Invariant Method Research Articles

Lie symmetries, invariant subspace method, and conservation laws for a time fractional generalized Broer–Kaup system

Lie symmetries, invariant subspace method, and conservation laws for a time fractional generalized Broer–Kaup system

Separable solutions of the Black-Scholes equation with three different time fractional-order derivatives

In this work, we use the invariant subspace method to obtain separable solutions for the well-known time-fractional Black-Scholes equation (tF-BSE) under three different kinds of fractional derivatives that are (i) Caputo derivative, (ii) regularized Prabhakar derivative, and (iii) Hilfer derivative. Also, the comparison of the obtained solutions of tF-BSE with those mentioned above three different fractional-order derivatives has been discussed. In addition, this work shows that generalized separable exact solutions include the two- and three-parameters of the Mittag-Leffler, the Euler-gamma, exponential, and polynomial functions. Additionally, we compare the obtained separable solutions in two-dimensional graphically under considered fractional-order derivatives for various values of fractional-order α, α ϵ (0, 1].

Жанрологія в національному мовознавстві: наукова школа Флорія Бацевича

The article summarizes the ideas of linguistic genreology in the context of the philological interpretation of the genre's nature. It is determined that the linguistic objectivity of its analysis is based on the ideas of communicative studies. In Ukrainian linguistics, they are systematically represented in the researches of the scientific school of F. Batsevych. The thesis is argued that his ideas that are related to the linguistic interpretation of the genre, its characteristics and communicative dominants, take into account, first of all, different forms and formats of intentions. The author's comment is given on their verbalization in dynamically changing variants as peculiar patterns of communicative situations, typed structure fixed by cultural tradition, as well as the fact that they acquire individual characteristics in the process of communication. It also defined that F. Batsevych emphasizes on the tactics of implementing of communicative strategies, which are interpreted as separate genres in micro-contexts. It is summarized that the research ideas of F. Batsevych in Ukrainian linguistics have developed into a consistent tradition, realized in the works of his colleagues. It allows us to talk about the formation and active functioning of an authoritative scientific school of linguistic genreology. It was determined that the concept of linguistic genreology, formed and systematically implemented by F. Batsevych in the author's texts and researches of his followers, generalizes the communicative dominants of the genre, which are based on extralinguistic parameters: social conditioning, typicality of the communicative situation, formal features, functionality, stability and variability. It is argued that F. Batsevych's linguistic ideas of genre analysis are meaningfully correlated with the objectivity of media genreology (in the context of functional parallelism with linguistic genreology). It was determined that its prospects lie in the implementation of methodological syncretism of the analysis of language in the dynamics of social communication and its functions in the media, in the emergence of invariant forms and methods of verbal mass interaction, in the motivated renewal of its stylistics and genre system. And this, in turn, determines the vectors that leadto the perspective of the ideas of neolinguistic research.

Mechanical Automation Design and Manufacturing of Production Equipment Combined with Artificial Intelligence Technology and Algorithm Implementation

Abstract This paper explores the impact of artificial intelligence and machine automation on productivity. It focuses on analyzing the production model of machinery automation based on Petri nets. Through the invariant analysis method, the article constructs a model and presents its structure as a correlation matrix. The study results show that the model has an error rate of only 2.26% and an accuracy of 90.14% in terms of operational performance. Regarding time performance, its training time is 3854 seconds and response time is 351 milliseconds, which are better than other algorithms. In the practical application of automotive parts production, the method significantly reduces the busy probability and blocking probability during order processing and material delivery, and also improves the equipment load rate, waiting rate and blocking rate in the production process. This indicates that the Petri net-based method of machine automation production has significant advantages in improving productivity and reducing costs.

Methods of ensuring the invariance of parameters in infocommunication networks in emergency situations to forecasting and random disturbances

Currently, the mode of operation of information and communication networks corresponds to the emergency mode. In this mode, it is necessary to ensure the invariance (insensitivity) of network parameters under random disturbances that actually act on the signal as various interferences. Thus, the main task of the information and communication network is to ensure that the deviation of the parameters from the norm is within acceptable limits. This quality of invariance of the information and communication network must be ensured both for predictable disturbances and unpredictable random facts. Ensuring the invariance of information transmission systems is characterized by such a parameter as noise immunity. The quantitative assessment of noise immunity is the probability of error. The task of ensuring invariance is to preserve the quantitative characterization of the error probability. It is necessary that the error probability be less than the specified one and remain unchanged despite the presence of interference that causes the information transmission system to be unstable in emergency situations. Thus, a given quality of the system’s functioning is achieved due to the invariance of the error probability, its independence from predictable and random unpredictable disturbances. That is, the system will have the properties of invariance. The article presents methods for achieving invariance. Examples are given to illustrate the basic concepts of the theory of invariance and practical methods for building information transmission systems invariant to various interferences in emergency situations.

A ternary mixture model with dynamic boundary conditions.

The influence of short-range interactions between a multi-phase, multi-component mixture and a solid wall in confined geometries is crucial in life sciences and engineering. In this work, we extend the Cahn-Hilliard model with dynamic boundary conditions from a binary to a ternary mixture, employing the Onsager principle, which accounts for the cross-coupling between forces and fluxes in both the bulk and surface. Moreover, we have developed a linear, second-order and unconditionally energy-stable numerical scheme for solving the governing equations by utilizing the invariant energy quadratization method. This efficient solver allows us to explore the impacts of wall-mixture interactions and dynamic boundary conditions on phenomena like spontaneous phase separation, coarsening processes and the wettability of droplets on surfaces. We observe that wall-mixture interactions influence not only surface phenomena, such as droplet contact angles, but also patterns deep within the bulk. Additionally, the relaxation rates control the droplet spreading on surfaces. Furthermore, the cross-coupling relaxation rates in the bulk significantly affect coarsening patterns. Our work establishes a comprehensive framework for studying multi-component mixtures in confined geometries.

Domain of Stability Characterization for Power Systems: A Novel Individual Invariance Method

In this paper, we approach the problem of stability in nonlinear systems through a new perspective that views them as a combination of individual artificial systems carefully chosen to simplify the complex structure of nonlinear systems. This is achieved by recasting nonlinear vector fields as an algebraic sum of individual vector fields for which artificial systems with known invariant sets or at least in forms that allow for tractable approximation of their invariant sets. This attempt to restructure nonlinear systems stands out in comparison to other previous attempts like Lure' systems or network based models as a purely mathematical structuring technique that transcends the physical constraints and dependencies within dynamical models and allows the user to creatively construct artificial systems with the sole focus on the overall stability. The theoretical foundation is provided for a theorem about individual invariance to relate the invariant sets of individual artificial systems to the invariant set of their original system in a way that significantly simplifies the task of approximating regions of attraction. Several examples are used to demonstrate this theorem and we also evaluate the use this theorem for the challenging power system stability problems in both AC and DC grids. The proposed method is successfully applied to the IEEE 39- bus New England system, and a DC converter with constant power load giving accurate and realistic estimations of the critical clearing time and stability regions in comparison to state of the art approaches.

A Noise Invariant Method for Bearing Fault Detection and Diagnosis Using Adapted Local Binary Pattern (ALBP) and Short-Time Fourier Transform (STFT)

A Noise Invariant Method for Bearing Fault Detection and Diagnosis Using Adapted Local Binary Pattern (ALBP) and Short-Time Fourier Transform (STFT)

Human Behavior Recognition Based on CNN-LSTM Hybrid and Multi-Sensing Feature Information Fusion

To address the human activity recognition problem and its application in practical situations, a CNN-LSTM hybrid neural network model capable of automatically extracting sensor data features and memorizing temporal activity data is designed and improved by integrating CNN and gated recurrent units as a variant of RNN. A multi-channel spatiotemporal fusion network-based two-person interaction behavior recognition method is proposed for two-person skeletal sequential behavior recognition. Firstly, a viewpoint invariant feature extraction method is used to extract two-player skeleton features, then a two-layer cascaded spatiotemporal fusion network model is designed, and finally, a multi-channel spatiotemporal fusion network is used to learn multiple sets of two-player skeleton features separately to obtain multi-channel fusion features, and the fusion features are used to recognize the interaction behavior, and the weights are shared among the channels. Applying the algorithm in the paper to the UCF101 dataset for experiments, the accuracy of the two-person cross-object experiment can reach 96.42% and the accuracy of the cross-view experiment can reach 97.46%. The method in the paper shows better performance in two-player interaction behavior recognition compared to typical methods in this field.

Invariant subspace method and exact solutions of the coupled system of time-fractional convection–reaction–diffusion equations

Invariant subspace method and exact solutions of the coupled system of time-fractional convection–reaction–diffusion equations

Formation of conjugate curved surfaces that exclude interference

The object of the study is the method of geometric design of conjugate curved surfaces. The subject of the study is the possibility of achieving the absence of interference of the designed surfaces of kinematic pairs of technical structures, for example, products in mechanical engineering (cutting tools, gearing), based on an invariant method. This problem is of significant importance for a wide class of products, but especially for gears from the point of view of the precision of manufacturing the tooth surface, load-bearing capacity, and, consequently, the reliability and durability of the transmission. When calculating the strength, each tooth of the gear can be considered as a cantilever beam, loaded at the free end by the force of interaction with the second gear wheel. In the presence of interference (for trimming gears), not only the shape of the tooth surface is disrupted, but also the cross-sectional area of the tooth base is significantly reduced. Therefore, solving such a problem is important when designing and manufacturing gears. That is why, when forming the initial curved tool surface of a cutting tool, the conjugacy condition between the points of the product and the tool is taken into account. As a result, when designing a cutting tool using the proposed invariant method using a unified methodology, a wide class of complex curved surfaces can be formed. In particular, this applies to technological operations on numerically controlled machines. The generated conjugate curvilinear transformations of the cutting tool using an invariant method make it possible to avoid interference of mating surfaces at the design stage. At the same time, the curvilinear characteristics of surfaces are analyzed, defining a family of normals as common to two conjugate surfaces with linear contact, which is essential for the design process

Security Analysis of Distribution Network Loop Closure Based on Half Invariant Method

The integration of distributed power sources requires active power systems to raise new concerns about their safety. In order to scientifically and effectively analyze the safety of active distribution network closing current, taking photovoltaic power supply as an example, a closed-loop equivalent model considering the influence of distributed power sources was proposed, and an equation based on the random fluctuation current of new energy sources was derived. On this basis, a semi invariant method is used to solve the random fluctuation variable of the required current, and corresponding indicators are developed based on the principle of closed loop safety to evaluate the safety of the closed loop current. Based on PSCAD and MATLAB platforms, simulation calculations were conducted, and the simulation and calculation values were compared to verify the feasibility and timeliness of the closed-loop security analysis model based on the semi invariant method.

Propagation of magnetogasdynamics spherical shock wave in a gravitating gas with radiation heat flux

This article presents a mathematical model for characterizing the dynamic behavior of spherical shock waves in a self-gravitating, radiating ideal gas with the presence of an azimuthal magnetic field, emphasizing adiabatic conditions. The analysis assumes that the environment just ahead of the shock wave is stationary, and it accounts for variations in density, magnetic field, and fluid velocity within the disturbed medium just behind the shock front. Furthermore, the impact of thermal radiation within the context of an optically thin limit is incorporated into the energy equation of the governing system. Employing the Lie invariance method, the set of partial differential equations governing the flow within this medium is transformed into a system of nonlinear ordinary differential equations through the use of similarity variables. Four distinct cases of similarity solutions are derived by selecting different values for the arbitrary constants associated with the generators. Among these four cases, only two yield similarity solutions, one assuming a power-law shock path and the other an exponential-law shock path. In the case of a power-law shock path, the resulting set of nonlinear ordinary differential equations is numerically solved using the 4th-order Runge-Kutta method in MATLAB software. The article thoroughly discusses the influence of various parameters, including γ (adiabatic index of the gas), Ma−2 (Alfvén–Mach number), ϕ (ambient density exponent), and G0 (gravitational parameter), on the flow properties. The findings are presented graphically to provide a comprehensive understanding of the effects of these parameters.

Diagnosing injection-production system faults in the same well using the rough set-LVQ neural network.

This study proposed a reverse calculation model of the unique rod pump injection and production system structures in the same well to diagnose and resolve defects, after which dynamometer diagrams of the system production and injection pumps were drawn. The invariant moment feature method was applied to identify seven such characteristics in the injection pump power graph, establishing a downhole system for fault diagnosis in rod pump injection and production systems in the same well using Rough Set(RS)-Learning Vector Quantization(LVQ). On the premise of keeping the classification ability unchanged, the Self-Organizing Map(SOM) neural network was used to discretize the original feature data, while RS theory was employed for attribute reduction. After establishing the LVQ fault diagnosis subsystem, the reduced decision table was entered for learning and training. The test results confirmed the efficacy and accuracy of this method in diagnosing downhole faults in rod pump injection-production systems in the same well. After comparing the test results with the actual working conditions, it can be seen that the rod pump injection-production diagnosis system based on RS-LVQ designed in this paper has a recognition rate of 91.3% for fault types, strong recognition ability, short diagnosis time, and A certain practicality. However, the research object of fault diagnosis in this paper is a single fault, and the actual downhole fault situation is complex, and there may be two or more fault types at the same time, which has certain limitations.

Similarity solution for magnetogasdynamic spherical shock wave in a self-gravitating non-ideal radiating gas using lie invariance method

Similarity solution for magnetogasdynamic spherical shock wave in a self-gravitating non-ideal radiating gas using lie invariance method

Optimizing option pricing: Exact and approximate solutions for the time-fractional Ivancevic model

This research investigates the time fractional Ivancevic option pricing model and presents two distinct solution methods: the invariant subspace method for obtaining exact solutions and the residual power series method for generating approximate solutions. In the invariant subspace method, we employ an algebraic approach to solve the time fractional Ivancevic option pricing model. By constructing an appropriate invariant subspace, we derive a system of fractional ordinary differential equations that characterizes the exact solution. This method provides a rigorous and efficient technique for generating various exact solutions. We also propose the residual power series method for obtaining approximate solutions. This method involves expressing the solution as an expansion of power functions and iteratively solving the residual equation to refine the approximation. By truncating the series expansion, we obtain an approximate solution that captures the essential features of the model while balancing computational efficiency and accuracy. Different graphs in 2-dimensions and 3-dimensions are presented to pioneer the obtained solutions. Our findings demonstrate the effectiveness of the invariant subspace method in generating exact solutions and shedding light on the model's dynamics. The residual power series method, on the other hand, provides a flexible and computationally efficient approach for obtaining reliable approximate solutions. The integration of exact and approximate methodologies presents a thorough structure for evaluating and valuing options in the time fractional Ivancevic option pricing model. This comprehensive approach yields valuable understandings for financial professionals and researchers alike.

Analyzing the decision-making process of international trade agreements using Petri nets

Abstract This paper aims to analyze regulatory cooperation in international trade agreements by combining petri net models with intuitionistic fuzzy petri net models. A security information system for international trade agreements combines formal mathematical methods with visual graphics. The correlation matrix and invariants method is utilized to analyze invariants in international trade agreements. The correlation matrix reorganization algorithm is employed to examine correlation factors in the decision-making process of international trade agreements. The results show that the fuzzy Petri net model has the least fluctuation in analyzing the information security posture value of international trade agreements, and the security posture value floats between 6.7 and 7.3. The newest ITA regulation is 0.2 higher than the traditional regulation in consistency, the embodiment of the newest ITA regulation in democracy is 0.75, and the transparency in the newest ITA regulation is increased by 0.3. This paper’s research enhances the useful data and information for analyzing the factors influencing ITAs’ decision-making.

Wavelet transform based image enhancement: A noise reduction approach

<span lang="EN-US">This paper introduces a new thresholding function that mixes the soft thresholding functions and Smoothly Clipped Absolute Deviation (SCAD) for denoising images using the decimated wavelet transform technique, which is widely popular in various applications. The proposed method is applied to denoise noisy images contaminated with additive white Gaussian noise, employing the Top rule. The efficiency of this new thresholding function is also evaluated within the context of the Translation Invariant method. The results are compared with existing methods such as SCAD, soft thresholding, and the Wiener filter-based denoising approach. Parameters such as Root Mean Square Error (RMSE) and Peak Signal Noise Ratio (PSNR) are employed to assess the quality of denoising.</span>

Active flutter suppression of nonlinear fin-actuator system via inverse system and immersion and invariance method

Structural nonlinearities such as freeplay will affect the stability and even flight safety of the fin-actuator system. There is a lack of a practical method for designing Active Flutter Suppression (AFS) control laws for nonlinear fin-actuator systems. A design method for the AFS controller of the nonlinear all-movable fin-electromechanical actuator system is established by combining the inverse system and the Immersion and Invariance (I&I) theory. First, the composite control law combining the inverse system principle and internal model control is used to offset the nonlinearity and dynamics of the actuator, so that its driving torque can follow the ideal signal. Then, the ideal torque of the actuator is designed employing the I&I theory. The unfavorable oscillation of the fin is suppressed by making the output torque of the actuator track the ideal signal. The simulation results reveal that the proposed AFS method can increase the flutter speed of the nonlinear fin-actuator system with freeplay, and a set of controller parameters is also applicable for wider freeplay within a certain range. The power required for the actuator does not exceed the power that can be provided by the commonly used aviation actuator. This method can also resist a certain level of noise and external disturbance.

An commercial area extraction approach using time series nighttime light remote sensing data——Take Wuhan city as a case

The degree of nighttime illumination in a region is closely related to its economic development, therefore, urban commercial areas can be located based on the intensity of the nighttime light. Aiming at the problem of discontinuous and incomparable brightness of nighttime remote sensing images in different periods, a method of urban commercial area extraction based on temporal nighttime remote sensing data is proposed. Firstly, multi- nighttime remote sensing image correction was carried out based on the invariant target region method, and stable time series NPP/VIIRS data set was generated. Secondly, the impervious water surface was extracted by three index synthesis method to obtain the candidate urban commercial area using Landsat-8 image. Finally, multi-scale segmentation and unsupervised classification are carried out on the temporal nighttime remote sensing data set of the candidate area to realize the extraction of urban commercial area. Taking Wuhan city as an example, the method in this paper is used to extract and verify the urban commercial area. The effectiveness and accuracy of the method are verified according to the commercial planning map of Wuhan city and previous studies.