A Synergistic Multi-Attribute Decision-Making Method for Educational Institutions Evaluation Using Similarity Measures of Possibility Pythagorean Fuzzy Hypersoft Sets

Due to the numerous variables to take into account as well as the inherent ambiguity and uncertainty,evaluating educational institutions can be difficult.The concept of a possibility Pythagorean fuzzy hypersoft set(pPyFHSS)is more flexible in this regard than other theoretical fuzzy set-like models,even though some attempts have been made in the literature to address such uncertainties.This study investigates the elementary notions of pPyFHSS including its set-theoretic operations union,intersection,complement,OR-and AND-operations.Some results related to these operations are also modified for pPyFHSS.Additionally,the similarity measures between pPyFHSSs are formulated with the assistance of numerical examples and results.Lastly,an intelligent decision-assisted mechanism is developed with the proposal of a robust algorithm based on similarity measures for solving multi-attribute decision-making(MADM)problems.A case study that helps the decision-makers assess the best educational institution is discussed to validate the suggested system.The algorithmic results are compared with the most pertinent model to evaluate the adaptability of pPyFHSS,as it generalizes the classical possibility fuzzy set-like theoretical models.Similarly,while considering significant evaluating factors,the flexibility of pPyFHSS is observed through structural comparison.

Solid Waste Management:A MADM Approach Using Fuzzy Parameterized Possibility Single-Valued Neutrosophic Hypersoft Expert Settings

The dramatic rise in the number of people living in cities has made many environmental and social problems worse.The search for a productive method for disposing of solid waste is the most notable of these problems.Many scholars have referred to it as a fuzzy multi-attribute or multi-criteria decision-making problem using various fuzzy set-like approaches because of the inclusion of criteria and anticipated ambiguity.The goal of the current study is to use an innovative methodology to address the expected uncertainties in the problem of solid waste site selection.The characteristics(or sub-attributes)that decision-makers select and the degree of approximation they accept for various options can both be indicators of these uncertainties.To tackle these problems,a novel mathematical structure known as the fuzzy parameterized possibility single valued neutrosophic hypersoft expert set(ρˆ-set),which is initially described,is integrated with a modified version of Sanchez’s method.Following this,an intelligent algorithm is suggested.The steps of the suggested algorithm are explained with an example that explains itself.The compatibility of solid waste management sites and systems is discussed,and rankings are established along with detailed justifications for their viability.This study’s strengths lie in its application of fuzzy parameterization and possibility grading to effectively handle the uncertainties embodied in the parameters’nature and alternative approximations,respectively.It uses specific mathematical formulations to compute the fuzzy parameterized degrees and possibility grades that are missing from the prior literature.It is simpler for the decisionmakers to look at each option separately because the decision is uncertain.Comparing the computed results,it is discovered that they are consistent and dependable because of their preferred properties.

Global Piecewise Analysis of HIV Model with Bi-Infectious Categories under Ordinary Derivative and Non-Singular Operator with Neural Network Approach

This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.

Impact of Pollutant Concentration and Particle Deposition on the Radiative Flow of Casson-Micropolar Fluid between Parallel Plates

Assessing the behaviour and concentration of waste pollutants deposited between two parallel plates is essential for effective environmental management.Determining the effectiveness of treatment methods in reducing pollution scales is made easier by analysing waste discharge concentrations.The waste discharge concentration analysis is useful for assessing how effectively wastewater treatment techniques reduce pollution levels.This study aims to explore the Casson micropolar fluid flow through two parallel plates with the influence of pollutant concentration and thermophoretic particle deposition.To explore the mass and heat transport features,thermophoretic particle deposition and thermal radiation are considered.The governing equations are transformed into ordinary differential equations with the help of suitable similarity transformations.The Runge-Kutta-Fehlberg’s fourthfifth order technique and shooting procedure are used to solve the reduced set of equations and boundary conditions.The integration of a neural network model based on the Levenberg-Marquardt algorithm serves to improve the accuracy of predictions and optimize the analysis of parameters.Graphical outcomes are displayed to analyze the characteristics of the relevant dimensionless parameters in the current problem.Results reveal that concentration upsurges as the micropolar parameter increases.The concentration reduces with an upsurge in the thermophoretic parameter.An upsurge in the external pollutant source variation and the local pollutant external source parameters enhances mass transport.The surface drag force declines for improved values of porosity and micropolar parameters.

Numerical Analysis of the Magnetic Dipole Effect on a Radiative Ferromagnetic Liquid Flowing over a Porous Stretched Sheet

The effects of a magnetic dipole on a nonlinear thermally radiative ferromagnetic liquidflowing over a stretched surface in the presence of Brownian motion and thermophoresis are investigated.By means of a similarity transformation,ordinary differential equations are derived and solved afterwards using a numerical(the BVP4C)method.The impact of various parameters,namely the velocity,temperature,concentration,is presented graphically.It is shown that the nanoparticles properties,in conjunction with the magnetic dipole effect,can increase the thermal conductivity of the engineered nanofluid and,consequently,the heat transfer.Comparison with earlier studies indicates high accuracy and effectiveness of the numerical approach.An increase in the Brow-nian motion parameter and thermophoresis parameter enhances the concentration and the related boundary layer.The skin-friction rises when the viscosity parameter is increased.A larger value of the ferromagnetic para-meter results in a higher skin-friction and,vice versa,in a smaller Nusselt number.

When Does Sora Show:The Beginning of TAO to Imaginative Intelligence and Scenarios Engineering

DURING our discussion at workshops for writing“What Does ChatGPT Say:The DAO from Algorithmic Intelligence to Linguistic Intelligence”[1],we had expected the next milestone for Artificial Intelligence(AI)would be in the direction of Imaginative Intelligence(II),i.e.,something similar to automatic wordsto-videos generation or intelligent digital movies/theater technology that could be used for conducting new“Artificiofactual Experiments”[2]to replace conventional“Counterfactual Experiments”in scientific research and technical development for both natural and social studies[2]-[6].Now we have OpenAI’s Sora,so soon,but this is not the final,actually far away,and it is just the beginning.

Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated.The DarcyBrinkman model is used to characterize the fluid flow dynamics in porous materials.The analytical solutions are obtained for the unidirectional and completely developed flow.Based on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is solved.The eigenvalue problem is then solved by the spectral method.Finally,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters.The results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the flow.Besides,the flow is the most unstable when the channel is vertically oriented.

COMPLETE KAHLER METRICS WITH POSITIVE HOLOMORPHIC SECTIONAL CURVATURES ON CERTAIN LINE BUNDLES(RELATED TO A COHOMOGENEITY ONE POINT OF VIEW ON A YAU CONJECTURE)

In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.

Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fin exposed to magnetic field in the presence of a shape-dependent trihybrid nanofluid

The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical(Fe_3O_4), cylindrical(Au), and platelet(Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method(ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.

A Study on the Transmission Dynamics of the Omicron Variant of COVID-19 Using Nonlinear Mathematical Models

This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delays eventually resulted in the pandemic’s containment.To ensure the safety of the host population,this concept integrates quarantine and the COVID-19 vaccine.We investigate the stability of the proposed models.The fundamental reproduction number influences stability conditions.According to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the community.The real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.

DISCUSSION ON″THE BOUNDEDNESS AND ASYMPTOTIC BEHAVIOR OR SOLUTION DIFFERENTIAL SYSTEM OF SECOND-ORDER WITH VARIABLE COEFFICIENT" (App1ied Mathematics and Mechanics,Vo1.3,No.4,1982)

After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:

Examining Mathematics Anxiety of Undergraduates Using a Brain-Based Measurement, EEG

This paper reports on an investigation of mathematics anxiety (MA) among 40 Korean undergraduate students, using cognitive neuroscience. In Spring 2015, we collected data on correct response rates and reaction times from computer-based activities related to quadratic functions. We also measured brain response through event related potentials (ERP). Results demonstrate that students with higher mathematics anxiety (HMA) took more time than students with lower mathematics anxiety (LMA), both in translating equations to graphs and in translating graphs to equations. Moreover, based on analysis of ERP, brain waves of the HMA group recorded higher amplitude. In specific, both groups showed higher amplitude in translation from graphs to equation than vice versa. Higher amplitudes indicate greater demands on working memory, which we discuss in the concluding section, especially with regard to MA.

Erratum to “Weierstrass’ Elliptic Function Solution to the Autonomous Limit of the String Equation of Type (2,5)” [Advances in Pure Mathematics 4 (2014), 494-497]

In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.

Effectiveness of serological markers of gastric mucosal atrophy in the gastric precancer screening and in cancer prevention

BACKGROUND New markers are needed to improve the effectiveness of serological screening for atrophic gastritis.AIM To develop a cost-effective method for serological screening of atrophic gastritis with a high level of sensitivity.METHODS Of the 169 patients with atrophic gastritis,selected by the visual endoscopic Kimura-Takemoto method,165 showed histological mucosal atrophy using the updated Kimura-Takemoto method.All 169 patients were examined for postprandial levels of gastrin-17(G17)and pepsinogen-1(PG1)using Gastro-Panel®(Biohit Plc,Helsinki,Finland).RESULTS We used the histological standard of five biopsies of the gastric mucosa,in accordance with the Kimura-Takemoto classification system to assess the sensitivity of G17 in detecting gastric mucosal atrophy.We also compared the morphofunctional relationships between the detected histological degree of gastric mucosal atrophy and the serological levels of G17 and PG1,as the markers of atrophic gastritis.The sensitivity of postprandial G17 was 62.2%for serological levels of G17(range:0-4 pmol/L)and 100%for serological G17(range:0-10 pmol/L)for the detection of monofocal severe atrophic gastritis.No strong correlation was found between the levels of PG1 and degree of histological atrophy determined by the Kimura-Takemoto classification system to identify the severity of mucosal atrophy of the gastric corpus.In the presented clinical case of a 63-year-old man with multifocal atrophic gastritis,there is a pronounced positive long-term dynamics of the serological marker of atrophy-postprandial G17,after five months of rennet replacement therapy.CONCLUSION Serological screening of multifocal atrophic gastritis by assessment of postprandial G17 is a cost-effective method with high sensitivity.Postprandial G17 is an earlier marker of regression of atrophic gastritis than a morphological examination of a gastric biopsy in accordance with the Sydney system.Therefore,postprandial G17 is recommended for dynamic monitoring of atrophic gastritis after treatment.

Music as Mathematics of Senses

It is often said that music has reached its supreme and highest level in the 18th and 19th centuries. One of the main reasons for this achievement seems to be the robust structure of compositions of music, somewhat remindful of robust structure of mathematics. One is reminded of the words of Goethe: Geometry is frozen music. Here, we may extend geometry to mathematics. For the Middle Age in Europe, there were seven main subjects in the universities or in higher education. They were grammar, logic and rhetoric—these three (tri) were regarded as more standard and called trivia (trivium), the origin of the word trivial. And the remaining four were arithmetic, geometry, astronomy and music—these four (quadrus) were regarded as more advanced subjects and were called quadrivia (quadrivium). Thus for Goethe, geometry and mathematics seem to be equivocal. G. Leibniz expresses more in detail in his letter to C. Goldbach in 1712 (April 17): Musica est exercitium arithmeticae occultum nescientis se numerari animi (Music is a hidden arithmetic exercise of the soul, which doesn’t know that it is counting). Or in other respects, J. Sylvester expresses more in detail: Music is mathematics of senses. Mathematics is music of reasons. Thus, the title arises. This paper is a sequel to [1] and examines mathematical structure of musical scales entailing their harmony on expanding and elaborating material in [2] [3] [4] [5], etc. In statistics, the strong law of large numbers is well-known which claims that This means that the relative frequency of occurrences of an event A tends to the true probability p of the occurrences of A with probability 1. In music, harmony is achieved according to Pythagoras’ law of small numbers, which claims that only the small integer multiples of the fundamental notes can create harmony and consonance. We shall also mention the law of cyclotomic numbers according to Coxeter, which elaborates Pythagoras’ law and suggests a connection with construction of n-gons by ruler and compass. In the case of natural scales (just intonation), musical notes appear in the form 2p3q5r (multiples of the basic note), where p∈Z,?q=-3, -2, -1, 0, 1, 2, 3 and r=-1, 0, 1. We shall give mathematical details of the structure of various scales.

Erratum to “Simple Method for Evaluating Singular Integrals” [American Journal of Computational Mathematics, Volume 7, Number 4, December 2017 PP. 444-450]

In this paper, we study the class of one-dimensional singular integrals that converge in the sense of Cauchy principal value. In addition, we present a simple method for approximating such integrals.

Exploration and Practice of Improving Higher Mathematics Teaching Quality of Teaching at Different Levels

Teaching content of Higher Mathematics is systematic and rigor with a high degree of abstraction. Because different students are on the different basis and different disciplines have various requirements, mathematics is generally difficult for students. In order to improve the quality of teaching mathematics, we should make use of individualized teaching and teaching by different levels in order to achieve the best teaching results.

Assessment on a Hybrid Master of Science Program in Mathematics

A fully online MS program in mathematical science using hybrid synchronous instruction developed at the University of West Florida （UWF） has been successfully implemented since fall 2009. Distance students are taught simultaneously with on-campus students in the same classes. The assessment results show that the developed model is flexible, cost efficient and benefits both groups of students. It also showed that the distance students do as well as the face-to-face students when this model is used.