Search Results (17)

Precipitation cyclicity plays a crucial role in regional water supply and climate predictions. In this study, we used observational data from 34 representative meteorological stations in the Xinjiang region, a major part of inland arid China, to characterize the interannual cyclicity of regional precipitation from 1951 to 2021 and analyze its contributing factors. The results indicated that the mean annual precipitation in Xinjiang (MAP_XJ) was dominated by a remarkably increasing trend over the past 70 years, which was superimposed by two bands of interannual cycles of approximately 3 years with explanatory variance of 56.57% (Band I) and 6–7 years with explanatory variance of 23.38% (Band II). This is generally consistent with previous studies on the cyclicity of precipitation in Xinjiang for both seasonal and annual precipitation. We analyzed the North Tropical Atlantic sea-surface temperature (NTA_SST), El Niño-Southern Oscillation (ENSO), North Atlantic Oscillation (NAO), Arctic Oscillation (AO), and Indian Summer Monsoon (ISM) as potential forcing factors that show similar interannual cycles and may contribute to the identified precipitation variability. Two approaches, multivariate linear regression and the Random Forest model, were employed to ascertain the relative significance of each factor influencing Bands I and II, respectively. The multivariate linear regression analysis revealed that the AO index contributed the most to Band I, with a significance score of −0.656, whereas the ENSO index with a one-year lead (ENSO_−1yr) played a dominant role in Band II (significance score = 0.457). The Random Forest model also suggested that the AO index exhibited the highest significance score (0.859) for Band I, whereas the AO index with a one-year lead (AO_−1yr) had the highest significance score (0.876) for Band II. Overall, our findings highlight the necessity of employing different methods that consider both the linear and non-linear response of climate variability to driving factors crucial for future climate prediction. Full article

The quantity of wind and photovoltaic power-based distributed generators (DGs) is continually rising within the distribution network, presenting obstacles to its safe, steady, and cost-effective functioning. Active distribution network dynamic reconfiguration (ADNDR) improves the consumption rate of renewable energy, reduces line losses, and optimizes voltage quality by optimizing the distribution network structure. Despite being formulated as a highly dimensional and combinatorial nonconvex stochastic programming task, conventional model-based solvers often suffer from computational inefficiency and approximation errors, whereas population-based search methods frequently exhibit premature convergence to suboptimal solutions. Moreover, when dealing with high-dimensional ADNDR problems, these algorithms often face modeling difficulties due to their large scale. Deep reinforcement learning algorithms can effectively solve the problems above. Therefore, by combining the graph attention network (GAT) with the deep deterministic policy gradient (DDPG) algorithm, a method based on the graph attention network deep deterministic policy gradient (GATDDPG) algorithm is proposed to online solve the ADNDR problem with the uncertain outputs of DGs and loads. Firstly, considering the uncertainty in distributed power generation outputs and loads, a nonlinear stochastic optimization mathematical model for ADNDR is constructed. Secondly, to mitigate the dimensionality of the decision space in ADNDR, a cyclic topology encoding mechanism is implemented, which leverages graph-theoretic principles to reformulate the grid infrastructure as an adaptive structural mapping characterized by time-varying node–edge interactions Furthermore, the GATDDPG method proposed in this paper is used to solve the ADNDR problem. The GAT is employed to extract characteristics pertaining to the distribution network state, while the DDPG serves the purpose of enhancing the process of reconfiguration decision-making. This collaboration aims to ensure the safe, stable, and cost-effective operation of the distribution network. Finally, we verified the effectiveness of our method using an enhanced IEEE 33-bus power system model. The outcomes of the simulations demonstrate its capacity to significantly enhance the economic performance and stability of the distribution network, thereby affirming the proposed method’s effectiveness in this study. Full article

We prove a conjecture on the second minimal odd periodic orbits with respect to Sharkovski ordering for the continuous endomorphisms on the real line. A $(2k+1)$-periodic orbit $\{{\beta }_1<{\beta }_2<\cdots <{\beta }_{2k+1}\}$, ($k\ge 3$) is called second minimal for the map f, if $2k-1$ is a minimal period of ${f|}_{[{\beta }_1,{\beta }_{2k+1}]}$ in the Sharkovski ordering. Full classification of second minimal orbits is presented in terms of cyclic permutations and directed graphs of transitions. It is proved that second minimal odd orbits either have a Stefan-type structure like minimal odd orbits or one of the $4k-3$ types, each characterized with unique cyclic permutations and directed graphs of transitions with an accuracy up to the inverses. The new concept of second minimal orbits and its classification have an important application towards an understanding of the universal structure of the distribution of the periodic windows in the bifurcation diagram generated by the chaotic dynamics of nonlinear maps on the interval. Full article

Utilizing an advanced machine learning algorithm, particularly the Artificial Neural Network (ANN) framework, this study reveals a significant nonlinear and even cyclical relationship between public concern about environmental issues and the ESG performance of Chinese A-share listed companies, covering the period from 2004 to 2020. The findings highlight the effectiveness of the Self-Organizing Map (SOM)-ANN framework in elucidating the empirical relationship between these variables. We contend that robust public monitoring can enhance companies’ ESG initiatives, and we recommend that policymakers implement a series of measures to safeguard and promote public involvement in decision-making processes. Furthermore, our analysis of the combined effects of public concern and various performance metrics on firms’ ESG outcomes indicates that the diversity among firms is crucial for determining the most appropriate level of public participation in their sustainable development efforts. Therefore, managers and policymakers should focus on firm-specific attributes instead of adopting a “one-size-fits-all” approach to maximize the benefits of public engagement. Full article

This paper introduces interpolative enriched cyclic Reich–Rus–Ćirić operators in normed spaces, expanding existing contraction principles by integrating interpolation and cyclic conditions. This class of operators addresses mappings with discontinuities or non-self mappings, enhancing the applicability of fixed-point theory to more complex problems. This class of operators expands on existing cyclic contractions, including interpolative Kannan mappings, interpolative Reich–Rus–Ćirić contractions, and other known contractions in the literature. We demonstrate the existence and uniqueness of fixed points for these operators and provide an example to illustrate our findings. Moreover, we discuss the applications of our results in solving nonlinear integral equations. Furthermore, we introduce the idea of a coupled interpolative enriched cyclic Reich–Rus–Ćirić operator and establish the existence of a strongly coupled fixed-point theorem for this contraction. Finally, we provide an application to fractional differential equations to show the validity of the main result. Full article

In the context of multi-array multi-target bearing-only localization, due to the existence of direction-finding errors, the crossing results of bearing lines cannot accurately determine correspondence with targets. Under conditions that clutter interference and missing of detection in direction-finding, the traditional method will produce false alarm targets and miss some targets. To address this issue, this paper draws on the idea of a spatial likelihood map which calculates the likelihood of target presence at each grid point within the observation area by partitioning the observation area into grids and utilizing bearing data from each array, yielding the distribution of targets in the observation area. Then, a multi-target cyclic peak extraction algorithm based on a statistical dual-threshold is proposed, which eliminates false peaks by cyclic extraction of target positions, so as to reduce false targets. Simulation results demonstrate that the spatial likelihood mapping-based localization exhibits good performance. Furthermore, when the multi-target cyclic peak extraction algorithm based on statistical dual-thresholds is applied, it outperforms direct target extraction from the spatial likelihood map, showcasing enhanced multi-target localization capabilities. Moreover, compared to the position non-linear least squares multi-target localization method, the proposed method has lower optimal sub-pattern assignment distance and lower localization error under the condition of interference and missing detection. Full article

Based on finite-dimensional time-frequency analysis, we study the properties of time-frequency shift equivariant maps that are generally nonlinear. We first establish a one-to-one correspondence between $\mathsf{\Lambda }$-equivariant maps and certain phase-homogeneous functions and also provide a reconstruction formula that expresses $\mathsf{\Lambda }$-equivariant maps in terms of these phase-homogeneous functions, leading to a deeper understanding of the class of $\mathsf{\Lambda }$-equivariant maps. Next, we consider the approximation of $\mathsf{\Lambda }$-equivariant maps by neural networks. In the case where $\mathsf{\Lambda }$ is a cyclic subgroup of order N in ${\mathbb{Z}}_N\times {\mathbb{Z}}_N$, we prove that every $\mathsf{\Lambda }$-equivariant map can be approximated by a shallow neural network whose affine linear maps are simply linear combinations of time-frequency shifts by $\mathsf{\Lambda }$. This aligns well with the proven suitability of convolutional neural networks (CNNs) in tasks requiring translation equivariance, particularly in image and signal processing applications. Full article

The essence of the stochastic processes behind the empirical data on infection and fatality during pandemics is the complex interdependence between biological and social factors. Their balance can be checked on the data of new virus outbreaks, where the population is unprepared to fight the viral biology and social measures and healthcare systems adjust with a delay. Using a complex systems perspective, we combine network mapping with K-means clustering and multifractal detrended fluctuations analysis to identify typical trends in fatality rate data. We analyse global data of (normalised) fatality time series recorded during the first two years of the recent pandemic caused by the severe acute respiratory syndrome coronavirus 2 as an appropriate example. Our results reveal six clusters with robust patterns of mortality progression that represent specific adaptations to prevailing biological factors. They make up two significant groups that coincide with the topological communities of the correlation network, with stabilising (group g1) and continuously increasing rates (group g2). Strong cyclic trends and multifractal small-scale fluctuations around them characterise these patterns. The rigorous analysis and the proposed methodology shed more light on the complex nonlinear shapes of the pandemic’s main characteristic curves, which have been discussed extensively in the literature regarding the global infectious diseases that have affected humanity throughout its history. In addition to better pandemic preparedness in the future, the presented methodology can also help to differentiate and predict other trends in pandemics, such as fatality rates, caused simultaneously by different viruses in particular geographic locations. Full article

Novel cyclic contractions of the Kannan and Chatterjea type are presented in this study. With the aid of these brand-new contractions, new results for the existence and uniqueness of fixed points in the setting of complete generalized metric space have been established. Importantly, the results are generalizations and extensions of fixed point theorems by Chatterjea and Kannan and their cyclical expansions that are found in the literature. Additionally, several of the existing results on fixed points in generalized metric space will be generalized by the results presented in this work. Interestingly, the findings have a variety of applications in engineering and sciences. Examples have been given at the end to show the reliability of the demonstrated results. Full article

To better cope with the significant nonlinear radiation distortions (NRD) and severe rotational distortions in multi-modal remote sensing image matching, this paper introduces a rotationally robust feature-matching method based on the maximum index map (MIM) and 2D matrix, which is called the rotation-invariant local phase orientation histogram (RI-LPOH). First, feature detection is performed based on the weighted moment equation. Then, a 2D feature matrix based on MIM and a modified gradient location orientation histogram (GLOH) is constructed and rotational invariance is achieved by cyclic shifting in both the column and row directions without estimating the principal orientation separately. Each part of the sensed image’s 2D feature matrix is additionally flipped up and down to obtain another 2D matrix to avoid intensity inversion, and all the 2D matrices are concatenated by rows to form the final 1D feature vector. Finally, the RFM-LC algorithm is introduced to screen the obtained initial matches to reduce the negative effect caused by the high proportion of outliers. On this basis, the remaining outliers are removed by the fast sample consensus (FSC) method to obtain optimal transformation parameters. We validate the RI-LPOH method on six different types of multi-modal image datasets and compare it with four state-of-the-art methods: PSO-SIFT, MS-HLMO, CoFSM, and RI-ALGH. The experimental results show that our proposed method has obvious advantages in the success rate (SR) and the number of correct matches (NCM). Compared with PSO-SIFT, MS-HLMO, CoFSM, and RI-ALGH, the mean SR of RI-LPOH is 170.3%, 279.8%, 81.6%, and 25.4% higher, respectively, and the mean NCM is 13.27, 20.14, 1.39, and 2.42 times that of the aforementioned four methods. Full article

In the current paper, we first introduce a new class of contractions via a new notion called p-cyclic contraction mapping by combining the ideas of cyclic contraction mapping and p-contraction mapping. Then, we give a new definition of a cyclically 0-complete pair to weaken the completeness condition on the partial metric spaces. Following that, we prove some best proximity point results for p-cyclic contraction mappings on $D\cup E$ where $\left(D,E\right)$ is a cyclically 0-complete pair in the setting of partial metric spaces. Hence, we generalize and unify famous and well-known results in the literature of metric fixed point theory. Additionally, we present some nontrivial examples to compare our results with earlier. Finally, we investigate the sufficient conditions for the existence of a solution to nonlinear Fredholm integral equations by the results in the paper. Full article

Power transmission covering long-distances has shifted from overhead high voltage cables to underground power cable systems due to numerous failures under severe weather conditions and electromagnetic pollution. The underground power cable systems are limited by the melting point of the insulator around the conductor, which depends on the surrounding soils’ heat transfer capacity or the thermal conductivity. In the past, numerical and theoretical studies have been conducted based on the mechanistic heat and mass transfer model. However, limited experimental evidence has been provided. Therefore, in this study, we performed a series of experiments for static and cyclic thermal loads with a cylindrical heater embedded in the sand. The results suggest thermal charging of the surrounding dry sand and natural convection within the wet sand. A comparison of heat transfer for dry, unsaturated and fully saturated sand is presented with graphs and colour maps which provide valuable information and insight of heat and mass transfer around an underground power cable. Furthermore, the measurements of thermal conductivity against density, moisture and temperature are presented showing positive nonlinear dependence. Full article

The combination of network sciences, nonlinear dynamics and time series analysis provides novel insights and analogies between the different approaches to complex systems. By combining the considerations behind the Lyapunov exponent of dynamical systems and the average entropy of transition probabilities for Markov chains, we introduce a network measure for characterizing the dynamics on state-transition networks with special focus on differentiating between chaotic and cyclic modes. One important property of this Lyapunov measure consists of its non-monotonous dependence on the cylicity of the dynamics. Motivated by providing proper use cases for studying the new measure, we also lay out a method for mapping time series to state transition networks by phase space coarse graining. Using both discrete time and continuous time dynamical systems the Lyapunov measure extracted from the corresponding state-transition networks exhibits similar behavior to that of the Lyapunov exponent. In addition, it demonstrates a strong sensitivity to boundary crisis suggesting applicability in predicting the collapse of chaos. Full article

The present research is concerned with the elastic–plastic responses of functionally graded material (FGM) pipe, undergoing two types of loading conditions. For the first case, the FGM is subjected to sustained internal pressure combined with a cyclic bending moment whereas, in the second case, sustained internal pressure is applied simultaneously with a cyclic through-thickness temperature gradient. The properties of the studied FGM are considered to be variable through shell thickness according to a power-law function. Two different designs of the FGM pipe are adopted in the present research, where the inner surface in one case and the outer surface in the other are made from pure 1026 carbon steel. The constitutive relations are developed based on the Chaboche nonlinear kinematic hardening model, classical normality rule and von Mises yield function. The backward Euler alongside the return mapping algorithm (RMA) is employed to perform the numerical simulation. The results of the proposed integration procedure were implemented in ABAQUS using a UMAT user subroutine and validated by a comparison between experiments and finite element (FE) simulation. Various cyclic responses of the two prescribed models of FGM pipe for the two considered loading conditions are classified and brought together in one diagram known as Bree’s diagram. Full article

The aim of this study is to investigate the existence of solutions for a non-linear neutral differential equation with an unbounded delay. To achieve our goals, we take advantage of fixed point theorems for self-mappings satisfying a generalized ( $\alpha ,\phi$ ) rational contraction, as well as cyclic contractions in the context of $\mathcal{F}$ -metric spaces. We also supply an example to support the new theorem. Full article