Different Types Of Solutions Research Articles

A Lie group treatment on a generalized evolution Fisher type equation with variable coefficients

In this study, a general second-order evolution equation of the Fisher-type, with time-dependent variable coefficients, is considered. This equation contains many well-known equations, and obtained results may be applicable in investigating other evolution equations. Lie symmetries and corresponding invariant solutions of the considered problem are studied by a non-traditional Lie symmetry method (LSM). Prolongation of the model is an essential part of the Lie symmetry method, which in the current work, we analyze by the heir-equations. Finally, different types of solutions depending on the variable coefficients, such as the exponential solutions, trigonometric solutions, Bessel solutions, and Mathieu solutions, are extracted.

High Sensitive and Selective Cu-doped ZnO Thin film for No2 Sensing with Chemical Root Method

Copper Doped Zinc Oxide-Thin films are prepared by the Sol-Gel method and annealing at 400°C, For sol preparation, we prepare 2- different types of solution, one is zinc nitrate hexahydrate and the second is copper nitrate, that are deeply discussed in this paper. The thin size was varied by XRD, the detected (h k l) peaks are confirmed with 2θ values and the morphology was also studied by field emission scanning electron microscopy (FESEM), the Nano-bubbles and nano-balls was observed. Electrical properties and VI- Characteristics were also done, and getting highly sensitive Performing results, finally, the gas sensing characteristic was taken by chemiresistive process. And the Gas Sensing performance was done with closed chamber methods and the High sensitive and selective performance result have been shown. The sensing parameters such as electrical properties, and VI- characteristics, for gases, are also observed we shown the response time and recovery time, The S=Rg/Ra formula is used for calculate the response of the films. The best of lower gas detection limits, towards NO2 gas, and also finalize the selectivity and sensitivity performance of the thin film. The final result shown that ZnO thinfilm can act as NO2 sensor and breath analyzer, for diabetes.

Some New Estimates of Fixed Point Results under Multi-Valued Mappings in G-Metric Spaces with Application

It is well known fact that fixed point results are very useful for finding the solution of different types of differential equations. In this paper, some new results of multi-valued functions involving rational inequality in G−metric spaces have been obtained. Some of the new concepts are also defined over G−metric spaces that are open set, interior of set, and limit point of set. Moreover, we have presented the application of our main results in the field of Homotopy. Some non-trivial examples are also provided to discuss the validation of the main finding.

Generating Weak Fuzzy Complex and Anti Weak Fuzzy Complex Integer Solutions for Pythagoras Diophantine Equation 𝑿𝟐 + 𝒀𝟐 = 𝒁𝟐

In this paper, we find necessary and sufficient conditions for a weak fuzzy complex integer triple (X,Y, Z) to be a pythagoras triple, and for an anti-weak fuzzy complex integer triple to be a Pythagoras triple (X,Y, Z), where we prove that the non-linear Fermat's Diophantine equation has three different types of solutions according to the value of . All types will be solved and discussed in terms of theorems and examples that explains how the algorithms work

Influence of ligands on the optical properties of rod-shaped Au25 nanoclusters.

In this study, we successfully synthesized rod-shaped [Au25(PPh3)10(S-Adm)5Cl2]2+ nanoclusters using kinetic controls. The complete molecular structure was determined by single-crystal X-ray crystallography and electrospray ionization mass spectrometry. In comparison with the previously reported [Au25(PPh3)10(PET)5Cl2]2+ clusters, both nanoclusters have an icosahedral composition of Au13 linked by Au atoms that share a vertex, but [Au25(PPh3)10(S-Adm)5Cl2]2+ clusters appear elongated due to the rigidity of adamantane. We conducted ultraviolet-visible spectrophotometry (UV-vis) measurements of [Au25(PPh3)10(PET)5Cl2]2+ and [Au25(PPh3)10(S-Adm)5Cl2]2+ in dichloromethane solvent to elucidate the modulation of the cluster properties of different ligands. The lowest energy absorption peak of [Au25(PPh3)10(S-Adm)5Cl2]2+ shifted to lower energies compared to the [Au25(PPh3)10(PET)5Cl2]2+ clusters in UV-vis measurements. Temperature-dependent absorption measurements revealed that [Au25(PPh3)10(S-Adm)5Cl2]2+ clusters were less affected by temperature compared to [Au25(PPh3)10(PET)5Cl2]2+. This result is attributed to the exciton phonon coupling of [Au25(PPh3)10(S-Adm)5Cl2]2+ clusters being weaker than [Au25(PPh3)10(PET)5Cl2]2+ clusters. Furthermore, the absorption spectra of [Au25(PPh3)10(PET)5Cl2]2+ and [Au25(PPh3)10(S-Adm)5Cl2]2+ clusters were measured using different types of solutions, and it was found that the lowest energy absorption peaks of [Au25(PPh3)10(S-Adm)5Cl2]2+ were shifted and affected by the solution at room temperature, which suggested that the [Au25(PPh3)10(S-Adm)5Cl2]2+ clusters with solution hydrogen bonds also interacted strongly at room temperature. Theoretical calculations show that changes in ligands affect the differences in the molecular orbitals and structures of the clusters, which cause changes in the optical properties.

Unsupervised Legendre–Galerkin Neural Network for Solving Partial Differential Equations

In recent years, machine learning methods have been used to solve partial differential equations (PDEs) and dynamical systems, leading to the development of a new research field called scientific machine learning, which combines techniques such as deep neural networks and statistical learning with classical problems in applied mathematics. In this paper, we present a novel numerical algorithm that uses machine learning and artificial intelligence to solve PDEs. Based on the Legendre-Galerkin framework, we propose an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unsupervised machine learning</i> algorithm that learns <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multiple instances</i> of the solutions for different types of PDEs. Our approach addresses the limitations of both data-driven and physics-based methods. We apply the proposed neural network to general 1D and 2D PDEs with various boundary conditions, as well as convection-dominated <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">singularly perturbed PDEs</i> that exhibit strong boundary layer behavior.

Influence in social networks with stubborn agents: From competition to bargaining

The literature on game-theoretic models of opinion dynamics in social networks mainly focuses on the Nash equilibrium, which reflects a competitive situation between influencing agents called players. In some real-world situations, however, players negotiate over a game; thus, a different type of solution needs to be considered to account for possible outcomes. In this paper, we examine an opinion dynamics game based on the Friedkin–Johnsen model for which we characterize the Pareto frontier, including the Nash bargaining solution. Next, we analyze this solution when there are changes in the susceptibility of noninfluencing agents with respect to their initial opinions. We also quantify how the Nash equilibrium outcome differs from the outcome prescribed by the Nash bargaining solution.

Soliton solutions and lump-type solutions to the (2+1)-dimensional Kadomtsev-Petviashvili equation with variable coefficient

In this article, the integrability, bilinear form, N-soliton solutions, lump solutions and rational function solutions of (2+1)-dimensional Kadomtsev-Petviashvili equation with variable coefficient (vcKP) are investigated. This has important implications for mathematicians and physicists to solve problems related to long water waves. The equation is proved to be Painlevé integrable by Painlevé analysis. With the help of Hirota bilinear method, the bilinear form of vcKP is obtained. Based on the bilinear form, the forms of four different types of solutions are constructed. In addition, taking the long wave limit method on two-soliton solutions, three-soliton solutions and four-soliton solutions to construct the lump solutions and the rational function solutions. As a result, some new solutions of vcKP are obtained, such as soliton solutions, lump solutions and interaction of different kinds of solutions. To describe better the change in solution with time, the dynamical behaviours of the exact solutions to the (2+1)-dimensional vcKP are analysed. The influence of parameters on the soliton solutions is analyzed. Moreover the evolution of several types of solutions is investigated depending on the change in time.

APPLICATION OF HOMOTOPY ANALYSIS METHOD (HAM) TO THE NON-LINEAR KDV EQUATIONS

In this work, approximate analytic solutions for different types of KdV equations are obtained using the homotopy analysis method (HAM). The convergence control parameter h helps us to adjust the convergence region of the approximate analytic solutions. The solutions are obtained in the form of power series. The obtained solutions and the exact solutions are shown graphically, highlighting the effects of non-linearity. We have compared the approximate analytical results which are determined by HAM, with the exact solutions and shown graphically with their absolute errors. By choosing an appropriate value of the convergence control parameter, we can obtain the solution in few iterations. All the computations have been performed using the software package MATHEMATICA.

On the Advantages of Distinguishing Between Predictive and Allocative Fairness in Algorithmic Decision-Making

The problem of algorithmic fairness is typically framed as the problem of finding a unique formal criterion that guarantees that a given algorithmic decision-making procedure is morally permissible. In this paper, I argue that this is conceptually misguided and that we should replace the problem with two sub-problems. If we examine how most state-of-the-art machine learning systems work, we notice that there are two distinct stages in the decision-making process. First, a prediction of a relevant property is made. Secondly, a decision is taken based (at least partly) on this prediction. These two stages have different aims: the prediction is aimed at accuracy, while the decision is aimed at allocating a given good in a way that maximizes some context-relative utility measure. Correspondingly, two different fairness issues can arise. First, predictions could be biased in discriminatory ways. This means that the predictions contain systematic errors for a specific group of individuals. Secondly, the system’s decisions could result in an allocation of goods that is in tension with the principles of distributive justice. These two fairness issues are distinct problems that require different types of solutions. I here provide a formal framework to address both issues and argue that this way of conceptualizing them resolves some of the paradoxes present in the discussion of algorithmic fairness.

Destabilization of Pickering emulsions by interfacial transport of mutually soluble solute

HypothesisPickering emulsions (PEs) once formed are highly stable because of very high desorption energies (∼107 kBT) associated with particles adsorbed to the interfaces. The destabilization of PEs is required in many instances for recovery of valuable chemicals, products and active compounds. We propose to exploit interfacial instabilities develop by the addition of different types of solutes to PEs as a route to engineer their destabilization. ExperimentsPEs stabilized by (i) spherical particles, (ii) non-spherical particles, (iii) oppositely charged particle–particle mixtures, and (iv) oppositely charged particle-polyelectrolyte mixtures are formulated. Different types of solutes are added to these highly stable PEs and the macroscopic as well as microscopic changes induced in the PEs is recorded by visual observation and bright field optical microscopy. FindingsOur results point to a simple yet robust method to induce destabilization of PEs by transiently perturbing the oil–water interface by transport of a mutually soluble solute across the interface. The generality of the method is demonstrated for different kind of solutes and stabilizers including particles of different sizes (nm to µm), shapes (sphere, spheroids, spherocylinders) and types (polystyrene, metal oxides). The method works for both oil-in-water (o/w) and water-in-oil (w/o) PEs with different kinds of non-polar solvents as oil-phase. However, the method fails when the solute is insoluble in one of the phases of PEs. The study opens up a new approach to destabilization of particle stabilized emulsions.

The Enhancement of Energy-Carrying Capacity in Liquid with Gas Bubbles, in Terms of Solitons

A generalized (3 + 1)-dimensional nonlinear wave is investigated, which defines many nonlinear phenomena in liquid containing gas bubbles. Basic theories of the natural phenomenons are usually described by nonlinear evolution equations, for example, nonlinear sciences, marine engineering, fluid dynamics, scientific applications, and ocean plasma physics. The new extended algebraic method is applied to solve the model under consideration. Furthermore, the nonlinear model is converted into an ordinary differential equation through the next wave transformation. A well-known analytical approach is used to obtain more general solutions of different types with the help of Mathematica. Shock, singular, mixed-complex solitary-shock, mixed-singular, mixed-shock singular, mixed trigonometric, periodic, mixed-periodic, mixed-hyperbolic solutions are obtained. As a result, it is found that the energy-carrying capacity of liquid with gas bubbles and its propagation can be increased. The stability of the considered model is ensured by the modulation instability gain spectrum generated and proposed with acceptable constant values. Two-dimensional, three-dimensional, and contour surfaces are plotted to see the physical properties of the obtained solutions.

Different coherent states for lightly supported coupled pendula

In this paper we discuss and explain the phenomenon of synchronization in lightly supported mechanical systems. The investigations are focused on the models of self–excited pendula hanged on the horizontally oscillating beam, which is lightly connected with the external support. Our results are based on the Centre-of-Mass (CoM) Theorem, which can be applied to the considered systems and allows to analytically confirm the observed behaviours. We present typical dynamical solutions, including periodic and quasiperiodic oscillations, within which the oscillators synchronize. The possible synchronous configurations are analyzed and examined, depending on the number of the pendula creating the system, their parameters and the initial conditions. We discuss bifurcations between different types of solutions, determining the regions and the conditions supporting the synchronization. Our investigations exhibit, that with the increase of the size of the network, the number of co–existing attractors also increases, leading to possible multistability and new types of behaviours (e.g., the traveling phase one). The results obtained numerically match with the analytical ones obtained from the CoM Theorem, which explains the existence of particular types of dynamical configurations. The study presented in this paper involves classical lightly supported pendula systems and due to their basic character, one can expect to observe similar behaviours in other types of mechanical models.

Are mussels and oysters capable of reducing the abundances of Picochlorum sp., responsible for a massive green algae bloom in Thau lagoon, France?

After an exceptional hydroclimatic year, a “massive green algae bloom”, dominated by the autotrophic picoeukaryote Picochlorum sp, was observed in 2018–2019 in the Thau lagoon. Oyster farmers informed decision-makers and scientists about an alarming halt to growth, loss of flesh weight and abnormal mortality in commercial size oysters, whereas mussel farmers observed no adverse effects. Two hypotheses were tested. First, Mediterranean mussels are capable of filtering Picochlorum spp. whereas Pacific and flat oysters are not. Second, picophytoplankton filtration rates vary with the size of the oyster, spats having greater ability than juveniles and commercial size oysters. A series of experiments was conducted in February 2019 using a series of beakers containing (i) three different types of solutions (1 L): water from the Thau lagoon containing Picochlorum at a rate of 45.2 million cells.L−1 (P) or diluted to 20.7 million cells. L−1 (D) and a solution of Isochrysis galbana containing 9.4 million cells. L−1; (ii) in the absence or presence of five types of bivalves: Pacific oysters of three different sizes (spat, juvenile and commercial size), flat oysters, and Mediterranean mussels of commercial size. Four separate water samples were taken during a 40-min incubation period to measure fluctuations in picophytoplankton and nanophytoplankton abundances using flow cytometry. Retention efficiency (%) was compared according to species and size. In contrast to Pacific and flat oysters, mussels with an average weight of 21.4 g, were able to drastically reduce the abundances of Picochlorum and depleted nearly one million Picochlorum cells per minute at 11.4 °C. These results suggest that the 1228 t of mussels that died in 2018 before the Picochlorum bloom could have helped limit the Picochlorum bloom if they had survived the heat and anoxia.

New Travelling Wave Solutions of Conformable Cahn-Hilliard Equation

In this article, two methods are proposed to solve the fractional Cahn-Hilliard equation. This model describes the process of phase separation with nonlocal memory effects. Cahn-Hilliard equations have numerous applications in real-world scenarios, e.g., material sciences, cell biology, and image processing. Different types of solutions have been obtained. For this, the fractional complex transformation has been used to convert fractional differential equation to ordinary differential equation of integer order. As a result, these solutions are new solutions that do not exist in the literature.

Keynote 2

Title of HEPA 2022 Keynote presentationPhysical activity, air pollution, and much more: the case for systems thinking in urban policies.Description of HEPA 2022 Keynote presentationPhysical activity may be one of greatest benefits of active travel -however there are many more, and in some cases there could be some trade-offs too. Yet, we create disjointed targets, campaigns and regulations to tackle in siloed and often piecemeal approaches major urban health and environmental challenges such as climate change, physical inactivity, air pollution, traffic injuries, social isolation, stress, inequalities, etc. The way we address these problems matters, and this lack of joined up thinking is a wasted opportunity. If we let the promotion of a healthier, more sustainable and resilient society be the goal of our policies rather than merely compliance with singularly focused standards and targets, we will find different types of solutions emerge as most advantageous. For example, in addition to providing a seamless way to integrate physical activity into daily routines, walking and cycling can be a convenient and low-cost alternatives to driving, thus reducing air pollution, green house gas emissions and noise; the infrastructure and urban design features conducive to walking and cycling may in turn have further benefits, such as traffic safety and greenspace exposure; etc. Evidence on benefits, co-benefits, and trade-offs of different types of urban policies that tackle some of our greatest urban health challenges jointly will be presented, making the case for holistic approaches to urban policy decision making, particularly through urban planning and design strategies. We will end by discussing avenues for greater integration of health in urban decision making.

The structure of optimal solutions for harvesting a renewable resource

AbstractWe consider the problem of optimal harvesting of a renewable resource whose dynamics are governed by logistic growth and whose payoff is proportional to the harvest. We consider both the case of a finite and an infinite time horizon and analyse the structure of the optimal solutions and their dependence on the parameters of the model. We show that the optimal policy can only have one of three structures: (1) maximal harvesting effort until the resource is depleted, (2) zero harvesting during an initial time interval followed by a subsequent switch to maximal harvesting effort, or (3) a singular solution, which corresponds to an intermediate level of harvesting, accompanied by the most rapid approach path. All three scenarios emerge, with minor variations, with finite and infinite time horizons, depending on the particular combination of parameters of the system. We characterize the conditions under which the singular solution is optimal and present suggestions for designing an optimal and sustainable harvesting strategy.Recommendations for Resource Managers: We have rigorously explored a standard optimal harvesting model and its steady states. We show that three different types of solutions may emerge: (i) maximal harvesting eventually leading to a complete depletion of the stock; (ii) maximal harvesting with a potential period of idleness leading to a positive stock; (iii) an initial phase of either no or full harvesting followed by a period of intermediate harvesting intensity leading to a positive stock (singular solution). With some modifications, similar results hold for a finite planning horizon. Which of these three scenarios emerges in the finite horizon case depends not only on the parameter values but also on the length of the planning horizon.

New business models in the Circular Economy

Abstract Circular Economy is becoming an important part of the trend on global business development. Companies and public organizations are facing new challenges and strive to integrate fresh concepts and instruments within their value chains. Strategic environmental goals are based upon reused resources and reintegrated materials, reduced carbon emissions, renewable energy, innovation, and overall optimization of models and processes. Governmental agencies are also preoccupied to enact specific regulations, to favor the economic and social integration of the circular economy. The advantages of the 6 R’s integration (recycle, reuse, reduce, repair, remanufacture, redesign) for businesses are straightforward, from cost optimizations, price volatility control, to increased automation and innovation. This paper is the first step of a more complex research endeavor, aiming to assess the feasibility of various fine tunings on specific business models that integrate circular economy principles. We have based our current assessment on six industries, with a major impact on the environment, and that can provide impacting solutions for environmental preservation. For each analyzed industry, a specific original diagram was provided, integrating the main industrial processes, outcomes, and reuse opportunities, derived from circularity principles. The literature review was intended to support each industry’s development pattern, highlighting different types of solutions for waste recycling, and business reorganization redesign.

Intervention Algorithm of Horse Racing for Students’ Psychological Disorders Based on Big Data

Horse racing is a competitive activity in which humans control horses. It is a worldwide traditional sports activity. In the history of human-horse racing, horse racing activities in various eras have been followed but also constantly innovated. According to the K-means clustering algorithm, a cluster analysis model is constructed for the model, and the algorithm model is applied to the students’ mental health counseling work. After six iterations to get the classification and six iterations of the cluster center algorithm, it was found that the mixed psychological population accounted for 50%. Horse racing can not only effectively relieve students’ psychological problems and exercise students’ willpower and thinking ability, but also promote traditional sports. Through K-means clustering algorithm research, frame design, and program design, a complete psychological disorder intervention system is established, which provides scientific, objective, and reliable data guarantee for the correct implementation of decision-making strategies. Integrating cluster analysis into the process of students’ mental health analysis makes it easier for decision-makers to understand and master all aspects of students’ information, to analyze and customize solutions for different types of students. It provides a good foundation for providing different psychotherapeutic methods for different groups of students.

Exact Solutions and Non-Traveling Wave Solutions of the (2+1)-Dimensional Boussinesq Equation

By the extended (G′G) method and the improved tanh function method, the exact solutions of the (2+1) dimensional Boussinesq equation are studied. Firstly, with the help of the solutions of the nonlinear ordinary differential equation, we obtain the new traveling wave exact solutions of the equation by the homogeneous equilibrium principle and the extended (G′G) method. Secondly, by constructing the new ansatz solutions and applying the improved tanh function method, many non-traveling wave exact solutions of the equation are given. The solutions mainly include hyperbolic, trigonometric and rational functions, which reflect different types of solutions for nonlinear waves. Finally, we discuss the effects of these solutions on the formation of rogue waves according to the numerical simulation.