Oscillation of Systems of Parabolic Differential Equations with Deviating Arguments

To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.

On a Class of Second Order Differential Inequality with Continuous Distributed Deviating Arguments

Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some sufficient conditions that ensure a class of second order delay differential inequality having no eventually positive solutions were obtained, which generalized some given results. Using the results, some oscillatory criteria for solutions of the hyperbolic equation with distributed deviating arguments can be established.

Periodic Solutions of Mixed Type p-Laplacian Equations with Deviating Arguments

Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.

The Existence and Uniqueness of Periodic Solutions for a Kind of Lienard Equation with a Deviating Argument

By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of periodic solutions are obtained.

Periodic Solutions for a Kind of Second Order Differential Equation with a Deviating Argument

By using the theory of coincidence degree, we study a kind of periodic solutions to second order differential equation with a deviating argument such as x″（t） ＋ f（x′（t）） ＋ h（x（t））x′（t） ＋ g（x（t - τ（t））） ≈ p（t）, some sufficient conditions on the existence of periodic solutions are obtained.

Periodic Solutions for p-Laplacian Neutral Functional Differential Equation with a Deviating Argument

In this paper, by using the continuation theorem of coincidence degree theory and some analysis methods, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with a deviating argument,some new results on the existence of periodic solutions is obtained.

Further Oscillation Results for a Class of Hyperbolic Equations with Continuous Distributed Deviating Arguments

A class of hyperbolic equations with continuous distributed deviating arguments is considered and its oscillation theorems are discussed.These theorems are of higher degree of generality and deal with the cases which are not covered by the known criteria.Particularly,these criteria extend and unify a number of existing results.

New Results on Oscillation of even Order Neutral Differential Equations with Deviating Arguments

In this paper, we point out some small mistakes in [6] and revise them, we obtain some new oscillation results for certain even order neutral differential equations with deviating arguments. Our results extend and improve many known oscillation criteria because the article just generalizes Meng and Xu’s results.

Oscillation of Differential Equations with Deviating Arguments

In this paper we establish new oscillation criteria for all solution of the first order differential equation with deviating argument. Our result can be applied to the case when coefficients and deviating arguments are oscillatory and essentially improve the known results in the literature.

Periodicity and Stability in Periodic n-Species Lotka-Volterra Competition System with Feedback Controls and Deviating Arguments

By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterracompetition system with feedback controls and several deviating arguments. The problem considered inthis paper is in many aspects more general and incorporate as special cases various problems whichhave been studied extensively in the literature. Moreover, our new criteria, which improve andgeneralize some well known results, can be easily checked.

Path Planning and Tracking Control for Parking via Soft Actor-Critic Under Non-Ideal Scenarios

Parking in a small parking lot within limited space poses a difficult task. It often leads to deviations between the final parking posture and the target posture. These deviations can lead to partial occupancy of adjacent parking lots, which poses a safety threat to vehicles parked in these parking lots. However, previous studies have not addressed this issue. In this paper, we aim to evaluate the impact of parking deviation of existing vehicles next to the target parking lot(PDEVNTPL) on the automatic ego vehicle(AEV) parking, in terms of safety, comfort, accuracy, and efficiency of parking. A segmented parking training framework(SPTF) based on soft actor-critic(SAC) is proposed to improve parking performance. In the proposed method, the SAC algorithm incorporates strategy entropy into the objective function, to enable the AEV to learn parking strategies based on a more comprehensive understanding of the environment. Additionally, the SPTF simplifies complex parking tasks to maintain the high performance of deep reinforcement learning(DRL). The experimental results reveal that the PDEVNTPL has a detrimental influence on the AEV parking in terms of safety, accuracy, and comfort, leading to reductions of more than 27%, 54%, and 26%respectively. However, the SAC-based SPTF effectively mitigates this impact, resulting in a considerable increase in the parking success rate from 71% to 93%. Furthermore, the heading angle deviation is significantly reduced from 2.25 degrees to 0.43degrees.

Spatiotemporal characteristics of cultivated land use eco-efficiency and its influencing factors in China from 2000 to 2020

Improving cultivated land use eco-efficiency(CLUE)can effectively promote agricultural sustainability,particularly in developing countries where CLUE is generally low.This study used provincial-level data from China to evaluate the spatiotemporal evolution of CLUE from 2000 to 2020 and identified the influencing factors of CLUE by using a panel Tobit model.In addition,given the undesirable outputs of agricultural production,we incorporated carbon emissions and nonpoint source pollution into the global benchmark-undesirable output-super efficiency-slacks-based measure(GB-US-SBM)model,which combines global benchmark technology,undesirable output,super efficiency,and slacks-based measure.The results indicated that there was an upward trend in CLUE in China from 2000 to 2020,with an increase rate of 2.62%.The temporal evolution of CLUE in China could be classified into three distinct stages:a period of fluctuating decrease(2000-2007),a phase of gradual increase(2008-2014),and a period of rapid growth(2015-2020).The major grain-producing areas(MPAs)had a lower CLUE than their counterparts,namely,non-major grain-production areas(non-MPAs).The spatial agglomeration effect followed a northeast-southwest strip distribution;and the movement path of barycentre revealed a"P"shape,with Luoyang City,Henan Province,as the centre.In terms of influencing factors of CLUE,investment in science and technology played the most vital role in improving CLUE,while irrigation index had the most negative effect.It should be noted that these two influencing factors had different impacts on MPAs and non-MPAs.Therefore,relevant departments should formulate policies to enhance the level of science and technology,improve irrigation condition,and promote sustainable utilization of cultivated land.

EXISTENCE AND UNIQUENESS OF ANTI-PERIODIC SOLUTIONS TO AN nTH-ORDER NONLINEAR DIFFERENTIAL EQUATION WITH MULTIPLE DEVIATING ARGUMENTS

In this paper,we use the Leray-Schauder degree theory to establish some new results on the existence and uniqueness of anti-periodic solutions to an nth-order nonlinear differential equation with multiple deviating arguments.

OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF FIRST ORDER DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DEVIATING ARGUMENTS

In this paper, we consider the oscillatory and asymptotic behavior of solu-tions of first order nonlinear neutral differential equation with piecewise constantdeviating arguments. Several criteria are obtained for oscillatory and asymptoticbehavior of solutions of the equation.

PERIODIC SOLUTION FOR p-LAPLACIAN DIFFERENTIAL EQUATION WITH A DEVIATING ARGUMENT

By using the theory of coincidence degree, we study a kind of periodic solution to p-Laplacian differential equation with a deviating argument such as （φp（x＇（t）））＇ ＋ f（x（t）） ＋ g（x（t - τ（t））） = e（t）, a result on the existence of periodic solution is obtained.

A Distortion Self-Calibration Method for Binocular High Dynamic Light Adjusting and Imaging System Based on Digital Micromirror Device

Dear Editor,In order to realize the pixel level light adjusting control of the binocular high dynamic light adjusting and imaging system, this letter proposed a novel self-calibration method. By analyzing the optical design of the system, the causes of the distortion are given and a distortion model is established. Then, a quick and accurate self-calibration method is designed. The experiments indicate that the method can calibrate the two image sensors of the system at the same time,the average pixel deviation of the calibrated system is less than 0.5pixels and the maximum deviation is less than 1 pixel.

Spatiotemporal patterns and drivers of cultivated land conversion in Inner Mongolia Autonomous Region,northern China

Protection and optimization of cultivated land resources are of great significance to national food security.Cultivated land conversion in northern China has increased in recent years due to the industrialization and urbanization of society.However,the assessment of cultivated land conversion in this area is insufficient,posing a potential risk to cultivated land resources.This study evaluated the evolution and spatiotemporal patterns of cultivated land conversion in Inner Mongolia Autonomous Region,China,and the driving factors to improve rational utilization and to protect cultivated land resources.The spatiotemporal patterns of cultivated land conversion in Inner Mongolia were analyzed using the cultivated land conversion index,kernel density analysis,a standard deviation ellipse model,and a geographic detector.Results showed that from 2000 to 2020,the trends in cultivated land conversion area and rate in Inner Mongolia exhibited fluctuating growth,with the total area of cultivated land conversion reaching 7307.59 km^(2) at a rate of 6.69%.Spatial distribution of cultivated land conversion was primarily concentrated in the Hetao Plain,Nengjiang Plain,Liaohe Plain,and the Hohhot-Baotou-Ordos urban agglomeration.Moreover,the standard deviational ellipse of cultivated land conversion in Inner Mongolia exhibited a directional southwest-northeast-southwest-northeast distribution,with the northeast-southwest direction identified as the main driving force of spatial change in cultivated land conversion.Meanwhile,cultivated land conversion exhibited an increase-decrease-increase change process,indicating that spatial distribution of cultivated land conversion in Inner Mongolia became gradually apparent within the study period.The geographic detector results further revealed that the main driving factors of cultivated land conversion in Inner Mongolia were the share of secondary and tertiary industries and per-unit area yield of grain,with explanatory rates of 57.00%,55.00%,and 51.00%,respectively.Additionally,improved agricultural production efficiency and the coordinated development of population urbanization and industry resulted in cultivated land conversion.Collectively,the findings of this study indicated that,from 2000 to 2020,the cultivated land conversion in Inner Mongolia was significant and fluctuated in time,and had strong spatial heterogeneity.The primary drivers of these events included the effects of agriculture,population,and social economy.

OSCILLATION CRITERIA FOR HIGHER-ORDER IMPULSIVE HYPERBOLIC SYSTEM WITH DISTRIBUTED DEVIATING ARGUMENTS

By the methods of differential inequality and eigenvalue, we obtain several sufficient conditions for oscillation of solutions for higher-order impulsive hyperbolic system with distributed deviating arguments under Robin and Dirichlet boundary value conditions.

Computing large deviation prefactors of stochastic dynamical systems based on machine learning

We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.

Path Planning of Multi-Axis Robotic Arm Based on Improved RRT*

An improved RRT∗algorithm,referred to as the AGP-RRT∗algorithm,is proposed to address the problems of poor directionality,long generated paths,and slow convergence speed in multi-axis robotic arm path planning.First,an adaptive biased probabilistic sampling strategy is adopted to dynamically adjust the target deviation threshold and optimize the selection of random sampling points and the direction of generating new nodes in order to reduce the search space and improve the search efficiency.Second,a gravitationally adjustable step size strategy is used to guide the search process and dynamically adjust the step-size to accelerate the search speed of the algorithm.Finally,the planning path is processed by pruning,removing redundant points and path smoothing fitting using cubic B-spline curves to improve the flexibility of the robotic arm.Through the six-axis robotic arm path planning simulation experiments on the MATLAB platform,the results show that the AGP-RRT∗algorithm reduces 87.34%in terms of the average running time and 40.39%in terms of the average path cost;Meanwhile,under two sets of complex environments A and B,the average running time of the AGP-RRT∗algorithm is shortened by 94.56%vs.95.37%,and the average path cost is reduced by 55.28%vs.47.82%,which proves the effectiveness of the AGP-RRT∗algorithm in improving the efficiency of multi-axis robotic arm path planning.