Global Solution Research Articles

Global existence and stability of the wave equation with boundary variable damping

AbstractIn this paper, we present the result of global existence of solution for the wave equation with boundary variable damping term. Then, we prove that this global solution is stable. Our study is based on the semi‐groups theory and some integral inequalities.

Glocalization: an analysis into it’s conceptual and strategic underpinnings

Glocalization is a “simultaneity—the co-presence—of both universalizing and particularizing tendencies” emphasizing the need for tempering the effects of local conditions on global pressures. While the increasing presence of best-known fast food chain restaurants worldwide such as McDonald’s and KFC is a manifestation of globalization, the shrewd and strategic adaptations of their menu to satiate the local palates and tastes by these “Glocal Enterprises” is illustrative of glocalization. Conversely, the chief point of glocalization perspective is: “even the most local ways of carrying out business operations are more and more co-constituted by economic and social trends that are most global.” Language has a huge role to play in addressing the cultural and linguistic barriers and designing a successful global talent management and language learning solution that is complemented by local support. When used as an extension of the “Think Global, Act Local” grassroots movement, glocalization also refers to market advantage of local businesses versus global companies. In the face of globalization, both the little guys and would-be entrepreneurs can emerge triumphant by tapping into their hometown markets and then scaling up. However, it is imperative that MNCs restructure the national economies to become and remain more resilient, sustainable, and inclusive in their globalization to glocalization migration odyssey. An attempt would be made in this conceptual Paper to address this issue—a challenge and an opportunity—for the key players by enumerating the stories of successful transition into glocalization by several popular Multi National Corporations in the Indian context.

Stability analysis for stochastic nonlinear systems with state-dependent switching and time-delay

The stability of stochastic nonlinear systems with time-delay and state-dependent switching is studied in this paper. Firstly, system maximal solution is constructed and further extended as the global solution under certain mild conditions. Secondly, several Krasovskii-type stability and Razumikhin-type theorems are proposed by uniformly asymptotically stable functions (UASFs). These stability criteria overcome some stringent constraints associated with Lyapunov functional/functions. Finally, the theoretical findings are validated through two simulation examples.

The Cd resistant mechanism of Proteus mirabilis Ch8 through immobilizing and detoxifying

Cadmium (Cd) pollution is a serious global environmental problem, which requires a global concern and practical solutions. Microbial remediation has received widespread attention owing to advantages, such as environmental friendliness and soil amelioration. However, Cd toxicity also severely deteriorates the remediation performance of functional microorganisms. Analyzing the mechanism of bacterial resistance to Cd stress will be beneficial for the application of Cd remediation. In this study, the bacteria strain, up to 1400 mg/L Cd resistance, was employed and identified as Proteus mirabilis Ch8 (Ch8) through whole genome sequence analyses. The results indicated that the multiple pathways of immobilizing and detoxifying Cd maintained the growth of Ch8 under Cd stress, which also possessed high Cd extracellular adsorption. Firstly, the changes in surface morphology and functional groups of Ch8 cells were observed under different Cd conditions through SEM-EDS and FTIR analyses. Under 100 mg/L Cd, Ch8 cells exhibited aggregation and less flagella; the Cd biosorption of Ch8 was predominately by secreting exopolysaccharides (EPS) and no significant change of functional groups. Under 500 mg/L Cd, Ch8 were present irregular polymers on the cell surface, some cells with wrapping around; the Cd biosorption capacity exhibited outstanding effects (38.80 mg/g), which was mainly immobilizing Cd by secreting and interacting with EPS. Then, Ch8 also significantly enhanced the antioxidant enzyme activity and the antioxidant substance content under different Cd conditions. The activities of SOD and CAT, GSH content of Ch8 under 500 mg/L Cd were significantly increased by 245.47%, 179.52%, and 241.81%, compared to normal condition. Additionally, Ch8 significantly induced the expression of Acr A and Tol C (the resistance-nodulation-division (RND) efflux pump), and some antioxidant genes (SodB, SodC, and Tpx) to reduce Cd damage. In particular, the markedly higher expression levels of SodB under Cd stress. The mechanism of Ch8 lays a foundation for its application in solving soil remediation.

Efficiency and sustainability: Evaluating and optimizing energy use and environmental impact in cucumber production

This study assesses the energy-economic-environmental aspects of cucumber production in the face of environmental issues and resource scarcity, which threaten global food security and demand sustainable agriculture solutions. Data were collected by questionnaire and analyzed for inputs from planting to harvesting. The results indicated that diesel fuel (37.41%) and nitrate fertilizer (37.22%) constitute the primary inputs. The energy ratio, energy efficiency and net energy gain were 0.43, 0.54 kgMJ−1 and -30,153.31 MJha−1, respectively. Input optimization by Data Envelopment Analysis (DEA) reduced the carbon footprint from 178.433 to 168.900 kg CO2 per ton, the abiotic depletion from 1228.291 to 964.305 MJ and the acidification from 0.838 to 0.749 kg SO2 eq. Also, the results of DEA showed that 52.5% and 35% of the units were fully efficient under Variable Return to Scale (VRS) and Constant Return to Scale (CRS) models, respectively, while the others were inefficient to varying degrees. The average of technical, pure technical and scale efficiencies were 92.88%, 97.64%, and 95.07%, respectively. The results of economic evaluation showed that production cost is 6058.84 $ha−1 with a benefit-cost ratio of 1.71. Based on the primary results, it is suggested to use precision agriculture techniques and the exploration of alternative energy sources, such as biofuel for machinery. Additionally, using slow-release fertilizers or organic substitutes can decrease nitrogen fertilizer dependency while maintaining crop yields and improve the sustainability in this production.

Dynamic properties, probability density, and estimation of an SIRIS epidemic model with an Ornstein-Uhlenbeck process

Abstract Considering the relapse and temporary immunity of some diseases, a stochastic SIRIS epidemic model with saturation incidence is developed in this paper, in which the Ornstein-Uhlenbeck process is introduced to describe the randomness of the model. The existence and uniqueness of the global solution are first proved to investigate the dynamic properties of the SIRIS model. By constructing a series of Lyapunov functions, the thresholds $\sR_0^E$ and $\sR_0^S$ are further derived to determine the extinction and persistence of the disease. Subsequently, we prove that the solution of the model admits a stationary distribution. The probability density function is obtained by the algebraic method. In addition, the unknown parameters of the density function are estimated by using the maximum likelihood estimation. Finally, numerical simulations verify the results of the above properties.

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.

Group sparsity residual constraint model with weighted log-sum penalty for image restoration

In the field of image restoration, non-convex penalties and non-local self-similarity (NSS) prior have been found to enhance image edges and textures. However, NSS-based methods often overlook the inherent variations within patch groups by treating them as a single entity for processing. Despite the existence of numerous convex or non-convex regularizers, few of them have been able to adaptively adjust penalty strength based on NSS information in order to preserve fine details in an image. To address this issue, we propose a novel group sparsity residual constraint model with weighted log-sum penalty (GSRC-Log) for image restoration in this paper. The proposed regularization term is parameterized by an adaptive scalar parameter that relates to NSS, allowing the model to prioritize high NSS group sparse coefficients while penalizing low NSS coefficients. For image denoising, we provide detailed analysis on the optimal condition of our proposed model and prove that it has a simple closed-form global solution. For image restoration tasks, we utilize the ADMM algorithm to solve the GSRC-Log problem and empirically verify its convergence. Extensive experimental results on both image denoising and compressive sensing (CS) recovery demonstrate that our proposed GSRC-Log outperforms many popular or state-of-the-art methods.

Global existence and blowup of solutions for nonlinear Love equation

In this paper, we are concerned with the nonlinear Love equation, which describes some sort of “propagation process” in physics. Firstly, we establish the local existence and uniqueness of the solution by using the contraction mapping principle and the regularity theory for the elliptic problem. Secondly, we construct a family of potential wells to obtain a threshold for the existence of global solutions and blowup in a finite time of the solution in both cases with subcritical and critical initial energy. Additionally, we provide the decay rate of the global solution and estimate the lifespan of a blow‐up solution. Moreover, at the supercritical initial energy level, we provide a sufficient condition for initial data leading to blow‐up results. This paper, along with the previous work of A. N. Carvalho, J. Cholewa, Local well‐posedness, asymptotic behavior, and asymptotic bootstrapping for a class of semilinear evolution equations of the second order in time, Trans. Amer. Math. Soc. 361 (5) (2009) 2567‐2586, provides us with a comprehensive and systematic study of the dynamic behavior of the solution to the nonlinear Love equation.

An automated multi-layer perceptron discriminative neural network based on Bayesian optimization achieves high-precision one-source single-snapshot direction-of-arrival estimation

This paper proposes an innovative global solution which is a pioneering work applying automated machine learning algorithms to remarkable precision sparse underwater direction-of-arrival (DOA) estimation that views the subaquatic sparse-sampling DOA estimation problem as a classification prediction task. The proposed solution, termed automated multi-layer perceptron discriminative neural network (AutoMPDNN), is built upon a Bayesian optimization framework. AutoMPDNN transforms sparsely sampled time-domain signals into the complex domain, preserving essential components in a one-source single-snapshot scenario. Leveraging Bayesian optimization principles, the algorithm embeds necessary hyperparameters into the loss function, effectively defining it as a maximum likelihood problem using the upper confidence bound function and incorporating sparse signal features. We also explore the model space architecture and introduce variants of AutoMPDNN, denoted as AutoMPDNNs_ln (n = 2,3,4). Through a series of plane wave simulation experiments, it is demonstrated that AutoMPDNN achieves the highest prediction performance for one-source single-snapshot scenarios compared to classical DOA estimation algorithms that incorporate sparse representation approaches, as well as contemporary deep learning DOA methods under varying conditions.

A sequence decomposition genetic algorithm for petrophysical inversion with spatial correlation

Predicting petrophysical properties based on seismic attributes is essential for accurate subsurface characterization. Typically, a forward model is first established to relate petrophysical properties to geophysical measurements, and then the petrophysical properties are inverted from actual measurements. Imposing prior constraints of spatial relationship is also desirable to regularize the ill-posed inverse problem. However, petrophysical inversion involving spatial correlation presents a high-dimensional optimization problem with multiple local extrema. This problem can be challenging to solve, particularly when discrete variables (such as lithofacies) and continuous variables (such as porosity and fluid saturation) are considered together. Therefore, we propose a global optimization algorithm that utilizes Markov chain decomposition and a genetic algorithm for joint discrete-continuous petrophysical inversion with spatial correlation. The innovation of this algorithm is to spatially decouple the sequence optimization problem into multiple low-dimensional sub-problems and overcome the initial value dependence to converge to the global optimal solution. Furthermore, an approximation operation is introduced to expedite the optimization algorithm. Numerical experiments demonstrate that after algorithmic acceleration, the spatially correlated inversion requires the same computational time as a simple spatially uncorrelated inversion and achieves significantly better accuracy than the latter. Finally, we apply the method to a case study in East China, where lithofacies, clay content, porosity, and water saturation are inferred from the data of wave velocities and density. The inversion results around the wells generally match the well logging data, verifying the feasibility of the new method.

Global mild solutions to the relativistic Vlasov–Poisson–Fokker–Planck system in the whole space

In this manuscript, we consider the Cauchy problem of the relativistic Vlasov–Poisson–Fokker–Planck system in the whole space. The global existence and the exponential time decay rates of the mild solutions around a global relativistic Maxwellian are obtained under assumption that initial data satisfies some smallness in the low regularity space Lk1LT∞Lv2.

Imagining Global Climate Solutions: Reflections on <em>The Ministry for the Future</em> and <em>Eleutheria</em>

Even though a scientific consensus has been building for many decades that the climate emergency is real, and despite many protests and conferences demanding action, global climate solutions remain elusive. What are the main sticking points to making climate progress, and how might they be overcome? This article draws on two novels to imagine possible solutions: The Ministry for the Future by Kim Stanley Robinson and Eleutheria by Allegra Hyde. Both envision effective social change over the next few decades. Themes and pathways include influencing public opinion, new religious movements, politics at global scale, tweaking the global economic system, geoengineering, and the various roles that people from all walks of life can play—especially young people—to deliver climate solutions. Not least, a common theme is how love can save the world.

Optimal distributed control for a Cahn-Hilliard-Darcy system with mass sources, unmatched viscosities and singular potential

We study a Cahn-Hilliard-Darcy system with mass sources, which can be considered as a basic, though simplified, diffuse interface model for the evolution of tumor growth. This system is equipped with an impermeability condition for the averaged velocity u as well as homogeneous Neumann boundary conditions for the phase function ϕ and the chemical potential µ. The source term in the convective Cahn-Hilliard equation contains a control R that can be thought as a drug or a nutrient in applications. Our goal is to study a distributed optimal control problem in the two-dimensional setting with a cost functional of tracking-type. In the physically relevant case with unmatched viscosities for the binary fluid mixtures and a singular potential, we first prove the existence and uniqueness of a global strong solution with ϕ being strictly separated from the pure phases ±1. This well-posedness result enables us to characterize the control-to-state mapping S: R→ϕ. Then we obtain the existence of an optimal control, the Frechet differentiability of S and first-order necessary optimality conditions expressed through a suitable variational inequality for the adjoint variables. Finally, we prove the differentiability of the control-to-costate operator and establish a second-order sufficient condition for the strict local optimality.

First image of a jet launching from a black hole accretion system: Kinematics

Jets are endemic to both Galactic solar mass and extragalactic supermassive black holes. A recent 86 GHz image of M 87 shows a jet emerging from the accretion ring around a black hole, providing the first direct observational constraint on the kinematics of the jet-launching region in any black hole jetted system. The very wide (∼280 μas), highly collimated, limb-brightened cylindrical jet base is not predicted in current numerical simulations. The emission was shown to be consistent with that of a thick-walled cylindrical source that apparently feeds the flow that produces the bright limbs of the outer jet at an axial distance downstream of 0.4 mas < z < 0.65 mas. The analysis here applies the conservation laws of energy, angular momentum, and magnetic flux to the combined system of the outer jet, the cylindrical jet, and the launch region. It also uses the brightness asymmetries of the jet and counterjet to constrain the Doppler factor. The only global solutions have a source that is located < 34 μas from the event horizon. This includes the Event Horizon Telescope annulus of emission and the regions interior to this annulus. The axial jet begins as a magnetically dominated flow that spreads laterally from the launch radius (< 34 μas). It becomes super-magnetosonic before it reaches the base of the cylindrical jet. The flow is ostensibly redirected and collimated by a cylindrical nozzle formed in a thick accretion disk. The flow emerges from the nozzle as a mildly relativistic (0.3c < v < 0.4c) jet with a significant protonic kinetic energy flux.

Hull form optimization research based on multi‐precision back‐propagation neural network approximation model

AbstractIn order to shorten the optimization cycle of ship design optimization and solve the time‐consuming problem of computational fluid dynamics (CFD) numerical calculation, this paper proposes a multi‐precision back‐propagation neural network (MP‐BP) approximation technology. Fewer high‐precision ship samples and more low‐precision ship samples were used to construct an approximate model, back‐propagation (BP) neural network was used to train multi‐precision samples. So that the approximate model is as close as possible to the real model, and achieving the effect of high‐precision approximation model. Subsequently, numerical verification and typical hull form verification are given. Based on CFD and Rankine theory, the multi‐objective design optimization framework for ship comprehensive navigation performance is constructed. The multi‐objective approximation model of KCS ship is constructed by MP‐BP approximation technology, and optimized by particle swarm optimization (PSO) algorithm. The results show that the multi‐objective optimization design framework using the MP‐BP approximation model can capture the global optimal solution and improve the efficiency of the entire hull form design optimization. It can provide a certain degree of technical support for green ship and low‐carbon shipping.

Super-targeting of non-minimal WHEN systems

Energy conservation and emission reduction have become critical issues due to increasing environmental policy pressures and high energy prices. Work and heat exchange network (WHEN) synthesis is a promising approach to enhance the energy efficiency of energy-intensive processes. WHEN considering single-stage compression/expansion can be divided into two classes by structure complexity: minimal structure and non-minimal structure. The synthesis problem of minimal structure has been addressed in our previous work, where the global optimal solution can be guaranteed. In contrast, the compressors/expanders are not at the beginning or end of the streams' paths in the non-minimal structure and therefore the inlet/outlet temperatures are now variables of the problem. Instead of solving this complicated problem directly, we propose a super-targeting model to screen and scope the solution space for primal promising options before detailed structure design which can be designed using regular HEN synthesis methods. The super-target is estimated by regulating the thermodynamic paths of hot and cold streams where the objective function uses classical HEN super-target to evaluate the costs of the heat exchanger network. Benefiting from the unimodal nature of non-minimal WHEN super-targeting problems, we develop two deterministic algorithms: one relies on derivatives and one is derivative-free. Case studies show the efficiency of the proposed algorithm. The resulting TAC can be 23.1% lower than the literature report and the solution of super-targeting problems are proven to be globally optimal. The derivative optimization algorithm has been found to exhibit superior efficiency in solving problems of relatively large scale.

Optimal design of mixed dielectric coaxial-annular TSV using GWO algorithm based on artificial neural network

The single-objective and single-parameter optimization method is commonly used in the structure optimization of TSV to improve the transmission characteristics, for which a structure design scheme that simultaneously satisfies multiple target requirements is difficult to obtain. Moreover, the method cannot simultaneously optimize different design parameters. Aiming at the above problems, a global optimization method based on the gray wolf optimization (GWO) algorithm and artificial neural network (ANN) model is proposed. With the presented mixed dielectric coaxial-annular TSV model, firstly six key design parameters A-F are selected as optimization variables by the control variable method. The L25(56) orthogonal experiment is designed for Taguchi analysis and analysis of variance (ANOVA). Then, three prediction models, ANN, support vector machine (SVM), and extreme learning machine (ELM), are developed with the extended orthogonal data as the training sets. It is found that the ANN model performed best. To search for the global optimal solution, the genetic algorithm (GA) and GWO algorithm, combined with the ANN model are applied, respectively. The results show that the GWO algorithm is more successful in solving the problem of falling into the local optimum than GA, and the convergence speed is faster and more stable. After GWO-ANN optimization, the performance of each S-parameter index is greatly improved, S11 reduces by 14.05 dB, S21 increases by 0.33 dB, and S31 reduces by 12.50 dB at 30 GHz.

Global existence and partial regularity for the Landau-Lifshitz-Gilbert equation with helicity

In this paper, the Landau-Lifshitz-Gilbert equation with helicity is considered. In R3 or a bounded regular domain Ω of R3, we establish the global existence of a weak solution. In Rn, a global existence criterion and uniqueness of the smooth solution are given. In R1, the local smooth solution is indeed global with large initial data. In R2, we prove the existence of a global weak solution, which is smooth with the exception of at most finite singular points.

Enhancing the structural performance of engineering components using the geometric mean optimizer

Abstract In this article, a newly developed optimization approach based on a mathematics technique named the geometric mean optimization algorithm is employed to address the optimization challenge of the robot gripper, airplane bracket, and suspension arm of automobiles, followed by an additional three engineering problems. Accordingly, other challenges are the ten-bar truss, three-bar truss, tubular column, and spring systems. As a result, the algorithm demonstrates promising statistical outcomes when compared to other well-established algorithms. Additionally, it requires less iteration to achieve the global optimum solution. Furthermore, the algorithm exhibits minimal deviations in results, even when other techniques produce better or similar outcomes. This suggests that the proposed approach in this paper can be effectively utilized for a wide range of critical industrial and real-world engineering challenges.