Groundwater modeling remains challenging due to heterogeneity and complexity of aquifer systems,necessitating endeavors to quantify Groundwater Levels(GWL)dynamics to inform policymakers and hydrogeologists.This study...Groundwater modeling remains challenging due to heterogeneity and complexity of aquifer systems,necessitating endeavors to quantify Groundwater Levels(GWL)dynamics to inform policymakers and hydrogeologists.This study introduces a novel Fuzzy Nonlinear Additive Regression(FNAR)model to predict monthly GWL in an unconfined aquifer in eastern Iran,using a 19-year(1998–2017)dataset from 11 piezometric wells.Under three distinct scenarios with progressively increasing input complexity,the study utilized readily available climate data,including Precipitation(Prc),Temperature(Tave),Relative Humidity(RH),and Evapotranspiration(ETo).The dataset was split into training(70%)and validation(30%)subsets.Results showed that among three input scenarios,Scenario 3(Sc3,incorporating all four variables)achieved the best predictive performance,with RMSE ranging from 0.305 m to 0.768 m,MAE from 0.203 m to 0.522 m,NSE from 0.661 to 0.980,and PBIAS from 0.771%to 0.981%,indicating low bias and high reliability.However,Sc2(excluding ETo)with RMSE ranging from 0.4226 m to 0.9909 m,MAE from 0.3418 m to 0.8173 m,NSE from 0.2831 to 0.9674,and PBIAS from−0.598%to 0.968%across different months offers practical advantages in data-scarce settings.The FNAR model outperforms conventional Fuzzy Least Squares Regression(FLSR)and holds promise for GWL forecasting in data-scarce regions where physical or numerical models are impractical.Future research should focus on integrating FNAR with deep learning algorithms and real-time data assimilation expanding applications across diverse hydrogeological settings.展开更多
Recent years have witnessed transformative changes brought about by artificial intelligence(AI)techniques with billions of parameters for the realization of high accuracy,proposing high demand for the advanced and AI ...Recent years have witnessed transformative changes brought about by artificial intelligence(AI)techniques with billions of parameters for the realization of high accuracy,proposing high demand for the advanced and AI chip to solve these AI tasks efficiently and powerfully.Rapid progress has been made in the field of advanced chips recently,such as the development of photonic computing,the advancement of the quantum processors,the boost of the biomimetic chips,and so on.Designs tactics of the advanced chips can be conducted with elaborated consideration of materials,algorithms,models,architectures,and so on.Though a few reviews present the development of the chips from their unique aspects,reviews in the view of the latest design for advanced and AI chips are few.Here,the newest development is systematically reviewed in the field of advanced chips.First,background and mechanisms are summarized,and subsequently most important considerations for co-design of the software and hardware are illustrated.Next,strategies are summed up to obtain advanced and AI chips with high excellent performance by taking the important information processing steps into consideration,after which the design thought for the advanced chips in the future is proposed.Finally,some perspectives are put forward.展开更多
With the increasing growth of online news,fake electronic news detection has become one of the most important paradigms of modern research.Traditional electronic news detection techniques are generally based on contex...With the increasing growth of online news,fake electronic news detection has become one of the most important paradigms of modern research.Traditional electronic news detection techniques are generally based on contextual understanding,sequential dependencies,and/or data imbalance.This makes distinction between genuine and fabricated news a challenging task.To address this problem,we propose a novel hybrid architecture,T5-SA-LSTM,which synergistically integrates the T5 Transformer for semantically rich contextual embedding with the Self-Attentionenhanced(SA)Long Short-Term Memory(LSTM).The LSTM is trained using the Adam optimizer,which provides faster and more stable convergence compared to the Stochastic Gradient Descend(SGD)and Root Mean Square Propagation(RMSProp).The WELFake and FakeNewsPrediction datasets are used,which consist of labeled news articles having fake and real news samples.Tokenization and Synthetic Minority Over-sampling Technique(SMOTE)methods are used for data preprocessing to ensure linguistic normalization and class imbalance.The incorporation of the Self-Attention(SA)mechanism enables the model to highlight critical words and phrases,thereby enhancing predictive accuracy.The proposed model is evaluated using accuracy,precision,recall(sensitivity),and F1-score as performance metrics.The model achieved 99%accuracy on the WELFake dataset and 96.5%accuracy on the FakeNewsPrediction dataset.It outperformed the competitive schemes such as T5-SA-LSTM(RMSProp),T5-SA-LSTM(SGD)and some other models.展开更多
In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.T...In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.展开更多
In this paper, we present our research on building computing machines consciousness about intuitive geometry based on mathematics experiments and statistical inference. The investigation consists of the following five...In this paper, we present our research on building computing machines consciousness about intuitive geometry based on mathematics experiments and statistical inference. The investigation consists of the following five steps. At first, we select a set of geometric configurations and for each configuration we construct a large amount of geometric data as observation data using dynamic geometry programs together with the pseudo-random number generator. Secondly, we refer to the geometric predicates in the algebraic method of machine proof of geometric theorems to construct statistics suitable for measuring the approximate geometric relationships in the observation data. In the third step, we propose a geometric relationship detection method based on the similarity of data distribution, where the search space has been reduced into small batches of data by pre-searching for efficiency, and the hypothetical test of the possible geometric relationships in the search results has be performed. In the fourth step, we explore the integer relation of the line segment lengths in the geometric configuration in addition. At the final step, we do numerical experiments for the pre-selected geometric configurations to verify the effectiveness of our method. The results show that computer equipped with the above procedures can find out the hidden geometric relations from the randomly generated data of related geometric configurations, and in this sense, computing machines can actually attain certain consciousness of intuitive geometry as early civilized humans in ancient Mesopotamia.展开更多
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.
The integration of the Czech Republic into the process of European space university education formation makes many demands on the higher education system--from creating new legislation and educational conception to ch...The integration of the Czech Republic into the process of European space university education formation makes many demands on the higher education system--from creating new legislation and educational conception to changes in the study programme structure. With regard to the study programme structure, permeability and modular construction of the programme and the actual European Credit Transfer and Accumulation System （ECTS） implementation are some of requirements coming to the fore. The aim of this work is to present an analysis of bachelor study programme Applied Mathematics Structure at the University of Ostrava within the context of the above mentioned requirements.展开更多
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
There are several challenges that hospitals are facing according to the emergency department(ED).Themain two issues are department capacity and lead time.However,the lack of consensus on performance criteria to evalua...There are several challenges that hospitals are facing according to the emergency department(ED).Themain two issues are department capacity and lead time.However,the lack of consensus on performance criteria to evaluateEDincreases the complication of this process.Thus,this study aims to evaluate the efficiency of the emergency department in 20 Egyptian hospitals(12 private and 8 general hospitals)based on 13 performance metrics.This research suggests an integrated evaluation model assess ED under a framework of plithogenic theory.The proposed framework addressed uncertainty and ambiguity in information with an efficient manner via presenting the evaluation expression by plithogenic numbers.Data Envelopment Analysis(DEA)technique is used in order to measure the efficiency of the emergency department of 20 hospitals according to the number of treated patients and effect on patient’s life quality based on 11 factors.Using the Analytic Hierarchy Process(AHP),the weight of efficiency factors will be measured based on neutrosophic linguistic scale pairwise comparison.Plithogenic operations provide more accurate aggregation result according to contradiction degree between criteria values.The results show that ten of the hospitals are providing efficient service in their emergency department,while the other ten are less efficient.The analysis of the results shows that 58%of private hospitals emergency department is operating efficiently,while the efficient general hospitals represent 38%.展开更多
This paper points out that delayed or no supply of software can kill potential benefits associated with new mathematical ideas that have led to development of new mathematics in OR. It also points out that it is a sel...This paper points out that delayed or no supply of software can kill potential benefits associated with new mathematical ideas that have led to development of new mathematics in OR. It also points out that it is a self-created situation by the scientific community. This situation needs attention and should be resolved urgently. Many illustrative examples have been given to justify the claim</span></span><span>.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
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
基金supported by the Iran National Science Foundation(INSF)the University of Birjand under grant number 4034771.
文摘Groundwater modeling remains challenging due to heterogeneity and complexity of aquifer systems,necessitating endeavors to quantify Groundwater Levels(GWL)dynamics to inform policymakers and hydrogeologists.This study introduces a novel Fuzzy Nonlinear Additive Regression(FNAR)model to predict monthly GWL in an unconfined aquifer in eastern Iran,using a 19-year(1998–2017)dataset from 11 piezometric wells.Under three distinct scenarios with progressively increasing input complexity,the study utilized readily available climate data,including Precipitation(Prc),Temperature(Tave),Relative Humidity(RH),and Evapotranspiration(ETo).The dataset was split into training(70%)and validation(30%)subsets.Results showed that among three input scenarios,Scenario 3(Sc3,incorporating all four variables)achieved the best predictive performance,with RMSE ranging from 0.305 m to 0.768 m,MAE from 0.203 m to 0.522 m,NSE from 0.661 to 0.980,and PBIAS from 0.771%to 0.981%,indicating low bias and high reliability.However,Sc2(excluding ETo)with RMSE ranging from 0.4226 m to 0.9909 m,MAE from 0.3418 m to 0.8173 m,NSE from 0.2831 to 0.9674,and PBIAS from−0.598%to 0.968%across different months offers practical advantages in data-scarce settings.The FNAR model outperforms conventional Fuzzy Least Squares Regression(FLSR)and holds promise for GWL forecasting in data-scarce regions where physical or numerical models are impractical.Future research should focus on integrating FNAR with deep learning algorithms and real-time data assimilation expanding applications across diverse hydrogeological settings.
基金supported by the Hong Kong Polytechnic University(1-WZ1Y,1-W34U,4-YWER).
文摘Recent years have witnessed transformative changes brought about by artificial intelligence(AI)techniques with billions of parameters for the realization of high accuracy,proposing high demand for the advanced and AI chip to solve these AI tasks efficiently and powerfully.Rapid progress has been made in the field of advanced chips recently,such as the development of photonic computing,the advancement of the quantum processors,the boost of the biomimetic chips,and so on.Designs tactics of the advanced chips can be conducted with elaborated consideration of materials,algorithms,models,architectures,and so on.Though a few reviews present the development of the chips from their unique aspects,reviews in the view of the latest design for advanced and AI chips are few.Here,the newest development is systematically reviewed in the field of advanced chips.First,background and mechanisms are summarized,and subsequently most important considerations for co-design of the software and hardware are illustrated.Next,strategies are summed up to obtain advanced and AI chips with high excellent performance by taking the important information processing steps into consideration,after which the design thought for the advanced chips in the future is proposed.Finally,some perspectives are put forward.
基金supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number(PNURSP2025R195)Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘With the increasing growth of online news,fake electronic news detection has become one of the most important paradigms of modern research.Traditional electronic news detection techniques are generally based on contextual understanding,sequential dependencies,and/or data imbalance.This makes distinction between genuine and fabricated news a challenging task.To address this problem,we propose a novel hybrid architecture,T5-SA-LSTM,which synergistically integrates the T5 Transformer for semantically rich contextual embedding with the Self-Attentionenhanced(SA)Long Short-Term Memory(LSTM).The LSTM is trained using the Adam optimizer,which provides faster and more stable convergence compared to the Stochastic Gradient Descend(SGD)and Root Mean Square Propagation(RMSProp).The WELFake and FakeNewsPrediction datasets are used,which consist of labeled news articles having fake and real news samples.Tokenization and Synthetic Minority Over-sampling Technique(SMOTE)methods are used for data preprocessing to ensure linguistic normalization and class imbalance.The incorporation of the Self-Attention(SA)mechanism enables the model to highlight critical words and phrases,thereby enhancing predictive accuracy.The proposed model is evaluated using accuracy,precision,recall(sensitivity),and F1-score as performance metrics.The model achieved 99%accuracy on the WELFake dataset and 96.5%accuracy on the FakeNewsPrediction dataset.It outperformed the competitive schemes such as T5-SA-LSTM(RMSProp),T5-SA-LSTM(SGD)and some other models.
文摘In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.
文摘In this paper, we present our research on building computing machines consciousness about intuitive geometry based on mathematics experiments and statistical inference. The investigation consists of the following five steps. At first, we select a set of geometric configurations and for each configuration we construct a large amount of geometric data as observation data using dynamic geometry programs together with the pseudo-random number generator. Secondly, we refer to the geometric predicates in the algebraic method of machine proof of geometric theorems to construct statistics suitable for measuring the approximate geometric relationships in the observation data. In the third step, we propose a geometric relationship detection method based on the similarity of data distribution, where the search space has been reduced into small batches of data by pre-searching for efficiency, and the hypothetical test of the possible geometric relationships in the search results has be performed. In the fourth step, we explore the integer relation of the line segment lengths in the geometric configuration in addition. At the final step, we do numerical experiments for the pre-selected geometric configurations to verify the effectiveness of our method. The results show that computer equipped with the above procedures can find out the hidden geometric relations from the randomly generated data of related geometric configurations, and in this sense, computing machines can actually attain certain consciousness of intuitive geometry as early civilized humans in ancient Mesopotamia.
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The integration of the Czech Republic into the process of European space university education formation makes many demands on the higher education system--from creating new legislation and educational conception to changes in the study programme structure. With regard to the study programme structure, permeability and modular construction of the programme and the actual European Credit Transfer and Accumulation System （ECTS） implementation are some of requirements coming to the fore. The aim of this work is to present an analysis of bachelor study programme Applied Mathematics Structure at the University of Ostrava within the context of the above mentioned requirements.
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There are several challenges that hospitals are facing according to the emergency department(ED).Themain two issues are department capacity and lead time.However,the lack of consensus on performance criteria to evaluateEDincreases the complication of this process.Thus,this study aims to evaluate the efficiency of the emergency department in 20 Egyptian hospitals(12 private and 8 general hospitals)based on 13 performance metrics.This research suggests an integrated evaluation model assess ED under a framework of plithogenic theory.The proposed framework addressed uncertainty and ambiguity in information with an efficient manner via presenting the evaluation expression by plithogenic numbers.Data Envelopment Analysis(DEA)technique is used in order to measure the efficiency of the emergency department of 20 hospitals according to the number of treated patients and effect on patient’s life quality based on 11 factors.Using the Analytic Hierarchy Process(AHP),the weight of efficiency factors will be measured based on neutrosophic linguistic scale pairwise comparison.Plithogenic operations provide more accurate aggregation result according to contradiction degree between criteria values.The results show that ten of the hospitals are providing efficient service in their emergency department,while the other ten are less efficient.The analysis of the results shows that 58%of private hospitals emergency department is operating efficiently,while the efficient general hospitals represent 38%.
文摘This paper points out that delayed or no supply of software can kill potential benefits associated with new mathematical ideas that have led to development of new mathematics in OR. It also points out that it is a self-created situation by the scientific community. This situation needs attention and should be resolved urgently. Many illustrative examples have been given to justify the claim</span></span><span>.
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.
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.
