Solving Procedure Research Articles

PERSEPSI MAHASISWA PENDIDIKAN MATEMATIKA TERHADAP MANFAAT APLIKASI PHOTOMATH DALAM MENYELESAIKAN PERSOALAN MATEMATIKA

This research explores how mathematics education students view the benefits of using the Photomath application in solving mathematics problems. The method applied is a qualitative research approach. Information was collected by distributing questionnaires to mathematics education students at the Sultan Syarif Kasim State Islamic University of Riau who had experience using Photomath to help them solve mathematical problems. A total of 30 subjek penetrants were the sample in this research. The collected data was analyzed based on perception themes related to the use of the Photomath application that had been determined by the researcher. The research results show that using the Photomath application is indeed suitable for making it easier for users to understand mathematical solving procedures both in terms of features and performance.

Functional generalized canonical correlation analysis for studying multiple longitudinal variables.

In this paper, we introduce functional generalized canonical correlation analysis, a new framework for exploring associations between multiple random processes observed jointly. The framework is based on the multiblock regularized generalized canonical correlation analysis framework. It is robust to sparsely and irregularly observed data, making it applicable in many settings. We establish the monotonic property of the solving procedure and introduce a Bayesian approach for estimating canonical components. We propose an extension of the framework that allows the integration of a univariate or multivariate response into the analysis, paving the way for predictive applications. We evaluate the method's efficiency in simulation studies and present a use case on a longitudinal dataset.

A non-uniform compound strip method for effective buckling analysis of stiffened structures

In this paper, a versatile compound strip method (CSM) with non-uniform spline functions is developed for buckling analysis of stiffened structures. The proposed method further extends the existing CSM by permitting the flexible modification of local knots to place the stiffeners along the strip arbitrarily. In addition, a reasonable knot arrangement can achieve an accurate solving procedure with improved convergence. The displacements of stiffeners are expressed compatibly by the fundamental parameters of skin according to the beam-plate model. Consequently, the reinforcement of stiffeners is naturally incorporated by adding the beam stiffness matrix to the corresponding strips. Based on the first-order shear deformation plate theory and non-uniform spline functions, the semi-analytical formulations of stiffened structures are established. The present method provides the possibility to achieve the local mesh refinement in the finite strip methods. The convergence and validation study is demonstrated through the comparisons with the results of the existing literature solution and finite element method. In conclusion, a more efficient and applicable CSM is proposed to analyze the buckling behaviors of stiffened structures.

Oscillatory systems with two degrees of freedom and van der Pol coupling: Analytical approach

In this paper steady‐state vibrations of the two‐degrees‐of‐freedom oscillatory systems with van der Pol coupling are investigated. The model is a system of two differential equations with weak nonlinearity. A new solving procedure based on D′Alembert's method and the method of time‐variable amplitude and phase is developed. The main advantage of the method in comparison to others is that it gives the solution of the system of two coupled weak nonlinear equations in the form that is simple to analyze, as it has the same form as the solution of the corresponding system of linear equations. In the paper two types of systems are considered: one, a two‐mass system with two degrees of freedom, and second, the one‐mass system with two degrees of freedom. The torsional vibrations of a two‐mass system and vibrations of a Jeffcott rotor with two‐degrees‐of‐freedom are analyzed. Analytically obtained results are numerically tested. It is obtained that the difference between analytic and numeric results is small and almost negligible. As the accuracy of the analytic solution is high, it is suitable for application in technics and engineering. Conclusions about steady‐state self‐sustainable oscillators, orbital, and limit cycle motions are given.

A spectral collocation scheme for solving nonlinear delay distributed-order fractional equations

The basic purpose of this paper is to implement a variant of the Jacobi–Gauss collocation scheme for solving nonlinear delay (in difference format) fractional differential equations of distributed-order type. At the first stage of the solving procedure, the Legendre–Gauss quadrature rule is implemented to approximate the main problem by a difference delay fractional differential equation of multi-term type. So, one can apply the Jacobi–Gauss collocation approach for localizing the resulting multi-term fractional differential equation with the difference delay factor. Moreover, some special cases of Jacobi–Gauss quadrature rules can be used for approximating the involved integrals in the aforementioned problem. By considering the Lagrange interpolating polynomials, as the numerical solutions, the solution of the main problem can be approximated by solving the associated system of nonlinear algebraic equations in terms of unknown Lagrange multipliers. Convergence analysis of the problem is investigated rigorously under some mild conditions at a spectral rate. Extensive test problems are considered to justify the theoretical analysis.

SRS-Net: a universal framework for solving stimulated Raman scattering in nonlinear fiber-optic systems by physics-informed deep learning

As a crucial nonlinear phenomenon, stimulated Raman scattering (SRS) plays multifaceted roles involved in forward and inverse problems. In fibre-optic systems, these roles range from detrimental interference that impairs optical performance to beneficial effects that enables various devices such as Raman amplifier. To obtain solutions of SRS, various numerical methods customized for different scenarios have been proposed. However, these methods are time-consuming, low-efficiency, and experience-orientated, particularly in combined scenarios consisting of both forward and inverse problems. Inspired by physics-informed neural networks, we propose SRS-Net, which combines the efficient automatic differentiation and powerful representation ability of neural networks with the regularization of SRS physical laws, to obtain universal solutions for SRS of forward, inverse, and combined problems. We showcase the intuitive solving procedure and high-speed performance of SRS-Net through extensive simulations covering different scenarios. Additionally, we validate its capabilities in experiments involving the high-fidelity modelling of a wavelength division multiplexing system spanning the C + L-band with approximately 10 THz. The versatility of the SRS-Net framework extends beyond SRS, indicating its potential as a promising universal solution in other engineering problems with nonlinear dynamics governed by partial differential equations.

Random and harmonic responses of plain woven carbon fiber reinforced conical-conical shell based on machine learning multiscale modelling

This study analyzes the frequency-response characteristics under non-stationary base random acceleration and harmonic points force excitations of plain woven carbon fiber reinforced polymers (PW-CFRP) conical-conical shells comprehensively. Artificial neural network (ANN) based machine learning multiscale modelling strategy is introduced in the process of predicting the mechanical properties of PW-CFRP. The dataset is generated by randomization, linear fitting and two-step homogenization and then trained to generate an ANN to predict the mechanical properties of PW-CFRP. The governing equations of the conical-conical shell under random acceleration excitation are obtained according to the first order shear deformation theory (FSDT) and Hamilton's principle. After the structure is split along the circumference at the excitation points, the harmonic points force excitations are introduced based on the discontinuity condition between conical segments. Generalized differential quadrature (GDQ) is applied during the solving procedure. After comparison studies focusing on the frequency-response characteristics under two types of excitations, two examples on harmonic and random responses of conical-conical shell and conical-cylindrical shell are carried out separately. In this process, the effects of excitation type, excitation and response points, geometric parameters on the frequency-response characteristics are extensively analyzed, which proves efficiency and accuracy of the ANN based machine learning multiscale modelling strategy and the constructed GDQ based computational strategy.

Deep reinforcement learning-based dynamic multi-beam power allocation for GEO-LEO co-existing satellites

This paper first formulates a novel long-term beam power allocation (BPA) problem to tackle the harmful co-linear interference issue in the geostationary earth orbit (GEO) and low earth orbit (LEO) co-existing satellite system. This BPA problem intends to optimize the long-term weighted sum rate of the LEO system while ensuring that GEO user’s received interference from the LEO satellite system is lower than a pre-fixed threshold. To solve it in a real-time manner, a deep reinforcement learning (DRL) framework based on the proximal policy optimization (PPO) algorithm is proposed, named as drlBPA. In addition, for the existing most relevant baseline, the fractional optimization (FO)-based BPA scheme, on the one hand, this paper improves it via a greedy strategy to fully exploit time resource. On the other hand, to further reduce the computational complexity stemming from its iterative solving procedure, a deep neural network approximation scheme is also developed. Simulation results demonstrate that (i) The trained DRL model of the proposed drlBPA scheme has good convergence and generality performance. (ii) Compared with the three FO-based benchmarks, the drlBPA scheme not only achieves the highest throughput of the LEO system within a significantly reduced computation time, but also yields the best system stability.

Robust dynamic train regulation integrated with stop-skipping strategy in urban rail networks: An outer approximation based solution method

In dense urban rail networks with high passenger demands, uncertain disturbances occur frequently, and the resulting train delays will likely spread over the whole network rapidly, hence degrading the service quality offered to passengers. To cope with the uncertainties of frequent disturbances in urban rail networks, this paper proposes a robust train regulation strategy based on the information gap decision theory, which allows the operators to adjust the conservativeness of adjustment schemes flexibly by varying system performances but without the need for prior knowledge of uncertain disturbances. Specifically, considering the coupling relationship between train dynamic flows and passenger dynamic flows, a mixed integer quadratically constrained programming (MIQCP) model is constructed for the robust train regulation problem to generate solutions with immunity against disturbance uncertainties, in which the envelope-bound model is used to characterizing the uncertain sets of disturbances. To meet the real-time requirements of train operation adjustment, a tailored outer approximation algorithm incorporating a two-phase heuristics method is devised to effectively solve the developed robust train regulation model, thereby quickly generating high-quality solutions. Moreover, the warm start technique and domain reduction technique are carefully developed to accelerate the solving procedure. Numerical experiments based on the Beijing metro network illustrate the robustness of the proposed train regulation strategies and the effectiveness of the designed solution approach.

Differential (Pukhov) transform method analysis of transient regimes in electrical circuits

The generalized classical method (GCM) was developed on the basis of the differential Taylor transform method, which was first used by the Ukrainian scientist G.E. Pukhov. In this study, some applications of the GCM to the analysis of transient events in simple electrical circuits are examined. It is shown that, if the solution can be decomposed into a steady-state part and a transient part, the use of the GCM becomes more effective, and the transient regime of the circuit solution can be analyzed without a full solving process of differential equations. The efficiency of the proposed approximation method is illustrated by comparing it with prior arts on similar problems. The results reveal that the proposed method is simple and can be applied successfully for the analysis of both linear and nonlinear problems in mathematical physics by similar solving procedures.

Three-dimensional hygro-thermo-mechanical bending analysis of anisotropic skewed parallelogram plates on a tri-parameter foundation using a wavelet method

In the paper, a brand-new three-dimensional hygro-thermo-mechanical bending model of anisotropic skewed parallelogram plates with extreme skew angle in large deformation supported by a tri-parameter nonlinear elastic foundation is proposed. By investigating the mutual coupled interaction of hygrothermal effects between in-plane distribution and thickness variation, nine kinds of spatially analytical hygrothermal fields in parallelogram domain are established by analyzing the Dirichlet, Neumann and Robin thermal boundary conditions of sinusoidally induced heat conduction at top and bottom surfaces. With coordinate transformation in oblique system considering the Von Kármán membrane strains, the highly coupled and strongly nonlinear governing partial differential equations have been derived. A wavelet solving procedure has been developed with the convergence process validated and precision of obtained solutions verified in good accordance with published results. Parametric studies have been carried out to investigate the large-deflection behavior of simply supported or clamped skew plates on Winkler–Pasternak foundation under combined mechanical and hygrothermal loads. The influence of skew angle, material orthotropy and foundation contact nonlinearity is examined, which reveals the geometrically nonlinear responses of plates are highly affected by large oblique angle, principle orientation of material orthotropy and foundation parameters.

Hydrodynamic performance of vertical cylindrical wave energy absorbers in front of a vertical wall

This paper studies the hydrodynamic performance of vertical cylindrical absorbers in front of a vertical wall. All the absorbers are independent of each other and restricted to only the heave motion. Based on a linear potential flow theory, an analytical solution is developed for the problems of wave diffraction and radiation by absorbers. In the solving procedure, the hydrodynamic problem is first transformed into an equivalent problem in an open water domain using the image principle. The number of absorbers in the equivalent problem is twice that in the real problem, and the plane layout is symmetric about the original vertical wall. The velocity potential of the fluid domain is obtained using the method of variable separation, and the unknown expansion coefficients in the velocity potential are determined by the matched boundary conditions. The heave excitation force, added mass, radiation damping, motion response, and energy capture width of the absorbers are calculated. Case studies are presented to show the effects of the wall reflection and hydrodynamic interaction on the energy extraction performance of the wave energy converter (WEC) system. Subsequently, the WEC performance under the action of irregular waves is analyzed by considering an incident wave spectrum, and the mean annual absorbed power of the device is estimated by considering the wave data statistics at the actual sites. The results indicate that when the wave motion resonates with the absorber motion, the energy extraction performance of the absorbers is significantly improved. The performance of the absorbers can be effectively improved when the structures are close to the antinodes of a standing wave field. By designing a reasonable plane layout, the hydrodynamic interaction can play a constructive role in the performance of the WEC system.

New Accurate Flexural Analysis for Different Types of Plates in a Rectangular Sewage Tank by Utilizing a Unified Analytic Solution Procedure

In the present paper, a modified Fourier series approach is developed for new precise flexural analysis of three different types of concrete plates in a rectangular sewage tank. The bending problems of the bottom plate, side-plate, and the fluid-guiding plate are not easily solved via using the traditional analytic approaches. Based on the Fourier series theory, the present approach provides a unified semi-inverse solving procedure for the above plates by means of choosing three different kinds of Fourier series as the trial functions. Although all the trial functions are quite similar to the classical Navier-form solution, new, precise analytic flexural solutions for plates without Navier-type edge conditions (all edges simply-supported) are achieved, which is mainly attributed to employing the Stoke’s transform technique. For each case, the plate-bending problems are finally altered to deal with linear algebra equations. Furthermore, owing to the orthogonality and completeness of the Fourier series, the obtained solutions perfectly satisfy both the edge conditions and the governing partial differential equation of plates, which paves an easily implemented and rational way for engineers and researchers to provide new, exact designs of plate structures. The main contribution of this study lies in the provision of a unified solution procedure for addressing complex plate-bending problems across diverse boundary conditions. By employing a range of Fourier series types, this approach offers a comprehensive solution framework that accommodates the complexities inherent in plate analysis. The correctness of the present analytic solutions is verified against precise finite element method (FEM) results and ones available in the literature. Finally, the influences of foundation, edge conditions, and aspect ratio on flexural behaviors of plates are discussed in detail.

Sliding Mode Control for Uncertain 2-D FMII Systems Under Stochastic Scheduling.

In this article, the sliding mode control (SMC) problem is addressed for two-dimensional (2-D) systems depicted by the second Fornasini-Marchesini (FMII) model. The communication from the controller to actuators is scheduled via a stochastic protocol modeled as Markov chain, by which only one controller node is permitted to transmit its data at each instant. A compensator for other unavailable controller nodes is introduced by means of previous transmitted signals at two most adjacent points. To characterize the features of 2-D FMII systems state recursion and stochastic scheduling protocol, a sliding function associated with the states at both the present and previous positions is constructed, and a scheduling signal-dependent SMC law is designed. By constructing token- and parameter-dependent Lyapunov functionals, both the reachability of the specified sliding surface and the uniform ultimate boundedness in the mean-square sense of the closed-loop system are analyzed and the corresponding sufficient conditions are derived. Furthermore, an optimization problem is formulated to minimize the convergent bound via searching desirable sliding matrices, meanwhile, a feasible solving procedure is provided by using the differential evolution algorithm. Finally, the proposed control scheme is further demonstrated via simulation results.

A Non-parametric Graph Clustering Framework for Multi-View Data

Multi-view graph clustering (MVGC) derives encouraging grouping results by seamlessly integrating abundant information inside heterogeneous data, and has captured surging focus recently. Nevertheless, the majority of current MVGC works involve at least one hyper-parameter, which not only requires additional efforts for tuning, but also leads to a complicated solving procedure, largely harming the flexibility and scalability of corresponding algorithms. To this end, in the article we are devoted to getting rid of hyper-parameters, and devise a non-parametric graph clustering (NpGC) framework to more practically partition multi-view data. To be specific, we hold that hyper-parameters play a role in balancing error item and regularization item so as to form high-quality clustering representations. Therefore, under without the assistance of hyper-parameters, how to acquire high-quality representations becomes the key. Inspired by this, we adopt two types of anchors, view-related and view-unrelated, to concurrently mine exclusive characteristics and common characteristics among views. Then, all anchors' information is gathered together via a consensus bipartite graph. By such ways, NpGC extracts both complementary and consistent multi-view features, thereby obtaining superior clustering results. Also, linear complexities enable it to handle datasets with over 120000 samples. Numerous experiments reveal NpGC's strong points compared to lots of classical approaches.

The comparing analysis of two parallelization schemes for computations with round memory

In this paper, we consider a tree-like recursion procedure of solving of binary decomposable problems. More specifically, we study some questions of parallelization of this procedure with using of shared round memory. We consider two parallelization schemes for parallel solving of binary decomposable problems by tree-like recursion procedures on a parallel computing system with shared round memory. We call these schemes the TAN-scheme and the TON-scheme of parallelization. We compare the efficiency of these schemes, using different parameters of parallelization. Based on this comparative analysis, we conclude the TON-scheme to be more effective.

Introducing electromagnetic effects in Soledge3X

AbstractIn the pedestal region, electromagnetic effects affect the evolution of micro‐instabilities and plasma turbulence. The transport code Soledge3X developed by the CEA offers an efficient framework for turbulent 3D simulation on an electrostatic model with a fixed magnetic field. The physical accuracy of the model is improved with electromagnetic induction, driven by the local value of the parallel component of the electromagnetic vector potential , known from Ampère's law. It is solved implicitly in a coupled system with the vorticity equation on the electric potential . The consequence is a basic electromagnetic behavior in the form of shear Alfvén waves. A finite electron mass prevents unphysical speeds but requires solving for the time evolution of the parallel current density in the generalized Ohm's law. This term can be analytically included with little computational overhead in the system on and and improves its numerical condition, facilitating the iterative solving procedure. Simulations on a periodic slab case let us observe the predicted bifurcation of the wave propagation speed between the Alfvén wave and the electron thermal wave speeds for varying perpendicular wavenumbers. The first results on a circular geometry with a limiter attest to the feasibility of turbulent electromagnetic scenarios.

Implementing Graph-Theoretic Feature Selection by Quantum Approximate Optimization Algorithm.

Feature selection plays a significant role in computer science; nevertheless, this task is intractable since its search space scales exponentially with the number of dimensions. Motivated by the potential advantages of near-term quantum computing, three graph-theoretic feature selection (GTFS) methods, including minimum cut (MinCut)-based, densest k -subgraph (DkS)-based, and maximal-independent set/minimal vertex cover (MIS/MVC)-based, are investigated in this article, where the original graph-theoretic problems are naturally formulated as the quadratic problems in binary variables and then solved using the quantum approximate optimization algorithm (QAOA). Specifically, three separate graphs are created from the raw feature set, where the vertex set consists of individual features and pairwise measure describes the edge. The corresponding feature subset is generated by deriving a subgraph from the established graph using QAOA. For the above three GTFS approaches, the solving procedure and quantum circuit for the corresponding graph-theoretic problems are formulated with the framework of QAOA. In addition, those proposals could be employed as a local solver and integrated with the Tabu search algorithm for solving large-scale GTFS problems utilizing limited quantum bit resource. Finally, extensive numerical experiments are conducted with 20 publicly available datasets and the results demonstrate that each model is superior to its classical scheme. In addition, the complexity of each model is only O(p n2) even in the worst cases, where p is the number of layers in QAOA and n is the number of features.

ANALYSIS OF CONCEPT UNDERSTANDING IN THE PYTHAGORAS THEOREM AT STUDENTS SMPN 1 KOTABARU

The aims of this study were 1) to analyze the conceptual understanding of students in class VIII F in understanding the Pythagorean theorem and 2) to find out the factors that cause misconceptions in class VIII F students in solving problems regarding the Pythagorean theorem. The approach used in this research is qualitative research. The method used in this research is the descriptive qualitative method. There are 3 subjects in this research. Data was collected using research instruments in the form of learning achievement tests and interviews. The results of the study stated that students' conceptual understanding subject S1 had a high conceptual understanding even though S1 was less thorough in checking answers. Whereas the S3 subject was able to explain the description of the Pythagorean theorem, it's just that the S3 could not continue the solving procedure on the Pythagorean triple problem due to lack of thoroughness, being in a hurry when working on the problem, and not understanding the Pythagorean theorem material. S2 was not able to understand some of the questions presented. It could not continue the completion procedure according to the questions due to not being thorough, easily forgetting the material that had been taught, being in a hurry when working on the questions, and not understanding the questions that had been given.

Efektivitas Budaya Literasi dalam Meningkatkan Keterampilan 4C Siswa UPT SD Negeri 060871 Medan

This research aims to find out how literacy culture influences the 4C skills of elementary school students. This research uses qualitative research methods with a descriptive approach. The descriptive method is a problem solving procedure by describing the condition of the subject or object of research based on facts that are seen as they really are. The data collection technique uses observation and interview techniques. The research results show that the implementation of literacy culture that has been implemented or carried out is quite effective. From the literacy culture implemented, students have begun to have quite good 4C skills, namely Communication, Collaboration, Critical Thinking, and Creativity and Innovation.