Multiple Solutions Research Articles

Mathematical Modelling Non Linearity Characteristic Analysis and Efficiency Enhancement Strategies for Hybrid Solar Photovoltaic Energy System

As the world continues to grapple with the challenges posed by climate change and the depletion of conventional energy sources, renewable energy systems such as solar photovoltaic (PV) technology have gained significant prominence. Hybrid solar PV systems, which combine multiple energy sources and storage solutions, offer a promising avenue to improve the reliability and efficiency of renewable energy generation. This research focuses on the mathematical modeling, non-linearity characteristic analysis, and the development of efficiency enhancement strategies for hybrid solar PV energy systems. The study begins with the development of comprehensive mathematical models that accurately represent the complex interactions within hybrid solar PV systems. These models consider various factors, including solar irradiance, temperature variations, load profiles, and the dynamic behavior of energy storage components. The incorporation of non-linear characteristics, often overlooked in conventional models, allows for a more realistic representation of system performance. To enhance the efficiency of hybrid solar PV systems, a range of strategies are proposed and evaluated. These strategies encompass advanced control algorithms, optimized sizing and placement of energy storage elements, and the integration of emerging technologies such as artificial intelligence and machine learning. The goal is to mitigate non-linear effects, maximize energy utilization, and improve system response to dynamic operating conditions.
 The findings from this research provide valuable insights into the design, operation, and performance optimization of hybrid solar PV energy systems. By addressing non-linearity characteristics and developing efficient strategies, this study contributes to the advancement of renewable energy technologies and fosters the transition towards a more sustainable and resilient energy future.

How brand loyalty and its marketing activities affect Japanese fashion companies' financial performance

PurposeTo investigate (1) the relationship between young adults' behavioural brand loyalty (BBL) and Japanese fashion companies' financial performance (FP) and (2) FP improvement from the perspectives of social media brand engagement (BE) and loyalty programmes (LPs) by applying the complexity theory.Design/methodology/approachA mixed methodology was employed by combining qualitative and quantitative approaches to examine the prediction of outcomes by various variables in a realistic context. The integrated model associated BE and LPs with BBL and FP, which are essential for fashion companies. We selected 14 fashion brands belonging to 14 publicly traded Japanese fashion companies and surveyed 183 Japanese consumers (aged 18–25 years) who chose these brands as their favourites, engaged with the brands and participated in LPs.FindingsThe findings reveal the positive and negative effects of the variables (BE and LP) on the outcomes (short- and long-term FP). They offer marketing implications regarding brand strategy and financial improvement by considering various combinations of causal factors and complex situations, such as the fashion brands' and consumers' characteristics.Originality/valueExisting empirical studies consider consumers' symmetric reactions to the benefits and losses from variables (BE, LP and BBL) but do not realistically reveal the negative and positive effects on outcomes (FP). This study addresses this gap by applying the complexity theory and offers multiple solutions to target different consumer types to predict high FP.

Multiplicity of solutions for a singular system with sign-changing potential

Abstract This paper focuses on a singular system with a sign-changing potential in Γ, a bounded domain with a Lipschitz boundary in ℝ d {\mathbb{R}^{d}} . By imposing appropriate conditions on the weight potential, which is allowed to change sign, we establish the existence of multiple solutions using the shape optimization approach. This study represents one of the earliest endeavors to explore and analyze the occurrence of multiple solutions in fractional singular systems involving sign-changing potentials. By explicitly addressing this particular aspect, our paper contributes significantly to the limited body of literature that exists in this specific field.

Stable non-BPS black holes and black strings in five dimensions

In this paper we study black hole and black string solutions in five dimensional N=2 supergravity theories arising from the compactification of M-theory on Calabi-Yau manifolds. In particular, we consider explicit examples of three parameter Calabi-Yau manifolds which are obtained as hypersurfaces in toric varieties. Using the attractor mechanism, we obtain Bogomol’nyi-Prasad-Sommerfield (BPS) as well as non-BPS black holes in these compactified supergravity theories. We also consider the black string solutions in these models. We analyze the stability of these extremal black brane configurations by computing the recombination factor. We find multiple stable non-BPS attractor solutions in some of these models. Published by the American Physical Society 2024

Multiplicative design and technological solutions in development and industrial application of pulse-cyclic electrochemical method

The article presents multiplicative design and technological directions in the development and application of the pulse-cyclic method of volumetric shaping. Previously published scientific and technical publications dealt with the consideration of technological and metal-physical aspects of pulse-cyclic shaping. At the same time, the achieved indicators of these parameters are largely determined by the implemented design and technological solutions of the equipment used. The applied modular principle of construction of metalworking equipment. Allows for the construction of multiplicative design and technological solutions in the development of equipment for the industrial application of the electrochemical pulse-cyclic method. On the basis of the proposed approach, electrochemical copy-piercing machines of the EHP-1 model were created and introduced into industrial production. The presented multiplicative solutions in this article show how it is possible to create high-tech domestic machine-tool equipment. Ensuring the scientific and technical competitiveness of the developed pulse-cyclic electrochemical processing allows solving complex industrial problems to provide electrochemical equipment with the required level of accuracy and performance.

Soliton molecules, Y-type soliton and complex multiple soliton solutions to the extended (3+1)-dimensional Jimbo-Miwa equation

Abstract The central purpose of this paper is extracting some novel and interesting soliton solutions of the extended (3+1)-dimensional Jimbo-Miwa equation(JME) which acts as an extension of the classic (3+1)-dimensional JME for the plasma and optics. First, we study the N-soltion solutions that is developed by the Hirota bilinear method (HBM). Then, the soliton molecules and Y-type soliton solutions are constructed via imposing the novel resonance conditions to the N-soltion solutions. In addition, we also explore the complex multiple soliton solutions via the HBM. The dynamic properties of the N-soltion, soliton molecules, Y-type soliton as well as the complex multiple soliton solutions are presented graphically. The developed soliton solutions of this research are all new and can enable us apprehend the nonlinear dynamic behaviors of the extended (3+1)-dimensional JME better.

Multi-Node Feature Learning Network Based on Maximum Spectral Harmonics-to-Noise Ratio Deconvolution for Machine Condition Monitoring

Since the cyclostationarity in vibration signals is the key to judge the rotating machine health state, spectral harmonics-to-interference ratio (SHIR) has been used to construct single node feature learning network (SHIR-based blind deconvolution, BD-SHIR) to realize condition monitoring of machine. However, BD-SHIR still has several obvious limitations, including the need for prior fault information and the tendency to fall into local optimal solutions which will affect its feature learning and state monitoring performance. Therefore, this paper proposes a multi-node feature learning network based on BDSHIR, which does not rely on prior information, multi-node adaptive BDSHIR (MABD-SHIR). It uses each filter in the 1/3 binary tree filter bank to design each initial node (filter) in the learning network correspondingly, and introduces an adaptive fault characteristic frequency (FCF) detection process. Since this initialization can give some filters close to the fault resonant band, iterations starting from these nodes are more likely to detect the precise FCF and converge to the optimal solution. Finally, MABD-SHIR can obtain multiple local optimal solutions, among which the one with the largest SHIR is generally closer to the global optimal solution than the one obtained by BD-SHIR. Simulation and experimental data of defective rotating machinery verify the effectiveness of MABD-SHIR in machinery condition monitoring and fault feature learning. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is motivated by the problems that the rotating machine condition monitoring based on BDSHIR is easy to prematurely fall into local optimal solution and requires prior fault information. These problems can be effectively solved by extending BDSHIR from single node structure to multi-node structure and introducing adaptive period detection technique (A-DPT). The core idea is to start iterations from multiple initial filters and to detect the FCF adaptively during each iteration. Multiple features conforming to filtered signals’ SHIR maximization can be finally learned. Therefore, in this paper, MABD-SHIR is proposed, which is equivalent to a multi-node feature learning network. Since the objective function of BD is usually non-convex, MABD-SHIR can obtain multiple local optimal solutions without requiring prior FCFs. This is more likely to achieve a global optimal solution than BDSHIR, which starts iteration from only one initial filter and ends up with one local optimal solution. In addition, the objective function of MABD-SHIR has lower mathematical complexity, which reduces the difficulty of optimization.

High-throughput 3D microfluidic chip for generation of concentration gradients and mixture combinations.

Concentration gradient generation and mixed combinations of multiple solutions are of great value in the field of biomedical research. However, existing concentration gradient generators for single or two-drug solutions cannot simultaneously achieve multiple concentration gradient formations and mixed solution combinations. Furthermore, the whole system was huge, and required expensive auxiliary equipment, which may lead to complex operations. To address this problem, we devised a novel 3D microchannel network design, which is capable of creating all the desired mixture combinations and concentration gradients of given small amounts of the input solutions. As a proof of concept, the device we presented was verified by both colorimetric and fluorescence detection methods to test the efficiency. This can enable the implementation of one to three solutions with no driving pump and facilitate unique multiple types of more concentration gradients and mixture combinations in a single operation. We envision that this will be a promising candidate for the development of simplified methods for screening of the appropriate concentration and combination, such as various drug screening applications.

Geometrical wetting boundary condition for complex geometries in lattice Boltzmann color-gradient model

A wetting boundary condition for dealing with moving contact lines on complex surfaces is developed in the lattice Boltzmann color-gradient model. The wetting boundary condition is implemented by combining the geometrical formulation of contact angle and the idea of the prediction–correction wetting scheme, which not only produces the desired contact angles with high accuracy but also avoids the necessity to select an appropriate interface normal vector from multiple solutions that satisfy the contact angle condition. Through the implementation in the framework of color-gradient model, the developed wetting boundary condition is validated against analytical solutions by a series of benchmark cases, including a droplet resting on a cylindrical surface and on a tilt wall, a liquid film migrating between two parallel plates, and the forced imbibition into a pore doublet. The simulation results of static contact angles show that the wetting boundary condition is able to simulate arbitrary values of contact angle and leads to negligible mass leakage across the boundary. For dynamic problems, the wetting boundary condition is found to correctly capture the imbibition dynamics under various flow and viscosity ratio conditions and produce dynamic contact angles that match well with the Cox–Voinov law.

Comparative analysis of Casson nanofluid flow over shrinking sheet under the influence of thermal radiation, electric variable, and cross diffusions: Multiple solutions and stability analysis

Comparative analysis of Casson nanofluid flow over shrinking sheet under the influence of thermal radiation, electric variable, and cross diffusions: Multiple solutions and stability analysis

Multiple soliton solutions of the Korteweg-de Vries in the frame of the time-dependent variable coefficient

Multiple soliton solutions of the Korteweg-de Vries in the frame of the time-dependent variable coefficient

Exploration of solitons and analytical solutions by sub-ODE and variational integrators to Klein-Gordon model

In this paper, we use the sub-ODE method to analyze soliton solutions for the renowned nonlinear Klein-Gordon model (NLKGM). This method provides a variety of soliton solutions, including three positive solitons, three Jacobian elliptic function solutions, bright solitons, dark solitons, periodic solitons, rational solitons and hyperbolic function solutions. Applications for these solitons can be found in optical communication, fiber optic sensors, plasma physics, Bose-Einstein condensation and other areas. We also study some numerical solutions by using forward, backward, and central difference techniques. Moreover, we discuss variational integrators (VIs) using the projection technique for NLKGM. We develop a numerical solution for NLKGM using the discrete Euler lagrange equation, the Lagrangian and the Euler lagrange equation. At the end, in various dimensions, covering 3D, 2D, and contour, we will also plot several graphs for the obtained NLKGM solutions. A contour plot is a type of graphic representation that displays a three-dimensional surface on a two-dimensional plane by using contour lines. Each contour line in the plotted function represents one of the function's constant values, mapping the function's value across the plane. This model has been studied across multiple soliton solutions using various methods in the open literature, but this model for VIs and finite deference scheme (FDS) is the first time it has been studied. Within the various numerical techniques accessible for solving Hamiltonian systems, variational integrators distinguish themselves because of their symplectic quality. Here are some of the symplectic properties: symplectic orthogonality, energy conservation, area preservation, and structure preservation.

Multiple positive solutions for a singular tempered fractional equation with lower order tempered fractional derivative

&lt;abstract&gt;&lt;p&gt;Let $ \alpha\in (1, 2], \beta\in (0, 1) $ with $ \alpha-\beta &amp;gt; 1 $. This paper focused on the multiplicity of positive solutions for a singular tempered fractional boundary value problem&lt;/p&gt; &lt;p&gt;&lt;disp-formula&gt; &lt;label/&gt; &lt;tex-math id="FE1"&gt; \begin{document}$ \begin{equation*} \left\{\begin{aligned}\ &amp;amp; -{^R _0}{{\mathbb{D}_t}^{\alpha,\lambda}} u(t) = p(t)h\left(e^{\lambda t} u(t), {^R _0}{{\mathbb{D}_t}^ {\beta,\lambda}}u(t)\right), t\in(0,1),\\&amp;amp; {^R _0}{{\mathbb{D}_t}^ {\beta,\lambda}}u(0) = 0, \ \ {^R _0}{{\mathbb{D}_t}^ {\beta,\lambda}}u(1) = 0, \end{aligned}\right. \end{equation*} $\end{document} &lt;/tex-math&gt;&lt;/disp-formula&gt;&lt;/p&gt; &lt;p&gt;where $ h\in C([0, +\infty)\times[0, +\infty), [0, +\infty)) $ and $ p \in L^1([0, 1], (0, +\infty)) $. By applying reducing order technique and fixed point theorem, some new results of existence of the multiple positive solutions for the above equation were established. The interesting points were that the nonlinearity contained the lower order tempered fractional derivative and that the weight function can have infinite many singular points in $ [0, 1] $.&lt;/p&gt;&lt;/abstract&gt;

Kinematic Analysis of Multi-Section Opposite Magnetic Catheter Robots With Solution Multiplicity

Magnetic catheter robots have great potential for application in minimally invasive surgical interventions that require submillimeter soft catheters to be inserted into the body. Compared to other medical continuum robots, the kinematic characteristics of the magnetic continuum robot are required to be improved, including operating dexterity. The opposite magnetic continuum robot (OMCR), which has oppositely-magnetized magnets on the robot, is capable of deforming in large and high-order curvatures and shows improved dexterity. However, unstable kinematic behaviors emerge owing to solution multiplicity and affect the actual operation. For example, snapping, which indicates the sudden jump from one state to another, induces danger for medical operations. In addition, the motion sequence of the external mobile magnet affects the final state of OMCR. Therefore, in this study, we first analyze the reason for these emerging behaviors by understanding the solution multiplicity of an OMCR. We then modified the OMCR kinematic model with instability analysis and additional constraints, to predict the critical point for snapping and avoid other unexpected behavior for path planning. Herein, our study aims to analyze the stability of the OMCR with relatively unstable configurations in their actuation space to ensure stable and dexterous motions for medical applications. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this work is to analyze, predict, and avoid the unexpected behaviors of the medical magnetic catheter robots, and ensure stable and dexterous operation. Submillimeter magnetic catheter robots have received considerable attention in the past ten years owing to their small size and dexterous motion. They have great potential for minimally invasive surgical interventions that require the navigation of “tighter corners” inside the human body. However, there may exist multiple local solutions under an external field, especially when the robot deforms in high-order curvature for dexterous operation. This situation induces unexpected behaviors and danger for medical use, such as a sudden jump from one state to another. Herein, we analyze the solution evolution as the external field varies and predict the unexpected behaviors using a modified kinematic model with instability analysis. Preliminary experiments demonstrated the effectiveness of the modified model, which can predict unexpected behaviors, and evaluate and enhance the stability during path planning. This method can be implemented for the dexterous and stable operation of magnetic catheter robots, which is significant for medical applications.

Safety Risk Assessment of an Autonomous Agricultural Machine

Highlights The safety guidelines outlined in ISO 18497 are not sufficient to guarantee the safe operation of autonomous agricultural machines. Since the risk assessment techniques specified in ISO 12100:2012 require historical failure data of the machine at hand, they cannot be used to effectively mitigate the risk associated with autonomous agricultural machines where such data are not readily available. Analysis from the perspective of ergonomics can potentially increase the safety of autonomous agricultural machines. Abstract. The goal of this study was to analyze the safety implications of an autonomous agricultural machine (TerraPreta) using the standards ISO 18497 (ISO, 2018) and ISO 12100:2012 (ISO, 2012), as well as to investigate the ergonomics associated with the use of the autonomous agricultural machine. First, three engineers involved in the robot's manufacturing process were asked to evaluate the robot's functionalities compliance with the applicable safety standards and protective measures outlined in standard ISO 18497 (ISO, 2018). Second, while the robot was planting cover crop seeds, an attempt was made to identify and evaluate every risk connected to the robot using the risk assessment techniques outlined in ISO 12100:2012 (ISO, 2012). (1) Half (50%) of the functionalities of the autonomous agricultural machine complied with the safety requirements and protective measures described within the standard ISO 18497 (ISO, 2018). (2) The heavy reliance on past incident data of the risk assessment procedure described within the standard ISO 12100:2012 (ISO, 2012) makes it ineffective for new and revolutionary technologies such as autonomous agricultural machines where such data are not available. (3) Lifting a bag to fill the robot hopper with seeds was found to be a moderately hazardous activity associated with human-robot interaction. Multiple tentative solutions were provided to avoid this moderately hazardous activity. Keywords: Autonomous agricultural machine, Ergonomics, Machine safety, NIOSH lifting equation, Risk assessment, Standards.

Simplicial decomposition of variational inequalities with multiple nonlinear column generation

&lt;abstract&gt; &lt;p&gt;Simplicial decomposition (SD) of variational inequalities experiences the long-tail convergence property. That is, the equilibrium solution rapidly progresses at first but then tails off, making only a tiny amount of progress per column generation iteration, which is a drawback of SD-VI. In the context of Dantzig-Wolfe of LP, it is reported that the more proposals are used to initialize the algorithm, the faster the solution can be found by reducing the number of decomposition steps. Therefore, I proposed to solve multiple nonlinear column generation (mNCG) subproblems in each SD-VI iteration (SD-VI-mNCG) instead of solving only one subproblem as in SD-VI. Generating multiple column generation subproblem solutions in each SD-VI iteration enabled the corresponding convex hull to be rapidly enlarged. Consequently, the number of SD-VI iterations could be greatly reduced. A transportation network equilibrium problem was used to study the performance of the SD-VI-mNCG.&lt;/p&gt; &lt;/abstract&gt;

Multiple Nontrivial Solutions for Biharmonic Systems Involving Rellich-type Potentials and Homogeneous Terms

Multiple Nontrivial Solutions for Biharmonic Systems Involving Rellich-type Potentials and Homogeneous Terms

Solitary waves of the generalized Zakharov equations via integration algorithms

&lt;abstract&gt;&lt;p&gt;In many applications, the investigation of traveling wave solutions is essential in obtaining an accurate description of the dynamical behavior of most physical phenomena. The exact solutions to nonlinear equations can provide more physical descriptions and insightful details for many problems of practical interest. This paper focuses on investigating the solitary wave solutions of the generalized Zakharov equations (GZEs) by using four integration algorithms, namely, the modified $ (g'/g^{2}) $-expansion method, the modified $ (g') $-expansion method, the generalized simple ($ w/g $)-expansion method, and the addendum to Kudryashov's method. The GZEs have been widely used to describe the propagation of Langmuir waves in the field of plasma physics. The efficiency and simplicity of these methods are evaluated based on their application to GZEs, which have yielded multiple new optical solitary wave solutions in the form of rational, trigonometric, and hyperbolic functions. By using a suitable wave transformation, the coupled nonlinear partial differential equations are converted into ordinary differential equations. The derived optical solutions are graphically depicted in $ 2 $D and $ 3 $D plots for some specific parameter values. The traveling wave solutions discovered in the current study constitute just one example of the desired solutions that may enable the exploration of the physical properties of many complex systems and could also contribute greatly to improving our understanding of many interesting natural phenomena that arise in different applications, including plasma physics, fluid mechanics, protein chemistry, wave propagation, and optical fibers.&lt;/p&gt;&lt;/abstract&gt;

Multiple positive solutions for the logarithmic Schrödinger equation with a Coulomb potential

Multiple positive solutions for the logarithmic Schrödinger equation with a Coulomb potential

Periodic solutions in reversible systems in second order systems with distributed delays

&lt;abstract&gt;&lt;p&gt;In this paper, we study the existence and multiplicity of periodic solutions to a class of second-order nonlinear differential equations with distributed delay. Under assumptions that the nonlinearity is odd, differentiable at zero and satisfies the Nagumo condition, by applying the equivariant degree method, we prove that the delay equation admits multiple periodic solutions. The results are then illustrated by an example.&lt;/p&gt;&lt;/abstract&gt;