Unique Solution Research Articles

An efficient Newton-type matrix splitting algorithm for solving generalized absolute value equations with application to ridge regression problems

A generalized Newton-based matrix splitting (GNMS) method is proposed for solving the generalized absolute value equations (GAVEs). Under mild conditions, the GNMS method converges to the unique solution of GAVEs. Moreover, we can obtain a few weaker convergence conditions for some existing methods. Numerical results verify the effectiveness of the proposed method.

An Optimal Multi-Modal Approach for Stock Market Price Forecasting with Fused Sentiment Analysis for Real Time Data

Abstract: This study presents an innovative fusion-based methodology that integrates real-time stock market technical indicators with news sentiment analysis from financial news feeds to enhance stock selection decisions. The proposed framework employs a Bidirectional Long Short-Term Memory (Bi-LSTM) model for forecasting stock prices and a Deep Neural Network (DNN) used in conjunction with transformer-based model for sentiment classification, both optimized through the incorporation of real-time datasets. To further refine feature selection, Artificial Bee Colony (ABC) and Firefly algorithms are utilized, significantly improving the accuracy of price trend predictions and sentiment analysis. Technical indicators from stock market data are processed using the Bi-LSTM model to predict future stock prices. Concurrently, sentiment data from the Economic Times is pre-processed through Term Frequency-Inverse Document Frequency (TF-IDF) vectorization and pre-trained transformer models to extract key sentiment scores. The ABC algorithm enhances textual feature selection, while the Firefly algorithm reduces skewness in the error distribution of technical indicators, thereby improving the alignment between forecasted and actual stock prices. The fusion mechanism integrates predicted price movements with sentiment analysis to provide actionable insights for stock selection. The decision-making framework classifies stocks based on the consistency between price movements and sentiment: stocks predicted to rise with positive sentiment are labelled as "Sure Selection"; rising prices with negative sentiment are categorized as "Dicey Selection"; declining prices with positive sentiment result in a "Risky Selection"; and negative sentiment with falling prices trigger an "Avoid Selection". The proposed approach achieved a prediction accuracy of 67.00% for the Bi-LSTM model, with a precision of 0.714, recall of 0.695, and an F1 score of 0.677, demonstrating the model's robustness. The mean absolute error (MAE) for the Bi-LSTM model was 4.30, indicating strong predictive performance. The combined use of ABC and Firefly algorithms optimizes both technical and sentiment features, significantly contributing to the overall performance of the prediction model. By fusing multiple data sources and employing advanced optimization techniques, this methodology offers a unique and effective solution for stock market prediction and decision-making

Propagation of wave insights to the Chiral Schrödinger equation along with bifurcation analysis and diverse optical soliton solutions

In this study, the modified Sardar sub-equation method is capitalised to secure soliton solutions to the (1+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1+1)$$\\end{document}-dimensional chiral nonlinear Schrödinger (NLS) equation. Chiral soliton propagation in nuclear physics is an extremely attractive field because of its wide applications in communications and ultrafast signal routing systems. Additionally, we perform bifurcation analysis to gain a deeper understanding of the dynamics of the chiral NLS equation. This highlights the complex behaviour of the system and exposes the conditions under which various types of bifurcations occur. Additionally, a sensitivity analysis is performed to assess how small changes in initial conditions and parameters influence the solutions, offering valuable perspectives on the stability and dependability of the acquired solutions. By employing the above-mentioned methodology, we derive a variety of exact solutions, including periodic, singular, dark, bright, mixed trigonometric, exponential, hyperbolic, and rational wave solutions. The study’s findings advance our theoretical knowledge of chiral NLS equations and have potential applications in optical communication and related fields.

Existence of extremal solutions for a class of fractional integro-differential equations

In the study the existence of solutions of a class of fractional integro-differential equations with boundary conditions was considered. The main tool, we employ, is the conventional monotone iterative technique, which is highly effective method to examine the quantitative and qualitative characteristics of various nonlinear problems. This technique produces monotone sequences whose iterations are unique solutions of the certain linear problems. These bounds converge uniformly to the maximal solutions of the given problems. Some types of coupled solutions are considered to obtain the claim of the main results under suitable conditions.

The Robin Problems in the Coupled System of Wave Equations on a Half-Line

This article investigates the local well-posedness of a coupled system of wave equations on a half-line, with a particular emphasis on Robin boundary conditions within Sobolev spaces. We provide estimates for the solutions to linear initial-boundary-value problems related to the coupled system of wave equations, utilizing the Unified Transform Method in conjunction with the Hadamard norm while considering the influence of external forces. Furthermore, we demonstrate that replacing the external force with a nonlinear term alters the iteration map defined by the unified transform solutions, making it a contraction map in a suitable solution space. By employing the contraction mapping theorem, we establish the existence of a unique solution. Finally, we show that the data-to-solution map is locally Lipschitz continuous, thus confirming the local well-posedness of the coupled system of wave equations under consideration.

Three Duopoly Game-Theoretic Models for the Smart Grid Demand Response Management Problem

Demand response management (DRM) significantly influences the prospective advancement of electricity smart grids. This paper introduces three distinct game-theoretic duopoly models for the smart grid demand response management problem. It delineates several rational assumptions regarding the model variables, functions, and parameters. The first model adopts a Cournot duopoly form, offering a unique closed-form equilibrium solution. The second model adopts a Stackelberg duopoly structure, also providing a unique closed-form equilibrium solution. Following a comparison of the economic viability of the two model equilibria and an assessment of their sensitivity to parametric changes, the paper proposes a third model with a Cartel structure and discusses its advantages over the earlier models. Finally, the paper examines how demand forecasting affects the equilibrium quantities and pricing solutions of each model.

Solutions of the system of dual matrix equation [formula omitted] in two partial orders

In this paper, we consider the solutions of the system of dual matrix equation AXB=B=BXA in P-star partial order and D-star partial order, respectively. The solvability condition are obtained by applying the singular value decomposition (SVD) and the expression of general solutions to the dual matrix equations are provided. The special case in which A=B is discussed and the properties of {1}−dual generalized inverse are used to verify the accuracy of the explicit solution of dual matrix equation BXB=B. Finally, the explicit formula for the unique minimum-norm solution is given.

Optical solitons, dynamics of bifurcation, and chaos in the generalized integrable (2+1)-dimensional nonlinear conformable Schrödinger equations using a new Kudryashov technique

In the present paper, the new Kudryashov approach is utilized to construct several novel optical soliton solutions for the generalized integrable (2 + 1)-dimensional nonlinear Schrödinger system with conformable derivative. Additionally, the dynamics of bifurcation behavior and chaos analysis in this system are investigated. We applied bifurcation and chaos theories to enhance our understanding of the planar dynamical system derived from the current model while we obtained and illustrated the chaotic solutions for the perturbed dynamical system using graphs. The study yields a class of new optical soliton solutions, including bell-shaped, wave, dark, dark-bright, dark, multi-dark, and singular soliton solutions. Three-dimensional, two-dimensional, and contour plots are presented to visually demonstrate the physical implications and dynamic characteristics of the current conformable equation system. Further, an analysis is discussed on how the conformable derivative parameter and the parameter of time impact the present optical solutions, demonstrating the system’s importance. It is believed that the solutions analyzed in this study are entirely new and have not been previously reported. These discoveries have the potential to significantly enhance our understanding of nonlinear physical phenomena, especially in nonlinear optics and traffic signaling effects with optical dromion transmission.

Semipositone elliptic equations in unbounded domains in Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbb{R}^{n}$\\end{document}

We investigate a class of semipositone nonlinear elliptic boundary value problems in unbounded domains D of Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbb{R}^{n}$\\end{document}, n≥3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$n\\geq 3$\\end{document}. Under some mild-assumptions, we obtain the existence of a unique positive continuous solution and provide information about its global behavior.

Lattice QCD estimates of thermal photon production from the QGP

Thermal photons produced in heavy-ion collision experiments are an important observable for understanding quark-gluon plasma (QGP). The thermal photon rate from the QGP at a given temperature can be calculated from the spectral function of the vector current correlator. Extraction of the spectral function from the lattice correlator is known to be an ill-conditioned problem, as there is no unique solution for a spectral function for a given lattice correlator with statistical errors. The vector current correlator, on the other hand, receives a large ultraviolet contribution from the vacuum, which makes the extraction of the thermal photon rate difficult from this channel. We therefore consider the difference between the transverse and longitudinal part of the spectral function, only capturing the thermal contribution to the current correlator, simplifying the reconstruction significantly. The lattice correlator is calculated for light quarks in quenched QCD at T=470 MeV (∼1.5Tc), as well as in 2+1 flavor QCD at T=220 MeV (∼1.2Tpc) with mπ=320 MeV. In order to quantify the nonperturbative effects, the lattice correlator is compared with the corresponding NLO+LPMLO estimate of correlator. The reconstruction of the spectral function is performed in several different frameworks, ranging from physics-informed models of the spectral function to more general models in the Backus-Gilbert method and Gaussian process regression. We find that the resulting photon rates agree within errors. Published by the American Physical Society 2024

Analysis of Hybrid NAR-RBFs Networks for complex non-linear Covid-19 model with fractional operators

The Hybrid NAR-RBFs Networks for COVID-19 fractional order model is examined in this scientific study. Hybrid NAR-RBFs Networks for COVID-19, that is more infectious which is appearing in numerous areas as people strive to stop the COVID-19 pandemic. It is crucial to figure out how to create strategies that would stop the spread of COVID-19 with a different age groups. We used the epidemic scenario in the Hybrid NAR-RBFs Networks as a case study in order to replicate the propagation of the modified COVID-19. In this research work, existence and stability are verified for COVID-19 as well as proved unique solutions by applying some results of fixed point theory. The developed approach to investigate the impact of Hybrid NAR-RBFs Networks due to COVID-19 at different age groups is relatively advanced. Also obtain solutions for a proposed model by utilizing Atanga Toufik technique and fractal fractional which are the advanced techniques for such type of infectious problems for continuous monitoring of spread of COVID-19 in different age groups. Comparisons has been made to check the efficiency of techniques as well as for finding the reliable solutions to understand the dynamical behavior of Hybrid NAR-RBFs Networks for non-linear COVID-19. Finally, the parameters are evaluated to see the impact of illness and present numerical simulations using Matlab to see actual behavior of this infectious disease for Hybrid NAR-RBFs Networks of COVID-19 for different age groups.

The existence of a unique solution and stability results with numerical solutions for the fractional hybrid integro-differential equations with Dirichlet boundary conditions

In this paper, we investigate the fractional hybrid integro-differential equations with Dirichlet boundary conditions. We first prove the existence of a unique solution for the equation using a fixed point technique. Our main goal is to obtain the best approximation using optimal controllers. After studying the stability, we present the reproducing kernel Hilbert space numerical method to obtain approximate solutions to the equation. We finally conclude with numerical results.

Interval pairwise comparisons in the presence of infeasibilities: Numerical experiments

Pairwise comparisons constitute a fundamental part of many multiple-criteria decision-making methods designed to solve complex real-world problems. One of the pervasive features associated with the complexity of any problem is uncertainty. Experts are rarely able to consistently and accurately evaluate a set of alternatives under consideration due to time pressure, cognitive bias, the intricacy or intangible essence of the problem, a lack of requisite knowledge or experience, or other reasons. Interval pairwise comparisons (IPCs) allow for this uncertainty in a natural way; however, the problem of inconsistency (or infeasibility) may arise. That is, a set of interval comparisons may not allow experts to find a solution in the form of a priority vector. The aim of this paper is to provide a comparison of existing priority deriving methods for inconsistent (infeasible) IPCs via numerical examples and simulations. Our results indicate that the Interval Stretching Method is the best with respect to preserving original preferences. In addition, the question of the uniqueness of the solution is investigated for selected methods, with the Fuzzy Preference Programming method being the best in providing a unique solution. Since the majority of examined methods provide mostly non-unique solutions, modifying these methods in order to provide unique solutions might be a research direction worth considering in the future.

Global Unique Solutions with Instantaneous Loss of Regularity for SQG with Fractional Diffusion

In this work we construct global unique solutions of the dissipative Surface quasi-geostrophic equation (α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}-SQG) that lose regularity instantly when there is super-critical fractional diffusion.

Relativistic two-fluid hydrodynamics with quantized vorticity from the nonlinear Klein-Gordon equation

Abstract We consider a relativistic two-fluid model of superfluidity, in which the superfluid is described by an order parameter that is a complex scalar field satisfying the nonlinear Klein-Gordon equation (NLKG). The coupling to the normal fluid is introduced via a covariant current-current interaction, which results in the addition of an effective potential, whose imaginary part describes particle transfer between superfluid and normal fluid. Quantized vorticity arises in a class of singular solutions and the related vortex dynamics is incorporated in the modified NLKG, facilitating numerical analysis which is usually very complicated in the phenomenology of vortex filaments. The dual transformation to a string theory description (Kalb-Ramond) of quantum vorticity, the Magnus force and the mutual friction between quantized vortices and normal fluid are also studied.

Dynamics analysis of a delayed stochastic SIRS epidemic model with a nonlinear incidence rate

. This article proposes a stochastic delayed SIRS epidemic model with nonlinear incidence to describe disease transmission in a stochastic environment. First, it proves that the model has a unique global positive solution and derives sufficient conditions for the extinction and persistence of the epidemic in the population under appropriate conditions. Then, by constructing suitable Lyapunov functions, the asymptotic behavior of the model around the disease-free equilibrium and endemic equilibrium points of the deterministic model is analyzed, and it is concluded that under certain conditions, the solution of the stochastic system randomly oscillates around these two equilibrium points. Finally, several numerical examples are provided to validate the theoretical results, illustrating the significant impact of stochastic perturbations and time delays on disease control.

Estimation of electrical conductivity models using multi-coil rigid-boom electromagnetic induction measurements

Electromagnetic induction measurements from multi-coil configuration instruments are used to obtain information about the electrical conductivity distribution in the subsurface. The resulting inverse problem might not have a unique and stable solution. In that case, a local inversion method can be trapped in a local minimum and lead to an incorrect solution. In this study, we evaluate the well-posedness of the inverse problem for two and three-layered electrical conductivity models. We show that for a two-layered model, uniqueness is ensured only when both in-phase and quadrature data are available from the measurements. Results from a Gauss–Newton inversion and a lookup table demonstrate that the solution space is convex. Furthermore, we demonstrate that for even a simple three-layered model, the data contained in such measurements are insufficient to reach a correct or stable solution. For models with more than 2 layers, independent prior information is necessary to solve the inverse problem. The insights from the numerical examples are applied in a field case.

A unique solar pond system integrated with chlor-alkali electrolyser for heat storage and hydrogen production

Solar ponds are recognized as a simple, but a unique solution for renewable heat storage to use later. A freshwater feed to solar ponds is considered a crucial requirement to maintain the salinity gradient accordingly for heat storage purposes. This study aims to benefit from this specific requirement for solar ponds by integrating chlor-alkali electrolysers to produce hydrogen along with heat storage, which is a common purpose of a solar pond. Therefore, the proposed system establishes a desirable synergy, as per the sustainable development goals, between a conventional solar pond and an innovative high-tech hydrogen production system. In order to produce hydrogen, the saline water withdrawn from the upper convective zone is used in a chlor-alkali electrolyser powered by solar PV in order to produce green hydrogen. Thus, a conventional solar pond is converted into an integrated energy system that produces hydrogen and chlorine for useful purposes, along with heat storage capability. The system’s performance has been assessed in terms of the energy and exergy efficiencies for five distinct cities located in different countries that are grappling with poverty. The system’s performance, which is assessed in five cities, demonstrates the energy and exergy efficiencies ranging from 11.66 % to 14.56 % and 6.84 % to 8.60 % for the solar pond. They vary from 21.95 % to 24.22 % and from 14.23 % to 14.66 % for the overall system, respectively. Furthermore, the system effectively captures and stores solar energy, and it reaches temperatures up to 89.1°C. Moreover, the proposed system is expected to contribute to the United Nations’ Sustainable Development Goals by addressing energy poverty, promoting clean energy, and fostering economic growth.

Multiple soliton solutions and other travelling wave solutions to new structured (2+1)-dimensional integro-partial differential equation using efficient technique

The Ito equation belongs to the Korteweg–de Vries (KdV) family and is commonly employed to predict how ships roll in regular seas. Additionally, it characterizes the interaction between two internal long waves. In the 1980s, Ito extended the bilinear KdV equation, resulting in the well-known (1+1)-dimensional and (2+1)-dimensional Ito equations. In this study finds numerous classes of exact solutions for a new structured (2 + 1)-dimensional Ito integro-differential equation using the help of the Mathematica software. The Improved Modified Extended Tanh Function Scheme (IMETFS) is utilised to address the aforementioned equation analytically. Bright, dark, and singular soliton solutions are produced. Additionally, periodic, exponential, rational, singular periodic, and Weierstrass elliptic doubly periodic results are achieved. The method employed includes the nonlinear evolution equations that arise in a variety of real-world situations, and it is efficient, applicable, and simple to handle. For certain obtained solutions, specific options of free constants are presented in 3D, 2D, and contour graphical depictions.

Soliton solutions of nonlinear coupled Davey–Stewartson Fokas system using modified auxiliary equation method and extended (G′/G2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(G'/G^{2})$$\\end{document}-expansion method

The captivating realm of the nonlinear coupled Davey–Stewartson Fokas system is explored in this research paper. As a powerful tool, the proposed system is utilized for the realistic representation of various non-linear dynamical mechanisms in different fields of sciences and engineering including non-linear optical fibers, plasma physics and water waves theory. Two distinct exact methods, namely the modified auxiliary equation method and the extended (G′/G2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(G'/G^{2})$$\\end{document}-expansion method, are utilized to acquire the exact soliton solutions of the non-linear coupled Davey–Stewartson Fokas system. A plethora of novel soliton solutions containing anti-kink, kink, bright, dark, dark-bright, bright-dark and some other singular soliton solutions, have been obtained using the employed exact methods. The significance of proposed manuscript lies in the novelty of obtained solutions. Kink, dark and bright solitons have wide applications in optical fiber communications, plasma physics and water waves dynamics. The acquired nontrivial exact solutions contain exponential, trigonometric, rational and hyperbolic functions. Some obtained solutions are visually represented through graphical simulations of 3D, 2D-contour and 2D-line plots, providing a comprehensive visualization of the soliton dynamics.The modulation instability of the proposed nonlinear system has been investigated, which ensures the stability of the system.