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. ...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:展开更多
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 f...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.展开更多
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 i...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.展开更多
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 re...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.展开更多
In this study, the mathematical models of dynamics of student populations in the university departments are formulated. As a case study, we employ the data of registration section from Department of Mathematics, Facul...In this study, the mathematical models of dynamics of student populations in the university departments are formulated. As a case study, we employ the data of registration section from Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Thailand, from calendar year 2006 to 2010. Using regression analysis, descriptive model and explanatory model are derived. The descriptive model is linear with R2 = 0.8864. Using log-transformation, the explanatory model gives the nonlinear approximation with R2 = 0.8293. The model predicts that the number of students of Department of Mathematics, KMUTNB has a tendency to linearly increase with slope of 20 with 95% CI (6.8417, 33.1583). The application of the models in educational management is discussed.展开更多
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.
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 ...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.展开更多
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 taugh...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.展开更多
This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreov...This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.展开更多
This study numerically examines the heat and mass transfer characteristics of two ternary nanofluids via converging and diverg-ing channels.Furthermore,the study aims to assess two ternary nanofluids combinations to d...This study numerically examines the heat and mass transfer characteristics of two ternary nanofluids via converging and diverg-ing channels.Furthermore,the study aims to assess two ternary nanofluids combinations to determine which configuration can provide better heat and mass transfer and lower entropy production,while ensuring cost efficiency.This work bridges the gap be-tween academic research and industrial feasibility by incorporating cost analysis,entropy generation,and thermal efficiency.To compare the velocity,temperature,and concentration profiles,we examine two ternary nanofluids,i.e.,TiO_(2)+SiO_(2)+Al_(2)O_(3)/H_(2)O and TiO_(2)+SiO_(2)+Cu/H_(2)O,while considering the shape of nanoparticles.The velocity slip and Soret/Dufour effects are taken into consideration.Furthermore,regression analysis for Nusselt and Sherwood numbers of the model is carried out.The Runge-Kutta fourth-order method with shooting technique is employed to acquire the numerical solution of the governed system of ordinary differential equations.The flow pattern attributes of ternary nanofluids are meticulously examined and simulated with the fluc-tuation of flow-dominating parameters.Additionally,the influence of these parameters is demonstrated in the flow,temperature,and concentration fields.For variation in Eckert and Dufour numbers,TiO_(2)+SiO_(2)+Al_(2)O_(3)/H_(2)O has a higher temperature than TiO_(2)+SiO_(2)+Cu/H_(2)O.The results obtained indicate that the ternary nanofluid TiO_(2)+SiO_(2)+Al_(2)O_(3)/H_(2)O has a higher heat transfer rate,lesser entropy generation,greater mass transfer rate,and lower cost than that of TiO_(2)+SiO_(2)+Cu/H_(2)O ternary nanofluid.展开更多
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(pP...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.展开更多
Mid-infrared(MIR)-polarized thermal emission has broad applications in areas such as molecular sensing,information encryption,target detection,and optical communication.However,it is difficult for objects in nature to...Mid-infrared(MIR)-polarized thermal emission has broad applications in areas such as molecular sensing,information encryption,target detection,and optical communication.However,it is difficult for objects in nature to produce polarized thermal emission.Moreover,simultaneously generating and modulating broadband MIR thermal emission with both circular and linear polarization is even more difficult.We present a chiral plasmonic metasurface emitter(CPME)composed of asymmetric L-shaped and I-shaped antennas.The CPME consists of In_(3)SbTe_(2)(IST)phase-change material(PCM)antennas,an Al_(2)O_(3) dielectric layer,and an Au substrate.It is demonstrated that the CPME can selectively emit polarized light with different polarization states.Numerical simulations show that the CPME can achieve full Stokes parameter control of MIR thermal emission.By changing the state of the PCM IST,the spectral emissivity of 0 deg,45 deg,90 deg,and 135 deg linearly polarized(LP)lights and left-handed/right-handed circularly polarized(LCP/RCP)lights can be adjusted.In the crystalline state,the CPME exhibits the total degree of polarization(DoP)greater than 0.5 in the wavelength range of 3.4 to 5.3μm,the degree of linear polarization(DoLP)greater than 0.4 in the range of 3.0 to 5.1μm,and the degree of circular polarization(DoCP)greater than 0.4 in the range of 4.5 to 5.6μm.The physical mechanism of polarized emission has been investigated fully based on the near-field intensity distribution and power loss distribution.Finally,the potential applications of the designed CPME in infrared polarization detection and antidetection are verified through numerical calculations.展开更多
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.Ma...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.展开更多
The level 3 case for Ramanujan-type series has been considered as the most mysterious and the most challenging,out of all possible levels for Ramanujan-type series.This motivates the development of new techniques for ...The level 3 case for Ramanujan-type series has been considered as the most mysterious and the most challenging,out of all possible levels for Ramanujan-type series.This motivates the development of new techniques for constructing Ramanujan-type series of level 3.Chan and Liaw introduced an alternating analogue of the Borwein brothers’identity for Ramanujan-type series of level 3;subsequently,Chan,Liaw,and Tian formulated another proof of the Chan–Liaw identity,via the use of Ramanujan’s class invariant.Using the elliptic lambda function and the elliptic alpha function,we prove,via a limiting case of the Kummer–Goursat transformation,a new identity for evaluating the summands for alternating Ramanujan-type series of level 3,and we apply this new identity to prove three conjectured formulas for quadratic-irrational,Ramanujan-type series that had been discovered via numerical experiments with Maple in 2012 by Aldawoud.We also apply our identity to prove a new Ramanujan-type series of level 3 with a quartic convergence rate and quartic coefficients.展开更多
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 i...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.展开更多
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 po...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.展开更多
Transformer models have emerged as pivotal tools within the realm of drug discovery,distinguished by their unique architectural features and exceptional performance in managing intricate data landscapes.Leveraging the...Transformer models have emerged as pivotal tools within the realm of drug discovery,distinguished by their unique architectural features and exceptional performance in managing intricate data landscapes.Leveraging the innate capabilities of transformer architectures to comprehend intricate hierarchical dependencies inherent in sequential data,these models showcase remarkable efficacy across various tasks,including new drug design and drug target identification.The adaptability of pre-trained trans-former-based models renders them indispensable assets for driving data-centric advancements in drug discovery,chemistry,and biology,furnishing a robust framework that expedites innovation and dis-covery within these domains.Beyond their technical prowess,the success of transformer-based models in drug discovery,chemistry,and biology extends to their interdisciplinary potential,seamlessly combining biological,physical,chemical,and pharmacological insights to bridge gaps across diverse disciplines.This integrative approach not only enhances the depth and breadth of research endeavors but also fosters synergistic collaborations and exchange of ideas among disparate fields.In our review,we elucidate the myriad applications of transformers in drug discovery,as well as chemistry and biology,spanning from protein design and protein engineering,to molecular dynamics(MD),drug target iden-tification,transformer-enabled drug virtual screening(VS),drug lead optimization,drug addiction,small data set challenges,chemical and biological image analysis,chemical language understanding,and single cell data.Finally,we conclude the survey by deliberating on promising trends in transformer models within the context of drug discovery and other sciences.展开更多
History and Pedagogy of Mathematics(HPM)is one of the important research fields in mathematics education,which has received widespread attention from the mathematics education community because of its educational valu...History and Pedagogy of Mathematics(HPM)is one of the important research fields in mathematics education,which has received widespread attention from the mathematics education community because of its educational value.Modem mathematics education technology plays an important auxiliary role in mathematics teaching.Hawgent is a dynamic mathematics software that can present abstract mathematical knowledge visually and static mathematical knowledge dynamically.In view of this,this research takes"the recognition of circle" as an example to conduct a research on HPM teaching supported by Hawgent Dynamic Mathematics Software in three aspects:analyze the contents and uncover the history of mathematics,make the products and show the history of mathematics,design the teaching and integrate the history of Mathematics.展开更多
The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic fu...The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.展开更多
A stochastic epidemic model with two age groups is established in this study,in which the susceptible(S),the exposed(E),the infected(I),the hospitalized(H)and the recovered(R)are involved within the total population,t...A stochastic epidemic model with two age groups is established in this study,in which the susceptible(S),the exposed(E),the infected(I),the hospitalized(H)and the recovered(R)are involved within the total population,the aging rates between two age groups are set to be constant.The existence-and-uniqueness of global positive solution is firstly showed.Then,by constructing several appropriate Lyapunov functions and using the high-dimensional Itô’s formula,the sufficient conditions for the stochastic extinction and stochastic persistence of the exposed individuals and the infected individuals are obtained.The stochastic extinction indicator and the stochastic persistence indicator are less-valued expressions compared with the basic reproduction number.Meanwhile,the main results of this study are modified into multi-age groups.Furthermore,by using the surveillance data for Fujian Provincial Center for Disease Control and Prevention,Fuzhou COVID-19 epidemic is chosen to carry out the numerical simulations,which show that the age group of the population plays the vital role when studying infectious diseases.展开更多
文摘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:
文摘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.
文摘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.
文摘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.
文摘In this study, the mathematical models of dynamics of student populations in the university departments are formulated. As a case study, we employ the data of registration section from Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Thailand, from calendar year 2006 to 2010. Using regression analysis, descriptive model and explanatory model are derived. The descriptive model is linear with R2 = 0.8864. Using log-transformation, the explanatory model gives the nonlinear approximation with R2 = 0.8293. The model predicts that the number of students of Department of Mathematics, KMUTNB has a tendency to linearly increase with slope of 20 with 95% CI (6.8417, 33.1583). The application of the models in educational management is discussed.
文摘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.
文摘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.
文摘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.
文摘This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.
基金supported by DST-FIST(Government of India)(Grant No.SR/FIST/MS-1/2017/13)and Seed Money Project(Grant No.DoRDC/733).
文摘This study numerically examines the heat and mass transfer characteristics of two ternary nanofluids via converging and diverg-ing channels.Furthermore,the study aims to assess two ternary nanofluids combinations to determine which configuration can provide better heat and mass transfer and lower entropy production,while ensuring cost efficiency.This work bridges the gap be-tween academic research and industrial feasibility by incorporating cost analysis,entropy generation,and thermal efficiency.To compare the velocity,temperature,and concentration profiles,we examine two ternary nanofluids,i.e.,TiO_(2)+SiO_(2)+Al_(2)O_(3)/H_(2)O and TiO_(2)+SiO_(2)+Cu/H_(2)O,while considering the shape of nanoparticles.The velocity slip and Soret/Dufour effects are taken into consideration.Furthermore,regression analysis for Nusselt and Sherwood numbers of the model is carried out.The Runge-Kutta fourth-order method with shooting technique is employed to acquire the numerical solution of the governed system of ordinary differential equations.The flow pattern attributes of ternary nanofluids are meticulously examined and simulated with the fluc-tuation of flow-dominating parameters.Additionally,the influence of these parameters is demonstrated in the flow,temperature,and concentration fields.For variation in Eckert and Dufour numbers,TiO_(2)+SiO_(2)+Al_(2)O_(3)/H_(2)O has a higher temperature than TiO_(2)+SiO_(2)+Cu/H_(2)O.The results obtained indicate that the ternary nanofluid TiO_(2)+SiO_(2)+Al_(2)O_(3)/H_(2)O has a higher heat transfer rate,lesser entropy generation,greater mass transfer rate,and lower cost than that of TiO_(2)+SiO_(2)+Cu/H_(2)O ternary nanofluid.
基金supported by the Deanship of Graduate Studies and Scientific Research at Qassim University(QU-APC-2024-9/1).
文摘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.
基金supported by the National Natural Science Foundation of China(Grant No.61775050).
文摘Mid-infrared(MIR)-polarized thermal emission has broad applications in areas such as molecular sensing,information encryption,target detection,and optical communication.However,it is difficult for objects in nature to produce polarized thermal emission.Moreover,simultaneously generating and modulating broadband MIR thermal emission with both circular and linear polarization is even more difficult.We present a chiral plasmonic metasurface emitter(CPME)composed of asymmetric L-shaped and I-shaped antennas.The CPME consists of In_(3)SbTe_(2)(IST)phase-change material(PCM)antennas,an Al_(2)O_(3) dielectric layer,and an Au substrate.It is demonstrated that the CPME can selectively emit polarized light with different polarization states.Numerical simulations show that the CPME can achieve full Stokes parameter control of MIR thermal emission.By changing the state of the PCM IST,the spectral emissivity of 0 deg,45 deg,90 deg,and 135 deg linearly polarized(LP)lights and left-handed/right-handed circularly polarized(LCP/RCP)lights can be adjusted.In the crystalline state,the CPME exhibits the total degree of polarization(DoP)greater than 0.5 in the wavelength range of 3.4 to 5.3μm,the degree of linear polarization(DoLP)greater than 0.4 in the range of 3.0 to 5.1μm,and the degree of circular polarization(DoCP)greater than 0.4 in the range of 4.5 to 5.6μm.The physical mechanism of polarized emission has been investigated fully based on the near-field intensity distribution and power loss distribution.Finally,the potential applications of the designed CPME in infrared polarization detection and antidetection are verified through numerical calculations.
文摘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.
基金supported by a Killam Postdoctoral Fellowship from the Killam Trusts.
文摘The level 3 case for Ramanujan-type series has been considered as the most mysterious and the most challenging,out of all possible levels for Ramanujan-type series.This motivates the development of new techniques for constructing Ramanujan-type series of level 3.Chan and Liaw introduced an alternating analogue of the Borwein brothers’identity for Ramanujan-type series of level 3;subsequently,Chan,Liaw,and Tian formulated another proof of the Chan–Liaw identity,via the use of Ramanujan’s class invariant.Using the elliptic lambda function and the elliptic alpha function,we prove,via a limiting case of the Kummer–Goursat transformation,a new identity for evaluating the summands for alternating Ramanujan-type series of level 3,and we apply this new identity to prove three conjectured formulas for quadratic-irrational,Ramanujan-type series that had been discovered via numerical experiments with Maple in 2012 by Aldawoud.We also apply our identity to prove a new Ramanujan-type series of level 3 with a quartic convergence rate and quartic coefficients.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-RP23066).
文摘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.
文摘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.
基金supported in part by National Institute of Health(NIH),USA(Grant Nos.:R01GM126189,R01AI164266,and R35GM148196)the National Science Foundation,USA(Grant Nos.DMS2052983,DMS-1761320,and IIS-1900473)+3 种基金National Aero-nautics and Space Administration(NASA),USA(Grant No.:80NSSC21M0023)Michigan State University(MSU)Foundation,USA,Bristol-Myers Squibb(Grant No.:65109)USA,and Pfizer,USAsupported by the National Natural Science Foundation of China(Grant Nos.:11971367,12271416,and 11972266).
文摘Transformer models have emerged as pivotal tools within the realm of drug discovery,distinguished by their unique architectural features and exceptional performance in managing intricate data landscapes.Leveraging the innate capabilities of transformer architectures to comprehend intricate hierarchical dependencies inherent in sequential data,these models showcase remarkable efficacy across various tasks,including new drug design and drug target identification.The adaptability of pre-trained trans-former-based models renders them indispensable assets for driving data-centric advancements in drug discovery,chemistry,and biology,furnishing a robust framework that expedites innovation and dis-covery within these domains.Beyond their technical prowess,the success of transformer-based models in drug discovery,chemistry,and biology extends to their interdisciplinary potential,seamlessly combining biological,physical,chemical,and pharmacological insights to bridge gaps across diverse disciplines.This integrative approach not only enhances the depth and breadth of research endeavors but also fosters synergistic collaborations and exchange of ideas among disparate fields.In our review,we elucidate the myriad applications of transformers in drug discovery,as well as chemistry and biology,spanning from protein design and protein engineering,to molecular dynamics(MD),drug target iden-tification,transformer-enabled drug virtual screening(VS),drug lead optimization,drug addiction,small data set challenges,chemical and biological image analysis,chemical language understanding,and single cell data.Finally,we conclude the survey by deliberating on promising trends in transformer models within the context of drug discovery and other sciences.
文摘History and Pedagogy of Mathematics(HPM)is one of the important research fields in mathematics education,which has received widespread attention from the mathematics education community because of its educational value.Modem mathematics education technology plays an important auxiliary role in mathematics teaching.Hawgent is a dynamic mathematics software that can present abstract mathematical knowledge visually and static mathematical knowledge dynamically.In view of this,this research takes"the recognition of circle" as an example to conduct a research on HPM teaching supported by Hawgent Dynamic Mathematics Software in three aspects:analyze the contents and uncover the history of mathematics,make the products and show the history of mathematics,design the teaching and integrate the history of Mathematics.
基金Supported by Natural Science Foundation of Guangdong Province in China(2018KTSCX161)。
文摘The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.
基金Supported by National Natural Science Foundation of China(61911530398,12231012)Consultancy Project by the Chinese Academy of Engineering(2022-JB-06,2023-JB-12)+3 种基金the Natural Science Foundation of Fujian Province of China(2021J01621)Special Projects of the Central Government Guiding Local Science and Technology Development(2021L3018)Royal Society of Edinburgh(RSE1832)Engineering and Physical Sciences Research Council(EP/W522521/1).
文摘A stochastic epidemic model with two age groups is established in this study,in which the susceptible(S),the exposed(E),the infected(I),the hospitalized(H)and the recovered(R)are involved within the total population,the aging rates between two age groups are set to be constant.The existence-and-uniqueness of global positive solution is firstly showed.Then,by constructing several appropriate Lyapunov functions and using the high-dimensional Itô’s formula,the sufficient conditions for the stochastic extinction and stochastic persistence of the exposed individuals and the infected individuals are obtained.The stochastic extinction indicator and the stochastic persistence indicator are less-valued expressions compared with the basic reproduction number.Meanwhile,the main results of this study are modified into multi-age groups.Furthermore,by using the surveillance data for Fujian Provincial Center for Disease Control and Prevention,Fuzhou COVID-19 epidemic is chosen to carry out the numerical simulations,which show that the age group of the population plays the vital role when studying infectious diseases.
