An Improved Version of Residual Power Series Method for Space-Time Fractional Problems

The task of present research is to establish an enhanced version of residual power series (RPS) technique for the approximate solutions of linear and nonlinear space-time fractional problems with Dirichlet boundary conditions by introducing new parameter λ . The parameter λ allows us to establish the best numerical solutions for space-time fractional differential equations (STFDE). Since each problem has different Dirichlet boundary conditions, the best choice of the parameter λ depends on the problem. This is the major contribution of this research. The illustrated examples also show that the best approximate solutions of various problems are constructed for distinct values of parameter λ . Moreover, the efficiency and reliability of this technique are verified by the numerical examples.

Human Position Detection Based on Depth Camera Image Information in Mechanical Safety

The devices used for human position detection in mechanical safety mainly include safety light curtain, safety laser scanner, safety pad, and vision system. However, these devices may be bypassed when used, and human or equipment cannot be distinguished. To solve this problem, a depth camera is proposed as a human position detection device in mechanical safety. The process of human position detection based on depth camera image information is given; it mainly includes image information acquisition, human presence detection, and distance measurement. Meanwhile, a human position detection method based on Intel RealSense depth camera and MobileNet-SSD algorithm is proposed and applied to robot safety protection. The result shows that the image information collected by the depth camera can detect the human position in real time, which can replace the existing mechanical safety human position detection device. At the same time, the depth camera can detect only human but not mobile devices and realize the separation and early warning of people and mobile devices.

Single Reflect-Mirror Laser Communication Tracking-Pointing System Load Technology for Micronanosatellite

In order to realize low-orbit microsatellite laser communication, L- and U-frame structures are designed, respectively, for the payload of single-lens reflex (SLR) laser communication tracking and pointing system. According to the characteristics of each load structure, the detailed system design is carried out, and the modal analysis is carried out on the key structural parts of the L- and U-frames to ensure the reliability of each load structure. The pointing accuracy of the two load structures is also calculated and analyzed. Finally, the conclusion is that both of the two load structures can meet the technical and accuracy requirements of low-orbit communication, but obviously, the U-frame structure has higher accuracy, greater pitching angle, and better reliability; eventually, the U-frame structure is adopted in this design. Then, we have completed the manufacture and assembly of the principle prototype and carried out a vibration test experiment on the principle prototype. The results show that the U-type loading structure SLR laser communication tracking and pointing system achieves the expected design purpose and can meet the technical requirements of the low-orbit microsatellite laser communication.

Motion Feature Retrieval in Basketball Match Video Based on Multisource Motion Feature Fusion

Both the human body and its motion are three-dimensional information, while the traditional feature description method of two-person interaction based on RGB video has a low degree of discrimination due to the lack of depth information. According to the respective advantages and complementary characteristics of RGB video and depth video, a retrieval algorithm based on multisource motion feature fusion is proposed. Firstly, the algorithm uses the combination of spatiotemporal interest points and word bag model to represent the features of RGB video. Then, the directional gradient histogram is used to represent the feature of the depth video frame. The statistical features of key frames are introduced to represent the histogram features of depth video. Finally, the multifeature image fusion algorithm is used to fuse the two video features. The experimental results show that multisource feature fusion can greatly improve the retrieval accuracy of motion features.

Novel Particular Solutions, Breathers, and Rogue Waves for an Integrable Nonlocal Derivative Nonlinear Schrödinger Equation

A determinant representation of the n -fold Darboux transformation for the integrable nonlocal derivative nonlinear Schödinger (DNLS) equation is presented. Using the proposed Darboux transformation, we construct some particular solutions from zero seed, which have not been reported so far for locally integrable systems. We also obtain explicit breathers from a nonzero seed with constant amplitude, deduce the corresponding extended Taylor expansion, and obtain several first-order rogue wave solutions. Our results reveal several interesting phenomena which differ from those emerging from the classical DNLS equation.

G -Chain Mixing and G -Chain Transitivity in Metric G-Space

Firstly, we introduce the concept of G -chain mixing, G -mixing, and G -chain transitivity in metric G -space. Secondly, we study their dynamical properties and obtain the following results. (1) If the map f has the G -shadowing property, then the map f is G -chain mixed if and only if the map f is G -mixed. (2) The map f is G -chain transitive if and only if for any positive integer k ≥ 2 , the map f k is G -chain transitive. (3) If the map f is G -pointwise chain recurrent, then the map f is G -chain transitive. (4) If there exists a nonempty open set U satisfying G U = U , U ¯ ≠ X , and f U ¯ ⊂ U , then we have that the map f is not G -chain transitive. These conclusions enrich the theory of G -chain mixing, G -mixing, and G -chain transitivity in metric G -space.

Superconvergence of Semidiscrete Splitting Positive Definite Mixed Finite Elements for Hyperbolic Optimal Control Problems

In this paper, we consider semidiscrete splitting positive definite mixed finite element methods for optimal control problems governed by hyperbolic equations with integral constraints. The state and costate are approximated by the lowest order Raviart-Thomas mixed rectangular finite element, and the control is approximated by piecewise constant functions. We derive some convergence and superconvergence results for the control, the state and the adjoint state. A numerical example is provided to demonstrate our theoretical results.

Noninteger Derivative Order Analysis on Plane Wave Reflection from Electro-Magneto-Thermo-Microstretch Medium with a Gravity Field within the Three-Phase Lag Model

The present research paper illustrates how noninteger derivative order analysis affects the reflection of partial thermal expansion waves under the generalized theory of plane harmonic wave reflection from a semivacuum elastic solid material with both gravity and magnetic field in the three-phase lag model (3PHL). The main goal for this study is investigating the fractional order impact and the applications related to the orders, especially in biology, medicine, and bioinformatics, besides the integer order considering an external effect, such as electromagnetic, gravity, and phase lags in a microstretch medium. The problem fractional form was formulated, and the boundary conditions were applied. The results were displayed graphically, considering the 3PHL model with magnetic field, gravity, and relaxation time. These findings were an explicit comparison of the effect of the plane wave reflection amplitude with integer derivative order analysis and noninteger derivative order analysis. The fractional order was compared to the correspondence integer order that indicated to the difference between them and agreement with the applications in biology, medicine, and other related topics. This phenomenon has more applications in relation to the biology and biomathematics problems.

Double Sumudu Transform Iterative Method for One-Dimensional Nonlinear Coupled Sine-Gordon Equation

In this paper, the combined double Sumudu transform with iterative method is successfully implemented to obtain the approximate analytical solution of the one-dimensional coupled nonlinear sine-Gordon equation (NLSGE) subject to the appropriate initial and boundary conditions which cannot be solved by applying double Sumudu transform only. The solution of the nonlinear part of this equation was solved by a successive iterative method, the proposed technique has the advantage of producing an exact solution, and it is easily applied to the given problems analytically. Two test problems from mathematical physics were taken to show the liability, accuracy, convergence, and efficiency of the proposed method. Furthermore, the results indicate that the introduced method is promising for solving other types of systems of NLPDEs.

Multifeature Contrast Enhancement Algorithm for Digital Media Images Based on the Diffusion Equation

This paper studies the processing of digital media images using a diffusion equation to increase the contrast of the image by stretching or extending the distribution of luminance data of the image to obtain clearer information of digital media images. In this paper, the image enhancement algorithm of nonlinear diffusion filtering is used to add a velocity term to the diffusion function using a coupled denoising model, which makes the diffusion of the original model smooth, and the interferogram is solved numerically with the help of numerical simulation to verify the denoising processing effect before and after the model correction. To meet the real-time applications in the field of video surveillance, this paper focuses on the optimization of the algorithm program, including software pipeline optimization, operation unit balancing, single instruction multiple data optimization, arithmetic operation optimization, and onchip storage optimization. These optimizations enable the nonlinear diffusion filter-based image enhancement algorithm to achieve high processing efficiency on the C674xDSP, with a processing speed of 25 posts per second for 640 × 480 size video images. Finally, the significance means a value of super pixel blocks is calculated in superpixel units, and the image is segmented into objects and backgrounds by combining with the Otsu threshold segmentation algorithm to mention the image. In this paper, the proposed algorithm experiments with several sets of Kor Kor resolution remote sensing images, respectively, and the Markov random field model and fully convolutional network (FCN) algorithm are used as the comparison algorithm. By comparing the experimental results qualitatively and quantitatively, it is shown that the algorithm in this paper has an obvious practical effect on contrast enhancement of digital media images and has certain practicality and superiority.