One-dimensional Research Articles

БІРӨЛШЕМДІ КОНСЕРВАТИВТІ ЖҮЙЕНІ ЗЕРТТЕУ ӘДІСІ

The article examines the movements of systems with equal degrees of freedom in a potential, stationary external field using the laws of theoretical mechanics. In order to study the system, the following generalized form of the Lagrange function was used [1,2]: If the force F acting on a particle depends only on the x coordinate, the Lagrange function is transformed as follows [1,2]: где, , , . We have written down the Lagrange equation for plane mathematical, physical, and cyclonic pendulums as follows [3,4]: +mgl где, , +mg l The moment of inertia compared to the axis of rotation J, the distance to the center of mass with the axis of rotation l, for the case under consideration , J , . For any conservative system, the law of conservation is respected: The motion of a particle in one-dimensional space is investigated using the Lagrange function and the laws of conservation of energy.

Triplet Epipolar Images for Spaceborne Three Linear Cameras

Abstract. Epipolar images can reduce conjugate points searching from a two-dimensional to a one-dimensional space, which significantly improves the robustness and efficiency of dense matching. However, two images matched the lack of redundancy and suffered from occlusions. The third image could introduce two more stereos and improve the accuracy and completeness of the three-dimension reconstruction, which were adopted by spaceborne three linear cameras (TLCs), the ALOS PRSIM and ZY-3. In this study, we propose a new triplet epipolar images generation method for spaceborne TLCs. Triplet epipolar images were defined as any two of the three epipolar image pairs. The triplet epipolar geometry requires the imaging rays of any conjugate point to be coplanar. For high-resolution satellite images, parallel projection can be used to approximate the imaging geometry of satellite images. Therefore, a coplanar principal optical axis is a fundamental requirement for spaceborne TLCs. We propose a general workflow to generate triplet epipolar images (TEIs), which includes free-net bundle adjustment of TLCs, building a triplet epipolar geometry, correcting the y-parallaxes, and generating a rational function model (RFM) for TEIs. The ZY3-02 satellite images were used to validate the proposed method. The root means square error (RMSEs) of the free-net bundle adjustment in the image space was 0.185 pixels, which proved the fine intrinsic accuracy. After compensation, the RMSEs of the y parallaxes of the three epipolar image pairs were 0.295, 0.310, and 0.370 pixels. Owing to the simple geometry of the TEIs, the RMSEs of the RFM replacements were within 0.001 pixels.

Numerical Study of Time-Fractional Schrödinger Model in One-Dimensional Space Arising in Mathematical Physics

This study provides an innovative and attractive analytical strategy to examine the numerical solution for the time-fractional Schrödinger equation (SE) in the sense of Caputo fractional operator. In this research, we present the Elzaki transform residual power series method (ET-RPSM), which combines the Elzaki transform (ET) with the residual power series method (RPSM). This strategy has the advantage of requiring only the premise of limiting at zero for determining the coefficients of the series, and it uses symbolic computation software to perform the least number of calculations. The results obtained through the considered method are in the form of a series solution and converge rapidly. These outcomes closely match the precise results and are discussed through graphical structures to express the physical representation of the considered equation. The results showed that the suggested strategy is a straightforward, suitable, and practical tool for solving and comprehending a wide range of nonlinear physical models.

Simulation of association rule mining based on sensor networks in Chinese language learning recommendation system for college students

Based on the increasing learning needs of students that cannot be met by traditional education in schools, the use of online learning platforms has become a way for many college students to learn Chinese, thereby improving their academic performance and literary literacy. However, it is difficult to guarantee the service quality of online platforms for Chinese learning at present, so this paper proposes an association rule mining algorithm to strengthen Chinese online learning. We using user service quality as a constraint to improve spectrum utilization and energy efficiency, and defining the user state space, borrowing the obtained resource allocation optimization function to reward a small portion of users' communication costs, ultimately obtaining user state space information and one-dimensional state space data. This algorithm performs grouping operations on the data estimated by a large amount of computation, and divides the data into balanced categories to reduce the amount of input data in the network. The performance test results show that this paper has made a great breakthrough in the personalization of Chinese learning, and has outstanding performance in the processing and classification of Big data. There are also some solutions to the problem of too much existing data. In a period of use experience analysis report, we found that the online platform for Chinese learning can give consideration to students' personalized needs and experience.

Random walk simulation by population dynamics P systems

PDP systems have been widely used for real-life applications, such as systems biology, ecosystems, physics or economy, among others. Complex systems related with these areas are simulated in the framework of Membrane Computing using objects and membranes that can represent entities or places in the real-life process. In physics, the study of a particle in different fluids, depending on their composition, is really interesting for several applications. A first approximation to this field is to think that particles move randomly in the available space, without any force that constrains their movements. This behavior is known as random walk, and it is used not only in physics but in economics, genetics, and ecology among other areas. In this paper, we introduce generic PDP systems for simulating the behavior of particles, both for one-dimensional spaces and for two-dimensional spaces, using different simulators to analyze the computational resources consumed.

Augmented projection Wasserstein distances: Multi-dimensional projection with neural surface

The Wasserstein distance is a fundamental tool for comparing probability distributions and has found broad applications in various fields, including image generation using generative adversarial networks. Despite its useful properties, the performance of the Wasserstein distance decreases when data is high-dimensional, known as the curse of dimensionality. To mitigate this issue, an extension of the Wasserstein distance has been developed, such as the sliced Wasserstein distance using one-dimensional projection. However, such an extension loses information on the original data, due to the linear projection onto the one-dimensional space. In this paper, we propose novel distances named augmented projection Wasserstein distances (APWDs) to address these issues, which utilize multi-dimensional projection with a nonlinear surface by a neural network. The APWDs employ a two-step procedure; it first maps data onto a nonlinear surface by a neural network, then linearly projects the mapped data into a multidimensional space. We also give an algorithm to select a subspace for the multi-dimensional projection. The APWDs are computationally effective while preserving nonlinear information of data. We theoretically confirm that the APWDs mitigate the curse of dimensionality from data. Our experiments demonstrate the APWDs’ outstanding performance and robustness to noise, particularly in the context of nonlinear high-dimensional data.

Discrete tensor product BGG sequences: Splines and finite elements

In this paper, we provide a systematic discretization of the Bernstein-Gelfand-Gelfand diagrams and complexes over cubical meshes in arbitrary dimension via the use of tensor product structures of one-dimensional piecewise-polynomial spaces, such as spline and finite element spaces. We demonstrate the construction of the Hessian, the elasticity, and div ⁡ div \operatorname {div}\operatorname {div} complexes as examples for our construction.

Model-free method for LQ mean-field social control problems with one-dimensional state space

Model-free method for LQ mean-field social control problems with one-dimensional state space

Probabilistic Context Neighborhood model for lattices

We present the Probabilistic Context Neighborhood model designed for two-dimensional lattices as a variation of a Markov random field assuming discrete values. In this model, the neighborhood structure has a fixed geometry but a variable order, depending on the neighbors’ values. Our model extends the Probabilistic Context Tree model, originally applicable to one-dimensional space. It retains advantageous properties, such as representing the dependence neighborhood structure as a graph in a tree format, facilitating an understanding of model complexity. Furthermore, we adapt the algorithm used to estimate the Probabilistic Context Tree to estimate the parameters of the proposed model. We illustrate the accuracy of our estimation methodology through simulation studies. Additionally, we apply the Probabilistic Context Neighborhood model to spatial real-world data, showcasing its practical utility.

On the symmetry algebra of a one-dimensional quantum-mechanical oscillator on a hyperbola

The quantum-mechanical problem of a harmonic oscillator on a hyperbola as a one-dimensional space of constant negative curvature is considered in this article. A generalization to the singular oscillator model in the context of one-dimensional Cayley – Klein geometries is given by the factorization method. The energy spectrum and wave functions of stationary states are found having the curvature of space as a parameter. For the energy levels of the singular oscillator, the effect of non-zero curvature is clearly manifested through a positive or negative term, depending on the sign of the curvature, which is quadratic in the level number. The results obtained are consistent with those previously published. The dynamical symmetry of the problem is shown explicitly as a quadratic Hahn algebra QH(3) or its isomorphic Higgs algebra.

A sub-grid scale model for Burgers turbulence based on the artificial neural network method

The present study proposes a sub-grid scale model for the one-dimensional Burgers turbulence based on the neural network and deep learning method. The filtered data of the direct numerical simulation is used to establish the training data set, the validation data set, and the test data set. The artificial neural network (ANN) method and Back Propagation method are employed to train parameters in the ANN. The developed ANN is applied to construct the sub-grid scale model for the large eddy simulation of the Burgers turbulence in the one-dimensional space. The proposed model well predicts the time correlation and the space correlation of the Burgers turbulence.

Complex pattern evolution of a two-dimensional space diffusion model of malware spread

In order to investigate the propagation mechanism of malware in cyber-physical systems (CPSs), the cross-diffusion in two-dimensional space is attempted to be introduced into a class of susceptible-infected (SI) malware propagation model depicted by partial differential equations (PDEs). Most of the traditional reaction-diffusion models of malware propagation only take into account the self-diffusion in one-dimensional space, but take less consideration of the cross-diffusion in two-dimensional space. This paper investigates the spatial diffusion behaviour of malware nodes spreading through physical devices. The formations of Turing patterns after homogeneous stationary instability triggered by Turing bifurcation are investigated by linear stability analysis and multiscale analysis methods. The conditions under the occurence of Hopf bifurcation and Turing bifurcation in the malware model are obtained. The amplitude equations are derived in the vicinity of the bifurcation point to explore the conditions for the formation of Turing patterns in two-dimensional space. And the corresponding patterns are obtained by varying the control parameters. It is shown that malicious virus nodes spread in different forms including hexagons, stripes and a mixture of the two. This paper will extend a new direction for the study of system security theory.

Binocular Visual Measurement Method Based on Feature Matching.

To address the issues of low measurement accuracy and unstable results when using binocular cameras to detect objects with sparse surface textures, weak surface textures, occluded surfaces, low-contrast surfaces, and surfaces with intense lighting variations, a three-dimensional measurement method based on an improved feature matching algorithm is proposed. Initially, features are extracted from the left and right images obtained by the binocular camera. The extracted feature points serve as seed points, and a one-dimensional search space is established accurately based on the disparity continuity and epipolar constraints. The optimal search range and seed point quantity are obtained using the particle swarm optimization algorithm. The zero-mean normalized cross-correlation coefficient is employed as a similarity measure function for region growing. Subsequently, the left and right images are matched based on the grayscale information of the feature regions, and seed point matching is performed within each matching region. Finally, the obtained matching pairs are used to calculate the three-dimensional information of the target object using the triangulation formula. The proposed algorithm significantly enhances matching accuracy while reducing algorithm complexity. Experimental results on the Middlebury dataset show an average relative error of 0.75% and an average measurement time of 0.82 s. The error matching rate of the proposed image matching algorithm is 2.02%, and the PSNR is 34 dB. The algorithm improves the measurement accuracy for objects with sparse or weak textures, demonstrating robustness against brightness variations and noise interference.

Machine learning-enhanced optical tweezers for defect-free rearrangement

Optical tweezers constitute pivotal tools in Atomic, Molecular, and Optical (AMO) physics, facilitating precise trapping and manipulation of individual atoms and molecules. This process affords the capability to generate desired geometries in both one-dimensional and two-dimensional spaces, while also enabling real-time reconfiguration of atoms. Due to stochastic defects in these tweezers, which cause catastrophic performance degradation especially in quantum computations, it is essential to rearrange the tweezers quickly and accurately. Our study introduces a machine learning approach that uses the Proximal Policy Optimization model to optimize this rearrangement process. This method focuses on efficiently solving the shortest path problem, ensuring the formation of defect-free tweezer arrays. By implementing machine learning, we can calculate optimal motion paths under various conditions, resulting in promising results in model learning. This advancement presents new opportunities in tweezer array rearrangement, potentially boosting the efficiency and precision of quantum computing research.

The collective dynamics of a stochastic Port-Hamiltonian self-driven agent model in one dimension

This paper studies the collective motion of self-driven agents in a one-dimensional space with periodic boundaries, using a stochastic Port-Hamiltonian system (PHS) with symmetric nearest-neighbor interactions and additive Brownian noise as an external input. In the case of a quadratic potential the PHS is an Ornstein-Uhlenbeck process for which we explicitly determine the distribution for any time t ≥ 0 and in the limit t → ∞. In particular, we characterize the collective motion by showing that the agents’ positions tend to build exactly one cluster. This is confirmed in simulations that show rapid and coordinated motion among agents, driven by noise, despite the absence of a preferred direction of motion in the model. Remarkably, the theoretical properties observed in the Ornstein-Uhlenbeck process also emerge in simulations of the nonlinear model incorporating a general interaction potential.

Multiple scattering theory in one dimensional space and time dependent disorder: average field [Invited

We theoretically study the propagation of light in one-dimensional space- and time-dependent disorder. The disorder is described by a fluctuating permittivity ε(x, t) exhibiting short-range correlations in space and time, without cross correlation between them. Depending on the illumination conditions, we show that the intensity of the average field decays exponentially in space or in time, with characteristic length or time defining the scattering mean-free path ℓ s and the scattering mean-free time τ s . In the weak scattering regime, we provide explicit expressions for ℓ s and τ s , that are checked against rigorous numerical simulations.

On codimension one stability of the soliton for the 1D focusing cubic Klein-Gordon equation

We consider the codimension one asymptotic stability problem for the soliton of the focusing cubic Klein-Gordon equation on the line under even perturbations. The main obstruction to full asymptotic stability on the center-stable manifold is a small divisor in a quadratic source term of the perturbation equation. This singularity is due to the threshold resonance of the linearized operator and the absence of null structure in the nonlinearity. The threshold resonance of the linearized operator produces a one-dimensional space of slowly decaying Klein-Gordon waves, relative to local norms. In contrast, the closely related perturbation equation for the sine-Gordon kink does exhibit null structure, which makes the corresponding quadratic source term amenable to normal forms (see Lührmann and Schlag [Duke Math. J. 172 (2023), pp. 2715–2820]). The main result of this work establishes decay estimates up to exponential time scales for small “codimension one type” perturbations of the soliton of the focusing cubic Klein-Gordon equation. The proof is based upon a super-symmetric approach to the study of modified scattering for 1D nonlinear Klein-Gordon equations with Pöschl-Teller potentials from Lührmann and Schlag [Duke Math. J. 172 (2023), pp. 2715–2820], and an implementation of a version of an adapted functional framework introduced by Germain and Pusateri [Forum Math. Pi 10 (2022), p. 172].

Asymptotic behaviour for a parabolic p-Laplacian equation with an advection force

The rescaling method is presented to allow us establishing the interface functions and the nonnegative local solutions to the evolution of nonlinear degenerate parabolic p-Laplacian process with conservation laws that are posed in one-dimensional space. This equation has a self-similar solution which represents the main feature of this work. The Cauchy problem (CP) for this equation with specific restrictions in the range of parameters and the negative advection coefficient is considered. In this work, there are several regions to discuss the qualitative analysis for the local weak solutions and the asymptotic interfaces in the irregular domains. The dominating of the advection force over the p-Laplacian type diffusion will appear clearly in these regions. Moreover, the solutions of the CP for the degenerate parabolic p-Laplacian advection equations are asymptotically equal to the solutions of advection equations under some restrictions.

Auditory free classification of gender diverse speakersa).

Auditory attribution of speaker gender has historically been assumed to operate within a binary framework. The prevalence of gender diversity and its associated sociophonetic variability motivates an examination of how listeners perceptually represent these diverse voices. Utterances from 30 transgender (1 agender individual, 15 non-binary individuals, 7 transgender men, and 7 transgender women) and 30 cisgender (15 men and 15 women) speakers were used in an auditory free classification paradigm, in which cisgender listeners classified the speakers on perceived general similarity and gender identity. Multidimensional scaling of listeners' classifications revealed two-dimensional solutions as the best fit for general similarity classifications. The first dimension was interpreted as masculinity/femininity, where listeners organized speakers from high to low fundamental frequency and first formant frequency. The second was interpreted as gender prototypicality, where listeners separated speakers with fundamental frequency and first formant frequency at upper and lower extreme values from more intermediate values. Listeners' classifications for gender identity collapsed into a one-dimensional space interpreted as masculinity/femininity. Results suggest that listeners engage in fine-grained analysis of speaker gender that cannot be adequately captured by a gender dichotomy. Further, varying terminology used in instructions may bias listeners' gender judgements.

Concept of introverted space: is multidimensional, extroverted space an illusion?

Abstract The quantum-phase-field concept of matter is revisited with special emphasis on the introverted view of space. Extroverted space surrounds physical objects, while introverted space lies in between physical objects. Space between objects leads to a network structure of matter: a network in which one-dimensional spaces connect individual particles.