Multiple Solutions Research Articles

Fractional Musielak spaces: study of nonlocal elliptic problem with Choquard-logarithmic nonlinearity

In this study, we thoroughly examine a specific type of complex mathematical problems involving a fractional ψ κ , y ( ⋅ ) -Laplacian operator and a Choquard-logarithmic nonlinearity, combined with a real parameter, known as non-homogeneous elliptic problems. Our approach involves setting-specific conditions for the Choquard nonlinearities and the continuous function ψ κ , y . This allows us to successfully identify multiple solutions to these problems. Our analysis is conducted in the area of fractional Musielak spaces. We rely heavily on the mountain pass theorem and Ekeland's variational principle, as well as the Hardy–Littlewood–Sobolev inequality, which is essential for supporting the theoretical basis of our research.

Comparison and analysis of new curriculum criteria for end-to-end ASR

Traditionally, teaching a human and a Machine Learning (ML) model is quite different, but organized and structured learning has the ability to enable faster and better understanding of the underlying concepts. For example, when humans learn to speak, they first learn how to utter basic phones and then slowly move towards more complex structures such as words and sentences. Motivated by this observation, researchers have started to adapt this approach for training ML models. Since the main concept, the gradual increase in difficulty, resembles the notion of the curriculum in education, the methodology became known as Curriculum Learning (CL). In this work, we design and test new CL approaches to train Automatic Speech Recognition systems, specifically focusing on the so-called end-to-end models. These models consist of a single, large-scale neural network that performs the recognition task, in contrast to the traditional way of having several specialized components focusing on different subtasks (e.g., acoustic and language modeling). We demonstrate that end-to-end models can achieve better performances if they are provided with an organized training set consisting of examples that exhibit an increasing level of difficulty. To impose structure on the training set and to define the notion of an easy example, we explored multiple solutions that use either external, static scoring methods or incorporate feedback from the model itself. In addition, we examined the effect of pacing functions that control how much data is presented to the network during each training epoch. Our proposed curriculum learning strategies were tested on the task of speech recognition on two data sets, one containing spontaneous Finnish speech where volunteers were asked to speak about a given topic, and one containing planned English speech. Empirical results showed that a good curriculum strategy can yield performance improvements and speed-up convergence. After a given number of epochs, our best strategy achieved a 5.6% and 3.4% decrease in terms of test set word error rate for the Finnish and English data sets, respectively.

Using Particle Filters to Solve the Problem of Symmetric Multiple Solutions in Robot Inverse Kinematics

Using Particle Filters to Solve the Problem of Symmetric Multiple Solutions in Robot Inverse Kinematics

Multiple jets in a rotating annulus model with an imposed azimuthal magnetic field

Zonal flows driven by rotation and convection are found commonly within astrophysical and geophysical bodies. Multiple jets are most famously observed on the surface of Jupiter, with prograde and retrograde zonal flows making up part of its banded structure of zones and belts. Non-magnetic studies of convection in a rotating annulus model have previously been shown to produce multiple jet structures, similar to those observed in atmospheres of giant planets such as Jupiter. These giant planets have strong magnetic fields which impact on convection in the electrically conducting regions of their atmospheres. Therefore the effect of a magnetic field on the multiple jet solutions of the annulus model is of astrophysical interest. In this work we impose a uniform azimuthal magnetic field to the annulus model and vary its strength and other control parameters to determine the parameter space where multiple jets exist. Zonal flows and multiple jet solutions are found at weak magnetic field strength and, indeed, the magnetic field can promote the production of these features. Simulations with a weak magnetic field or no magnetic field are also found to match well with the Rhines scaling theory. For cases with multiple jets, a strong inertial force must be present, combined with either a weak Lorentz force, or a Lorentz force entering the main balance with increased contributions from the viscous force. At strong magnetic field strengths two regimes are found. For weak magnetic diffusion zonal flows can be retained, albeit without the multiple jet structure. For larger magnetic diffusion non-axisymmetric solutions without clear bands are found. In these regimes, the Lorentz force appears in the primary balance of forces and zonal flows are only retained at strong driving when inertia is able to also enter the balance at leading order.

Pseudo grid-based physics-informed convolutional-recurrent network solving the integrable nonlinear lattice equations

Traditional discrete learning methods involve discretizing continuous equations using difference schemes, necessitating considerations of stability and convergence. Integrable nonlinear lattice equations possess a profound mathematical structure that enables them to revert to continuous integrable equations in the continuous limit, particularly retaining integrable properties such as conservation laws, Hamiltonian structure, and multiple soliton solutions. The pseudo grid-based physics-informed convolutional-recurrent network (PG-PhyCRNet) is proposed to investigate the localized wave solutions of integrable lattice equations, which significantly enhances the model’s extrapolation capability to lattice points beyond the temporal domain. We conduct a comparative analysis of PG-PhyCRNet with and without pseudo grid by investigating the multi-soliton solutions and rational solitons of the Toda lattice and self-dual network equation. The results indicate that the PG-PhyCRNet excels in capturing long-term evolution and enhances the model’s extrapolation capability for solitons, particularly those with steep waveforms and high wave speeds. Finally, the robustness of the PG-PhyCRNet method and its effect on the prediction of solutions in different scenarios are confirmed through repeated experiments involving pseudo grid partitioning.

Dynamic analysis and multiple solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid

Dynamic analysis and multiple solutions for a (3+1)-dimensional generalized Kadomtsev–Petviashvili equation in fluid

Examining firearm-related deaths in Mexico, 2015–2022

BackgroundGlobally, Mexico is one of six countries with the highest level of firearm mortality. While previous studies have examined firearm mortality in Mexico before 2015, increases in violence since then highlight the need for an updated analysis. In this study, we examined changes in firearm-related deaths in Mexico from 2015 to 2022 and described these deaths by key demographic groups, incident location, and state of occurrence. Data came from Mexico’s Instituto Nacional de Estadistica y Geografia (INEGI), a federal agency that collects and reports national population data. We used descriptive statistics to analyze rates, proportions, and percentage changes in firearm mortality, and we displayed temporal trends using time plots and special trends using maps.ResultsFirearm deaths increased in Mexico from 2015 to 2018 but slightly decreased from 2018 to 2022. Homicides presented the highest increase and the highest proportion of firearm-related deaths from 2015 to 2022. Victims were primarily males but rates among women increased at a higher proportion (99.5% vs 53.5%). One third of victims were 20–29y but rates among children and adolescents (10–9y) increased at a higher proportion. Most firearm-related deaths occurred in streets or public spaces but the percentage of incidents occurring in households have increased. State-level rates and percentage changes varied significantly. States with higher rates of firearm mortality coincide with those involving conflict among organized criminal organizations.ConclusionFirearm mortality in Mexico is a major public health burden. The epidemiology of firearm-related deaths in Mexico varies by intent, demographics, location, and states. To mitigate this challenge, multiple solutions are required.

Leveraging innovization and transfer learning to optimize best management practices in large-scale watershed management

Recent research in evolutionary multi-objective optimization (EMO) highlights the concept of “Innovization”, which identifies essential patterns in high-quality, non-dominated solutions. This study introduces a novel method to pinpoint influential Best Management Practices (BMPs) in the Chesapeake Bay Watershed, optimizing the trade-off solution process. This approach, though innovative, demands considerable expertise and involves generating multiple solutions for expert analysis to detect commonly used BMPs. We devised three re-optimization strategies from these findings using an innovized BMP list, efficiently producing high-quality solutions. We also implemented transfer learning to adapt these strategies for new counties, demonstrating effectiveness in four West Virginia counties by reducing decision variables by 3% to 33% and achieving similar reductions in four additional counties. This showcases the potential of combining innovization with transfer learning to simplify complex optimization challenges, emphasizing its significant applicability in real-world settings.

Peristaltic transport with multiple solutions of heat and mass transfer using modified Buongiorno nanofluid model over tapered channel with long wave‐length at small Reynolds number

AbstractThis research paper aims to investigate the peristaltic transport of a nanofluid (NF) in a tapered asymmetric channel. Initially, the governing equations for the balance of mass, momentum, temperature, and volume fraction for the NF using Reiner–Philippoff (RP) based NF are formulated. Subsequently, these equations are employed to analyze long wavelength and small Reynolds number scenarios. The numerical results for various flow features are thoroughly examined and discussed. Dual solutions have been examined for some factors. So, stability assessment is implemented to find stable solution. Novelty of the existing is to investigate the peristaltic motion of Buongiorno's NF model and its stability which has not investigated in the previous literatures. It has been demonstrated that modifying the RPF parameter leads to a transition in the fluid's velocity, changing it from a dilatant liquid to a Newtonian fluid and from Newtonian to pseudoplastic. The findings indicate that the temperature curves rise as Brownian motion and thermophoretic factors increase, while they decrease as the Prandtl number increases. Furthermore, a concise mathematical and graphical analysis is carried out to examine the impact of each key parameter on the flow characteristics.

Multiple Solutions to the Fractional p-Laplacian Equations of Schrödinger–Hardy-Type Involving Concave–Convex Nonlinearities

This paper is concerned with nonlocal fractional p-Laplacian Schrödinger–Hardy-type equations involving concave–convex nonlinearities. The first aim is to demonstrate the L∞-bound for any possible weak solution to our problem. As far as we know, the global a priori bound for weak solutions to nonlinear elliptic problems involving a singular nonlinear term such as Hardy potentials has not been studied extensively. To overcome this, we utilize a truncated energy technique and the De Giorgi iteration method. As its application, we demonstrate that the problem above has at least two distinct nontrivial solutions by exploiting a variant of Ekeland’s variational principle and the classical mountain pass theorem as the key tools. Furthermore, we prove the existence of a sequence of infinitely many weak solutions that converges to zero in the L∞-norm. To derive this result, we employ the modified functional method and the dual fountain theorem.

The consistency discretization adjustment method of interval fuzzy preference relationship based on individual agreement and group consensus

Constrained by the limited knowledge and fuzzy cogitation, it is often difficult to guarantee the consistency of decision makers’ preference judgments. To effectively avoid the distortion of information about the original preferences, a discrete scale consistency adjustment model based on integer variables under the individual interval fuzzy preference relationship is established. The research shows that the proposed method can not only validly enhance the differentiation between alternatives, but also drop the occurrence of zero weights to a larger extent. Furthermore, aiming at the potential multiplicity of optimal adjustment strategies for interval fuzzy preference relations, an efficient algorithm for screening multiple optimal solutions under single-person decision making is proposed by setting multiple screening dimensions. The algorithm makes up for the deficiency of ignoring potential optimal solutions in traditional methods, and greatly raises the decision flexibility of the ranking optimization process. The validity and applicability of the algorithm are verified through filtering and analyzing multiple optimal solutions under different scenarios. Considering the differences in the decision making tendencies of exclusive and altruistic groups in the interval fuzzy environment, a discrete compatible adjustment model of group consensus under different decision making behaviors is established. Finally, the efficient screening system is matched for different groups, which provides a valid path for the optimal solution selection of group consensus.

Growth of α-Ga2O3 from Gallium Acetylacetonate under HCl Support by Mist Chemical Vapor Deposition.

α-Ga2O3 films were grown on a c-plane sapphire substrate by HCl-supported mist chemical vapor deposition with multiple solution chambers, and the effect of HCl support on α-Ga2O3 film quality was investigated. The growth rate monotonically increased with increasing Ga supply rate. However, as the Ga supply rate was higher than 0.1 mmol/min, the growth rate further increased with increasing HCl supply rate. The surface roughness was improved by HCl support when the Ga supply rate was smaller than 0.07 mmol/min. The crystallinity of the α-Ga2O3 films exhibited an improvement with an increase in the film thickness, regardless of the solution preparation conditions, Ga supply rate, and HCl supply rate. These results indicate that there is a low correlation between the improvement of surface roughness and crystallinity in the α-Ga2O3 films grown under the conditions described in this paper.

A ~40-kb flavi-like virus does not encode a known error-correcting mechanism

It is commonly held that there is a fundamental relationship between genome size and error rate, manifest as a notional "error threshold" that sets an upper limit on genome sizes. The genome sizes of RNA viruses, which have intrinsically high mutation rates due to a lack of mechanisms for error correction, must therefore be small to avoid accumulating an excessive number of deleterious mutations that will ultimately lead to population extinction. The proposed exceptions to this evolutionary rule are RNA viruses from the order Nidovirales (such as coronaviruses) that encode error-correcting exonucleases, enabling them to reach genome lengths greater than 40 kb. The recent discovery of large-genome flavi-like viruses (Flaviviridae), which comprise genomes up to 27 kb in length yet seemingly do not encode exonuclease domains, has led to the proposal that a proofreading mechanism is required to facilitate the expansion of nonsegmented RNA virus genomes above 30 kb. Herein, we describe a ~40 kb flavi-like virus identified in a Haliclona sponge metatranscriptome that does not encode a known exonuclease. Structural analysis revealed that this virus may have instead captured cellular domains associated with nucleic acid metabolism that have not been previously found in RNA viruses. Phylogenetic inference placed this virus as a divergent pesti-like lineage, such that we have provisionally termed it "Maximus pesti-like virus." This virus represents an instance of a flavi-like virus achieving a genome size comparable to that of the Nidovirales and demonstrates that RNA viruses have evolved multiple solutions to overcome the error threshold.

On simulations of 3D fractional WBBM model through mathematical and graphical analysis with the assists of fractionality and unrestricted parameters

This study retrieves some novel exact solutions to the family of 3D space–time fractional Wazwaz–Benjamin–Bona–Mahony (WBBM) equations in the context of diverse nonlinear physical phenomena resulting from water wave mechanics. The family of WBBM equations is transformed for this purpose using a space and time fractional transformation into an ordinary differential equation (ODE). The ODE then uses a strong method, namely the Unified Method. Consequently, lump solutions, dark-bright soliton, singular and multiple soliton solutions, and periodic solutions are investigated. The disparities between the current study's conclusions and previously acquired solutions via other approaches are examined. All wave solutions produced are determined to be novel in terms of fractionality, unrestricted parameters, and implemented technique sense. The impact of unrestricted parameters and fractionality on the obtained solutions are visually presented, along with physical explanations. It is observed that the wave portents are varied with the increase of unrestricted parameters as well as fractionality. We dynamically showed that the appropriate transformation and the applied Unified approach more proficient in the study of water wave dynamics and might be used in future researches to clarify the many physical phenomena. The novelty of this work validate that the proposed method seem simple and useful tools for obtaining the solutions in PDEs and it is expected to use in mathematical physics and optical engineering.

Existence and simulation of multiple solutions to an optimization model for completing incomplete fuzzy preference relations

Existence and simulation of multiple solutions to an optimization model for completing incomplete fuzzy preference relations

Impact of various DIII-D diagnostics on the accuracy of neural network surrogates for kinetic EFIT reconstructions

Kinetic equilibrium reconstructions make use of profile information such as particle density and temperature measurements in addition to magnetics data to compute a self-consistent equilibrium. They are used in a multitude of physics-based modeling. This work develops a multi-layer perceptron (MLP) neural network (NN) model as a surrogate for kinetic Equilibrium Fitting (EFITs) and trains on the 2019 DIII-D discharge campaign database of kinetic equilibrium reconstructions. We investigate the impact of including various diagnostic data and machine actuator controls as input into the NN. When giving various categories of data as input into NN models that have been trained using those same categories of data, the predictions on multiple equilibrium reconstruction solutions (poloidal magnetic flux, global scalars, pressure profile, current profile) are highly accurate. When comparing different models with different diagnostics as input, the magnetics-only model outputs accurate kinetic profiles and the inclusion of additional data does not significantly impact the accuracy. When the NN is tasked with inferring only a single target such as the EFIT pressure profile or EFIT current profile, we see a large increase in the accuracy of the prediction of the kinetic profiles as more data is included. These results indicate that certain MLP NN configurations can be reasonably robust to different burning-plasma-relevant diagnostics depending on the accuracy requirements for equilibrium reconstruction tasks.

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In this article, we investigated the solitary wave solutions of the KdV–mKdV equation using Hirota’s bilinear method. Closed-form analytical single and multiple solitary wave solutions were obtained. Through qualitative methods and the analysis of solitary waveforms, we discovered that in addition to sech-type solitary waves, the system also contains Sech2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{Sech}^{2}$$\\end{document}-type solitary waves. By employing the trial functions method, we obtained a single Sech2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{Sech}^{2}$$\\end{document}-type solitary wave and verified its existence and stability using the split-Step Fourier Transform method. Furthermore, we use the collision of two Sech2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{Sech}^{2}$$\\end{document}-type single solitary waves to excite a stable Sech2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{Sech}^{2}$$\\end{document}-type double solitary wave. Similarly, we excite a stable triple solitary wave with three Sech2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{Sech}^{2}$$\\end{document}-type single solitary waves. This method can also be used to excite stable multiple solitary waves. It is shown that these solitary wave solutions enrich the dynamic behavior of the KdV–mKdV equation and provide methods for solving Sech2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext{Sech}^{2}$$\\end{document}-type solitary waves, which hold significant theoretical value.

Dynamics of a 3D Piezo-Magneto-Elastic Energy Harvester with Axisymmetric Multi-Stability.

In this investigation, a three-dimensional (3D) axisymmetric potential well-based nonlinear piezoelectric energy harvester is proposed to increase the broadband frequency response under low-strength planar external excitation. Here, a two-dimensional (2D) planar bi-stable Duffing potential is generalized into three dimensions by utilizing axial symmetry. The resulting axisymmetric potential well has infinitely many stable equilibria and one unstable equilibria at the highest point of the potential barrier for this cantilevered oscillator. Dynamics of such a 3D piezoelectric harvester with axisymmetric multi-stability are studied under planar circular excitation motion. Bifurcations of average power harvested from the two pairs of piezoelectric patches are presented against the frequency variation. The results show the presence of several branches of large-amplitude cross-well type period-1 and subharmonic solutions. Subharmonics involved in such responses are verified from the Fourier spectra of the solutions. The identified subharmonic solutions perform interesting patterns of curvilinear oscillations, which do not cross the potential barrier through its highest point. These solutions can completely or partially avoid the climbing of the potential barrier, thereby requiring low input excitation energy for barrier crossing. The influence of excitation amplitude on the bifurcations of normalized power is also investigated. Through multiple solution branches of subharmonic solutions, producing comparable power to the period-1 branch, broadband frequency response characteristics of such a 3D axisymmetically multi-stable harvester are highlighted.

Surface Plasmon Resonance Sensor Based on Fe2O3/Au for Alcohol Concentration Detection.

Hematite (α-Fe2O3) is widely used in sensor sensitization due to its excellent optical properties. In this study, we present a sensitivity-enhanced surface plasmon resonance alcohol sensor based on Fe2O3/Au. We describe the fabrication process of the sensor and characterize its structure. We conduct performance testing on sensors coated multiple times and use solutions with the same gradient of refractive indices as the sensing medium. Within the refractive index range of 1.3335-1.3635, the sensor that was coated twice achieved the highest sensitivity, reaching 2933.2 nm/RIU. This represents a 30.26% enhancement in sensitivity compared to a sensor with a pure gold monolayer film structure. Additionally, we demonstrated the application of this sensor in alcohol concentration detection by testing the alcohol content of common beverages, showing excellent agreement with theoretical values and highlighting the sensor's potential in food testing.

Exploring the chaotic structure and soliton solutions for (3 + 1)-dimensional generalized Kadomtsev–Petviashvili model

The study of the Kadomtsev–Petviashvili (KP) model is widely used for simulating several scientific phenomena, including the evolution of water wave surfaces, the processes of soliton diffusion, and the electromagnetic field of transmission. In current study, we explore some multiple soliton solutions of the (3+1)-dimensional generalized KP model via applying modified Sardar sub-equation approach (MSSEA). By extracting the novel soliton solutions, we can effectively obtain singular, dark, combo, periodic and plane wave solutions through a multiple physical regions. We also investigate the chaotic structure of governing model using the chaos theory. The behavior of the collected solutions is visually depicted to demonstrate the physical properties of the proposed model. The solutions obtained in this paper can expand the existing solutions of the (3+1)-dimensional KP model and enhance our understanding of the nonlinear dynamic behaviors. This approach allows for consistent and effective treatment of the computation process for nonlinear KP model.