Different Types Of Solutions Research Articles

Plane Symmetric Cosmological Model with Strange Quark Matter in f(R,T) Gravity

A plane symmetric Bianchi-I model filled with strange quark matter (SQM) was explored in f(R,T)=R+2λT gravity, where R is the Ricci scalar, T is the trace of the energy-momentum tensor, and λ is an arbitrary constant. Three different types of solutions were obtained. In each model, comparisons of the outcomes in f(R,T) gravity and bag constant were made to comprehend their roles. The first power-law solution was obtained by assuming that the expansion scalar is proportional to the shear scalar. This solution was compared with a similar one obtained earlier. The second solution was derived by assuming a constant deceleration parameter q. This led to two solutions: one power-law and the other exponential. Just as in the case of general relativity, we can obtain solutions for each of the different eras of the universe, but we cannot obtain a model which shows transitional behavior from deceleration to acceleration. However, the third solution is a hybrid solution, which shows the required transition. The models start off with anisotropy, but are shear free at late times. In general relativity, the effect of SQM is to accelerate the universe, so we expect the same in f(R,T) gravity.

Analytical solutions of the extended Kadomtsev–Petviashvili equation in nonlinear media

Abstract This manuscript attempts to construct diverse exact traveling wave solutions for an important model called the (3+1)-dimensional Kadomtsev–Petviashvili equation. In order to achieve that, the Jacobi elliptic function technique and the Kudryashov technique are chosen in favor of their noticeable efficacy in dealing with nonlinear dynamical models. As expected, the used approaches lead to a variety of traveling wave solutions of different types. Finally, we have graphically illustrated some of the obtained wave solutions to further make sense of their representation. Also, we provide an overview of the main results at the end.

Exact coherent structures in fully developed two-dimensional turbulence

This paper reports several new classes of unstable recurrent solutions of the two-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions are in many ways analogous to recurrent solutions of the Navier–Stokes equation which are often referred to as exact coherent structures. In particular, we find that recurrent solutions of the Euler equation are dynamically relevant: they faithfully reproduce large-scale flows in simulations of turbulence at very high Reynolds numbers. On the other hand, these solutions have a number of properties which distinguish them from their Navier–Stokes counterparts. First of all, recurrent solutions of the Euler equation come in infinite-dimensional continuous families. Second, solutions of different types are connected, e.g. an equilibrium can be smoothly continued to a travelling wave or a time-periodic state. Third, and most important, they are only weakly unstable and, as a result, fully developed turbulence mimics some of these solutions remarkably frequently and over unexpectedly long temporal intervals.

Explanation of Student Attendance AI Prediction with the Isabelle Infrastructure Framework

Right from the beginning, attendance has played an important role in the education systems, not only in student success but in the overall interest of the matter. Although all schools try to accentuate good attendance, still some schools find it hard to achieve the required level (96% in UK) of average attendance. The most productive way of increasing the pupils′ attendance rate is to predict when it is going to go down, understand the reasons—why it happened—and act on the affecting factors so as to prevent it. Artificial intelligence (AI) is an automated machine learning solution for different types of problems. Several machine learning (ML) models like logistic regression, decision trees, etc. are easy to understand; however, complicated (Neural Network, BART etc.) ML models are not transparent but are black-boxes for humans. It is not always evident how machine intelligence arrived at a decision. However, not always, but in critical applications it is important that humans can understand the reasons for such decisions. In this paper, we present a methodology on the application example of pupil attendance for constructing explanations for AI classification algorithms. The methodology includes building a model of the application in the Isabelle Insider and Infrastructure framework (IIIf) and an algorithm (PCR) that helps us to obtain a detailed logical rule to specify the performance of the black-box algorithm, hence allowing us to explain it. The explanation is provided within the logical model of the IIIf, thus is suitable for human audiences. It has been shown that the RR-cycle of IIIf can be adapted to provide a method for iteratively extracting an explanation by interleaving attack tree analysis with precondition refinement, which finally yields a general rule that describes the decision taken by a black-box algorithm produced by Artificial intelligence.

Brief classification and latest therapy for lactose intolerance

Lactose intolerance is a digestive problem with a high incidence worldwide. The disease occurs mainly due to a lack or deficiency of lactase in the body, which prevents effective digestion of lactose. Congenital lactose intolerance is caused by a genetic defect that prevents the body from producing enough lactase, and its incidence is relatively low. Secondary lactose intolerance is caused by other gastrointestinal disorders, such as celiac disease, and is relatively common. Functional lactose intolerance is the most common form of lactose intolerance, in which lactase activity is reduced or lactose absorption is impaired, but there is no apparent organic disease. This article lists several possible solutions for different types of lactose intolerance based on the latest research. In studies of lactose intolerance, scientists have found that the rate of lactose intolerance varies widely across populations, with significant differences in prevalence by race and region. In addition, several studies have shown a link between lactose intolerance and the composition of the gut microbiome. Therefore, the study of lactose intolerance has important implications for understanding how the human digestive system works and the relationship between the gut microbiome and health.

Adherence of polystyrene microspheres on cave sediment: implications for organic contaminants and microplastics in karst systems.

Interactions of karst aquifer sediments with organic contaminants or microplastics (MPs) have received relatively little attention even though the susceptibility of karst aquifers to contamination and their ability to store and transport sediment is well documented. Studies using polystyrene microspheres as surrogate tracers for bacteria transport in karst systems have generally observed low recovery of microspheres and attributed this to microsphere adsorption onto aquifer sediments. In addition to being used as surrogate tracer for bacteria, microspheres have the potential to be used as surrogate material for organic contaminants and MPs. Using cave sediments as a proxy for karst aquifer sediments, the adherence of two types of microspheres (carboxylated and nonfunctionalized) was measured in three different types of solutions: deionized water, a calcium carbonate solution, and a karst spring water. Both types of microspheres adhered to the sediments; the most influential factor in adherence was solution type not microsphere type. Average adherence ranged from 51%-94% with average adsorption coefficients (KD) ranging from 11.8-442. Average estimated organic-carbon water partition coefficients (KOC) and retardation factors (RF) ranged from 1.64×103 - 6.13×104 and 6.20×101 - 2.29 × 103, respectively. KD, KOC, and RF were an order of magnitude higher in the karst water than in DI or CaCO3 solution. The results illustrate the importance of sediment interactions with potential organic or MP contaminants in karst systems.

Location Selection of Electric Vehicles Charging Stations Based on Analytical Hierarchy Process and Clustering Algorithm

In recent years, the charging infrastructure for electric vehicles (EVs) in China has been developing quickly, yet the charging station industry still faces problems such as unreasonable layout, difficulty in profitability and limited coverage. Based on this, this paper systematically compared the key factors of charging facility location and used the AHP method to measure the degree of influence of various factors at different levels on the location of charging stations of enterprises, so as to establish a scientific and reasonable evaluation model for the location of charging stations. Secondly, we selected 12 typical enterprises such as TELD NEW ENERGY Co., Ltd.from the dimensions of company scale and strategic objectives, and then classified them into state-owned enterprises, vehicle enterprises and specialized operating enterprises through k-means clustering. Finally it turns out that various types of enterprises are in the stage of differentiation in the investment and construction speed of charging station enterprises. In addition, this study proposes personalized siting solutions for different types of charging piles, and makes referenceable suggestions for the siting of charging stations.
 
 
 atasets MNIST and CIFAR-10. After a few epochs, the model is convergent and reaches high accuracy of 99.34% in MNIST and 92.04% in CIFAR-10. This model outperforms the single CNN and some state-of-the-art models in classifying both datasets, especially in distinguishing similar images like ‘6’ and ‘9’, ‘bird’ and ‘plane’. These results indicate the model's good robustness and generality.

Soliton solutions of the space–time fractional nonlocal nonlinear Schrödinger equation

In this paper, the space–time fractional nonlocal nonlinear Schrödinger equations under Jumarie modified Riemann–Liouville derivative is studied. The soliton solutions are formally derived by using the extended tanh method of fractional Riccati subequation and the ansatz method combined with the Hermite–Gaussian function and Mittag-Leffler function. Different types of solutions are obtained and the necessary conditions for the existence of solutions are given. With the help of Maple, we plot figures exhibit that solitons are forming as fractional order λ increasing, and also, we noticed that at different order n of the Hermite–Gaussian function Hn(y), mainly affects the amplitude of soliton. Furthermore, we have discussed the new soliton solutions in the fractional case. It is of great significance to understand complex physical phenomena described by fractional nonlocal nonlinear equations.

Approximate water vertical infiltration extremum path in unsaturated soils

According to the principle of stationary action, water vertically infiltrates unsaturated soils along an infiltration-duration extremum path with linear deviation. The solution of the Euler–Lagrange equation with appropriate boundary conditions yields a linear relationship between the moisture diffusion function and the ratio of the spatial location to the wetting front distance. By integrating the law of mass conservation at the boundary, the temporal evolution of the wetting front is implicitly derived. A linear term is introduced to compensate for the deviation in calculating the position of the wetting front owing to the Taylor series approximation. Based on the representation of the diffusion function in relation to the boundary diffusivity, the spatial location and the position of the wetting front, a direct way to determine hydraulic conductivity is presented. Unlike existing methods, the proposed approach involves fewer hypotheses and is more theoretically robust. Moreover, the material parameters in the proposed approach have a clear physical meaning and can be explicitly determined. Using the Brooks–Corey hydraulic function, the evolution and distribution characteristics of the water content are explicitly determined, while the advancing wetting front is implicitly represented. The results of the proposed solution for different types of soil are in agreement with these numerical and analytical solutions.

Exact traveling wave solutions for the (2+1)-dimensional double sine-Gordon equation using direct integral method

In this paper, the direct integral method and complete discrimination system for quartic polynomial in standard form are applied to the (2+1)-dimensional double sine-Gordon equation. All possible exact traveling wave solutions of different types are successfully obtained from nine subcases. These exact solutions include kink solutions, and periodic solutions. Different from traditional methods (the Jacobi elliptic function method, the Exp-function method, extended Tanh method and the algebraic mapping method, etc.), the direct integral method described in this work is very natural and simple, and gives a new idea to obtain exact solutions for the mathematical physics equations considered.

P-harmonic functions with nonlinear Neumann conditions on the sphere and measure data

We study renormalized solutions to the problem 1\\right\\rbrace \\\\ \\left\\lvert {\ abla u} \\right\\rvert^{p-2}u_\ u + g(u) = \\mu & \\mbox{ on } \\left\\lbrace x \\in \\mathbb{R}^N : \\left\\lvert {x} \\right\\rvert=1\\right\\rbrace \\end{cases} \\end{align*} $$]]> { − Δ p u = 0 in { x ∈ R N : | x | > 1 } | ∇ u | p − 2 u ν + g ( u ) = μ on { x ∈ R N : | x | = 1 } where 1<p<N, N ≥ 2 , u ν is the normal derivative of u, μ is a bounded Radon measure, and g : R → R is a continuous function. We consider first the case when g is trivial where, by making use of the symmetries of the problem and the stability of renormalized solutions, we obtain an existence theory. Afterwards, we show existence of solutions for different types of nonlinearities, including power functions. We also provide a characterization of removable sets for the problem with source.

An approach of flow velocity measurement on microfluidic chip by near-field scanning microwave microscopy

A novel approach for flow velocity measurements on a microfluidic chip using near-field scanning microwave microscopy (NSMM) is proposed. It does not require the tested sample to contain visible particles, as the intrinsic electromagnetic properties of the fluid can be detected. Compared with conventional flowmetry, NSMM can measure flow velocity of the tested specimen without any invasive detectors inside or in contact with the specimen, and it can preserve original characteristics of the sample. The flow velocity of different types of solutions is obtained in point scanning, and flow velocity distribution in a microfluidic channel is illustrated in line scanning of NSMM measurement. The flow velocity distribution in microfluidic channel demonstrates distinctive differences between flow velocities of adjacent points, and the microfluidic channel is recognized with a lateral resolution of 10 μm. This approach can help optimize localized flow velocity measurement in drug screening and chemical reaction, and it can be developed for 2D/3D flow velocity imaging in chemical industry and biomedical field.

X-in-the-Loop-Based High Accuracy Test Facility for Industrial Development of Electric Vehicles

The present paper offers a complete, flexible and adaptable solution for electric vehicles industrial developers to test their designs from all the perspectives required by a V-mode development approach. Construction of high accuracy mechanical and electrical real-time digital-twin models fuzzing dedicated software was proven to be the proper solution to reach results confirmed by actual measurements. Methods for transitioning from real-time simulations to emulations or hardware in the loop testing are presented in detail. The digital-twin solution performing real-time simulations are considered to be the virtual test facility presented in the paper. For actual validation, preliminary the battery is studied via hardware emulation and hardware testing. The same approach is then applied to the vehicle motor together with its electronics and control. The added value of the paper is brought by several aspects such as the real-time co-simulation, performed using National Instruments VeriStand software aggregator, the methods of virtual, emulation and hardware testing of the same assemblies, all being confirmed by comparative analysis. The increased precision obtained, proved by actual measurements, estimates the value and usefulness of this study for those working in electric vehicles development. The content of the paper is an extended genuine study giving hands-on solutions for different types of approaches when it comes to developing and testing mechanical or electrical assemblies. The paper gives a theoretical background pushed to the application side confirmed by actual laboratory testing.

Business model comparison of slum-based PV to realize low-cost and flexible power generation in city-level

Photovoltaics (PVs) have become an essential part of the energy transition in recent years, and decision-makers have gradually entered the era of PV markets without subsidies. Consequently, the importance of PV policy and business models has been further demonstrated. However, in the case of rooftop PVs in urban areas, most PV promotion policies only focus on formal areas, whereas there is a lack of suitable policies directly applicable to slums with informal built environments. This study focused on a method for realizing low-cost and flexible PV power generation for urban slums with competitive business models. First, an analysis of rooftop PV in slums revealed three business models as dominant including slums, high-rise buildings, governments, power systems, and energy service providers. Afterward, considering Shenzhen as a case study, different loads of various buildings were provided, and the overall power generation potential at the city level was analyzed. Subsequently, 11 typical building groups were selected to evaluate the business model profits. Consequently, considering the construction rate caused by the energy policy of PVs, the most suitable solutions for different types of areas and various construction-rate combinations were discussed. Thus, this study argued that our novel analysis could serve as a powerful tool for policymakers to plan the future development of sustainable cities and alleviate poverty.

Investigation of influence of electrical field and solution of the surface-active substance (SAS) on water flood oil recovery factor

Influence of the electrical current fields and various type solutions of the surface-active substances on an interfacial tension, adsorption, desorption and on oil recovery factor from heavily clay porous medium has been investigated in the article. Nonionic alfenol, cation-active DMABACH (Dimethyl Alkyl Benzyl Ammonium Chloride) and anion-active sulfonic acid have been used as SAS. Quartz sand and rock from surface exposure of Kirmakian Suite (KS) of Balakhany field are as an adsorbent. It was revealed that direct and alternating current at 50 and 100 V through solutions of different type of SAS doesn’t practically influence on their interfacial tension on the boundary of nonpolar hydrocarbon liquid. Direct and alternating current through the porous medium containing clays and carbonates doesn’t influence on value of dynamic adsorption of nonionic SAS but promotes a decrease of their desorption from the rocks surface. It was determined that shared use of the direct-current field and solution of nonionic surface-active substance in comparison with mineralized water doesn’t practically influence on value of the oil recovery factor due to high adsorption of its molecules on surface of the heavily clay rock of Kirmakian suite. The use of direct current at 100 V considerably allowed (up to 23 %) to increase the Kirmakian oil recovery factor by the stratal alkaline water

Piston driven shock waves in non-homogeneous planar media

In this work, we analyze in detail the problem of piston driven shock waves in planar media. Similarity solutions to the compressible hydrodynamics equations are developed, for a strong shock wave, generated by a time dependent pressure piston, propagating in a non-homogeneous planar medium consisting of an ideal gas. Power law temporal and spatial dependency is assumed for the piston pressure and initial medium density, respectively. The similarity solutions are written in both Lagrangian and Eulerian coordinates. It is shown that the solutions take various qualitatively different forms according to the value of the pressure and density exponents. We show that there exist different families of solutions, for which the shock propagates at a constant speed, accelerates, or slows down. Similarly, we show that there exist different types of solutions, for which the density near the piston is either finite, vanishes, or diverges. Finally, we perform a comprehensive comparison between the planar shock solutions and Lagrangian hydrodynamic simulations, by setting proper initial and boundary conditions. A very good agreement is reached, which demonstrates the usefulness of the analytic solutions as a code verification test problem.

Degenerate and bound-state solitons of a novel Kundu-nonlinear Schrödinger equation based on generalized Darboux transformation

In this paper, we derive a novel Kundu-nonlinear Schrödinger equation through a 2 × 2 matrix spectral problem, which can be used to describe the phenomena in optical propagation, and the determinant expression of generalized (n,N−n)-fold Darboux transformation for the Kundu-nonlinear Schrödinger equation is given by solving algebraic equations. In addition, through the generalized (n,N−n)-fold Darboux transformation, we obtain three different types of solutions, (i) soliton solutions, (ii) degenerate soliton solutions, (iii) interaction solutions between solitons and degenerate solitons, which are divided into elastic interaction and bound-state. At the same time, the conditions for their generation are discussed. The properties of the aforementioned solutions are analyzed graphically ultimately.

Solutions of Multiplicative İntegral Equations via The Multiplicative Power Series Method

In this study, definitions of types of multiplicative integral equations are given. And solutions of different types of multiplicative integral equations are investigated using the multiplicative power series method. These are supported by numerical examples.

Weak-anchoring effects in a thin pinned ridge of nematic liquid crystal.

A theoretical investigation of weak-anchoring effects in a thin two-dimensional pinned static ridge of nematic liquid crystal resting on a flat solid substrate in an atmosphere of passive gas is performed. Specifically, we solve a reduced version of the general system of governing equationsrecently derived by Cousins etal. [Proc. R. Soc. A 478, 20210849 (2022)10.1098/rspa.2021.0849] valid for a symmetric thin ridge under the one-constant approximation of the Frank-Oseen bulk elastic energy with pinned contact lines to determine the shape of the ridge and the behavior of the director within it. Numerical investigations covering a wide range of parameter values indicate that the energetically preferred solutions can be classified in terms of the Jenkins-Barratt-Barbero-Barberi critical thickness into five qualitatively different types of solution. In particular, the theoretical results suggest that anchoring breaking occurs close to the contact lines. The theoretical predictions are supported by the results of physical experiments for a ridge of the nematic 4^{'}-pentyl-4-biphenylcarbonitrile (5CB). In particular, these experiments show that the homeotropic anchoring at the gas-nematic interface is broken close to the contact lines by the stronger rubbed planar anchoring at the nematic-substrate interface. A comparison between the experimental values of and the theoretical predictions for the effective refractive index of the ridge gives a first estimate of the anchoring strength of an interface between air and 5CB to be (9.80±1.12)×10^{-6}Nm^{-1} at a temperature of (22±1.5)^{∘}C.

Phase diagram of Einstein-Weyl gravity

Thanks to their interpretation as the first order correction of general relativity at high energies, quadratic theories of gravity have gained much attention in recent times. Particular attention has been drawn to the Einstein-Weyl theory, where the addition of the squared Weyl tensor to the action opens the possibility of having non-Schwarzschild black holes in the classical spectrum of the theory. Static and spherically symmetric solutions of this theory have been studied and classified in terms of their small scales behavior; however, a classification of these solutions in terms of the asymptotic gravitational field is still lacking. In this paper we address this point and present a phase diagram of the theory, where the different types of solutions are shown in terms of their mass and the strength of a Yukawa-like correction to the gravitational field. In particular we will show that, in the case of compact stars, different equations of state imply different Yukawa corrections to the gravitational potential, with possible phenomenological implications.