Mixed Problem Research Articles

An Explicit–Implicit Upwind Difference Splitting Scheme in Directions for a Mixed Boundary Control Problem for a Two-Dimensional Symmetric t-Hyperbolic System

In this paper, we introduce a numerical integration method for hyperbolic systems problems known as the splitting method, which serves as an effective tool for solving complex multidimensional problems in mathematical physics. The exponential stability of the upwind explicit–implicit difference scheme split into directions is established for the mixed problem of a linear two-dimensional symmetric t-hyperbolic system with variable coefficients and lower-order terms. It is noteworthy that there are control functions in the dissipative boundary conditions. A discrete quadratic Lyapunov function was devised to address this issue. A condition for the problem’s boundary data, ensuring the exponential stability of the difference scheme with directional splitting for the mixed problem in the l2 norm, has been identified.

The forward–backward splitting method for finding the minimum like-norm solution of the mixed variational inequality problem

We consider a general class of convex optimization problems in which one seeks to minimize a strongly convex function over a closed and convex set, which is by itself an optimal set of another mixed variational inequality problem in a Hilbert space. Regularized forward–backward splitting method is applied to find the minimum like-norm solution of the mixed variational inequality problem under investigation.

Research on early fault feature extraction technology of aviation bearing based on noise estimation ITD

Early indications of faults in aircraft bearings are frequently accompanied by excessive noise. To enhance the accuracy of signal decomposition, this study presents the ensemble noise-reconstructed intrinsic time-scale decomposition (ENITD) technique. In addition, a highly sensitive mode component selection method is suggested to attain the goal of improving the precision of fault feature extraction. The findings demonstrate that the ENITD approach is successful in addressing the mode mixing issue and enhancing the precision of fault feature extraction. Unlike established decomposition methods, the estimated noise is applied for denoising instead of incorporating white noise. Furthermore, the estimated noise can introduce diverse frequency signals to their corresponding proper rotation component (PRCs), aiding in resolving the mode mixing problem. This paper examines the efficacy of the ENITD approach for extracting early fault features in aircraft bearings using both simulated and experimental signals.

Implementasi Model Pembelajaran Means Ends Analysis (MEA) pada Pembelajaran Matematika

The purpose of this study was to describe plans, implementation, constraints and solutions, as well as the results of implementing the MEA learning model on mixed arithmetic problem solving materials with integers. The research was conducted with a qualitative approach. Research data were collected through interviews, observation, and documentation studies. The data analysis technique uses descriptive analysis with the steps: data collection, data reduction, data display, verification and confirmation of conclusions (Conclusion Drawing and Verification). The results of the study concluded that teacher preparation carried out by teachers in implementing MEA learning was: (1) preparing lesson plans, (2) preparing learning materials according to core competencies, basic competencies and learning objectives, (3) preparing learning media according to the MEA learning model in the form of interactive powerpoints and learning materials to be studied, (4) developing learning strategies and steps, (5) compiling assessment instruments accompanied by answer sheets and assessment criteria. The stages of implementing the MEA model learning are: (1) preliminary activities, (2) core activities, (3) closing, and (4) assessment of learning outcomes. The internal obstacles to MEA learning are: (1) students' difficulties in completing and solving math problems, (2) students' lack of enjoyment in learning material, (3) students with low math mastery tend to be passive, (4) the process of compiling math problem solving questions requires thinking mature and long process, (5) difficulty expressing math problems to students. External constraints: (1) Limited time and space for interaction between teachers and students due to the COVID-19 pandemic so that learning is less effective, (2) patterns of learning mathematics that are abstract in nature that have not been supported by concrete learning media cause the completion of problem solving questions to be less understandable by learners.

Joint Slot Scheduling and Power Allocation for Throughput Maximization of Clustered UASNs

In the last decades, independent consideration of underwater acoustic medium access control (MAC) layer has received much attention for designing a reliable data transmission protocol. Although it can simplify the system design, it is often insufficient for the enhancement of overall system performance. The focus of this paper is on the cross-layer optimization to maximize the network throughput (NT) of clustered underwater acoustic sensor networks (UASNs) by jointly optimizing the sensor nodes’ slot scheduling and power allocation. The formulated problem is a mixed integer non-linear programming problem, which is NP-hard. An alternating-optimization-based centralized algorithm is proposed first to solve it, which can achieve the best NT performance but at the price of high complexity. Therefore, a multi-leader multi-follower Stackelberg game based distributed algorithm is also proposed to achieve a better tradeoff between system performance and complexity. Simulation results demonstrate that our proposed schemes considering the information causality constraint have a better NT performance than those without a “systematic” consideration over such joint optimization, like CMS-MAC algorithm.

Numerical algorithms and simulations of boundary dynamic control for optimal mixing in unsteady Stokes flows

This work develops an efficient and accurate optimization algorithm to study the optimal mixing problem driven by boundary control of unsteady Stokes flows, based on the theoretical foundation laid by Hu and Wu in a series of work. The scalar being mixed is purely advected by the flow and the control is a force exerted tangentially on the domain boundary through the Navier slip conditions. The control design has potential applications in many industrial processes such as rotating wall driven mixing, mircomixers with acoustic waves, and artificial cilia mixing.The numerical algorithms have high complexity, high accuracy demand, and high computing expense, due to the multiscale nature of the mixing problem and the optimization requirements. A crucial problem is the computation of the Gâteaux derivative of the cost functional. To this end, a hybrid approach based on variational formula and finite difference is built with high accuracy and efficiency to treat various types of control input functions. We have experimented with various optimization algorithms including the steepest descent algorithm, the conjugate gradient method and two line search options (backtracking and exact line search). We are able to identify and implement the best combinations.The numerical simulations show that the mixing efficacy is limited when only one single type of control is applied, but can be enhanced when more diverse control types and more time segmentation are utilized. The mix-norm in the optimal mixings decays exponentially. The numerical study in this work demonstrates that boundary control alone could be an effective strategy for mixing in incompressible flows.

Optimal Hardy‐weights for elliptic operators with mixed boundary conditions

AbstractWe construct families of optimal Hardy‐weights for a subcritical linear second‐order elliptic operator with degenerate mixed boundary conditions. By an optimal Hardy‐weight for a subcritical operator we mean a nonzero nonnegative weight function W such that is critical, and null‐critical with respect to W. Our results rely on a recently developed criticality theory for positive solutions of the corresponding mixed boundary value problem.

Nonlinear fuzzy chance constrained approach for multi-objective mixed fuzzy-stochastic optimization problem

Nonlinear fuzzy chance constrained approach for multi-objective mixed fuzzy-stochastic optimization problem

Constrained evolutionary variational–hemivariational inequalities with application to fluid flow model

We study a new class of abstract evolution variational–hemivariational inequalities with constraints in the framework of evolution triples of spaces. Existence of solution is established based on the so-called mixed equilibrium problem formulation. Then, we apply this result to a mathematical analysis of the unsteady Oseen model for a generalized Newtonian incompressible fluid. A variational–hemivariational inequality for the flow problem is derived and sufficient conditions for existence of weak solutions are obtained. The mixed boundary conditions involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier–Fujita slip condition, and the threshold slip and leak condition of frictional type.

An optimization-based partial marginal pricing method to reduce excessive consumer payment in electricity markets

Among the pricing schemes, locational marginal pricing is the most widely adopted scheme in current electricity markets. Despite the nice properties, theoretical study and practical experience have shown that considering the strategic bidding behaviors of market participants, locational marginal pricing may result in excessive consumer payment and prejudices market efficiency. In this paper, we propose an optimization-based partial marginal pricing method to reduce consumer payment under strategic bidding. The advantages of the locational marginal pricing method are reserved to the best extent while the remaining problems are delicately handled. To achieve this, we first analyze the characteristics and problems of the locational marginal pricing scheme and present a partial marginal pricing structure. Second, we establish an optimization-based partial marginal pricing model, in which discriminatory price components are introduced in price formulation and the pricing properties including competitive equilibrium and revenue adequacy are formulated as constraints. Third, to verify the performance of the proposed pricing scheme considering the strategic bidding, a bi-level strategic bidding problem of the generator under the proposed pricing method is established and transformed into a mixed integer linear programming problem. The numerical results indicate that under the conventional pricing methods, the consumer payments under strategic bidding can be up to 16.67 times higher than those under truthful bidding, while the proposed method can effectively reduce excessive consumer payments by 92.1% while maintaining the desired pricing properties.

Pulse parameter optimizer: an efficient tool for achieving prescribed dose and dose rate with electron FLASH platforms

Purpose. Commercial electron FLASH platforms deliver ultra-high dose rate doses at discrete combinations of pulse parameters including pulse width (PW), pulse repetition frequency (PRF) and number of pulses (N), which dictate unique combinations of dose and dose rates. Additionally, collimation, source to surface distance, and airgaps also vary the dose per pulse (DPP). Currently, obtaining pulse parameters for the desired dose and dose rate is a cumbersome manual process involving creating, updating, and looking up values in large spreadsheets for every treatment configuration. This work presents a pulse parameter optimizer application to match intended dose and dose rate precisely and efficiently. Methods. Dose and dose rate calculation methods have been described for a commercial electron FLASH platform. A constrained optimization for the dose and dose rate cost function was modelled as a mixed integer problem in MATLAB (The MathWorks Inc., Version9.13.0 R2022b, Natick, Massachusetts). The beam and machine data required for the application were acquired using GafChromic film and alternating current current transformers (ACCTs). Variables for optimization included DPP for every collimator, PW and PRF measured using ACCT and airgap factors. Results. Using PW, PRF, N and airgap factors as parameters, a software was created to optimize dose and dose rate, reaching the closest match if exact dose and dose rates are not achievable. Optimization took 20 s or less to converge to results. This software was validated for accuracy of dose calculation and precision in matching prescribed dose and dose rate. Conclusion. A pulse parameter optimization application was built for a commercial electron FLASH platform to increase efficiency in dose, dose rate, and pulse parameter prescription process. Automating this process reduces safety concerns associated with manual look up and calculation of these parameters, especially when many subjects at different doses and dose rates are to be safely managed.

On an annular crack near an arbitrarily graded interface in FGMs

Annular cracks can be generated during the fabrication of materials and around the pre-existing defects. Previous works on the annular crack problems were most limited to homogenous materials. This paper extends the analysis and examines the axisymmetric problem of a flat mixed-mode annular crack near and parallel to an arbitrarily graded interface in functionally graded materials (FGMs). The crack is modelled as plane circular dislocation loop and an efficient solution for dislocation in FGMs is used to calculate the stress field at the crack plane. The three-parts mixed boundary value problem is solved by a series expansion method. Analytical solutions of the stress intensity factors are obtained. Compared with many other existing analytical treatments to the crack problems in FGMs with the assumption of special gradation, the present method can consider arbitrarily graded shear modulus and Poisson's ratio. It is shown that the present solution can reduce to existing solutions in literatures for annular crack in homogenous materials. Numerical study is conducted to investigate the fracture mechanics of annular crack in FGMs. A practical example of an annular crack in a real Epoxy-Glass FGM with measured data of material properties is also considered.

Analysis of a cracked neo-Hookean substrate with initial stress under a rigid punch

The coupling problem of a cracked neo-Hookean substrate with initial stress under a rigid punch is examined in the current work. Fourier series is used to transform the mixed boundary value problem(MBVP) into singular integral equations (SIEs). The obtained SIEs is solved by using Gauss-Chebyshev collocation method. The stress distributions on the contact zone and crack surface, and related singularities are present. The numerical experiments examine how the punch position, punch width, crack length and propagation parameter affect the stress field. The result showed that: for k = 1 and unchanged material property parameters, the incremental stress distribution on the initially stressed neo-Hookean base is very similar to the Cauchy stress distribution of the isotropic linear elastic base.

Locality Preserved Selective Projection Learning for Rice Variety Identification Based on Leaf Hyperspectral Characteristics

Rice has an important position in China as well as in the world. With the wide application of rice hybridization technology, the problem of mixing between individual varieties has become more and more prominent, so the variety identification of rice is important for the agricultural production, the phenotype collection, and the scientific breeding. Traditional identification methods are highly subjective and time-consuming. To address this issue, we propose a novel locality preserved selective projection learning (LPSPL) method for non-destructive rice variety identification based on leaf hyperspectral characteristics. The proposed LPSPL method can select the most discriminative spectral features from the leaf hyperspectral characteristics of rice, which is helpful to distinguish different rice varieties. In the experiments, support vector machine (SVM) is adopted to conduct the rice variety identification based on the selected spectral features. The experimental results show that the proposed method here achieves higher identification rates, 96% for the early rice and 98% for the late rice, respectively, which are superior to some state-of-the-art methods.

Quad Mesh Quantization Without a T‐Mesh

AbstractGrid preserving maps of triangulated surfaces were introduced for quad meshing because the 2D unit grid in such maps corresponds to a sub‐division of the surface into quad‐shaped charts. These maps can be obtained by solving a mixed integer optimization problem: Real variables define the geometry of the charts and integer variables define the combinatorial structure of the decomposition. To make this optimization problem tractable, a common strategy is to ignore integer constraints at first, then to enforce them in a so‐called quantization step. Actual quantization algorithms exploit the geometric interpretation of integer variables to solve an equivalent problem: They consider that the final quad mesh is a sub‐division of a T‐mesh embedded in the surface, and optimize the number of sub‐divisions for each edge of this T‐mesh. We propose to operate on a decimated version of the original surface instead of the T‐mesh. It is easier to implement and to adapt to constraints such as free boundaries, complex feature curves network etc.

Optimal decarbonization strategies for an industrial port area by using hydrogen as energy carrier

This article discusses possible strategies for decarbonizing the energy systems of an existing port. The approach consists in creating a complete superstructure that includes the use of renewable and fossil energy sources, the import or local production of hydrogen, vehicles and other equipment powered by Diesel, electricity or hydrogen and the associated refuelling and storage units. Two substructures are then identified, one including all these options, the other considering also the addition of the energy demand of an adjacent steel industry. The goal is to select from each of these two substructures the most cost-effective configurations for 2030 and 2050 that meet the emission targets for those years under different cost scenarios for the energy sources and conversion/storage units, obtained from the most reliable forecasts found in the literature. To this end, the minimum total cost of all the energy conversion and storage units plus the associated infrastructures is sought by setting up a Mixed Integer Linear Programming optimization problem, where integer variables handle the inclusion of the different generation and storage units and their activation in the operational phases. The comprehensive picture of possible solutions set allows identifying which options can most realistically be realized in the years to come in relation to the different assumed cost scenarios. Optimization results related to the scenario projected to 2030 indicate the key role played by Diesel hybrid and electric systems, while considering the most stringent, or much more stringent, scenarios for emissions in 2050, almost all vehicles energy demand and industry hydrogen demand is met by hydrogen imported as ammonia by ship.

Task Assignment Optimization in Multi-UAV-Assisted WSNs Considering Energy Budget and Sensor Distribution Characteristics.

In emergency situations, such as disaster area monitoring, deadlines for data collection are strict. The task time minimization problem concerning multi-UAV-assisted data collection in wireless sensor networks (WSNs), with different distribution characteristics, such as the geographical or importance of the information of the sensors, is studied. Our goal is to minimize the mission time for UAVs by optimizing their assignment, trajectory, and deployment locations, while the UAV energy constraint is taken into account. For the coupling relationship between the task assignment, trajectory, and hover position, it is not easy to solve the mixed integer non-convex problem directly. The problem is divided into two sub-problems: (1) UAV task assignment problem and (2) trajectory and hover position optimization problem. To solve this problem, an assignment algorithm, based on sensor distribution characteristics (AASDC), is proposed. The simulation results show that the collection time of our scheme is shorter than that of existing comparison schemes when using the same data size.

Asymptotic analysis of perturbed Robin problems in a planar domain

We consider a perforated domain \(\Omega(\epsilon)\) of \(\mathbb{R}^2\) with a small hole of size \(\epsilon\) and we study the behavior of the solution of a mixed Neumann-Robin problem in \(\Omega(\epsilon)\) as the size \(\epsilon\) of the small hole tends to \(0\). In addition to the geometric degeneracy of the problem, the nonlinear \(\epsilon\)-dependent Robin condition may degenerate into a Neumann condition for \(\epsilon=0\) and the Robin datum may diverge to infinity. Our goal is to analyze the asymptotic behavior of the solutions to the problem as \(\epsilon\) tends to \(0\) and to understand how the boundary condition affects the behavior of the solutions when \(\epsilon\) is close to \(0\). The present paper extends to the planar case the results of [36] dealing with the case of dimension \(n\geq 3\).
 For more information see https://ejde.math.txstate.edu/Volumes/2023/57/abstr.html

Mixed Pixel Classification on Hyperspectral Image Using Imbalanced Learning and Hyperparameter Tuning Methods

Hyperspectral image technology in land classification is a distinct advantage compared to ordinary RGB and multispectral images. This technology has a wide spectrum of electromagnetic waves, which can be more detailed than other types of imagery. Therefore, with its hyperspectral advantages, the characteristics of an object should have a high probability of being recognized and distinguished. However, because of the large data, it becomes a challenge to lighten the computational burden. Hyperspectral has a huge phenomenon that makes computations heavy compared to other types of images because this image is 3D. The problem faced in hyperspectral image classification is the high computational load, especially if the spatial resolution of the image also has mixed pixel problems. This research uses EO-1 satellite imagery with a spatial resolution of 30 meters and a mixed pixel problem. This study uses a classification method to lighten the computational burden and simultaneously increase the value of classification accuracy. The method used is satellite image pre-processing, including geometric correction and image enhancement using FLAASH while the corrections are geometric correction and atmospheric correction. Then to lighten the computational burden, the steps carried out are using the Slab and PCA method. After obtaining the characteristics, they are entered into a guided learning model using a support vector machine (SVM) for the five-class or multiclass classification. Moreover, the imbalance learning method is proven to produce increased accuracy. The best results were achieved by the ADASYN method with an accuracy of 96.58%, while the computational time became faster with the feature extraction method.

Identification and Analysis of Obstacles to the Revitalization and the Use of Agricultural Rituals in the Development of Tourism in Iran

Purpose: in order to develop agritourism, agricultural rituals are considered as one of the main potentials. for this purpose, the present study was aimed to identify and analyze the barriers to revitalization and application of agricultural rituals in the development of tourism in Iran. Research Method: This study consists of two main sections. In the first section, the obstacles to the revitalization and application of rituals in the development of tourism have been examined using a qualitative research method. In this section, theoretical saturation was achieved by using the grounded theory and performing interviews with 104 experts. and in the second part, in order to investigate and evaluate the obstacles and challenges identified in the first part, a questionnaire with a Likert spectrum scale in four dimensions (economic, social and cultural, environmental, physical and institutional) was prepared by the research team and given to 130 people. It was selected from the experts and finally after scoring (1 to 5) by them, it was analyzed in SPSS environment with Cronbach's alpha value of 0.982% and using binomial, correlation and Friedman tests.Findings: The results show that 11 core categories (management and planning, research and education, social, cultural, economic, marketing and advertising, tourism, agriculture, services and infrastructure, environment and rules and regulations) are the most important obstacles to the revitalization and application of agricultural rituals in the development of tourism in Iran.Originality/value: This research has been conducted for the first time in Iran, and until the time of compiling this research, a similar issue was not observed. This research has been compiled using mixed research method and problem solving approach. and for the first time, he brings up the discussion of agricultural rituals as an approach in the development of tourism and on the axis of agricultural tourism, which is unique in its kind. Also, the findings of the project have been provided to an Iranian government institution, which is very important from this point of view.