Solution Of Problem Research Articles

A novel linear discriminant analysis based on alternate ratio sum minimization

Linear discriminant analysis (LDA) and its variants are popular supervised dimension reduction methods, which have been widely used to handle high-dimensional data. Since most of previous LDA methods are developed based on the trace ratio (TR) criterion, they usually obtain the low-dimensional data feature with weak discriminative ability, due to the projections with small variance. The ratio sum (RS) criterion was developed to alleviate this drawback. However, the conventional ratio sum is formulated to maximize the arithmetic mean of items which suffers from the domination of the largest objectives and might deteriorate the recognition accuracy in practical applications. In this paper, a novel ratio sum minimization based linear discriminant analysis (RSM-LDA) method is proposed in this paper. Specifically, a new ratio sum minimization (RSM) criterion is developed, which is based on the properties of the harmonic mean and effectively avoids the dominance problem to discover more discriminative features of the data. However, obtaining a closed solution for the RSM-LDA problem is challenging. For this purpose, three optimization methods are used to solve the optimization problem of RSM-LDA, and the inherent relationships between the methods are discussed. Experimental results demonstrate that the proposed RSM-LDA method has better performance in classification tasks on several datasets, when compared with some comparison methods based dimensionality reduction methods. In addition, combined with other experimental results, the effectiveness of RSM-LDA was verified.

Economic Load Dispatch Problem Solution Based on Linear Variational Inequalities-dynamic Neural Network

Economic Load Dispatch Problem Solution Based on Linear Variational Inequalities-dynamic Neural Network

Bi-Objective Inventory Policy with Comprehensive Environmental Factors Formulation and Service Level Constraints

As firms and consumers engage with environmental issues, decisions for inventory control need to entail this perspective of sustainability. Most green inventory models employ methods such as carbon caps or taxes for dealing with environmental sustainability. This problem can be more generally tackled via an explicit estimation of the environmental drivers of maintaining inventory in a warehouse, paired with the economic perspective within a transparent multi-objective optimization framework. With this goal, this paper builds on a detailed estimation of environmental and cost factors for a continuous-review inventory policy. The bi-objective problem is tackled by keeping the objective functions separate. In particular, the modeling of greenhouse gas emission or cost performance factors for the inventory encompasses factors that can depend on the decision variables, taking into account aspects such as warehouse location, building characterization, energy usage, and transport requirements. The effects of the emission drivers on the multi-objective optimization decisions are analyzed, considering that the problem can be constrained by multiple service level measures. Stockout response can be multifaceted and different service level measures capture different aspects of inventory shortages, affecting the resulting efficient solutions differently. The results highlight the impact of aspects such as warehouse location and supply capacity on solutions for the multi-objective inventory problem. Managerial decisions are thus influenced by warehousing and supply attributes via a traceable link to specific cost and emission determinants.

Interval Constrained Multi-Objective Optimization Scheduling Method for Island-Integrated Energy Systems Based on Meta-Learning and Enhanced Proximal Policy Optimization

Multiple uncertainties from source–load and energy conversion significantly impact the real-time dispatch of an island integrated energy system (IIES). This paper addresses the day-ahead scheduling problems of IIES under these conditions, aiming to minimize daily economic costs and maximize the output of renewable energies. We introduce an innovative algorithm for Interval Constrained Multi-objective Optimization Problems (ICMOPs), which incorporates meta-learning and an improved Proximal Policy Optimization with Clipped Objective (PPO-CLIP) approach. This algorithm fills a notable gap in the application of DRL to complex ICMOPs within the field. Initially, the multi-objective problem is decomposed into several single-objective problems using a uniform weight decomposition method. A meta-model trained via meta-learning enables fine-tuning to adapt solutions for subsidiary problems once the initial training is complete. Additionally, we enhance the PPO-CLIP framework with a novel strategy that integrates probability shifts and Generalized Advantage Estimation (GAE). In the final stage of scheduling plan selection, a technique for identifying interval turning points is employed to choose the optimal plan from the Pareto solution set. The results demonstrate that the method not only secures excellent scheduling solutions in complex environments through its robust generalization capabilities but also shows significant improvements over interval-constrained multi-objective evolutionary algorithms, such as IP-MOEA, ICMOABC, and IMOMA-II, across multiple multi-objective evaluation metrics including hypervolume (HV), runtime, and uncertainty.

A NEW ALGORITHM FOR GENERATING POWER SERIES SOLUTIONS FOR A BROAD CLASS OF FRACTIONAL PDES: APPLICATIONS TO INTERESTING PROBLEMS

This research offers a precise analytical solution for initial value problems of both linear and nonlinear fractional order partial differential equations. A new approach called the limit residual function method is developed and utilized to generate a series solution for the equations. The key tools of this method are the concepts of power series, residual function, and the limit at zero. The new method is characterized by the speed of determining the series solution coefficients and the limited mathematical operations used. The study examines five significant applications of fractional partial differential equations using this new method. To validate the accuracy of the results, they are compared with exact solutions in the classical case for the discussed applications. We conclude that the proposed approach is straightforward, effective, and successful in solving linear and nonlinear fractional differential equations.

Managing Social Impact Bonds: Intermediary Work and Designing Institutional Infrastructure

Collaborations addressing grand challenges seek social impact; whether such social innovations will endure beyond initial enthusiasm is a major issue. Over the last decade, Social Impact Bonds (SIBs) emerged to diffuse globally as a new form of cross sector collaboration to finance solutions for social problems. Crucially, SIBs rely on intermediary organizations to coordinate and govern relations across diverse actors with competing and conflicting interests and values. How an intermediary goes about this work has significant effects on whether the collaboration achieves the desired social impact and whether it endures. In this article, we examine the intermediary work that enables such a cross-sector collaboration by analyzing two of the first completed SIBs in Continental Europe. Our findings identify three main types of interweaving intermediary work of aligning, stitching, and knotting, that are supported by three distinct forms of institutional infrastructure (ideational, operational, and relational respectively) providing a significant contribution to the analysis of cross-sector collaboration by connecting intermediary work to institutional infrastructure.

A Non-Standard Finite Difference Schemes for the Solution of Stiff Initial Value Problems

In this study, we introduce a novel non-standard finite difference (NSFD) scheme designed to address the challenges posed by stiff initial value problems. Stiffness in differential equations often leads to numerical instability and requires specialized methods for stable and accurate solutions. A novel set of numerical schemes for solving stiff ordinary differential equations caused by the decay of radioactive substances developed. This paper demonstrates the power of normalization in the discretization function. We employed non-local approximation and renormalization of the denominator function to create qualitatively stable schemes for a stiff ordinary differential equation. The schemes' stability properties were verified using numerical experiments. The schemes' performance is evaluated in comparison to other typical finite difference schemes

On the inverse problem of time dependent coefficient in a time fractional diffusion problem by sinc wavelet collocation method

The object of this study is to establish the unknown function in a time fractional diffusion problem and the solution as well by utilizing Sinc wavelet collocation method (SWCM) and residual power series method (RPSM) together. SWCM enables us to convert time fractional diffusion problem into a system of fractional ordinary differential and algebraic equations. At this stage, the unknown function and the solution are constructed in the series form by employing RPSM. The novelty of this study is that the combination of SWCM and RPSM is utilized to establish the solution of inverse coefficient problem for the first time. Demonstrative examples are presented to articulate the implementation and importance of the proposed method.

Analysis of Mathematical Critical Thinking Ability based on Students' Ability Level

Analyzing and testing mathematical critical thinking skills based on the ability level of class VIII students of junior high school is the aim of this research. By understanding the level of students' abilities, educators can determine students' mathematical critical thinking abilities and develop appropriate teaching strategies to improve students' abilities. This study uses a qualitative descriptive research method. This research was conducted at one of the junior high schools in Cipatat, West Bandung Regency with heterogeneous abilities of 8 students. This research uses data collection techniques by providing mathematical critical thinking ability questions on SPLDV material which consists of 5 essay test questions based on the following indicators: (1) Checking the completeness of problem solving steps. (2) Look for alternative solutions to problems. (3) Identify spldv equations with certain characteristics. (4) Choose the best way to solve the problem from alternative ways of solving it. (5) Identifying the adequacy of data on a problem. In this study, the results of the analysis have shown that students at a high level of ability can check the completeness of problem solving steps, students with a medium level of ability have little difficulty in identifying spldv equations with certain characteristics, and students with a low level of ability have difficulty finding alternatives problem solution.

Existence of solutions for critical Neumann problem with superlinear perturbation in the half‐space

AbstractIn this paper, we consider the existence and multiplicity of solutions for the critical Neumann problem where , , , , , is the outward unit normal vector at the boundary , is the usual critical exponent for the Sobolev embedding and is the critical exponent for the Sobolev trace embedding . By establishing an improved Pohozaev identity, we show that problem () has no nontrivial solution if . Applying the mountain pass theorem without the condition and the delicate estimates for the mountain pass level, we obtain the existence of a positive solution for all and the different values of the parameters and . Particularly, for , , , we prove that problem () has a positive solution if and only if . Moreover, the existence of multiple solutions for () is also obtained by dual variational principle for all and suitable .

Continuous solutions for a two-dimensional cross-diffusion problem involving doubly degenerate diffusion and logistic proliferation

Emerging from the modeling of intricate structures formed by bacterial motion in nutrient-deficient environments, the doubly degenerate nutrient taxis system [Formula: see text] is considered in smoothly bounded domains [Formula: see text]. In contrast to frameworks devoid of logistic growth where only small-data global solutions have so far been found in the literature, quadratic degradation in the logistic growth is shown to markedly amplify the overall dissipative effects to the extent that, for arbitrary smooth initial data, an associated no-flux type initial-boundary problem possesses global continuous weak solutions. Central to our findings is the identification of an advantageous dissipative structure subtly embedded in the system, the exploitation of which leads to the establishment of a positive lower bound for nutrients levels within any finite time interval, thereby ruling out the appearance of cross-degeneracies within such timeframes.

Towards Calculation of Anisotropic Constructive Elements with Elastic-Plastic Properties

Calculation improvement of asphalt concrete possessing parameters of structurally unstable material is based on the problem of increasing the bearing capacity in terms of the expansion of borders of elastic and plastic material deformation.Purpose: Determination of elastic-plastic characteristics of asphalt concrete during non-equiibrium deformation and elastic aftereffect.Practical implications: The estimation of strength of asphalt concrete pavement of carriageway is based on a solution of the contact problem for structurally unstable material.

On the existence and Lipschitz-like property of the solution map to parametric equilibrium problems governed by trifunction with applications

In this paper, we study a class of parametric equilibrium problems governed by a trifunction. We apply the Fan-KKM theorem under new type of monotonicity and coercivity conditions for trifunctions to obtain the existence result of a solution for the equilibrium problem. For the solution map of parametric equilibrium problems, we obtain the Hölder-type Lipschitz-like property relative to a closed and convex set, which generalizes some existing results in the literature. We illustrate the application of our abstract results in the study of a new model of a fluid flow problem with slip and leak boundary conditions of frictional type.

Enhancing extraction efficiency of carpaine in Carica papaya L. leaves: coupling acid-base extraction with surfactant-assisted micro-flotation.

Carpaine, a major alkaloid in papaya leaves, has considerable cardiovascular benefits alongside its notable effects on muscle relaxation when utilized in medicine. In this study, the coupling of acid-base extraction and flotation was developed to completely remove the use of toxic solvents. This method entails the extraction of carpaine from Carica papaya L. leaves using hot water extraction alongside ultrasound-assisted extraction followed by the condensation of the species using surfactant-assisted flotation. The acid-base extraction was applied to alter the solubility of carpaine as desired at different stages of the process. The results showed that the carpaine extraction yield using all the treatments in conjunction was significantly higher compared to the control samples in which the acid-base extraction or flotation was not applied. The TLC and GC-FID results suggested that the bubbles introduced during the flotation were highly specific toward their interactions with carpaine in its hydrophobic complex form. The quantity of carpaine extracted using our method, in comparison to the amount of carpaine obtained using a different method from a previous study that utilized ethanolic extraction, exhibited a 2.32-fold greater extraction yield. This work demonstrates the importance of flexible utilization of both surface and bulk chemistry in achieving an improved solution for a technical problem.

Integrated aircraft routing and cargo routing problem for combination airlines

The combination airlines operate both passenger aircraft and freighter aircraft to meet passenger and cargo demand. At present, combination airlines employ a sequential approach to allocating their capacity for passenger and cargo demand. Nevertheless, implementing an integrated resource allocation procedure has the potential to improve overall resource allocation efficiency. In this paper, we introduce an integrated model to help combination airlines integrate their aircraft routing and cargo routing decisions to maximize the expected overall profits derived from both passenger and cargo demand. We considered the stochastic nature of passenger baggage and proposed a set of individual chance constraints to ensure the robustness of the integrated solution. We reformulate the chance constraints using piecewise linear approximation to ensure solution efficiency. In addition, we proposed a column-and-row generation based solution approach that removes the through-connection related constraints at the beginning of the solution process and then adds the columns and rows during the iterations as needed. We proved that the proposed column-and-row generation approach can obtain an optimal solution for the LP relaxation problem. The model and the solution approach were tested in a number of scenarios obtained from a major Chinese combination airline. The computational results show that the combination airline can improve their expected profits by integrating capacity allocation. The results also demonstrated that the proposed column-and-row generation solution approach can decrease the solution time of the integrated model. These findings indicate that the model and the solution method are useful and efficient tools for combination airlines when planning their aircraft and cargo routes.

Inverse scattering transform for the higher-order integrable discrete nonlinear Schrödinger equation with nonzero boundary conditions

The inverse scattering transform is a tool for solving the initial value problem of nonlinear equations, and the solution of the initial-value problem by inverse scattering transform proceeds in three steps: direct scattering, time evolution and inverse problem. In this paper, we discuss the higher-order integrable discrete nonlinear Schrödinger equation which is subjected to inverse scattering transform under nonzero boundary conditions, and the corresponding soliton solutions are obtained and illustrated.

An innovative bio-inspired Aquila technique for efficient solution of combined power and heat economic dispatch problem

In the field of power systems, the optimization challenge of combined heat and power units economic dispatch (CHPUED) holds immense importance. This study presents an improved Aquila optimization technique (IAQT) that effectively tackles the CHPUED. The primary objective of the enhanced IAQT model is to minimize the overall cost of power generation in CHP systems while satisfying demand and operational constraints. However, to achieve more accurate cost estimations and avoid suboptimal solutions, it is crucial to consider transmission losses in the optimization model. By incorporating transmission losses, the IAQT algorithm can allocate power generation resources more effectively, leading to improved system efficiency and reduced operational costs. The proposed IAQT algorithm addresses the limitations of the standard AQT and introduces novel features to enhance its search capabilities. One key limitation of the standard AQT is its heavy reliance on the best solution found during optimization. To overcome this drawback, the enhanced IAQT model eliminates the dependency on the best solution and enables a more thorough exploration of the search space. Moreover, the algorithm incorporates specific limitations and constraints for each dimension of the newly generated solutions, ensuring their feasibility and validity. The standard AQT and proposed IAQT are tested on CEC 20 benchmark functions. Moreover, the proposed approach is extensively evaluated through experimentation and testing on various scenarios, including 7–48-unit and large 96-unit systems with/without losses. Furthermore, the overall costs for the 7 unit-system are considered including the reserve constraint. The results exhibit the remarkable performance and efficiency of the enhanced IAQT model, outperforming the standard version and several previously reported results. This validation underscores the significant contribution of the study in addressing the CHPUED and highlights its potential for real-world applications.

Bounded solutions in anisotropic degenerate parabolic problems with a singular term

Bounded solutions in anisotropic degenerate parabolic problems with a singular term

Taylor theory in quantum calculus: a general approach

Let the function β be strictly increasing and continuous on an interval I ⊂ ℝ. The β-difference operator is defined by Dβ f (t) = (f(β(t)) − f(t)/(β(t) – t), where t ≠ β(t), and Dβ f (t) = f′ t(t) when t = s 0 is a fixed point of the function β. This quantum operator is a generalization of q-Jackson, Hahn, power and other quantum operators. As a convenience of the β-function: β(t) turns into the probability distribution function with the probability measure 1, and the sample space ℝ, in the case of its conditions are relaxed to be increasing and continuous from the right, that is, lim t →∞ β(t) = 1 and lim t →∞ β(t) = 0, and also by using the Lebesgue-Stieltjes measure of the interval [a, b] to be β(b) − β(a). In this paper, we investigate a β-Taylor’s formula associated with the operator Dβ when the function β has a unique fixed point s 0 ∈ I, which may allow for more flexible and accurate approximations of functions. An estimation of its remainder is given. Additionally, the β-power series is defined. Furthermore, as application, the β-expansion form of some fundamental functions is introduced. Finally, we find the unique solution of the β-shifting problem.

The overdetermined Cauchy problem for the hyperbolic Gellerstedt equation

Abstract Overdetermined boundary value problems and the minimal operators generated by them are extremely important in the description of regular boundary value problems for differential equations, and are also widely used in the study of local properties of solutions. In addition, for inverse problems of mathematical physics arising from applications, when determining unknown data, it is necessary to study problems with overdetermined boundary conditions, which is reflected in the study of problems, including for hyperbolic equations and systems, arising in physics, geophysics, seismic tomography, geoelectrics, electrodynamics, medicine, ecology, economics and many other practical areas. Thus, the study of overdetermined boundary value problems is of both theoretical and applied interest. In this paper, a criterion for the regular solvability of the overdetermined Cauchy problem for the Gellerstedt equation and the minimal differential operator generated by it in a hyperbolic domain is established, as which both the case of a characteristic triangle and the case of a more general domain with fairly general assumptions about the boundary of the domain are considered. Due to overdetermined boundary conditions, the problem under consideration will be ill-posed in the general case, therefore, for its regular solvability, additional conditions must be imposed on the initial data. In other words, we have considered the inverse problem: to determine what requirements the initial data of the problem, in particular the right part of the Gellerstedt equation, should meet, in question, so that the overdetermined Cauchy problem is regularly solvable. The proof is based on the Gellerstedt potential, the properties of solutions of the Goursat problem in the characteristic triangle, and the properties of special functions.