Local Solution Research Articles

Local Weak Solution of the Isentropic Compressible Navier–Stokes Equations with Variable Viscosity

Local Weak Solution of the Isentropic Compressible Navier–Stokes Equations with Variable Viscosity

Adap-BDCM: Adaptive Bilinear Dynamic Cascade Model for Classification Tasks on CNV Datasets.

Copy number variation (CNV) is an essential genetic driving factor of cancer formation and progression, making intelligent classification based on CNV feasible. However, there are a few challenges in the current machine learning and deep learning methods, such as the design of base classifier combination schemes in ensemble methods and the selection of layers of neural networks, which often result in low accuracy. Therefore, an adaptive bilinear dynamic cascade model (Adap-BDCM) is developed to further enhance the accuracy and applicability of these methods for intelligent classification on CNV datasets. In this model, a feature selection module is introduced to mitigate the interference of redundant information, and a bilinear model based on the gated attention mechanism is proposed to extract more beneficial deep fusion features. Furthermore, an adaptive base classifier selection scheme is designed to overcome the difficulty of manually designing base classifier combinations and enhance the applicability of the model. Lastly, a novel feature fusion scheme with an attribute recall submoduleis constructed, effectively avoiding getting stuck in local solutions and missing some valuable information. Numerous experiments have demonstrated that our Adap-BDCM model exhibits optimal performance in cancer classification, stage prediction, and recurrence on CNV datasets. This study can assist physicians in making diagnoses faster and better.

Blind Super-Resolution Via Meta-Learning and Markov Chain Monte Carlo Simulation.

Learning based approaches have witnessed great successes in blind single image super-resolution (SISR) tasks, however, handcrafted kernel priors and learning based kernel priors are typically required. In this paper, we propose a Meta-learning and Markov Chain Monte Carlo based SISR approach to learn kernel priors from organized randomness. In concrete, a lightweight network is adopted as kernel generator, and is optimized via learning from the MCMC simulation on random Gaussian distributions. This procedure provides an approximation for the rational blur kernel, and introduces a network-level Langevin dynamics into SISR optimization processes, which contributes to preventing bad local optimal solutions for kernel estimation. Meanwhile, a meta-learning based alternating optimization procedure is proposed to optimize the kernel generator and image restorer, respectively. In contrast to the conventional alternating minimization strategy, a meta-learning based framework is applied to learn an adaptive optimization strategy, which is less-greedy and results in better convergence performance. These two procedures are iteratively processed in a plug-and-play fashion, for the first time, realizing a learning-based but plug-and-play blind SISR solution in unsupervised inference. Extensive simulations demonstrate the superior performance and generalization ability of the proposed approach when comparing with state-of-the-arts on synthesis and real-world datasets.

Local solutions for nonhomogeneous Navier–Stokes equations with large flux

The local existence of solutions to nonhomogeneous Navier–Stokes equations in cylindrical domains with arbitrary large flux is demonstrated. The existence is proved by the method of successive approximations. To show the existence with the lowest possible regularity the special Besov spaces called the Sobolev–Slobodetskii spaces are used. The inflow and outflow are prescribed on the parts of the boundary which are perpendicular to the ‐axis. Since the inflow and outflow are positive the crucial point of this paper is to verify that ‐coordinate of velocity is also positive. Finally, we conclude the local existence such that the velocity belongs to , the gradient of pressure to and the density to , where .

Angel CCS project – decarbonising the hard-to-abate industries of WA

The Angel CCS Project is a proposed large-scale multi-user carbon capture and storage (CCS) hub located near Karratha, WA. It is being progressed by the Angel CCS Joint Venture (JV). Angel CCS is ideally located to aggregate emissions from existing sources in the Pilbara region and has the potential to facilitate the development of new lower-carbon industries, such as the production of hydrogen and ammonia, by providing a local solution for emissions. The JV has been awarded greenhouse gas assessment permit G-10-AP, located in the Northern Carnarvon Basin off the north-western coast of Western Australia and is now assessing the technical, regulatory and commercial feasibility of aggregating emissions from existing and potential future facilities and the geological storage of carbon dioxide in the permit area. Notionally, the Angel CCS project is expected to be able to handle up to 5 Mtpa. The proposed project could be the first large scale CCS hub with offshore storage in Australia and potentially one of the largest CCS hubs in the Asia Pacific. The paper provides an overview of the Angel CCS Project, outlines key enabling factors for CCS Hub developments, and explains the key considerations that informed the development concept.

On the well-posedness of the Cauchy problem for the two-component peakon system in Ck∩Wk,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^k\\cap W^{k,1}$$\\end{document}

This study focuses on the Cauchy problem associated with the two-component peakon system featuring a cubic nonlinearity, constrained to the class (m,n)∈Ck(R)∩Wk,1(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(m,n)\\in C^{k}(\\mathbb {R}) \\cap W^{k,1}(\\mathbb {R})$$\\end{document} with k∈N∪{0}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k\\in \\mathbb {N}\\cup \\{0\\}$$\\end{document}. This system extends the celebrated Fokas–Olver–Rosenau–Qiao equation and the following nonlocal (two-place) counterpart proposed by Lou and Qiao: ∂tm(t,x)=∂x[m(t,x)(u(t,x)-∂xu(t,x))(u(-t,-x)+∂x(u(-t,-x)))],\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\partial _t m(t,x)= \\partial _x[m(t,x)(u(t,x)-\\partial _xu(t,x)) (u(-t,-x)+\\partial _x(u(-t,-x)))], \\end{aligned}$$\\end{document}where m(t,x)=1-∂x2u(t,x)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m(t,x)=\\left( 1-\\partial _{x}^2\\right) u(t,x)$$\\end{document}. Employing an approach based on Lagrangian coordinates, we establish the local existence, uniqueness, and Lipschitz continuity of the data-to-solution map in the class Ck∩Wk,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^k\\cap W^{k,1}$$\\end{document}. Moreover, we derive criteria for blow-up of the local solution in this class.

Multi-Strategy Improved Dung Beetle Optimization Algorithm and Its Applications

The dung beetle optimization (DBO) algorithm, a swarm intelligence-based metaheuristic, is renowned for its robust optimization capability and fast convergence speed. However, it also suffers from low population diversity, susceptibility to local optima solutions, and unsatisfactory convergence speed when facing complex optimization problems. In response, this paper proposes the multi-strategy improved dung beetle optimization algorithm (MDBO). The core improvements include using Latin hypercube sampling for better population initialization and the introduction of a novel differential variation strategy, termed “Mean Differential Variation”, to enhance the algorithm’s ability to evade local optima. Moreover, a strategy combining lens imaging reverse learning and dimension-by-dimension optimization was proposed and applied to the current optimal solution. Through comprehensive performance testing on standard benchmark functions from CEC2017 and CEC2020, MDBO demonstrates superior performance in terms of optimization accuracy, stability, and convergence speed compared with other classical metaheuristic optimization algorithms. Additionally, the efficacy of MDBO in addressing complex real-world engineering problems is validated through three representative engineering application scenarios namely extension/compression spring design problems, reducer design problems, and welded beam design problems.

Stable stripe and vortex solitons in two-dimensional spin-orbit coupled Bose–Einstein condensates

We present a flexible manipulation and control of solitons via Bose–Einstein condensates. In the presence of Rashba spin–orbit coupling and repulsive interactions within a harmonic potential, our investigation reveals the numerical local solutions within the system. By manipulating the strength of repulsive interactions and adjusting spin–orbit coupling while maintaining a zero-frequency rotation, diverse soliton structures emerge within the system. These include plane-wave solitons, two distinct types of stripe solitons, and odd petal solitons with both single and double layers. The stability of these solitons is intricately dependent on the varying strength of spin–orbit coupling. Specifically, stripe solitons can maintain a stable existence within regions characterized by enhanced spin–orbit coupling while petal solitons are unable to sustain a stable existence under similar conditions. When rotational frequency is introduced to the system, solitons undergo a transition from stripe solitons to a vortex array characterized by a sustained rotation. The rotational directions of clockwise and counterclockwise are non-equivalent owing to spin–orbit coupling. As a result, the properties of vortex solitons exhibit significant variation and are capable of maintaining a stable existence in the presence of repulsive interactions.

An Improved Golden Jackal Optimization Algorithm Based on Mixed Strategies

In an effort to overcome the problems with typical optimization algorithms’ slow convergence and tendency to settle on a local optimal solution, an improved golden jackal optimization technique is proposed. Initially, the development mechanism is enhanced to update the prey’s location, addressing the limitation of just relying on local search in the later stages of the algorithm. This ensures a more balanced approach to both algorithmic development and exploration. Furthermore, incorporating the instinct of evading natural predators enhances both the effectiveness and precision of the optimization process. Then, cross-mutation enhances population variety and facilitates escaping from local optima. Finally, the crossbar strategy is implemented to change both the individual and global optimal solutions of the population. This technique aims to decrease blind spots, enhance population variety, improve solution accuracy, and accelerate convergence speed. A total of 20 benchmark functions are employed for the purpose of comparing different techniques. The enhanced algorithm’s performance is evaluated using the CEC2017 test function, and the results are assessed using the rank-sum test. Ultimately, three conventional practical engineering simulation experiments are conducted to evaluate the suitability of IWKGJO for engineering issues. The results obtained demonstrate the beneficial effects of the altered methodology and illustrate that the expanded golden jackal optimization algorithm has superior convergence accuracy and a faster convergence rate.

PPSwarm: Multi-UAV Path Planning Based on Hybrid PSO in Complex Scenarios

Evolutionary algorithms exhibit flexibility and global search advantages in multi-UAV path planning, effectively addressing complex constraints. However, when there are numerous obstacles in the environment, especially narrow passageways, the algorithm often struggles to quickly find a viable path. Additionally, collaborative constraints among multiple UAVs complicate the search space, making algorithm convergence challenging. To address these issues, we propose a novel hybrid particle swarm optimization algorithm called PPSwarm. This approach initially employs the RRT* algorithm to generate an initial path, rapidly identifying a feasible solution in complex environments. Subsequently, we adopt a priority planning method to assign priorities to UAVs, simplifying collaboration among them. Furthermore, by introducing a path randomization strategy, we enhance the diversity of the particle swarm, thereby avoiding local optimum solutions. The experimental results show that, in comparison to algorithms such as DE, PSO, ABC, GWO, and SPSO, the PPSwarm algorithm demonstrates significant advantages in terms of path quality, convergence speed, and runtime when addressing path planning issues for 40 UAVs across four different scenarios. In larger-scale experiments involving 500 UAVs, the proposed algorithm also exhibits excellent processing capability and scalability.

Intelligent optimization algorithm-driven informational teaching model for English reading and writing in universities

English reading and writing are important parts of language teaching. In order to improve the English reading and writing ability of college students, the TLBO (teaching learning-based optimization) algorithm is used in this research to improve the way that English reading and writing are taught in colleges and universities. It is chosen as the primary model for this study. The TLBO algorithm is further optimized in this paper, and a convergence analysis is performed between the optimized model M-TLBO (multi-learning teaching learning-based optimization) algorithm and other TLBO algorithms in order to address the issues that the TLBO algorithm has an excessively single teaching ability and readily settles into local optimal solutions for some large-scale complex problems. In terms of stability and convergence accuracy, M-TLBO outperforms other algorithms. In order to investigate the impact of the M-TLBO algorithm on students’ writing performance, this paper uses the teaching-learning optimization algorithm to conduct a pre-and post-test on students’ English reading and writing performance in five dimensions. The study’s findings revealed that students’ pre-test writing scores had a mean value of 8.4770 and a standard deviation of 1.72449, and that their post-study writing scores had increased by 5.05 points. The English reading and writing information-based teaching model can improve students’ English writing performance. It is hoped to promote the development of English teaching and improve the efficiency of students’ English learning.

Gradient projection-based trajectory tracking control for automatic guided vehicle

In order to solve the problems of long operation time for solving the trajectory tracking controller and low real-time tracking. This paper proposes an improved model predictive control algorithm. By introducing the gradient projection method (GPM), the projection direction is used as the fastest descent direction of the objective function, which is used to reduce the number of iterations of the operation. Meanwhile, this paper adds constraints and relaxation factors to improve the trajectory tracking accuracy and prevent the controller operations from falling into local optimal solutions. Simulation by Simulink, the improved model predictive control algorithm reduces the average operation time by 24.74% and the single maximum operation time by 36.04%, effectively improving the real-time trajectory tracking performance. Finally, the verification experiment of trajectory tracking control is carried out by actual vehicle, proving the method’s effectiveness.

Making a U-turn on the Purfleet Interchange: Stone Tool Technology in Marine Isotope Stage 9 Britain and the Emergence of the Middle Palaeolithic in Europe

This paper re-examines earlier Palaeolithic core technology from British sites assigned to MIS 11, 9, and 7 using primarily a châine opératoire approach, with the objective of better understanding the earliest occurrence and distribution of Levallois and other prepared-core technologies across the Old World. Contrary to previous interpretations (White and Ashton in Current Anthropology, 44: 598–609, 2003), we find no evidence for a true Levallois concept in MIS 11 or MIS 9 in Britain. Cores previously described as ‘simple prepared cores’ or ‘proto-Levallois’ cores show neither evidence of core management nor predetermination of the resulting flakes. They can instead be explained as the coincidental result of a simpler technological scheme aimed at exploiting the largest surface area of a core, thereby maximising the size of the flakes produced from it. This may be a more widespread practice, or a local solution derived from existing principles. Levallois appears fully formed in Britain during terminal MIS 8/initial MIS 7. Consequently, Britain does not provide evidence for an in situ evolution of Levallois, rather we argue it was introduced by new settlers after a glacial abandonment: the solution to the emergence and significance of Levallois lies in southern Europe, the Levant and Africa.

Entrepreneurial thinking and Education 4.0 in communities with development gaps: an approach through the Sustainable Development Goals

Entrepreneurial thinking is considered a desirable competency in the profile of today’s professionals because it includes sub-competencies that strengthen individuals’ leadership capacity and stimulate the development of creative solutions that present a high impact on society. However, it has been detected that disadvantaged communities located in areas with underdeveloped conditions and rural areas present a significant disparity in access to training models, current infrastructure, and activities that promote entrepreneurship compared to developed communities frequently found in large cities. Through a comparative analysis with quantitative methods, we seek to argue the need that these types of communities have. In addition, the design of a training model based on the design framework for Education 4.0 is presented; this training model seeks to train in the sub-competences of entrepreneurial thinking using the “push and pull” technique with the Sustainable Development Goals (SDGs) as its central axis. This seeks to close the existing gap, provide affordable resources to these types of disadvantaged communities, and, at the same time, promote local solutions through the SDGs. The study is conducted in the eastern region of Michoacán, Mexico, and will present the preliminary results.

A class of static spherically symmetric solutions in f(T)-gravity

We study a class of static spherically symmetric vacuum solutions in modified teleparallel gravity solving the field equations for a specific model Ansatz, requiring the torsion scalar T to be constant. We discuss the models falling in this class. After some general considerations, we provide and investigate local solutions in the form of black holes and traversable wormholes as well as configurations that can match the anomalous rotation curves of galaxies.

Numerical Simulation and Deformation Prediction of Deep Pit Based on PSO-BP Neural Network Inversion of Soil Parameters

The finite element numerical simulation results of deep pit deformation are greatly influenced by soil layer parameters, which are crucial in determining the accuracy of deformation prediction results. This study employs the orthogonal experimental design to determine the combinations of various soil layer parameters in deep pits. Displacement values at specific measurement points were calculated using PLAXIS 3D under these varying parameter combinations to generate training samples. The nonlinear mapping ability of the Back Propagation (BP) neural network and Particle Swarm Optimization (PSO) were used for sample global optimization. Combining these with actual onsite measurements, we inversely calculate soil layer parameter values to update the input parameters for PLAXIS 3D. This allows us to conduct dynamic deformation prediction studies throughout the entire excavation process of deep pits. The results indicate that the use of the PSO-BP neural network for inverting soil layer parameters effectively enhances the convergence speed of the BP neural network model and avoids the issue of easily falling into local optimal solutions. The use of PLAXIS 3D to simulate the excavation process of the pit accurately reflects the dynamic changes in the displacement of the retaining structure, and the numerical simulation results show good agreement with the measured values. By updating the model parameters in real-time and calculating the pile displacement under different working conditions, the absolute errors between the measured and simulated values of pile top vertical displacement and pile body maximum horizontal displacement can be effectively reduced. This suggests that inverting soil layer parameters using measured values from working conditions is a feasible method for dynamically predicting the excavation process of the pit. The research results have some reference value for the selection of soil layer parameters in similar areas.

Optimal coordination of directional overcurrent protection relays using hybrid optimizer

In order to minimize or maximize an objective function, electrical engineering problems might benefit from optimization methodologies inspired by nature. This study employs a hybrid particle swarm optimizer (HPSO) to get rid of local optimum solutions and find the best global one for directional overcurrent protection relays (DOPR) protection. DOPR coordination is a highly constrained, mixed-integral nonlinear optimization problem. An adaptive defense method has been created to counteract the intentionally challenging design. Therefore, design variables such as time multiplier setting (TMS) and plug setting (PS) are utilized for each relay in the circuit. The goal function is to reduce the amount of time spent to trace the fault by all the relays. Reducing the time required for each relay to trace the fault is the aim of function. After analyzing and comparing two test studies of the IEEE benchmark using various optimization strategies, we found that the results for the IEEE 15-bus system has minimum time of 8.9 s, which is improved by 22.92% to 82.89%, and those for the IEEE 30-bus system minimum time of 22.45 s that is improved by 4.41% to 39.6%. In terms of overall DOPR operation and computational time needed to get the global optimum solution, the acquired results are demonstrably superior to those obtained using conventional and state-of-the-art methods.

Falkner–Skan boundary layer flow of a fluid with pressure-dependent viscosity past a stretching wedge with suction or injection

In this paper we study the boundary layer flow of a particular class of non-Newtonian fluids, namely piezo-viscous fluids, past a stretching wedge (Falkner–Skan flow). These fluids are essentially Navier–Stokes fluids with pressure-dependent viscosity. We consider the two-dimensional steady flow and introduce some similarity variables, so that the problem is reduced to a third-order nonlinear BVP. We solve the problem numerically by means of a shooting procedure combined with Newton’s method, and we find local similarity solutions. We investigate the behaviour of the velocity field, of the drag and of the thickness of the boundary layer for different values of the involved parameters, making a comparison between the piezo-viscous and the Newtonian case. We find that, depending on some material parameters, the effect of pressure is that of reducing or increasing the boundary layer with respect to the Newtonian case.

Develop a Program Design and Coding Standard

The use of programming language is increasing in the real world in all domains. So it’s important to follow and maintain coding guidelines & standard and follow the best practice. This article gives an overview of naming & coding standard, use of it, comparison of the main features of different programming languages(C++, Java, Python), data management approaches for local, mobile and cloud solutions for ERP and EHR implementations, the structure of each proposed algorithm and use, Few examples for in-house development, ERP solutions, packaged software implementations, and mobile applications, few proposals, and recommendations for further research. Also explain how to create the corporate standards a sample database and application design and development.

Effects of Continuous Analgesic Titrated Spinal Anesthesia in Elderly Patients Undergoing Hip Fracture Surgery

Background and Objectives: Anesthetizing elderly patients with hip fractures poses a significant challenge in emergency settings, particularly given the aging population both in Algeria and worldwide. With a high prevalence of comorbidities and polypharmacy, effective anesthetic management becomes paramount. Continuous titrated spinal anesthesia (CTSA) has emerged as a promising technique for addressing these complexities by proposing lower doses of local anesthetic (LA) in this patient population. Methods: This retrospective study involved 40 elderly patients (>65 years) undergoing hip fracture repair. Patients received intermittent dosing of a local anesthetic solution via an intrathecal catheter, utilizing 0.25 ml increments of 0.5% isobaric bupivacaine and 0.25 ml of fentanyl (12.5 μg). Evaluation criteria included hemodynamic stability, incidence of hypotension, extent of sensory and motor blockade, total ephedrine consumption, and patient and surgeon satisfaction. Results: A female predominance was noted, with a mean age of 75 years, and 72% classified as ASA ≥ III. Pertrochanteric fractures accounted for 47% of cases, followed by femoral neck fractures at 53%. Nearly all patients achieved a sensory level ≥ D10, with a failure rate of only 2%. Sedation supplementation was required in 20% of cases, with conversion to general anesthesia in one patient. Complications were minimal, including arterial hypotension (3%), vasoconstrictor use (2%), and bradycardia (0.8%). Overall, both patients and surgeons reported high levels of satisfaction. Conclusions: Our findings demonstrate that CTSA is an effective technique for elderly patients undergoing hip fracture repair, offering the advantages of reduced LA doses, excellent hemodynamic stability, and minimal side effects. Its simplicity and cost-effectiveness further enhance its appeal in clinical practice.