Velocity and Thought on Correcting Lorentz Transformation——The Superluminal Neutrino’s Influence on Special Relativity and Other Physical Theories

After discovery of the superluminal particle and consideration on development of contemporary physical theory research, also on the existing errors and omissions, the principle of constant light speed is found not a necessary condition in derivation of Lorentz Transformation;instead, this thesis proposes the velocity of graviton may feature superluminal, constant velocity in different directions, and independence of inertial reference frame speeds. This is an optional thought of correction. According serial hypothesis, an equation of graviton’s motion trace, i.e., the central curve of nebula density, is established for spiral galaxy. Thus we gain the method to measure velocity of graviton. If to totally avoid problem of limit speed, we have to search for independent of inertia frames, and relevant to space-time properties. Regarding current difficulties of singular points in the Theory of Limited Universe, this thesis points out that the document [1] is the best solution to these difficulties.

Auto-Backlund Transformation and Extended Tanh-Function Methods to Solve the Time-Dependent Coefficients Calogero-Degasperis Equation

In this paper, the Auto-B?cklund transformation connected with the homogeneous balance method (HB) and the extended tanh-function method are used to construct new exact solutions for the time-dependent coefficients Calogero-Degasperis (VCCD) equation. New soliton and periodic solutions of many types are obtained. Furthermore, the soliton propagation is discussed under the effect of the variable coefficients.

A Study on the Effects of Internal Heat Generation on the Thermal Performance of Solid and Porous Fins using Differential Transformation Method

In this study,the impacts of internal heat generation on heat transfer enhancement of porous fin is theoretical investigated using differential transform method.The parametric studies reveal that porosity enhances the fin heat dissipating capacity but the internal heat generation decreases the heat enhancement capacity of extended surface.Also,it is established that when the internal heat parameter increases to some certain values,some negative effects are recorded where the fin stores heat rather than dissipating it.This scenario defeats the prime purpose of the cooling fin.Additionally,it is established in the present study that the limiting value of porosity parameter for thermal stability for the passive device increases as internal heat parameter increases.This shows that although the internal heat parameter can help assist higher range and value of thermal stability of the fin,it produces negative effect which greatly defeats the ultimate purpose of the fin.The results in the work will help in fin design for industrial applications where internal heat generation is involved.

Mean Square Solutions of Second-Order Random Differential Equations by Using the Differential Transformation Method

The differential transformation method (DTM) is applied to solve the second-order random differential equations. Several examples are represented to demonstrate the effectiveness of the proposed method. The results show that DTM is an efficient and accurate technique for finding exact and approximate solutions.

New Generalized Transformation Method and Its Application in Higher-Dimensional Soliton Equation

一个新概括转变方法被介绍发现更多非线性的部分微分方程的准确答案。作为方法的应用，我们选择(3+1 ) 说明方法的维的碎 soliton 方程。作为结果，明确、准确的 travehng 波浪解决方案的许多类型，包含独居的波浪解决方案，三角法的函数解决方案， Jacobian 椭圆形的函数解决方案，和合理解决方案，被获得。Thenew 方法能在数学物理被扩大到另外的非线性的部分微分方程。