Solution Of Problem Research Articles

An efficient computational approach for basic feasible solution of fuzzy transportation problems

An efficient computational approach for basic feasible solution of fuzzy transportation problems

Genetic Algorithm as the Solution of Non-Linear Inverse Heat Conduction Problems: a Novel Sequential Approach

Genetic Algorithm as the Solution of Non-Linear Inverse Heat Conduction Problems: a Novel Sequential Approach

Editorial: Psychotropic overprescribing to youth: scope of the problem, causes, and possible solutions

Editorial: Psychotropic overprescribing to youth: scope of the problem, causes, and possible solutions

The improved residual power series method for the solutions of higher-order linear and nonlinear boundary value problems

AbstractIRPSM is the extended form of RPSM that gives an approximate solution to boundary value problems without requiring an exact solution. This method creates a truncated series for the determination of the missing initial conditions. The present study is conducted to evaluate semi-numerical solutions to differential equations using the Improved Residual Power Series Method (IRPSM). Our main objective is to check whether the proposed scheme is efficient for solving such equations or not. The solution of differential equations has been approximated using truncated residual power series. The method is used to solve differential equations for higher-order linear and non-linear boundary value problems. Absolute errors for the solved problems are calculated to ensure accuracy. It is also compared with some known methods, like the Differential Transform Method (DTM) and the Homotopy Perturbation Method (HPM). For the calculations, Mathematica 12.0 software is used. The computed results are compared to the exact solutions as well as the available results in the literature. The results showed that the results obtained by IRPSM are closely related to the exact solution when compared to the DTM and HPM results.

A Deep Learning Approach to Dental Image Analysis and Problem Identification

Panoramic Images are key tool for dentists to spot dental issues early and plan the best course of treatment. In this paper we propose a approach of dental problem detection using images. Model can detect 2 types of issues which are decay and cavity. Model is trained using CNN algorithm. Image processing is perform for detection. After detection of dental problem solution to that problem is also provided such as for decay tooth preventive measures

Stabilization‐free virtual element method for 2D elastoplastic problems

AbstractIn this paper, a novel first‐ and second‐order stabilization‐free virtual element method is proposed for two‐dimensional elastoplastic problems. In contrast to traditional virtual element methods, the improved method does not require any stabilization, making the solution of nonlinear problems more reliable. The main idea is to modify the virtual element space to allow the computation of the higher‐order projection operator, ensuring that the strain and stress represent the element energy accurately. Considering the flexibility of the stabilization‐free virtual element method, the elastoplastic mechanical problems can be solved by radial return methods known from the traditional finite element framework. plasticity with hardening is considered for modeling the nonlinear response. Several numerical examples are provided to illustrate the capability and accuracy of the stabilization‐free virtual element method.

Sensitivity Analysis of the Cost Coefficients in Multiobjective Integer Linear Optimization

This paper considers sensitivity analysis of the cost coefficients in multiobjective integer linear programming problems. We define the sensitivity region as the set of simultaneous changes to the coefficients for which the efficient set and its structure remain the same. In particular, we require that the component-wise relation between efficient solutions is preserved and that inefficient solutions remain inefficient, and we show that this is sufficient for the efficient set to be the same upon changes. For a single coefficient, we show that a subset of the inefficient solutions can be excluded from consideration. More specifically, we prove that it suffices to inspect the inefficient solutions of a q-objective problem that are efficient in one of two related q + 1-objective problems. Finally, we show that the sensitivity region is a convex set (an interval). Our approach generalizes to simultaneous changes in multiple coefficients. For illustration, we consider mean-variance capital budgeting and determine the region for which the set of efficient portfolios remains the same, despite a misspecification or a change in the net present values of the projects. Further computational experience with multiobjective binary and integer knapsack problems demonstrates the general applicability of our technique. For instance, we obtain all sensitivity intervals for changes to single coefficients of biobjective problems with 500 binary variables in less than half an hour of CPU time by excluding a large number of inefficient solutions. In fact, the number of excluded solutions is above 100 orders of magnitude larger than the number of remaining solutions. This paper was accepted by Chung Piaw Teo, optimization. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.01406 .

About a new nonlinear integro-differential equation of Volterra-Strum-Liouville type with a weakly singular kernel

This present paper proposes an analytical and numerical study of a new integro-differential Volterra-Strum-Liouville equation of the second type, having a weak singularity. We provide conditions that guarantee the existence and uniqueness of the solution of the nonlinear problem. Then, we develop a numerical technique using the production integration method. The numerical application shows the efficiency of the proposed procedure.

Characterization of E-Benson proper efficient solutions of vector optimization problems with variable ordering structures in linear spaces

Characterization of E-Benson proper efficient solutions of vector optimization problems with variable ordering structures in linear spaces

Procrustes problem for the inverse eigenvalue problem of normal (skew) J-Hamiltonian matrices and normal J-symplectic matrices

ABSTRACT A square complex matrix A is called (skew) J-Hamiltonian if AJ is (skew) Hermitian where J is a real normal matrix such that J 2 = − I , where I is the identity matrix. In this paper, we solve the Procrustes problem to find normal (skew) J-Hamiltonian solutions for the inverse eigenvalue problem. In addition, a similar problem is investigated for normal J-symplectic matrices.

Closed-Loop Subspace Predictive Control of Gyroscope

Control moment gyroscope (CMG) is used in many applications, especially related to spacecraft navigation. Hence, the trajectory tracking problem of the CMG control is important and worth researching. To address this problem, a closed-loop subspace predictive control (CSPC) of the gyroscope is presented in this paper. The proposed control technique constructs an auxiliary variable based on the known controller information. The constructed auxiliary variable assists to handle the inherent correlation between control inputs and noises in the closed-loop system. Additionally, an unbiased prediction of the system output is obtained to calculate the optimal control input. The theoretical analysis of the recursive feasibility and stability of the proposed control technique is also provided. Ultimately, the effectiveness of the proposed control technique is verified on a real-time experimental platform of the CMG. The experimental results demonstrate the improved trajectory tracking and predictive performance of the proposed control technique. Overall, this paper provides a solution for the trajectory tracking problem of the CMG control.

Informed Adaptive Sensing.

For many inverse problems, the data on which the solution is based is acquired sequentially. We present an approach to the solution of such inverse problems where a sensor can be directed (or otherwise reconfigured on the fly) to acquire a particular measurement. An example problem is magnetic resonance image reconstruction. We use an estimate of mutual information derived from an empirical conditional distribution provided by a generative model to guide our measurement acquisition given measurements acquired so far. The conditionally generated data is a set of samples which are representative of the plausible solutions that satisfy the acquired measurements. We present experiments on toy and real world data sets. We focus on image data but we demonstrate that the method is applicable to a broader class of problems. We also show how a learned model such as a deep neural network can be leveraged to allow generalisation to unseen data. Our informed adaptive sensing method outperforms random sampling, variance based sampling, sparsity based methods, and compressed sensing.

Subdifferential calculus and ideal solutions for set optimization problems

Subdifferential calculus and ideal solutions for set optimization problems

A complex transdisciplinary approach to achieve water sustainability: lessons from a case study in Morelia, Mexico

AbstractAlthough the theoretical–methodological complexity theory and transdisciplinary approach is increasingly accepted within sustainability science, its application at local-scale work with rural communities in the global south is still incipient and requires further research on its scope and limitations. The general objective of this work was to contribute to the knowledge on how a complexity and transdisciplinary approach applied to water problems at local scales can facilitate the process for water sustainability. The research took as study area the ejido of Coro Grande located in the municipality of Morelia, in the rural vicinity of Morelia City, capital of Michoacán State (Mexico). The theoretical–methodological scheme was based on the combination of the concepts of complexity–sustainability–transdisciplinarity to analyze the local water metabolism and generate actions to mitigate present and future water risk. The activities carried out involved a participatory diagnosis and the development of activities for the restoration of degraded environments with a double purpose: to generate conditions for the water sustainability of the system, and to promote the involvement of the population in a transdisciplinary research–action process. The results obtained show the effectiveness of the framework chosen to identify problems, achieve transformation in the short term, and improve both ecosystem functions and participation of the population in the solution of problems in the medium and long terms.

Determining the parameters of the functioning for a nonlinear ballistic system in a real external environment

Purpose. Development of an approximate nonlinear model for the solution of the external ballistics problem with determination of the nonlinear system parameters and development of a methodology for calculating the aerodynamic characteristics of the cargo, located on the external suspension of unmanned aerial vehicle (UAV) in order to increase the efficiency of their delivery to the specified landing target by means of asymptotic approach with given parameters of the studied system and external load. Methodology. The development of an effective model was carried out using analytical and numerical research algorithms based on a nonlinear system of differential equations in a general form with time-varying coefficients. In order to obtain a solution to the nonlinear problem of external ballistics in a two-dimensional formulation, the assumption of a significant influence of the projection of the velocity function on the ordinate axis in relation to the component on the abscissa axis is introduced. The problem is reduced to the solution of a related system of differential equations with variable coefficients along the corresponding coordinates using the asymptotic approach for a small parameter of the coefficient of frontal aerodynamic resistance. Applied mathematical analysis and modeling have been used for the problem formulation considering studied environmental parameters. Findings. Analytical dependences of the nonlinear problem of ballistics and application of finite-element analysis (FEA) with respect to the cargo motion from the UAV in the presence of the initial speed and wind load in the plane of motion are proposed. It is shown that the obtained analytical solution is correlated with the direct numerical calculation of the basic differential equation with respect to the ordinate axis. Originality. A mathematical nonlinear model of the dynamic process is proposed, assuming the prevailing influence of the speed function along the ordinate axis compared to the function along the abscissa axis. To obtain an approximate analytical solution of the basic nonlinear system of differential equations with variable coefficients the asymptotic perturbation method is applied. The dependence for the axial displacement function is presented considering actual time-flight parameter. Practical value. The obtained analytical dependencies for estimating the time and distance reaching the target with the initial speed of movement and the presence of wind load can be used in applied problems of mathematical physics and engineering calculations of functional dependencies and control of the cargo delivery process and target reaching from an UAV. The obtained analytical results and the solution algorithm can be integrated into applied problems of mathematical physics and engineering calculations, particularly the development of ballistic system control algorithms.

Finding and implementing the numerical solution of an optimal control problem for oscillations in a coupled objects system

Finding and implementing the numerical solution of an optimal control problem for oscillations in a coupled objects system

Schwarz Problem for Model Partial Differential Equations with One Complex Variable

This paper investigates the Schwarz problem. Initially, the focus lies on analyzing the problem for the first, second orders. Subsequently, attention shifts towards studying the same problem for equations of higher order. In the realm of second-order equations, the Schwarz problem is specifically examined for some operators; Laplace, Bitsadze and its complex conjugate. The findings demonstrate that the Schwarz problem for an n-order equation, when equipped with solely one boundary condition, exhibits an infinite number of solutions. However, by incorporating additional boundary conditions, it becomes feasible to obtain a unique solution for problem concerning n-order equations, effectively rendering it a well-posed problem.

The Impact of a Sterinberg Theory-Based Training Program on Secondary School Students' Development of Critical and Creative Thinking Skills

This study aimed to test the impact of a training program based on Sternberg's theory of problem solving on the development of critical and creative thinking skills among secondary school students, using a semi-experimental approach. The sample consisted of 70 students from the first grade of literary secondary school at Al-Baraa bin Malik Secondary School in the Directorate of Education of Naour in Jordan and was divided equally into two groups: experimental and control. The researcher built a training program based on Sternberg's theory of problem solving, known as the 'thinking circle', which consists of seven dimensions: feeling the problem, identifying the problem, representing the problem, choosing or inventing a solution strategy, effectively allocating resources for the solution, monitoring the problem solution, and evaluating the problem solution. The program was implemented during 11 six-week training sessions in the second semester of 2021–2022. The California 2000 Critical Thinking Scale and the Torrens Creative Thinking Scale (A) were also used in both the pre- and post-group assessment processes. To answer the questions of the study, it was found that the average performance of the groups was control and experimental for the pre-measurement of the critical thinking scale (10.55) and (10.75), respectively, while the average performance of the groups was on the dimensional measurement (11.67) and (17.78), respectively. To examine the differences in each of the arithmetic averages, the researcher used the analysis of covariance (ANCOVA) for performance for the total score of the critical thinking scale. The average performance of the control and experimental groups in the pre-evaluation of the creative thinking test was (71.68) and (70.35) respectively, and the average performance of the control and experimental groups in the dimensional measurement was (72.12) and (129.65) respectively, and the common multiple covariance analysis (MANCOVA) was used to test the differences in the arithmetic mean of performance in the sub-dimensions of the creative thinking test. It was found that there were statistically significant differences in the arithmetic mean in the level of significance (α = 0.05), and the difference was in favor of the experimental group in critical and creative thinking skills, which confirms that the program has a significant impact on the development of creative and critical thinking skills.

Using Genetic Algorithms and Core Values of Cooperative Games to Solve Fuzzy Multiobjective Optimization Problems

A new methodology for solving the fuzzy multiobjective optimization problems is proposed in this paper by considering the fusion of cooperative game theory and genetic algorithm. The original fuzzy multiobjective optimization problem needs to be transformed into a scalar optimization problem, which is a conventional optimization problem. Usually, the assignments of suitable coefficients to the corresponding scalar optimization problem are subjectively determined by the decision makers. However, these assignments may cause some biases by their subjectivity. Therefore, this paper proposes a mechanical procedure to avoid this subjective biases. We are going to formulate a cooperative game using the α-level functions of the multiple fuzzy objective functions. Under this setting, the suitable coefficients can be determined mechanically by involving the core values of the cooperative game, which is formulated using the multiple fuzzy objective functions. We shall prove that the optimal solutions of the transformed scalar optimization problem are indeed the nondominated solutions of fuzzy multiobjective optimization problem. Since the core-nondominated solutions will depend on the coefficients that are determined by the core values of cooperative game, there will be a lot of core-nondominated solutions that will also depend on the corresponding coefficients. In order to obtain the best core-nondominated solution, we shall invoke the genetic algorithms by evolving the coefficients.

Uncertainty relation and the constrained quadratic programming

The uncertainty relation is a fundamental concept in quantum theory, plays a pivotal role in various quantum information processing tasks. In this study, we explore the additive uncertainty relation pertaining to two or more observables, in terms of their variance, by utilizing the generalized Gell-Mann representation in qudit systems. We find that the tight state-independent lower bound of the variance sum can be characterized as a quadratic programming problem with nonlinear constraints in optimization theory. As illustrative examples, we derive analytical solutions for these quadratic programming problems in lower-dimensional systems, which align with the state-independent lower bounds. Additionally, we introduce a numerical algorithm tailored for solving these quadratic programming instances, highlighting its efficiency and accuracy. The advantage of our approach lies in its potential ability to simultaneously achieve the optimal value of the quadratic programming problem with nonlinear constraints but also precisely identify the extremal state where this optimal value is attained. This enables us to establish a tight state-independent lower bound for the sum of variances, and further identify the extremal state at which this lower bound is realized.