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The combination of the time-scaling transformation and control parameterization has proven to be an effective approach in addressing optimal control problems involving switching systems with predefined subsystem sequences. However, this approach has certain limitations. First, the number of control switchings is required to be no less than the number of subsystem switchings. Second, the switching of the subsystem must be accompanied by the switching of the control. Third, this scheme introduces many hyperparameters, leading to combinatorial explosion. To address these drawbacks, we introduce a novel computational approach such that the control switching can be independent of subsystem switching. The superiority of this novel approach can be clearly observed from the solutions obtained using the proposed method for solving two illustrative examples. [ABSTRACT FROM AUTHOR]

We show that the distribution class ℒ(γ) \ 풪풮 is not closed under infinitely divisible distribution roots for γ > 0, that is, we provide some infinitely divisible distributions belonging to the class, whereas the corresponding Lévy distributions do not. In fact, one part of these Lévy distributions belonging to the class 풪ℒ\ℒ(γ) have different properties, and the other parts even do not belong to the class 풪ℒ. Therefore, combining with the existing related results, we give a completely negative conclusion for the subject and Embrechts–Goldie conjecture. Then we discuss some interesting issues related to the results of this paper. [ABSTRACT FROM AUTHOR]

Accurate evaluation of the impact range of hydraulic fracturing (HF) in coal seams is the key to optimizing HF design schemes. In this study, multistage HF processes in Well No. 1 of the Xinji No. 2 coal mine were monitored and analyzed using ground microseismic (MS) monitoring technology. An improved particle swarm optimization algorithm and waveform similarity superposition method were used to locate HF-induced MS events with different signal-to-noise ratios. The results showed that the seismic source location points were distributed horizontally within a 120 m range on both sides of the fracturing well, and vertically distributed from − 615 to − 675 m. The MS events envelope method was used to calculate the stimulated reservoir volume (SRV) of nine fracturing sections, totaling approximately 1,977,000 m3, with the largest SRV in Sections Nos. 2 and 6. Through continuous fracture network (CFN) modeling, the overall fracture extension of the HF was revealed to be rectangular and evenly distributed on both sides of the fracturing well. The main direction of the fracture extended outward along the vertical direction, in line with the direction of the injection hole. By calculating the CFN branch index (BI) and CFN length, the results showed that the fracture networks of Sections Nos. 1, 4, and 6 were more complex, and the CFN lengths of Sections Nos. 1, 2, 6, and 9 were longer. Combining the fracture network size, MS event parameters, and SRV, we determined that Sections Nos. 2 and 6 have longer fracture networks, larger HF ranges, and the best HF effect. This study is important for the evaluation of the effective range of HF in coal seams and for the design and parameter optimization of HF schemes. Highlights: Microseismic events with different signal-to-noise ratios were accurately located. The stimulated reservoir volume and the number of microseismic events in the fractured area are positively correlated. The fracture extension pattern of hydraulic fracturing was obtained by continuous fracture network modeling. [ABSTRACT FROM AUTHOR]

Microseismic (MS) events generated during coal and rock hydraulic fracturing (HF) include wet events caused by fracturing fluid injection, in addition to dry events caused by stress perturbations. The mixture of these two events makes effective fracturing MS events pickup difficult. This study is based on physical experiments of different coal and rock HF and uniaxial compression. The differences of waveform characteristic parameters of various coal and rock ruptures were analyzed using the Hilbert–Huang transform, leading to some useful conclusions. The phase characteristics of the acoustic emission (AE) energy differed significantly and responded well to the pumping pressure curve. The AE waveforms of HF exhibit similar energy and frequency distribution characteristics after Empirical mode decomposition. The main frequency bands for coal, sandstone, and shale samples are 100–300 kHz, while the mudstone sample is in the range of 50–150 kHz. The decay ratios for coal, sandstone, shale and mudstone samples are 0.78, 0.83, 0.67 and 0.85, respectively. When compared to the uniaxial compression test, the main frequency bands of HF were reduced for coal, sandstone and mudstone samples, whereas shale remained essentially unchanged. The duration, instantaneous energy, and total energy of the HF waveform are smaller than those of uniaxial compression, while the decay ratio is greater, especially for the mudstone samples. The waveform characteristic parameters, trained using the multilayer perceptron neural network, can effectively identify HF and uniaxial compression events with an accuracy of 96%. [ABSTRACT FROM AUTHOR]

In this paper, a computational method is proposed for solving a class of fractional optimal control problems subject to canonical constraints of equality and inequality. Fractional derivatives are described in the Atangana–Baleanu-Caputo sense, and their fractional orders can be different. To solve this problem, we present a discretization scheme based on the trapezoidal rule and a novel numerical integration technique. Then, the gradient formulas of the cost and constraint functions with respect to the decision variables are derived. Furthermore, a gradient-based optimization algorithm for solving the discretized optimal control problem is developed. Finally, the applicability and effectiveness of the proposed algorithm are verified through three non-trivial example problems. [ABSTRACT FROM AUTHOR]

Circular RNAs (circRNAs) have emerged as a multifunctional class of RNAs, while there is limited knowledge on their functions in the development of cancers. Herein, we performed the current study to probe into the regulatory mechanism of circ_0044516 in malignant behaviors of gastric cancer (GC) cells with the involvement of microRNA (miR)-149-5p/human antigen R (HuR) axis. Firstly, the expression levels of circ_0044516 in GC cell lines and normal gastric mucosal epithelial cells were determined by qRT-PCR, and GC cell lines with the highest expression of circ_0044516 were screened for further cell experiments. Subsequently, the biological functions of silenced circ_0044516 in GC were identified by CCK-8, colony formation, and transwell assays. Xenograft mouse models were established for in vivo verification. Furthermore, luciferase reporter, RIP, RNA pull-down assay and rescue experiments were performed to explore the sponge regulatory mechanism of circ_0044516. circ_0044516 was suggested to be highly expressed in GC cell lines, and circ_0044516 could promote GC cell proliferation, migration and invasion, as well as in vivo tumor growth. In addition, silenced circ-0044516 reversed the promotive roles in cell viability caused by overexpressed HuR. Furthermore, circ_0044516 mainly localized in the cytoplasm, which may act as a miR-149-5p sponge to modulate HuR expression, thereby playing an essential role in GC development. This study suggests that circ_0044516 may promote HuR expression through sponging miR-149-5p, thereby playing a part in GC progression. [ABSTRACT FROM AUTHOR]

For some γ > 0, we show that the distribution class (ℒ(γ) ∩풪S)\S(γ) is not closed under infinitely divisible distribution roots, that is, we provide examples showing that some infinitely divisible distributions belong to this class but their corresponding Lévy distributions do not. To this end, we explore the structural properties of some distribution classes, give a positive conclusion to the Embrechts–Goldie conjecture, and study some properties of a transformation from a heavy-tailed distribution to a light-tailed one. [ABSTRACT FROM AUTHOR]

In this paper, a numerical method is developed for solving a class of delay fractional optimal control problems involving nonlinear time-delay systems and subject to state inequality constraints. The fractional derivatives in this class of problems are described in the sense of Caputo, and they can be of different orders. First, we propose a numerical integration scheme for the fractional time-delay system and prove that the convergence rate of the numerical solution to the exact one is of second order based on Taylor expansion and linear interpolation. This gives rise to a discrete-time optimal control problem. Then, we derive the gradient formulas of the cost and constraint functions with respect to the decision variables and present a gradient computation procedure. On this basis, a gradient-based optimization algorithm is developed to solve the resulting discrete-time optimal control problem. Finally, several example problems are solved to demonstrate the effectiveness of the developed solution approach. [ABSTRACT FROM AUTHOR]