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Based on Nijenhuis-Richardson bracket and bidegree on the cohomology complex for a Lie conformal algebra, we develop a twisting theory of Lie conformal algebras. By using derived bracket constructions, we construct L ∞ -algebras from (quasi-)twilled Lie conformal algebras. And we show that the result of the twisting by a C [ ∂ ] -module homomorphism on a (quasi-)twilled Lie conformal algebra is also a (quasi-)twilled Lie conformal algebra if and only if the C [ ∂ ] -module homomorphism is a Maurer-Cartan element of the L ∞ -algebra. In particular, we show that relative Rota-Baxter type operators on Lie conformal algebras are Maurer-Cartan elements. Besides, we propose a new algebraic structure, called NS-Lie conformal algebras, that is closely related to twisted relative Rota-Baxter operators and Nijenhuis operators on Lie conformal algebras. As an application of twisting theory, we give the cohomology of twisted relative Rota-Baxter operators and study their deformations. [ABSTRACT FROM AUTHOR]

In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and give some constructions of them. Then we introduce the notion of conformal formal deformations of commutative associative conformal algebras and show that Poisson conformal algebras are the corresponding semi-classical limits. At last, we develop the cohomology theory of noncommutative Poisson conformal algebras and use this cohomology to study their deformations. [ABSTRACT FROM AUTHOR]

Given a (quasi-)twilled pre-Lie algebra, we first construct a differential graded Lie algebra (L∞-algebra). Then we study the twisting theory of (quasi-)twilled pre-Lie algebras and show that the result of the twisting by a linear map on a (quasi-)twilled pre-Lie algebra is also a (quasi-)twilled pre-Lie algebra if and only if the linear map is a solution of the Maurer–Cartan equation of the associated differential graded Lie algebra (L∞-algebra). In particular, the relative Rota–Baxter operators (twisted relative Rota–Baxter operators) on pre-Lie algebras are solutions of the Maurer–Cartan equation of the differential graded Lie algebra (L∞-algebra) associated to the certain quasi-twilled pre-Lie algebra. Finally, we use the twisting theory of (quasi-)twilled pre-Lie algebras to study quasi-pre-Lie bialgebras. Moreover, we give a construction of quasi-pre-Lie bialgebras through symplectic Lie algebras, which is parallel to that a Cartan 3-form on a semi-simple Lie algebra gives a quasi-Lie bialgebra. [ABSTRACT FROM AUTHOR]

In this paper, first we give the cohomology theory of a 3-Lie algebra with a representation (called a 3- L i e R e p pair) and study the linear deformation theory of a 3- L i e R e p pair. We introduce the notion of a Nijenhuis structure on a 3- L i e R e p pair, which generates a trivial linear deformation. Then by adding compatibility conditions between Nijenhuis structures and relative Rota-Baxter operators, we introduce the notion of a relative Rota-Baxter-Nijenhuis structure on a 3- L i e R e p pair. Finally we construct relative Rota-Baxter-Nijenhuis structures on 3- L i e R e p pairs from those on L i e R e p pairs through certain linear functions. [ABSTRACT FROM AUTHOR]

The evaluation of the state of transformer oil-immersed insulation based on the traditional methods becomes unreliable due to the nonuniform aging effect. To address this issue, a novel model for accessing the aging information of transformer oil-immersed insulation at the hotspot is proposed. In this article, frequency-domain spectroscopy (FDS) is selected as the carrier for characterizing the aging states of oil-immersed insulation. The multiobjective function for reversing the FDS of the hotspot is constructed based on the dielectric response equivalent circuit. Then, the nondominated sorting genetic algorithm with the multiconstraint scheme is proposed to solve the multiobjective function, by which the FDS data of the transformer hotspot region are acquired. The verification results indicate that the average standard deviation between the computed FDS of the hotspot region and the measured data is less than 0.26. The contribution of this article is in the exploration of the proposed model as a potential tool to extract the FDS data of the hotspot region. This will promote a more reliable aging evaluation of the transformer oil-immersed paper insulation at the hotspot. [ABSTRACT FROM AUTHOR]

In this paper, we first study infinitesimal deformations of a Lie conformal algebra and a Lie conformal algebra with a module (called an LCMod pair), which lead to the notions of the Nijenhuis operator on the Lie conformal algebra and the Nijenhuis structure on the LCMod pair, respectively. Then, by adding compatibility conditions between Nijenhuis structures and O -operators, we introduce the notion of an O N -structure on an LCMod pair and show that an O N -structure gives rise to a hierarchy of pairwise compatible O -operators. In particular, we show that compatible O -operators on a Lie conformal algebra can be characterized by Nijenhuis operators on Lie conformal algebras. Finally, we introduce the notions of the conformal r-matrix-Nijenhuis structure and symplectic-Nijenhuis structure on Lie conformal algebras and study their relations. [ABSTRACT FROM AUTHOR]

In this paper, we study pre-Lie analogues of Poisson-Nijenhuis structures and introduce N -structures on bimodules over pre-Lie algebras. We show that an N -structure gives rise to a hierarchy of pairwise compatible -operators. We study solutions of the strong Maurer–Cartan equation on the twilled pre-Lie algebra associated to an -operator, which gives rise to a pair of N -structures which are naturally in duality. We show that KVN-structures and HN-structures on a pre-Lie algebra are corresponding to N -structures on the bimodule ( ∗ ; ad ∗ , − R ∗) , and KVB-structures are corresponding to solutions of the strong Maurer–Cartan equation on a twilled pre-Lie algebra associated to an -matrix. [ABSTRACT FROM AUTHOR]

The traditional method for transformer moisture diagnosis is to establish empirical equations between feature parameters extracted from frequency domain spectroscopy (FDS) and the transformer’s moisture content. However, the established empirical equation may not be applicable to a novel testing environment, resulting in an unreliable evaluation result. In this regard, it is acknowledged that FDS combined with machine learning is more suitable for estimating moisture content in a variety of test environments. Nonetheless, the accuracy of the estimation results obtained using the existing method is limited by the algorithm’s inability to generalize. To address this issue, we propose an AdaBoost algorithm-enhanced back-propagation neural network (BP_AdaBoost). This study creates a database by extracting feature parameters from the FDS that characterize the insulation states of the prepared samples. Then, using the BP_AdaBoost algorithm and the newly constructed database, the moisture estimation models are trained. Finally, the results of the estimation are discussed in terms of laboratory and field transformers. By comparing the proposed BP_AdaBoost algorithm to other intelligence algorithms, it is demonstrated that it not only performs better in generalization, but also maintains a high level of accuracy. [ABSTRACT FROM AUTHOR]

The generation and distribution of furfural are significantly affected by moisture content in the insulating paper. However, the diffusion mechanism of furfural under moisture effect is not clear, hence, this study investigates the effect of moisture on the diffusion characteristics of furfural by combining macro experiment and micro molecular dynamics simulation. The simulation results demonstrate that the increased moisture content in paper accelerates the diffusion of furfural from paper to oil, which is also proved by the experimental data. Then, the results of interaction energy analysis indicate that the increase of moisture enhances the van der Waals force between oil and furfural. The present findings are expected to improve the theoretical level of furfural analysis, which will facilitate the aging evaluation of the transformer insulating paper based on furfural. [ABSTRACT FROM AUTHOR]

An admissible Poisson algebra (or briefly, an adm-Poisson algebra) gives an equivalent presentation with only one operation for a Poisson algebra. We establish a bialgebra theory for adm-Poisson algebras independently and systematically, including but beyond the corresponding results on Poisson bialgebras given in [27]. Explicitly, we introduce the notion of adm-Poisson bialgebras which are equivalent to Manin triples of adm-Poisson algebras as well as Poisson bialgebras. The direct correspondence between adm-Poisson bialgebras with one comultiplication and Poisson bialgebras with one cocommutative and one anti-cocommutative comultiplications generalizes and illustrates the polarization–depolarization process in the context of bialgebras. The study of a special class of adm-Poisson bialgebras which include the known coboundary Poisson bialgebras in [27] as a proper subclass in general, illustrating an advantage in terms of the presentation with one operation, leads to the introduction of adm-Poisson Yang–Baxter equation in an adm-Poisson algebra. It is an unexpected consequence that both the adm-Poisson Yang–Baxter equation and the associative Yang–Baxter equation have the same form and thus it motivates and simplifies the involved study from the study of the associative Yang–Baxter equation, which is another advantage in terms of the presentation with one operation. A skew-symmetric solution of adm-Poisson Yang–Baxter equation gives an adm-Poisson bialgebra. Finally, the notions of an -operator of an adm-Poisson algebra and a pre-adm-Poisson algebra are introduced to construct skew-symmetric solutions of adm-Poisson Yang–Baxter equation and hence adm-Poisson bialgebras. Note that a pre-adm-Poisson algebra gives an equivalent presentation for a pre-Poisson algebra introduced by Aguiar. [ABSTRACT FROM AUTHOR]

This work investigates which acid can mainly lead to the reduction of alcohols contents in insulating oil during transformer oil-paper insulation aging. In terms of the activation free energy barrier theory, the microscopic mechanisms for the preferential reactions of methanol and ethanol with formic, acetic, naphthenic and stearic acids are analyzed. It is revealed that the decrease in alcohols concentrations in the middle and late stages of transformer oil-paper insulation aging is mainly caused by the reaction between alcohols and naphthenic acid. The results are cross-validated by utilizing the frontier molecular orbital theory and accelerated thermal aging experiments. Additionally, it is observed that methanol is more susceptible to the effect of acids than ethanol in the middle and late stages of aging. The obtained conclusions, in this paper, could provide a theoretical basis for using alcohols in oil as aging indicators to characterize the full-stage aging status of transformer paper insulation. [ABSTRACT FROM AUTHOR]

The heterocharge accumulated in the oil‐paper insulation system of the converter transformer will enhance the local electric field and cause insulation deterioration. Numerical simulation is an effective method to analyze heterocharge. Currently, the numerical simulation of heterocharge is mainly based on the bipolar charge transport (BCT) model and the impurity ion transport (IIT) model. However, the effects of temperature, conductivity, and thickness of oil‐impregnated paper on charge transport have not been considered in these models. In view of this, a modified charge transport (MCT) model by introducing the Maxwell–Wagner model and heat conduction equation is proposed in this paper based on the BCT model and IIT model. Then, the influence of multi‐factors (temperature gradient, moisture content, and oil‐impregnated paper thickness) on heterocharge accumulation is investigated by using the MCT model. The simulation results obtained by the MCT model are more consistent with the experimental results than the BCT model, which proves the accuracy and superiority of the MCT model. Moreover, the increase in temperature gradient, moisture content, and oil‐impregnated paper thickness will enlarge the ion dissociation rate, conductivity, and trap density, and thus promote the generation of heterocharge. In that respect, the MCT model is expected to optimize the insulation design and provide a reference for space charge dynamic simulation. [ABSTRACT FROM AUTHOR]

The total/partial oil change treatment can affect the furfural partitioning in oil-paper-pressboard insulation, resulting in poor accuracy of furfural analysis. Moreover, due to the high cost of total oil change, partial oil change is more practical during transformer operation. This paper investigates the furfural partitioning in the oil-paper-pressboard insulation under partial oil change conditions. First, the initial furfural partitioning equation with non-oil change is proposed based on the obtained furfural content in oil, paper, and pressboard. Then, the modified furfural partitioning model under partial oil change condition is established by introducing a correction factor. Moreover, a preliminary correction scheme for the furfural partitioning model considering the influence of moisture and acid is provided. Finally, furfural content in oil-Kraft paper and oil-thermally upgraded Kraft (TUK) paper insulation are discussed, and results indicate that the proposed modified furfural partitioning model is not suitable for the oil-TUK paper insulation. This work can provide theoretical support for furfural analysis of oil-immersed transformers. [ABSTRACT FROM AUTHOR]

Background: The purpose of this study is to investigate and analyze the prevalence and influencing factors of stroke in hypertensive patients aged 60 and above in Jiading District, Shanghai. Methods: The population-based study included 18,724 screened people with hypertension (age ≥ 60 years, 48.7% women). From 2016 to 2019, data on demographics, potential influencing factors and health status were collected through face-to-face interviews, physical examinations, and laboratory tests. Logistic multivariate logistic regression model was used to analyze the influencing factors associated with stroke. Results: Among the object of study from 2016 to 2019, 2,025 patients were screened for stroke, with the overall prevalence rate of 10.82% (10.41%-11.23%). Multivariate adjusted model analysis showed that dyslipidemia (OR:1.31,95%CI:1.19–1.45), lack of exercise (OR:1.91,95%CI:1.32–2.76), atrial fibrillation [OR:1.49,95%CI:1.35–1.65), family history of stroke (OR:2.18,95%CI:1.6–2.88) were the significant independent influencing factors of stroke in hypertensive patients over 60 years old. When these four factors were combined, compared with participants without any of these factors, the multi-adjusted odds ratios (95% confidence interval) of risk of stroke for persons concurrently having one, two and three or more of these factors were 1.89 (1.67–2.13), 2.15 (1.86–2.47) and 6.84 (4.90–9.55), respectively (linear trend P < 0.001); after multivariate adjustment, the family history of stroke had additive interaction with lack of exercise [RERI = 1.08(0.22–1.94), AP = 0.19(0.04–0.35), S = 1.31(1.02–1.69)], dyslipidemia [RERI = 0.87(0.41–1.33), AP = 0.23(0.08–0.38), S = 1.46(1.04–2.05)]. Conclusion: The prevalence of stroke was high in hypertensive patients aged 60 and above in Jiading District, Shanghai. Dyslipidemia, lack of exercise, atrial fibrillation and family history of stroke were significantly associated with stroke in hypertensive population. Stroke risk can be increased especially when multiple factors coexisting, and family history of stroke combined with a lack of exercise or dyslipidemia. [ABSTRACT FROM AUTHOR]

Moisture accumulates with the growing aging progress of oil-paper insulation and further shortens the remaining life of the transformer. The frequency-domain spectroscopy (FDS) technique can be used to realize the moisture estimation. However, the moisture estimation results would be unreliable once the aging effect on FDS was ignored. Given this issue, an alternative model including the aging effect is thus proposed using FDS and intelligent algorithm. In this work, the feature parameters of FDS data are used to build the databases for characterizing the aging degree and moisture. Then, the moisture estimation models are developed using the weighted K-nearest neighbor (K-NN) algorithm. The accuracy and applicability of the proposed models are finally discussed in laboratory and field conditions. In that respect, the findings reveal that the reported model is available for moisture estimation of transformer oil-paper insulation under various aging degrees and test temperatures. [ABSTRACT FROM AUTHOR]

The influence of nonuniform aging has not been considered in the prediction of the frequency domain spectroscopy (FDS) of the transformer oil-paper insulation (OPI) when using the finite element method (FEM). Given this issue, the modified simulation model was constructed based on the XY model and FEM. In the current work, the dielectric response property of the pressboards with different aging conditions in the modified model was characterized by its dielectric response parameters measured in the lab. Then the modified simulation model constructed in a 3-D system would be applied to study the effect of both nonuniform aging and the axial geometry on the FDS of OPI. Finally, the feasibility of the proposed models was verified by comparing the measured FDS and the predicted FDS. This article is expected to provide a model for predicting the FDS of the transformer OPI including the effect of nonuniform aging. [ABSTRACT FROM AUTHOR]

The accuracy and feasibility of the traditional XY model of transformer oil–paper insulation system are disputable since it ignored the effect of non‐uniform aging and conductance on dielectric response property. Given this issue, this work attempted to report a modified XY model to overcome these defects. The novelty of this work is in the exploration of the modified XY model as a potential tool for establishing the quantitative correlation among the complex relative permittivity of the liquid insulation, solid insulation, and liquid–solid composite insulation. In that respect, the presented verification experiments proved the feasibility and accuracy of the reported model. The contributions are expected to provide a theoretical basis for the condition evaluation of transformer solid insulation under non‐uniform aging conditions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of Koszul–Vinberg–Nijenhuis (KVN) structures on a left-symmetric algebroid as analogues of Poisson–Nijenhuis structures on a Lie algebroid, and show that a KVN-structure gives rise to a hierarchy of Koszul–Vinberg structures. We introduce the notions of KV Ω -structures, pseudo-Hessian–Nijenhuis structures and complementary symmetric 2 -tensors for Koszul–Vinberg structures on left-symmetric algebroids, which are analogues of P Ω -structures, symplectic-Nijenhuis structures and complementary 2 -forms for Poisson structures. We also study the relationships between these various structures. [ABSTRACT FROM AUTHOR]

The notion of an F -manifold algebra is the underlying algebraic structure of an F -manifold. We introduce the notion of pre-Lie formal deformations of commutative associative algebras and show that F -manifold algebras are the corresponding semi-classical limits. We study pre-Lie infinitesimal deformations and extension of pre-Lie n -deformation to pre-Lie (n + 1) -deformation of a commutative associative algebra through the cohomology groups of pre-Lie algebras. We introduce the notions of pre- F -manifold algebras and dual pre- F -manifold algebras, and show that a pre- F -manifold algebra gives rise to an F -manifold algebra through the sub-adjacent associative algebra and the sub-adjacent Lie algebra. We use Rota-Baxter operators, more generally O -operators and average operators on F -manifold algebras to construct pre- F -manifold algebras and dual pre- F -manifold algebras. [ABSTRACT FROM AUTHOR]

To investigate the contamination levels of respirable dust released in the work environment and the induced workers' health risk at a coal-fired power plant, we collected 405 dust samples from different dusty workstations by personal sampling during the coal-fired power generation process. Then, an inhalation risk assessment model from the USEPA was combined with the Monte Carlo simulation method to quantitatively evaluate the health risk caused by dust inhalation. Of 10 workstations researched, the dust concentration in the most workstations exceeded the prescribed occupational exposure limit. Workers engaged in ash removal suffered the highest health risk at 4.08 × 10−6 ± 2.85 × 10−6 (95% CI), closely followed by those involved in other job categories. The results can contribute to the formulation of targeted dust prevention measures and implementation of risk management for the coal-fired power sector. [ABSTRACT FROM AUTHOR]

The dielectric modulus Μ∗(ω) is used for studying the frequency domain response and activation energy (E a) of transformer immersed cellulose insulation. Existing literatures show that the temperature is a crucial factor affecting the Μ∗(ω) and aging rate of transformer oil-paper insulation, while the E a can be regarded as an indicator to reflect the average aging rate of the transformer immersed cellulose insulation. Therefore, the discussion of the temperature-dependence on both Μ∗(ω) and E a is of great significance. This paper attempts to report an approach for understanding the temperature impact on both Μ∗(ω) and E a. The obtained knowledge can be used to establish two available models for temperature correction on Μ∗(ω) and activation energy prediction of transform immersed cellulose insulation, respectively. These findings are expected to promote the reliability of the condition prediction result of transformer immersed cellulose insulation by using Μ∗(ω) and E a technique. [ABSTRACT FROM AUTHOR]

Background and Aims. To investigate the clinical effect of preservation or nonpreservation of the left colic artery (LCA) in total mesorectal excision (TME) under laparoscopy. Methods. The words, like "rectal cancer," "left colonic artery," and "laparoscopy," were used as the retrieval terms, and the keyword retrieval method was adopted. The retrieval period was set as from January 1, 2013, to June 1, 2018. We searched databases including PubMed, Web of Science, and China National Knowledge Infrastructure (CNKI) to collect randomized and controlled trials which compared the effect of preservation or nonpreservation of the LCA in TME under laparoscopy. Two researchers independently carried out literature screening, data extraction, and literature quality evaluation; Review Manager 5.3 was used for the meta-analysis. Results. Seven studies including 1467 cases were identified for the meta-analysis. As showed by the meta-analysis, compared with the LCA nonpreservation group, the LCA preservation group had significantly reduced incidence of anastomotic leakage (OR = 0.44 , CI = 0.30 , 0.65 , P < 0.0001) and postoperative urinary and sexual dysfunction (OR = 0.26 , CI = 0.09 , 0.78 , P = 0.02) and significantly shorter time for intestinal function recovery (WMD = − 0.26 , CI = − 0.41 , − 0.11 , P = 0.0008). There were no significant differences between the two groups in the duration of surgery, blood loss, number of dissected lymph nodes, or postoperative hospital stay. Conclusions. From the results, the LCA preservation group seems to achieve comparable success with acceptable safety outcomes. Therefore, this surgical method can be recommended in the clinical practice. [ABSTRACT FROM AUTHOR]

Two‐dimensional (2D) materials have unique structural and optoelectronic properties and have very important applications in energy, environment, and high‐performance optoelectronic sensing. Among them, the nonlinear optical properties and related applications are hot research fields. Herein, a novel 2D Bi2Te3–FeTe2 heterostructure is successfully prepared by Fe3+ induction and site‐selective overgrowth using a seed‐mediated growth method. This heterostructure has a plate−satellite geometry with an open spatially separated surface. The Z‐scan measurement characterizes the nonlinear transmittance of the heterostructure and proves the broadband saturation absorption behavior experimentally, which are superior to those of some mainstream 2D materials. In addition, the femtosecond‐transient absorption spectra reveal an ultrashort recovery time of 1.7 ps at pump wavelength of 780 nm. By integrating the Bi2Te3–FeTe2 saturable absorber into fiber laser, a 164.7‐ps pulse and a 481‐fs pulse are produced at center wavelengths of 1064 and 1550 nm, respectively, which are better than that of the Bi2Te3 nanoplate‐based mode‐locking. A new approach for the synthesis of 2D composites with spatially separated structures is provided. It is demonstrated that the synthesized Bi2Te3–FeTe2 heterojunction can be a promising broadband nonlinear optical material in ultrafast optical applications. [ABSTRACT FROM AUTHOR]

The results of frequency domain spectroscopy (FDS) will be affected by moisture which often leads to an unreliable condition prediction of oil-immersed cellulose insulation in transformers. In view of this, a solution is proposed in this study by adopting a fitting fingerprint database (FFD) technique, which can be utilized for condition prediction of aging and moisture content. In the current work, the relevant fingerprints that could characterize the insulation aging condition and moisture content are extracted from the FDS curves and the DC conductivity of the transformer oil. The FFD is then constructed by fitting fingerprints. The accuracy of the reported FFD technique is verified from tests on oil-immersed pressboard prepared in the lab and a transformer from the field. In this respect, the present contribution highlights FFD might be used as a powerful tool for condition prediction of oil-immersed cellulose insulation in transformers. [ABSTRACT FROM AUTHOR]

We recall the definition of the O -operators on bimodules over associative algebras (also called generalized Rota-Baxter operators), and we introduce the notions of compatible O -operators and of O N -structures. We show that an O N -structure gives rise to a hierarchy of O -operators and that a solution of the strong Maurer-Cartan equation on the associative twilled algebra associated to an O -operator gives rise to a pair of O N -structures which are naturally in duality. We introduce the notions of PN-, ΩN- and P Ω -structures on associative algebras and study their relations. [ABSTRACT FROM AUTHOR]

Over the past few years, frequency domain spectroscopy (FDS) has been widely utilized to assess transformer insulation. Many investigations have revealed that the FDS measurement has been observed to be dependent on service conditions (aging, moisture, geometry, and temperature). During the onsite FDS measurement, the inner insulation temperature of the de-energized transformer gradually decreases, which affects the FDS results due to moisture migration from oil to the cellulose insulation. This process gives rise to misinterpreting of the condition of the transformer insulation. Presently, the master curve technique reported by several researchers is utilized for temperature correction in FDS measurements. In fact, various researchers have obtained different master curves, so making a universal approach to temperature correction has become an important topic. In the present investigations, a series of experiments was performed on oil-impregnated pressboard insulation under laboratory conditions which was followed by FDS measurements at lower than operating temperature and a universal master curve for temperature correction was studied. Activation energies from oil-impregnated pressboard tests support the effectiveness of the proposed universal approach for temperature correction. [ABSTRACT FROM AUTHOR]

In this paper, first we study infinitesimal deformations of a Lie algebra with a representation and introduce the notion of a Nijenhuis pair, which gives a trivial deformation of a Lie algebra with a representation. Then we introduce the notion of a Kupershmidt-(dual-)Nijenhuis structure on a Lie algebra with a representation, which is a generalization of the r − n structure (r-matrix-Nijenhuis structure) introduced by Ravanpak, Rezaei-Aghdam, and Haghighatdoost. We show that a Kupershmidt-(dual-)Nijenhuis structure gives rise to a hierarchy of Kupershmidt operators. Finally, we define a Rota-Baxter-Nijenhuis structure to be a Kupershmidt-Nijenhuis structure on a Lie algebra with respect to the adjoint representation and study the relation between Rota-Baxter-Nijenhuis structures and r-matrix-Nijenhuis structures. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of a left-symmetric bialgebroid as a geometric generalization of a left-symmetric bialgebra and construct a left-symmetric bialgebroid from a pseudo-Hessian manifold. We also introduce the notion of a Manin triple for left-symmetric algebroids, which is equivalent to a left-symmetric bialgebroid. The corresponding double structure is a pre-symplectic algebroid rather than a left-symmetric algebroid. In particular, we establish a relation between Maurer–Cartan type equations and Dirac structures of the pre-symplectic algebroid which is the corresponding double structure for a left-symmetric bialgebroid. [ABSTRACT FROM AUTHOR]

Based on the differential graded Lie algebra controlling deformations of an n -Lie algebra with a representation (called an n - LieRep pair), we construct a Lie n -algebra, whose Maurer-Cartan elements characterize relative Rota-Baxter operators on n - LieRep pairs. The notion of an n -pre-Lie algebra is introduced, which is the underlying algebraic structure of the relative Rota-Baxter operator. We give the cohomology of relative Rota-Baxter operators and study infinitesimal deformations and extensions of order m deformations to order m + 1 deformations of relative Rota-Baxter operators through the cohomology groups of relative Rota-Baxter operators. Moreover, we build the relation between the cohomology groups of relative Rota-Baxter operators on n - LieRep pairs and those on (n + 1) - LieRep pairs by certain linear functions. [ABSTRACT FROM AUTHOR]

• Considered the significant impact of the COVID-19 on electricity load of metropolitan, ISOs and countries. • Developed a novel method based on multi-task learning, temporal convolutional network and long-short-term memory network. • Used the real mobility data from Google and Apple and load data from large power enterprises and public institutions. • Provides a feasible solution for reliable load forecasting model training and forecasting in long-sequence input scenarios. • Implemented the Shapley additive explanations technology to enhance interpretability by visualizing the Shapley values. The spread of the global COVID-19 epidemic has resulted in significant shifts in electricity consumption compared to regular days. It is unknown if standard single-task, single-indicator load forecasting algorithms can accurately reflect COVID-19 load patterns. Power practitioners urgently want a simple, efficient, and accurate solution for anticipating reliable load. In this paper, we first propose a unique collaborative TCN-LSTM-MTL short-term load forecasting model based on mobility data, temporal convolutional networks, and multi-task learning. The addition of the parameter sharing layers and the structure with residual convolution improves the data input diversity of the forecasting model and enables the model to obtain a wider time series receptive field. Then, to demonstrate the usefulness of the mobility optimized TCN-LSTM-MTL, tests were conducted in three levels and twelve base regions using 19 different benchmark models. It is capable of controlling predicting mistakes to within 1 % in the majority of tasks. Finally, to rigorously explain the model, the Shapley additive explanations (SHAP) visual model interpretation technology based on game theory is introduced. It examines the TCN-LSTM-MTL model's internal mechanism at various time periods and establishes the validity of the mobility indicators as well as the asynchronous relationship between indicator significance and real contribution. [ABSTRACT FROM AUTHOR]

Investigation of the rheological characteristics of deep-sea sediments is very important for understanding submarine disasters. Three reconstituted deep-sea soils with different plasticity and activity values from the South Sea China are considered in this study. A series of steady rheological tests are conducted on samples of three soils with different water contents and temperatures by a rate-controlled rotational rheometer operated in a steady-state regime. Rheological results show that shear stress and apparent viscosity can be decreased by a maximum of 65% when the temperature varies from 1 °C to 25 °C, and the three deep-sea soils are typical shear thinning non-Newtonian fluids with yield stress. The state of the samples can be divided into three phases during the shearing process, which implies that with an increase in the shear strain rate, all samples first behave as a solid, then transition from solid to liquid, and last behave as a liquid. The three phases are distinguished by the static yield stress (SYS) and fluidic yield stress (FYS), and a simple method for dividing the three phases is proposed. The SYS and FYS decreased with increasing temperature and water content. The relationships between yield stresses (SYS and FYS) and soil properties (water content and activity) and temperature are established. In addition, a unified strength model for deep-sea sediments is suggested, and the validity of the model is verified by comparing the prediction results of the model and test results. The results of this study could be useful for deep-sea submarine mudflow and landslide modelling. • A simple method to determine the values of SYS and FYS in steady rheological shearing tests is proposed. • Model for SYS and FYS that considering influence of LI, activity and temperature is established. • A unified strength model that considering effects of shear rate, temperature, water content, and activity is proposed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of a pre-symplectic algebroid and show that there is a one-to-one correspondence between pre-symplectic algebroids and symplectic Lie algebroids. This result is the geometric generalization of the relation between left-symmetric algebras and symplectic (Frobenius) Lie algebras. Although pre-symplectic algebroids are not left-symmetric algebroids, they still can be viewed as the underlying structures of symplectic Lie algebroids. Then we study exact pre-symplectic algebroids and show that they are classified by the third cohomology group of a left-symmetric algebroid. Finally, we study para-complex pre-symplectic algebroids. Associated with a para-complex pre-symplectic algebroid, there is a pseudo-Riemannian Lie algebroid. The multiplication in a para-complex pre-symplectic algebroid characterizes the restriction to the Lagrangian subalgebroids of the Levi–Civita connection in the corresponding pseudo-Riemannian Lie algebroid. [ABSTRACT FROM AUTHOR]

In this paper, we study non-abelian extensions of Leibniz algebras using two different approaches. First we construct two Leibniz 2-algebras using biderivations of Leibniz algebras and show that under a condition on centers, a non-abelian extension of Leibniz algebras can be described by a Leibniz 2-algebra morphism. Furthermore, under this condition, non-abelian extensions are classified by homotopy classes of Leibniz 2-algebra morphisms. Then we give a description of non-abelian extensions of Leibniz algebras in terms of Maurer-Cartan elements in a differential graded Lie algebra. [ABSTRACT FROM AUTHOR]

The life expectancy of a transformer is largely depended on the service life of transformer polymer insulation materials. Nowadays, several papers have reported that the traditional system poles obtained from polarization and depolarization current (PDC) data can be used to assess the condition of transformer insulation systems. However, the traditional system poles technique only provides limited ageing information for transformer polymer insulation. In this paper, the modified system poles obtained from PDC data are proposed to assess the ageing condition of transformer polymer insulation. The aim of the work is to focus on reporting a comparative investigation on the performance of modified system poles and traditional system poles for assessing the ageing condition of a transformer polymer insulation system. In the present work, a series of experiments have been performed under controlled laboratory conditions. The PDC measurement data, degree of polymerization (DP) and moisture content of the oil-immersed polymer pressboard specimens were carefully monitored. It is observed that, compared to the relationships between traditional system poles and DP values, there are better correlations between the modified system poles and DP values, because the modified system poles can obtain much more ageing information on transformer polymer insulation. Therefore, the modified system poles proposed in the paper are more suitable for the diagnosis of the ageing condition of transformer polymer insulation. [ABSTRACT FROM AUTHOR]

In this paper, first we modify the definition of a Hom-Lie algebroid introduced by Laurent-Gengoux and Teles and give its equivalent dual description. Many results that are parallel to Lie algebroids are given. In particular, we give the notion of a Hom-Poisson manifold and show that there is a Hom-Lie algebroid structure on the pullback of the cotangent bundle of a Hom-Poisson manifold. Then we give the notion of a Hom-Lie bialgebroid, which is a natural generalization of a purely Hom-Lie bialgebra and a Lie bialgebroid. We show that the base manifold of a Hom-Lie bialgebroid is a Hom-Poisson manifold. Finally, we introduce the notion of a Hom-Courant algebroid and show that the double of a Hom-Lie bialgebroid is a Hom-Courant algebroid. The underlying algebraic structure of a Hom-Courant algebroid is a Hom-Leibniz algebra, or a Hom-Lie 2-algebra. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of an omni -Lie algebra and show that it is the linearization of the higher analogue of the standard Courant algebroid. We also introduce the notion of a nonabelian omni -Lie algebra and show that it is the linearization of the higher analogue of the Courant algebroid associated to a Nambu-Poisson manifold. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of a left-symmetric algebroid, which is a generalization of a left-symmetric algebra from a vector space to a vector bundle. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie algebroid. We construct left-symmetric algebroids from [ABSTRACT FROM AUTHOR]

The statement in [2, Example 3.6] is not true in general. [ABSTRACT FROM AUTHOR]

For the oil-impregnated power transformers in service, the condition of the main insulation system is very important. This article reports a non-destructive evaluation technique based on time-frequency domain dielectric characteristics. First, the polarization/depolarization current and frequency-domain spectroscopy were well measured under controlled laboratory conditions. Then, the recovery voltage curves and recovery voltage polarization spectroscopy were also obtained by using the conversion method between polarization/depolarization current and recovery voltage based on the extended Debye model. After that, the time-domain dielectric characteristics, which can represent oil-paper insulation aging, were extracted from the polarization/depolarization current curves, recovery voltage curves and recovery voltage polarization spectroscopy. In addition, the frequency-domain dielectric characteristics, which can represent the oil-paper insulation aging, were also proposed in terms of frequency domain spectroscopy. Finally, the change rules of time-frequency domain dielectric characteristics under different aging times were investigated in depth. Results show that the time-frequency domain dielectric characteristics are sensitive to the aging states of power transformers, which could be utilized to diagnose the aging state of oil-paper insulation in field power transformers. [ABSTRACT FROM PUBLISHER]

In modern power transmission and distribution systems, power transformers are critical components and their electrical properties together with service lives are determined by the insulation property of oil-paper insulation. To better apply the frequency domain spectroscopy technique to assess transformer insulation condition, a series of experiments were performed under controlled laboratory conditions. First, this article presents the frequency domain dielectric response measurement results of oil-paper insulation samples under different moisture contents and aging states, and then the extracted frequency dielectric characteristic parameters determined from the imaginary part of relative permittivity (ϵr′′) and dielectric dissipation factor (tanδ) curves are used to assess the moisture contents and aging states of oil-paper insulation. Finally, the quantitative relationships among dielectric characteristic parameters, moisture content, and degree of polymerization are also established. Results show that in the frequency range of 10–3–102Hz, ϵr′′ and tanδ obviously increase as the moisture content of oil-paper insulation rises, while ϵr′′ and tanδ are very sensitive to aging only in 10–3–10–1Hz. Consequently, ϵr′′ and tanδ in different frequency ranges can be used to distinguish the influences of moisture content and aging state on frequency domain spectroscopy measurement results. [ABSTRACT FROM AUTHOR]

The ageing rate of cellulose insulation materials (paper/pressboard) in oil‐impregnated transformers is largely determined by moisture. In this paper, several experiments were conducted under controlled laboratory conditions to quantitatively diagnose the amount of moisture in cellulose insulation using frequency domain spectroscopy (FDS) technique, which has been proven to be an effective tool to predict the insulation condition in oil‐impregnated power equipment. The frequency dielectric response in oil‐impregnated pressboards, moisture content as well as test temperature, was monitored carefully, and a new dielectric characteristic parameter for the diagnosis of moisture content was proposed. In addition, the master curve technique was introduced to calibrate the temperature effect on FDS measurement results. These experiments revealed that a strong correlation exists between frequency dielectric parameter and moisture content in cellulose insulation. Such correlation can be utilised for better prediction of moisture content in paper–oil insulation. A modified assessment method for the diagnosis of moisture content in paper–oil insulation was investigated and its effectiveness was also demonstrated using a case. [ABSTRACT FROM AUTHOR]

In order to distinguish the influences of moisture and aging on the frequency domain dielectric response of oil-paper insulation and better apply frequency domain spectroscopy (FDS) to assess the insulation condition of power transformers, the oil-paper insulation samples with different moisture contents and different aging states were prepared in the laboratory. The FDS of the samples were tested and a group of characteristic parameters were extracted from dissipation factor (tan?) curves which could be used to assess the moisture content and aging states of oil-paper insulation respectively. The quantitative relationship among characteristic parameters, degree of polymerization (DP) and moisture contents (Km.c) was accurately established. The observations show that the proposed characteristic parameters are sensitive to the moisture in 10-3-102Hz, while the aging states influence the characteristic parameters in 10-3-10-1Hz. Meanwhile, an exponential relationship equation which could be used to assess the oil-paper insulation condition was established among the characteristic parameters, DP and the moisture content. Finally, the evaluation technique proposed in this paper was used to diagnose the insulation condition of several field transformers in this way, and its validity was preliminary and reasonably verified. [ABSTRACT FROM AUTHOR]

• Considered the significant impact of the COVID-19 on electricity load. • Developed a novel method based on multi-task learning using parameters sharing layers. • Used the real mobility data from Google and Apple and load data from large power enterprises and public institutions. • The universally adaptable model can control the forecasting error at a low level in the COVID-19. • Implemented the Shapley additive explanations technology to enhance interpretability. Affected by the new coronavirus (COVID-19) pandemic, global energy production and consumption have changed a lot. It is unknown whether conventional short-term load forecasting methods based on single-task, single-region, and conventional indicators can accurately capture the load pattern during the COVID-19 and should be carefully studied. In this paper, we make the following contributions: 1) A mobility-optimized load forecasting method based on multi-task learning and long short-term memory network is innovatively proposed to alleviate the impact of the COVID-19 on short-term load forecasting. The incorporation of mobility data and data sharing layers potentially reduces the difficulty of capturing the load patterns and improves the generalization of the load forecasting models. 2) The real public data collected from multiple agencies and companies in the United States and European countries are used to conduct horizontal and vertical tests. These tests prove the failure of the conventional models and methods in the COVID-19 and demonstrate the high accuracy (error mostly less than 1%) and robustness of the proposed model. 3) The Shapley additive explanations technology based on game theory is innovatively introduced to improve the objectivity of the models. It visualizes that mobility indicators are of great help to the accurate load forecasting. Besides, the non-synchronous relationships between the indicators' correlations and contributions to the load have been proved. [ABSTRACT FROM AUTHOR]

In this paper, first we give the cohomology theory of a Poisson algebra with a module (called a PoiMod pair) and study the linear deformation theory of a PoiMod pair. We introduce the notion of a Nijenhuis structure on a PoiMod pair, which gives a trivial linear deformation. Then by adding compatibility conditions between Nijenhuis structures and O -operators, we introduce the notion of an O N -structure on a PoiMod pair and show that an O N -structure gives rise to a hierarchy of pairwise compatible O -operators. Finally we introduce the notions of PN- and Ω N -structures on Poisson algebras and study their relations. [ABSTRACT FROM AUTHOR]

Biosurfactants are biologically active metabolites, and the efficiency of direct screening of new biosurfactants from nature using traditional methods is low, which should be enhanced in the following studies by adopting advanced biotechnologies. Rapid development and wide application of microbial culture independent methods, such as metagenomics, metatranscriptomics, metaproteomics and metabonomics, etc., contributes to quickly and precisely screening of novel biological surfactants. We mainly represented the current status of research and applications of biosurfactants in the remediation of petrochemical polluted environment, and also prospected avenues for future research. [ABSTRACT FROM AUTHOR]

• The effect of the aging of paper/pressboard on furfural content in oil was studied. • The effect of oil/paper/pressboard ratio on furfural- DP equation was studied. • The effect of oil replacement on aging evaluation results is corrected. The furfural analysis is an effective method to evaluate the aging state of transformer cellulose insulation. However, the existing research on the furfural analysis mainly focuses on 'oil-paper' system, without considering the oil-paper-pressboard system. In fact, the mass of insulating pressboard occupies a large proportion in the transformer, and there are obvious differences in the mass ratio of oil-paper-pressboard among transformers with different voltage levels, which will affect the effectiveness of furfural analysis. In addition, oil replacement is an oil treatment method to improve the insulation performance of oil, which will lead to the loss of furfural content in oil. In view of this, a series of experiments and studies were carried out to obtain the modified equation between furfural and degree of polymerization (DP) of paper/pressboard insulation with different oil-paper-pressboard mass ratios under oil replacement condition. Firstly, accelerated thermal aging experiment of insulation samples with various oil-paper-pressboard mass ratios was conducted in the lab, and the effect of oil-paper-pressboard mass ratio on furfural was analyzed. Then, the oil replacement experiments were performed, and the oil replacement compensation factor was proposed. Finally, a modified furfural -DP equation was established. This paper attempts to report a method for analyzing the effect of oil-paper-pressboard mass ratio and oil replacement on furfural- DP equation. These findings are expected to improve the application of furfural analysis in field transformers. [ABSTRACT FROM AUTHOR]

In this paper, first we introduce the notions of quasi-triangular pre-Lie bialgebras and factorizable pre-Lie bialgebras. A factorizable pre-Lie bialgebra leads to a factorization of the underlying pre-Lie algebra. We show that the symplectic double of a pre-Lie bialgebra naturally enjoys a factorizable pre-Lie bialgebra structure. Then we give the Rota-Baxter characterization of factorizable pre-Lie bialgebras. More precisely, we introduce the notion of quadratic Rota-Baxter pre-Lie algebras and show that there is a one-to-one correspondence between factorizable pre-Lie bialgebras and quadratic Rota-Baxter pre-Lie algebras. Finally, we develop the theories of matched pairs, bialgebras and Manin triples of Rota-Baxter pre-Lie algebras. In particular, a factorizable pre-Lie bialgebra gives rise to a Rota-Baxter pre-Lie bialgebra, and conversely a Rota-Baxter pre-Lie bialgebra gives rise to a factorizable pre-Lie bialgebra structure on the double space. [ABSTRACT FROM AUTHOR]

Oil–paper insulation is the critical insulation element in the modern power system. Under a harsh operating environment, oil–paper insulation will deteriorate gradually, resulting in electrical accidents. Thus, it is important to evaluate and monitor the insulation state of oil–paper insulation. Firstly, this paper introduces the geometric structure and physical components of oil–paper insulation and shows the main reasons and forms of oil–paper insulation's degradation. Then, this paper reviews the existing condition assessment techniques for oil–paper insulation, such as the dissolved gas ratio analysis, aging kinetic model, cellulose–water adsorption isotherm, oil–paper moisture balance curve, and dielectric response technique. Additionally, the advantages and limitations of the above condition assessment techniques are discussed. In particular, this paper highlights the dielectric response technique and introduces its evaluation principle in detail: (1) collecting the dielectric response data, (2) extracting the feature parameters from the collected dielectric response data, and (3) establishing the condition assessment models based on the extracted feature parameters and the machine learning techniques. Finally, two full potential studies are proposed, which research hotspots' oil–paper insulation and the electrical–chemical joint evaluation technique. In summary, this paper concludes the principles, advantages and limitation of the existing condition assessment techniques for oil–paper insulation, and we put forward two potential research avenues. [ABSTRACT FROM AUTHOR]

The distribution behavior of furfural in insulation systems is influenced by the oil–pressboard mass ratio. In addition, the equilibrium distribution of furfural between oil and pressboard will be disturbed after oil replacement. Therefore, it is of great significance to study the distribution ratio of furfural in oil with various oil–pressboard mass ratios after oil replacement. In this research, an accelerated thermal aging experiment and oil replacement experiment were conducted in the lab. Furthermore, the equilibrium characteristics of furfural dissolved in oil with various oil–pressboard mass ratios were studied. Multiple regression analysis was used to analyze the relationship between the oil–pressboard mass ratios and the distribution ratio of furfural in oil. The equilibrium distribution model of furfural was thus obtained. Afterwards, the modified furfural distribution model under oil replacement conditions was established. A novel scheme is provided for analyzing the equilibrium characteristics of furfural under various oil–pressboard mass ratios after oil replacement. The work of this paper is expected to improve the accuracy of furfural analysis. [ABSTRACT FROM AUTHOR]

Operating temperature is an important parameter of thyristors to ensure the stable operation of power electronic devices. Thermal management technology is of great significance for improving the reliability of thyristors. In this study, the performance of a phase change material (PCM) mesh-finned heat sink is investigated for the thermal management of thyristors. A multi-physical coupling model of the PCM mesh-finned heat sink is established to analyze the effects of different power losses, air velocities, heights of fins, and thickness of PCM on the thermal performance of the PCM heat sink. The influence of thermal and flow fields on PCM is considered in this model. Furthermore, the heat sink design is optimized to improve the thermal performance based on the calculation results of thermal network parameters. The results show that the power losses, the air velocity, the height of fins, and the thickness of PCM significantly affect the protection ability of the PCM heat sink. After optimizing the heat sink, the PCM heat sink provides 80 s protection time and 100 s recovery time. The PCM mesh-finned heat sink demonstrated good potential for the thermal management of thyristors. [ABSTRACT FROM AUTHOR]