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Long non-coding RNAs (lncRNAs) associate with RNA-binding proteins (RBPs) to form lncRNA-protein complexes that act in a wide range of biological processes. Understanding the molecular mechanism of how a lncRNA-protein complex is assembled and regulated is key for their cellular functions. In this mini-review, we outline molecular methods used to identify lncRNA-protein interactions from large-scale to individual levels using bulk cells as well as those recently developed imaging and single-molecule approaches that are capable of visualizing RNA-protein assemblies in single cells and in real-time. Focusing on the latter group of approaches, we discuss their applications and limitations, which nevertheless have enabled quantification and comprehensive dissection of RNA-protein interactions possible.

Keeping the nucleolus a liquid condensate The nucleolus is a multilayered, membraneless nuclear condensate in which DNA polymerase I (Pol I)–mediated ribosomal DNA (rDNA) transcription and pre-rRNA processing occur in fibrillar center and dense fibrillar component (FC/DFC) units. How its biophysical properties are regulated has remained elusive. Wu et al . found that the RNA helicase DDX21 forms a shell coating each FC/DFC unit in the nucleolus (see the Perspective by Yamazaki and Hirose). The authors found that a long noncoding RNA called SLERT facilitates the transition from the open to the closed configuration of the helicase using a chaperone-like mechanism. DDX21 in the closed conformation forms loose clusters that confer the FC/DFC unit sufficient liquidity and space required for Pol I processivity. In addition, DDX21 within the loose clusters cannot approach and wrap rDNA, thus licensing rDNA for transcription. —DJ

Polyhedral oligomeric silsesquioxane (POSS) has a total of eight substituents. The number of substituents determines the modification effect of POSS. Through simulation of molecular dynamics, this paper explores how the number of substituents affects the POSS-modified cellulose insulation paper. Specifically, the mechanical properties, thermal stability and polarizability were calculated for cellulose models with 1-phenyl POSS, 2-phenyl POSS, 3-phenyl POSS, 4-phenyl POSS, 5-phenyl POSS, 6-phenyl POSS, 7-phenyl POSS, and 8-phenyl POSS, respectively. The results show that the cellulose model modified by 6-phenyl POSS achieved better effect than the other seven models, as evidenced by its distinctively large bulk modulus, shear modulus, and elastic modulus. Besides, the cellulose model modified by 6-phenyl POSS had the most stable and the minimum mean square displacement (MSD). This is because the mechanical properties of the insulation paper are improved, as the motion of cellulose chains is inhibited by the nano-size effect of POSS and the effect of phenyls. Further, the cellulose model modified by 6-phenyl POSS also had the smallest polarizability among the modified models. Therefore, the 6-phenyl POSS-modified cellulose model can effectively reduce the polarizability of cellulose, uniform the electric field distribution in oil-paper insulation system, and thus enhance the insulation property of transformers.

The dynamic assembly of the Synaptic-soluble N-ethylmaleimide-sensitive factor Attachment REceptor (SNARE) complex is crucial to the membrane fusion. Traditional ensemble studies lack the information of dynamic assembly of the protein complex. Here, we apply minute force on a tethered protein complex through dual-trap optical tweezers and study the folding dynamics of SNARE complex under mechanical force regulated by complexin-1 (CpxI). We reconstructed the clamp and facilitate functions of CpxI in vitro. Specially, the 1–83 amino acids (aa) of CpxI mainly implement the facilitate function, while the N-terminal domain (NTD) plays a dominant role. CTD is mainly related to Clamping, and separate 1-83aa and C-terminal domain (CTD) of CpxI can efficiently reconstitute the inhibitory signal identical to that the full-length CpxI functions. Our observation identifies the important chaperone role of the CpxI molecule in the dynamic assembly of SNARE complex under mechanical tension, and elucidates the specific function of each fragment of CpxI molecules in the chaperone process. Additionally, the developed technique may also be applied to study the mechanobiology and folding dynamics of single molecular protein complex.

DNA mismatch repair (MMR) is accomplished by highly conserved MutS and MutL homologs. MutS proteins recognize mismatch nucleotides and in the presence of ATP form a stable sliding clamp on the DNA. The MutS sliding clamp then promotes the cascade assembly of a MutL sliding clamp, which ultimately coordinates downstream mismatch excision. The MutS clamp-loader mechanics are unknown. Here we have examined a conserved positively charged cleft (PCC) located on the MutL N-terminal domain (NTD) proposed to mediate stable DNA binding events in several MMR models. We show that MutL does not bind DNA in physiological ionic conditions. Instead, the MutS sliding clamps and DNA together exploit the PCC to position the MutL NTD for clamp loading. Once in a sliding clamp form, the MutL PCC aids in UvrD helicase capture but not interactions with MutH during mismatch excision. The MutS-DNA clamp-loader progressions are significantly different from the replication clamp-loaders that attach polymerase processivity factors such as β-clamp and PCNA to the DNA. These studies underlining the breadth of mechanisms for stably linking crucial genome maintenance proteins to the DNA.

MutS homologs (MSHs) are highly conserved core components of DNA mismatch repair. Mismatch recognition provokes ATP-binding by MSH proteins that drives a conformational transition from a short-lived lesion-searching clamp to an extremely stable sliding clamp on the DNA. Here, we have expanded on previous bulk biochemical studies to examine the stability, lifetime, and kinetics of bacterial and human MSH sliding clamps on mismatched DNA using surface plasmon resonance and single-molecule analysis of fluorescently labeled proteins. We found that ATP-bound MSH complexes bound to blocked-end or very long mismatched DNAs were extremely stable over a range of ionic conditions. These observations underpinned the development of a high-throughput Förster resonance energy transfer system that specifically detects the formation of MSH sliding clamps on mismatched DNA. The Förster resonance energy transfer system is capable of distinguishing between HsMSH2-HsMSH3 and HsMSH2-HsMSH6 and appears suitable for chemical inhibitor screens. Taken together, our results provide additional insight into MSH sliding clamps as well as methods to distinguish their functions in mismatch repair.

Energy consumption prediction plays an important role in pipeline operation regulation and energy management. Accurate energy consumption prediction is helpful to make important decisions, including unit commitment, batch scheduling, load dispatching, energy consumption target setting, etc. The energy consumption of crude oil pipeline is mainly the electrical energy of pump unit. The average annual electrical energy consumption of China’s crude oil pipelines accounts for more than half of the annual operating cost of pipelines. Therefore, the prediction of electrical energy consumption of crude oil pipelines is critical. The energy consumption prediction of crude oil pipelines is very complicated. Firstly, it depends on the variables related to operation parameter, crude oil physical property parameter, environmental parameter and equipment parameter. Secondly, its nonlinearity is strong. Thirdly, the available samples are too little. Through the study on the monthly operation data collected by the Supervisory Control And Data Acquisition (SCADA) system and energy consumption analysis, the turnover and the electrical energy consumption is selected as input variable and output variable, respectively. The support vector machines (SVM) is introduced to predict the monthly electric energy consumption of crude oil pipelines driving oil pumps. However, the generalization capability of SVM is highly dependent on appropriate parameter setting, such as penalty coefficient and kernel parameter. The selection of the optimal parameters is critical to achieving good performance in the learning process. Therefore, in order to improve the generalization ability, GridSearchCV was adopted to optimize the hyperparameters of SVM. Taking a crude oil pipeline from Qinhuangdao City, Hebei Province to Fangshan District, Beijing as an example, the actual operation data for four consecutive years (48 months) are used for this study. The data are divided into training set and test set by stratified sampling method, which consist of 28 samples and 20 samples respectively. The mean absolute percentage error (MAPE), root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R2) on the test set are 3.42, 21.64, 14.31 and 0.94 respectively. Compared with other five state-of-the-art prediction methods in predictive accuracy, the result shows that GSCV-SVM has the best performance in the case of small samples, and the prediction results are in good agreement with the actual data.

The process of oil-gas separation is an important part of oilfield surface engineering. The oil-gas separator is the key equipment in this process. The composition of produced fluid from oil well is complex and the flow state of it changes frequently, which leads to the abnormal operating condition of the separator and affects the continuity of oil production. Therefore, the operating condition diagnosis of the oil-gas separator is extremely important for the system of oil production. Compared with the traditional threshold-based alarm method, the data-driven diagnosis method is more accurate and intelligent. According to the multivariate time series properties of the data of supervisory control and data acquisition (SCADA) system, the convolution neural network (CNN) is proposed to extract the multi-dimensional features of the oil-gas separator. Then based on the extracted features, the slug flow conditions of oil-gas separator are diagnosed, whose process is visually analyzed by t-distributed stochastic neighbour embedding (t-SNE). Finally, the data-driven diagnosis method of the oil-gas separator is realized, and the simulation data show that the average fault diagnosis rate of this method reaches 97.78%, which is 26.95% higher than that of the traditional method. The method proposed can diagnose the operating conditions of the separator accurately and quickly.

In this paper, we study the existence of localized nodal solutions for a class of semiclassical quasilinear Schrodinger equations including, as a special case, the Modified Nonlinear Schrodinger Equation (MNLS) e 2 ( Δ v + 1 2 v Δ v 2 ) − V ( x ) v + | v | q − 2 v = 0 , in R N , v ( x ) → 0 as | x | → ∞ . We establish for small e the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function, by developing new variational perturbation method to treat this class of non-smooth variational problems. The new method allows the perturbed variational functionals to share critical points with the original functional. This method allows us to avoid any limiting process from the perturbed problems to the original problem, and it is effective in dealing with multiple existence of solutions.

For semiclassical nonlinear Schrodinger equations with Sobolev critical exponent we propose and implement a procedure to construct an unbounded sequence of semiclassical bound states which are localized nodal solutions and are concentrated at a local minimum set of the potential. Our approach does not need any non-degeneracy condition of the limiting equation and is robust for more general problems.

In this paper we consider the system of p-Laplacian equations in R N − Δ p u j + μ j ( x ) | u j | p − 2 u j = ∑ i = 1 k β i j | u i | q | u j | q − 2 u j in R N , u j ( x ) → 0 as | x | → ∞ , j = 1 , … , k , where 1 p N , max { 2 , p } 2 q p ∗ = N p N − p , β i j are constants, i , j = 1 , … , k , β j j > 0 , j = 1 , 2 , … , k , β i j ≤ 0 , i ≠ j , i , j = 1 , … , k ; μ j , j = 1 , … , k are the potential functions and satisfy suitable decay assumptions. The existence of infinitely many sign-changing solutions is proved by the truncation method and by the concentration-compactness analysis on the approximating solutions.

Consider the critical p-Laplacian equation in R + N { − Δ p u = 0 , in R + N , | ∇ u | p − 2 ∂ u ∂ n = | u | p ‾ − 2 u , on R N − 1 , where R + N = R N − 1 × ( 0 , ∞ ) , 1 p N , p ‾ = ( N − 1 ) p N − p is the critical exponent of the Sobolev imbedding from W 1 , p ( R + N ) to L q ( R N − 1 ) , p ≤ q ≤ p ‾ and Δ p is the p-Laplacian operator, Δ p u = ∇ ( | ∇ u | p − 2 ∇ u ) . We prove polynomial decay of the solutions | u ( x ) | ≤ c ( 1 + | x | ) − N − p p − 1 , for x ∈ R + N . The decay exponent is the best possible.

The pathogenic consequences of 369 unique human HsMLH1 missense variants has been hampered by the lack of a detailed function in mismatch repair (MMR). Here single-molecule images show that HsMSH2-HsMSH6 provides a platform for HsMLH1-HsPMS2 to form a stable sliding clamp on mismatched DNA. The mechanics of sliding clamp progression solves a significant operational puzzle in MMR and provides explicit predictions for the distribution of clinically relevant HsMLH1 missense mutations.

RNA polymerase I (Pol I) transcription takes place at the border of the fibrillar center (FC) and the dense fibrillar component (DFC) in the nucleolus. Here, we report that individual spherical FC/DFC units are coated by the DEAD-box RNA helicase DDX21 in human cells. The long noncoding RNA (lncRNA)

The electrical energy consumption forecasting for crude oil pipeline is critical in many aspects, such as energy consumption target setting, batch scheduling, unit commitment, etc. For actual crude oil pipelines, the nonlinearity of the sample is strong. The electrical energy consumption of crude pipeline is affected by many parameters, including oil physical property parameter, pipe parameter, station parameter, environmental parameter and operating parameter. At the same time, the whole process has the characteristics of intermittency and complex fluctuations. The above three main reasons make the energy consumption forecasting of crude oil pipeline complicated. In the past few years, several intelligence-based models have been introduced to accurately forecast energy consumption. Among them, back-propagation neural network (BPNN) seems to be more effective and can handle the nonlinear energy behavior and achieve accurate forecast results. However, due to its over-fitting problem, the accuracy of energy consumption forecasting will be reduced. To overcome this problem, the paper proposes a hybrid method for short-term energy consumption forecasting, namely PSO-BPNN. Back propagation neural network is integrated with particle swarm optimization to find optimal network weight. In this research, an effective technique called principal component analysis is applied to eliminate redundant noise and extract the primary characteristics of transportation data. The stratified sampling method is used to divide the training set and the test set to avoid large deviations caused by the randomness of sampling. Taking a crude oil pipeline in northeast china as a case study, SCADA system data are collected daily from December 31, 2016 to June 18, 2019. Comparing the evaluation indicators of PSO-BPNN with that of five state-of-the-art forecasting methods of GA-BPNN, SA-BPNN, DE-BPNN, FOA-BPNN, BPNN, the effectiveness of PSO-BPNN algorithm is evaluated. Compared with other five forecasting methods, the forecast results of PSO-BPNN are in best agreement with the actual data. The results indicate that the proposed PSO-BPNN model outperforms all five models used for comparison, which demonstrates its superior ability to generate forecasts in terms of forecasting accuracy.

Aiming at problems such as slow training speed, poor prediction effect, and unstable detection results of traditional anomaly detection algorithms, a data mining method for anomaly detection based on the deep variational dimensionality reduction model and MapReduce (DMAD-DVDMR) in cloud computing environment is proposed. First of all, the data are preprocessed by a dimensionality reduction model based on deep variational learning and based on ensuring complete data information as much as possible, the dimensionality of the data is reduced, and the computational pressure is reduced. Secondly, the data set stored on the Hadoop Distributed File System (HDFS) is logically divided into several data blocks, and the data blocks are processed in parallel through the principle of MapReduce, so the k-distance and LOF value of each data point can only be calculated in each block. Thirdly, based on stochastic gradient descent, the concept of k-neighboring distance is redefined, thus avoiding the situation where there are greater than or equal to k-repeated points and infinite local density in the data set. Finally, compared with CNN, DeepAnt, and SVM-IDS algorithms, the accuracy of the scheme is increased by 10.3%, 18.0%, and 17.2%, respectively. The experimental data set verifies the effectiveness and scalability of the proposed DMAD-DVDMR algorithm.

DNA mismatch repair (MMR) is a DNA excision-resynthesis process that principally enhances replication fidelity. Highly conserved MutS (MSH) and MutL (MLH/PMS) homologs initiate MMR and in higher eukaryotes act as DNA damage sensors that can trigger apoptosis. MSH proteins recognize mismatched nucleotides, whereas the MLH/PMS proteins mediate multiple interactions associated with downstream MMR events including strand discrimination and strand-specific excision that are initiated at a significant distance from the mismatch. Remarkably, the biophysical functions of the MLH/PMS proteins have been elusive for decades. Here we consider recent observations that have helped to define the mechanics of MLH/PMS proteins and their role in choreographing MMR. We highlight the stochastic nature of DNA interactions that have been visualized by single molecule analysis as well as the plasticity of protein complexes that employ thermal diffusion to complete the progressions of MMR.

Li7La3Zr2O12 (LLZO) garnet-type oxide has become a promising inorganic electrolyte for solid-state lithium-ion batteries due to its high ionic conductivity and good chemical stability with the lithium metal. However, the poor wettability of LLZO garnet-type oxide with lithium metal and its incompact structure have impeded their extensive applications in solid-state lithium-ion batteries. Herein, Li6.75La3Zr1.75Ta0.25O12 (LLZTO) particles were embedded in the amorphous Li3OCl to form an integrated composite electrolyte (LLZTO-2wt.% Li3OCl) with compact and stable structure at 350 °C, which presents high ionic conductivity (2.27 × 10−4 S cm−1), low interfacial resistance and high electrochemical stability (up to 10 V vs. Li/Li+) at room temperature. The amorphous Li3OCl acting as a binder, filler and bridge promotes the formation of an integrated composite electrolyte and continuous ionic conductive network among LLZTO particles. Furthermore, the Li3OCl with excellent affinity to lithium metal in-situ reacts with the lithium metal to form a stable and dense interfacial layer, which greatly decreases the interfacial resistance between the composite electrolyte and lithium metal (from 1850 to 90 Ω cm2). The interfacial layer allied compact composite electrolyte also effectively suppresses the lithium dendrite growth during lithium plating-striping. The symmetrical Li/LLZTO-2wt.% Li3OCl/Li cell can stably cycle 1000 h without short circuit. The stable specific capacity of solid-state LiFePO4/LLZTO-2wt.% Li3OCl/Li battery is as high as 157.5 mAh g−1 and 85.7 mAh g−1 at 0.05 C and 0.5 C, respectively. Combining the garnet-type electrolyte with amorphous Li3OCl is a promising way to develop the compact garnet-type electrolyte at low temperature for solid-state lithium-ion batteries.

Sliding clamps on DNA consist of evolutionarily conserved enzymes that coordinate DNA replication, repair, and the cellular DNA damage response. MutS homolog (MSH) proteins initiate mismatch repair (MMR) by recognizing mispaired nucleotides and in the presence of ATP form stable sliding clamps that randomly diffuse along the DNA. The MSH sliding clamps subsequently load MutL homolog (MLH/PMS) proteins that form a second extremely stable sliding clamp, which together coordinate downstream MMR components with the excision-initiation site that may be hundreds to thousands of nucleotides distant from the mismatch. Specific or nonspecific binding of other proteins to the DNA between the mismatch and the distant excision-initiation site could conceivably obstruct the free diffusion of these MMR sliding clamps, inhibiting their ability to initiate repair. Here, we employed bulk biochemical analysis, single-molecule fluorescence imaging, and mathematical modeling to determine how sliding clamps might overcome such hindrances along the DNA. Using both bacterial and human MSH proteins, we found that increasing the number of MSH sliding clamps on a DNA decreased the association of the Escherichia coli transcriptional repressor LacI to its cognate promoter LacO. Our results suggest a simple mechanism whereby thermal diffusion of MSH sliding clamps along the DNA alters the association kinetics of other DNA-binding proteins over extended distances. These observations appear generally applicable to any stable sliding clamp that forms on DNA.

The diagnosis of slug flow is extremely important for the efficient operation of the gas-liquid separator. Traditional fault diagnosis based on the convolutional neural network has not involved the explainability of the convolutional neural network, which makes the model difficult to interpret from the perspective of physical meaning. An explainable diagnostic method based on a fully convolutional neural network is proposed. The class activation mapping, multivariate mutual information, global average pooling and t-distributed stochastic neighbor embedding are combined to analyze the diagnostic process of the network. The experimental results based on simulation data showed that the proposed method can be utilized to interpret the correlation degree between different operating conditions, the importance of each period in the measurement variable, and the engineering significance of the convolutional kernels of the last layer, which provides information supplement for fault reasoning of human experts.

In this paper, we consider the problem − Δ p u + a ( x ) | u | p − 2 u = | u | p ⁎ − 2 u + μ | u | q − 2 u in R N , where 1 p N , max ⁡ { p , p ⁎ − 1 } q p ⁎ = N p N − p , μ > 0 , Δ p is the p-Laplacian operator, and the potential a ( x ) is positive and verifies suitable decay assumptions. We prove that the problem has infinitely many solutions by using truncation method.

A novel glass-ceramic electrolyte of (100-x)(70Li 2 S-30P 2 S 5 )-xLi 2 ZrO 3 (x = 0, 1, 2, 5) is successfully prepared by a vibratory ball-milling method and followed by a heat-treatment process. Composition of the ternary sulfide electrolyte and the heat-treatment process are optimized by physical characterizations and electrochemical measurements. The testing results show that the optimal substitution quantity of Li 2 ZrO 3 into the Li 2 S-P 2 S 5 electrolyte substrate is 1 mol %. An appropriate heat-treatment temperature of 99(70Li 2 S-30P 2 S 5 )-1Li 2 ZrO 3 glass-ceramic electrolyte is 285 °C. Among the as-prepared ternary electrolyte samples, 99(70Li 2 S-30P 2 S 5 )-1Li 2 ZrO 3 glass-ceramic electrolyte may exhibit the highest conductivity of 2.85 × 10 −3 S cm −1 at room temperature, which is much higher than that of the 70Li 2 S-30P 2 S 5 glass-ceramic electrolyte. Compared to that of the all-solid-state lithium-ion battery of LiCoO 2 /70Li 2 S-30P 2 S 5 /In-Li, discharge capacities of all-solid-state lithium-ion battery of LiCoO 2 /99(70Li 2 S-30P 2 S 5 )-1Li 2 ZrO 3 /In-Li may increase 41.0% at the 10th charge-discharge cycle and 21.9% at the 50th charge-discharge cycle, respectively. Furthermore, electrochemical impedance spectroscopy (EIS) analyses of all-solid-state lithium-ion batteries reveal that addition of Li 2 ZrO 3 into the Li 2 S-P 2 S 5 electrolyte substrate may decrease the interfacial resistance between the electrodes and solid electrolyte. The improvement of electrochemical performances of 99(70Li 2 S-30P 2 S 5 )-1Li 2 ZrO 3 glass-ceramic electrolyte is ascribed to both the stable crystal structure and a high lithium-ion diffusion coefficient of Li 2 ZrO 3 .

A Li-rich layered oxide Li[Li 0.17 Ni 0.17 Co 0.10 Mn 0.56 ]O 2 is synthesized by a chemical deposition method. The surface modification with the LiV 3 O 8 is introduced onto Li-rich layered Li[Li 0.17 Ni 0.17 Co 0.10 Mn 0.56 ]O 2 oxide for the first time. The pristine and LiV 3 O 8 -coated Li[Li 0.17 Ni 0.17 Co 0.10 Mn 0.56 ]O 2 cathode materials are investigated by X-ray diffraction (XRD), Special surface area analysis (BET), scanning electron microscopy (SEM), transmission electron microscopy (TEM), electrochemical measurement and charge-discharge testing techniques. After coating of LiV 3 O 8 , the bulk crystallographic structure, morphology and grain size of the layered Li[Li 0.17 Ni 0.17 Co 0.10 Mn 0.56 ]O 2 are not essentially changed. Compared to the pristine sample, electrochemical performance of LiV 3 O 8 -coated samples has been obviously enhanced. Especially, the capacity retention of 3 wt% LiV 3 O 8 -coated sample reaches 94.3% after 100 charge/discharge cycles. Moreover, the rate capability is obviously increased for LiV 3 O 8 -coated samples with suitable thickness of coating. The discharge capacity of 3 wt% LiV 3 O 8 -coated sample at 2C rate is more than 157.9 mAh g −1 . Therefore, the surface modification with the LiV 3 O 8 is an effective way to improve the electrochemical performance of Li-rich layered oxides.

A shared paradigm of mismatch repair (MMR) across biology depicts extensive exonuclease-driven strand-specific excision that begins at a distant single-stranded DNA (ssDNA) break and proceeds back past the mismatched nucleotides. Historical reconstitution studies concluded that Escherichia coli (Ec) MMR employed EcMutS, EcMutL, EcMutH, EcUvrD, EcSSB and one of four ssDNA exonucleases to accomplish excision. Recent single-molecule images demonstrated that EcMutS and EcMutL formed cascading sliding clamps on a mismatched DNA that together assisted EcMutH in introducing ssDNA breaks at distant newly replicated GATC sites. Here we visualize the complete strand-specific excision process and find that long-lived EcMutL sliding clamps capture EcUvrD helicase near the ssDNA break, significantly increasing its unwinding processivity. EcSSB modulates the EcMutL–EcUvrD unwinding dynamics, which is rarely accompanied by extensive ssDNA exonuclease digestion. Together these observations are consistent with an exonuclease-independent MMR strand excision mechanism that relies on EcMutL–EcUvrD helicase-driven displacement of ssDNA segments between adjacent EcMutH–GATC incisions., The mechanics of MMR strand specific excision that begins at a distant ssDNA break are not yet clear. Here the authors have used multiple single molecule imaging techniques to visualize the behavior of MMR components on mismatched DNA substrates and reveal an exonuclease-independent mechanism for E.coli MMR.

The mid-term electrical energy consumption forecasting for crude oil pipelines is helpful for making important decisions, such as energy consumption target setting, unit commitment, batch scheduling, and equipment monitoring with degraded performance. The electricity energy consumption forecasting during operation is complicated. Therefore, A hybrid prediction method combining genetic algorithm and support vector machine is proposed, which includes four parts: data preprocessing part, optimization part, forecasting part, and evaluation part. The stratified sampling method is adopted to divide the training set and the test set to avoid large deviation caused by sampling stochasticity of small samples. According to the nonlinear relationship between input variable and output variable mapped by SVM technology, genetic algorithm was proposed to optimize the hyperparameters of SVM. For the operation data of three crude oil pipelines in China, the different proportions of data sets are compared and analyzed, the ratio of training set to test set for Pipeline 1, Pipeline 2, and Pipeline 3 is 6:4, 7:3, 8:2, respectively. Comparing the evaluation indicators of GA-SVM with that of five state-of-the-art prediction methods, GA-SVM hybrid model has the best effect in improving the predictive accuracy, and the forecast results are in the best agreement with the actual data.

We study elliptic equations with quasilinear perturbation { Δ u + 1 2 κ u Δ u 2 + e ∑ i , j = 1 N ( a i j ( u ) D i j u + 1 2 D z a i j ( u ) D i u D j u ) + f ( u ) + e h ( u ) = 0 , in Ω , u = 0 , on ∂ Ω , where Ω ⊂ R N , N ≥ 3 is a smooth bounded domain, κ ∈ { 0 , 1 } , e is a small parameter. Multiplicity result is proved by elliptic regularization method.

We consider quasilinear elliptic equations, including the following Modified Nonlinear Schrodinger Equation as a special example: \begin{document}$ \begin{equation*} \left\{ \begin{aligned} &\Delta u+\frac{1}{2}u\Delta u^2+\lambda |u|^{r-2}u = 0, \ \ \ \text{in}\,\,\Omega,\\ u'>where \begin{document}$ \Omega\subset\mathbb{R}^N(N\geq3) $\end{document} is a bounded domain with smooth boundary, \begin{document}$ \lambda>0,\, r\in(2,4) $\end{document} . We prove as \begin{document}$ \lambda $\end{document} becomes large the existence of more and more sign-changing solutions of both positive and negative energies.

We consider the following nonlinear Schrodinger system with critical growth − Δ u j = λ j u j + ∑ i = 1 k β i j | u i | 2 ⁎ 2 | u j | 2 ⁎ 2 − 2 u j , in Ω , u j = 0 , on ∂ Ω , j = 1 , ⋯ , k , where Ω is a bounded smooth domain in R N , 2 ⁎ = 2 N N − 2 , 0 λ j λ 1 ( Ω ) , j = 1 , ⋯ , k , λ 1 ( Ω ) is the first eigenvalue of −Δ with zero Dirichlet boundary condition. We consider the repulsive case, namely β j j > 0 , j = 1 , ⋯ , k , β i j = β j i ≤ 0 , i ≠ j , i , j = 1 , ⋯ , k . The existence of infinitely many sign-changing solutions as bound states is proved, provided N ≥ 7 , by approximations of systems with subcritical growth and by the concentration analysis on approximating solutions.

In this paper, we consider the following quasilinear equation with critical exponent, a quasilinear version of the classical Brezis–Nirenberg problem: $$\begin{aligned} \left\{ \begin{array}{rlll} -\displaystyle \sum _{i, j=1}^ND_j(a_{ij}(u)D_i u)+\frac{1}{2}\displaystyle \sum _{i, j=1}^Na'_{ij}(u)D_i uD_j u &{}= au+|u|^{2^*-2}u &{} \quad \hbox { in } \Omega \\ u&{}=0 &{} \quad \hbox { on } \partial \Omega ,\\ \end{array}\right. \quad {(P)} \end{aligned}$$ where \( 2^*=\frac{2N}{N-2}\) is the Sobolev critical exponent for the embedding of \(H_0^1(\Omega )\) into \(L^p(\Omega )\), \(\Omega \subset \mathbb {R}^N\) is an open-bounded domain with smooth boundary, \(a>0\) is a constant. We prove that if \(N\ge 7,\) the problem (P) admits an unbounded sequence of solutions. These solutions are obtained from subcritical approximations. This is done by analyzing the asymptotic behavior and the concentration compactness of the approximation solutions for the subcritical problems. The existence of infinitely many solutions to the subcritical problems is obtained via a p-Laplacian regularization process.