Using intermediate and advanced Chinese students as the research subjects,HSK corpus and questionnaire surveys were used to explore the error types in the construction of"X什么(Y)+都+Z."The types of errors c...Using intermediate and advanced Chinese students as the research subjects,HSK corpus and questionnaire surveys were used to explore the error types in the construction of"X什么(Y)+都+Z."The types of errors can be divided into component errors,relationship errors between components,and collocation errors between components and sentences.The main reasons for the errors are the particularity of the construction,the immature development of construction teaching,the negative transfer of students5 mother tongue,as well as the generalization and avoidance of the target language.展开更多
In this paper, we investigate the problem of approximating solutions of the equations of Lipschitzian ψ-strongly accretive operators and fixed points of Lipschitzian ψ-hemicontractive operators by lshikawa type iter...In this paper, we investigate the problem of approximating solutions of the equations of Lipschitzian ψ-strongly accretive operators and fixed points of Lipschitzian ψ-hemicontractive operators by lshikawa type iterative sequences with errors. Our results unify, improve and extend the results obtained previously by several authors including Li and Liu (Acta Math. Sinica 41 (4)(1998), 845-850), and Osilike (Nonlinear Anal. TMA, 36(1)(1999), 1-9), and also answer completely the open problems mentioned by Chidume (J. Math. Anal. Appl. 151 (2)(1990), 453-461).展开更多
An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to swit...An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to switch from bad to good status. A matrix based on error logic is used to express current status u, expectant status u1 and transformation matrix T. It is u, u1, and T that are used to build error matrix equation T (u)= u1. This allows us to find a method whereby bad status “u” changes to good status “u1” by solving the equation. The conversion method that transform from current to expectant status can be obtained from the transformation matrix T. On this basis, this paper proposes a new kind of error matrix equation named “containing-type error matrix equation”. This equation is more suitable for analyzing the realistic question. The method of solving, existence and form of solution for this type of equation have been presented in this paper. This research provides a potential useful new technique for decision analysis.展开更多
Heteroscedasticity and multicollinearity are serious problems when they exist in econometrics data. These problems exist as a result of violating the assumptions of equal variance between the error terms and that of i...Heteroscedasticity and multicollinearity are serious problems when they exist in econometrics data. These problems exist as a result of violating the assumptions of equal variance between the error terms and that of independence between the explanatory variables of the model. With these assumption violations, Ordinary Least Square Estimator</span><span style="font-family:""> </span><span style="font-family:""><span style="font-family:Verdana;">(OLS) will not give best linear unbiased, efficient and consistent estimator. In practice, there are several structures of heteroscedasticity and several methods of heteroscedasticity detection. For better estimation result, best heteroscedasticity detection methods must be determined for any structure of heteroscedasticity in the presence of multicollinearity between the explanatory variables of the model. In this paper we examine the effects of multicollinearity on type I error rates of some methods of heteroscedasticity detection in linear regression model in other to determine the best method of heteroscedasticity detection to use when both problems exist in the model. Nine heteroscedasticity detection methods were considered with seven heteroscedasticity structures. Simulation study was done via a Monte Carlo experiment on a multiple linear regression model with 3 explanatory variables. This experiment was conducted 1000 times with linear model parameters of </span><span style="white-space:nowrap;"><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">0</span></sub><span style="font-family:Verdana;"> = 4 , </span><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">1</span></sub><span style="font-family:Verdana;"> = 0.4 , </span><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;">= 1.5</span></span></span><span style="font-family:""><span style="font-family:Verdana;"> and </span><em style="font-family:""><span style="font-family:Verdana;">β</span><span style="font-family:Verdana;"><sub>3 </sub></span></em><span style="font-family:Verdana;">= 3.6</span><span style="font-family:Verdana;">. </span><span style="font-family:Verdana;">Five (5) </span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">levels of</span><span style="white-space:nowrap;font-family:Verdana;"> </span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">mulicollinearity </span></span><span style="font-family:Verdana;">are </span><span style="font-family:Verdana;">with seven</span><span style="font-family:""> </span><span style="font-family:Verdana;">(7) different sample sizes. The method’s performances were compared with the aids of set confidence interval (C.I</span><span style="font-family:Verdana;">.</span><span style="font-family:Verdana;">) criterion. Results showed that whenever multicollinearity exists in the model with any forms of heteroscedasticity structures, Breusch-Godfrey (BG) test is the best method to determine the existence of heteroscedasticity at all chosen levels of significance.展开更多
When a statistical test of hypothesis for a population mean is performed, we are faced with the possibility of committing a Type II error by not rejecting the null hypothesis when in fact the population mean has chang...When a statistical test of hypothesis for a population mean is performed, we are faced with the possibility of committing a Type II error by not rejecting the null hypothesis when in fact the population mean has changed. We consider this issue and quantify matters in a manner that differs a bit from what is commonly done. In particular, we define the probability distribution function for Type II errors. We then explore some interesting properties that we have not seen mentioned elsewhere for this probability distribution function. Finally, we discuss several Maple procedures that can be used to perform various calculations using the distribution.展开更多
This study aimed to examine the performance of the Siegel-Tukey and Savage tests on data sets with heterogeneous variances. The analysis, considering Normal, Platykurtic, and Skewed distributions and a standard deviat...This study aimed to examine the performance of the Siegel-Tukey and Savage tests on data sets with heterogeneous variances. The analysis, considering Normal, Platykurtic, and Skewed distributions and a standard deviation ratio of 1, was conducted for both small and large sample sizes. For small sample sizes, two main categories were established: equal and different sample sizes. Analyses were performed using Monte Carlo simulations with 20,000 repetitions for each scenario, and the simulations were evaluated using SAS software. For small sample sizes, the I. type error rate of the Siegel-Tukey test generally ranged from 0.045 to 0.055, while the I. type error rate of the Savage test was observed to range from 0.016 to 0.041. Similar trends were observed for Platykurtic and Skewed distributions. In scenarios with different sample sizes, the Savage test generally exhibited lower I. type error rates. For large sample sizes, two main categories were established: equal and different sample sizes. For large sample sizes, the I. type error rate of the Siegel-Tukey test ranged from 0.047 to 0.052, while the I. type error rate of the Savage test ranged from 0.043 to 0.051. In cases of equal sample sizes, both tests generally had lower error rates, with the Savage test providing more consistent results for large sample sizes. In conclusion, it was determined that the Savage test provides lower I. type error rates for small sample sizes and that both tests have similar error rates for large sample sizes. These findings suggest that the Savage test could be a more reliable option when analyzing variance differences.展开更多
In this simulation study, five correlation coefficients, namely, Pearson, Spearman, Kendal Tau, Permutation-based, and Winsorized were compared in terms of Type I error rate and power under different scenarios where t...In this simulation study, five correlation coefficients, namely, Pearson, Spearman, Kendal Tau, Permutation-based, and Winsorized were compared in terms of Type I error rate and power under different scenarios where the underlying distributions of the variables of interest, sample sizes and correlation patterns were varied. Simulation results showed that the Type I error rate and power of Pearson correlation coefficient were negatively affected by the distribution shapes especially for small sample sizes, which was much more pronounced for Spearman Rank and Kendal Tau correlation coefficients especially when sample sizes were small. In general, Permutation-based and Winsorized correlation coefficients are more robust to distribution shapes and correlation patterns, regardless of sample size. In conclusion, when assumptions of Pearson correlation coefficient are not satisfied, Permutation-based and Winsorized correlation coefficients seem to be better alternatives.展开更多
Smartphone-based electrocardiograms(ECGs)are increasingly utilized for monitoring atrial fibrillation(AF)recurrence after catheter ablation(CA),referred to as smartphone AF burden(SMURDEN).The SMURDEN data often exhib...Smartphone-based electrocardiograms(ECGs)are increasingly utilized for monitoring atrial fibrillation(AF)recurrence after catheter ablation(CA),referred to as smartphone AF burden(SMURDEN).The SMURDEN data often exhibit complex patterns of zero AF episodes,which may arise from either true AF-free status(structural zeros)or missed AF episodes due to intermittent monitoring(random zeros).Such a mixture of AF-free and at-risk patients can lead to zero-inflation in the data.The authors propose a novel zero-inflation test for binomial regression models to identify recurrence-free AF populations.Unlike traditional approaches requiring fully specified zero-inflated models,the proposed test utilizes a weighted average of the discrepancies between observed and expected zero proportions,with weights determined by binomial sizes.A closed-form test statistic is developed,and its asymptotic distribution is derived using estimating equations.Simulations demonstrate superior performance over existing methods,and real-world AF monitoring data validate the practical utility of our proposed test.展开更多
Error correction, in recent times, is seen as one of the important teaching processes in L2 （second language） learning, because comprehensible inputs alone is insufficient for acquisition of language. However, few L...Error correction, in recent times, is seen as one of the important teaching processes in L2 （second language） learning, because comprehensible inputs alone is insufficient for acquisition of language. However, few L2 teachers know much about error analysis and how to correct errors in the L2 classroom. Error correction is a very complicated and a thorny issue in L2 teaching and learning. L2 teachers, therefore, need to be armed with ways in which errors can be treated to ensure maximum effect yet with less harm to learners. Identifying learners＇ errors is very important in L2 learning, but how to correct them to give the desired effect is equally important and very challenging to L2 teachers. It is therefore crucial to initiate a study in Ghana to find out how errors are corrected in the Ghanaian English language classroom. This case study used complete observation and semi-structured interview as data collection strategies to identify error correction strategies/types English teachers use in the Ghanaian JHS （Junior High School） classroom and how error correction/treatment can be improved to facilitate English language teaching and learning. The findings of the study showed that explicit error correction technique was the most commonly used followed by recast, elicitation, metalinguistic clues, clarification request, repetition, and cues. It was also found that the causes of the disparity in the use of the various error correction types were inadequate teacher preparation, incompetence in English language, limited knowledge in error correction, caliber of students, and insufficient teaching time. This study identified that the situation can be improved through effective teacher training, in-service training, learner involvement, and effective planning.展开更多
English writing instruction plays an important role in foreign language education. This study aims to explore EFL learners' major writing problems by analyzing the nature and distribution of the writing errors of ...English writing instruction plays an important role in foreign language education. This study aims to explore EFL learners' major writing problems by analyzing the nature and distribution of the writing errors of 98 second-year non-English majors of Xingtai College. The error analysis found that there were four major error types, they were: word choice, verb form, subject missing and verb tense. The author suggested four appropriate instructional strategies for English teachers to help to enhance students' writing proficiency.展开更多
The comparison of dec1inations from the Preliminary Compilation of DS-Pr0grammeStar Positions (PCDS) with those contained in the catalogues observed with meridian circlesof several northern observatories (Belgrade, Ki...The comparison of dec1inations from the Preliminary Compilation of DS-Pr0grammeStar Positions (PCDS) with those contained in the catalogues observed with meridian circlesof several northern observatories (Belgrade, Kiev, Moscow l, Moscow 2, Kazan) shows thesystematic differences depending on the spectral type of stars involved. The effect canprobably be explained by the differences in the atmospheric refraction for different spectraltypes.展开更多
The use of Statistical Hypothesis Testing procedure to determine type I and type II errors was linked to the measurement of sensitivity and specificity in clinical trial test and experimental pathogen detection techni...The use of Statistical Hypothesis Testing procedure to determine type I and type II errors was linked to the measurement of sensitivity and specificity in clinical trial test and experimental pathogen detection techniques. A theoretical analysis of establishing these types of errors was made and compared to determination of False Positive, False Negative, True Positive and True Negative. Experimental laboratory detection methods used to detect Cryptosporidium spp. were used to highlight the relationship between hypothesis testing, sensitivity, specificity and predicted values. The study finds that, sensitivity and specificity for the two laboratory methods used for Cryptosporidium detection were low hence lowering the probability of detecting a “false null hypothesis” for the presence of cryptosporidium in the water samples using either Microscopic or PCR. Nevertheless, both procedures for cryptosporidium detection had higher “true negatives” increasing its probability of failing to reject a “true null hypothesis” with specificity of 1.00 for both Microscopic and PCR laboratory detection methods.展开更多
Csiszar's strong coding theorem for discrete memoryless scarce is generalized to arbitrarily varying source.We also determine the asymptotic error exponent for arbitrarily wrying source.
In the present paper, we study the polynomial approximation of analytic functions of several complex variables. The characterizations of generalized type of analytic functions of several complex variables have been ob...In the present paper, we study the polynomial approximation of analytic functions of several complex variables. The characterizations of generalized type of analytic functions of several complex variables have been obtained in terms of approximation and interpolation errors.展开更多
The reduced-order finite element method （FEM） based on a proper orthogo- nal decomposition （POD） theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general ...The reduced-order finite element method （FEM） based on a proper orthogo- nal decomposition （POD） theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general FEM. It can significantly save mem- ory space and effectively relieve the computing load due to its reconstruction of POD basis functions. Furthermore, the reduced-order finite element （FE） scheme is shown to be un- conditionally stable, and error estimation is derived in detail. Two numerical examples are presented to show the feasibility and effectiveness of the method for time fractional differential equations （FDEs）.展开更多
文摘Using intermediate and advanced Chinese students as the research subjects,HSK corpus and questionnaire surveys were used to explore the error types in the construction of"X什么(Y)+都+Z."The types of errors can be divided into component errors,relationship errors between components,and collocation errors between components and sentences.The main reasons for the errors are the particularity of the construction,the immature development of construction teaching,the negative transfer of students5 mother tongue,as well as the generalization and avoidance of the target language.
基金supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Educations of MOE,P.R.C.the National Natural Science Foundation of P.R.C.No.19801023
文摘In this paper, we investigate the problem of approximating solutions of the equations of Lipschitzian ψ-strongly accretive operators and fixed points of Lipschitzian ψ-hemicontractive operators by lshikawa type iterative sequences with errors. Our results unify, improve and extend the results obtained previously by several authors including Li and Liu (Acta Math. Sinica 41 (4)(1998), 845-850), and Osilike (Nonlinear Anal. TMA, 36(1)(1999), 1-9), and also answer completely the open problems mentioned by Chidume (J. Math. Anal. Appl. 151 (2)(1990), 453-461).
文摘An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to switch from bad to good status. A matrix based on error logic is used to express current status u, expectant status u1 and transformation matrix T. It is u, u1, and T that are used to build error matrix equation T (u)= u1. This allows us to find a method whereby bad status “u” changes to good status “u1” by solving the equation. The conversion method that transform from current to expectant status can be obtained from the transformation matrix T. On this basis, this paper proposes a new kind of error matrix equation named “containing-type error matrix equation”. This equation is more suitable for analyzing the realistic question. The method of solving, existence and form of solution for this type of equation have been presented in this paper. This research provides a potential useful new technique for decision analysis.
文摘Heteroscedasticity and multicollinearity are serious problems when they exist in econometrics data. These problems exist as a result of violating the assumptions of equal variance between the error terms and that of independence between the explanatory variables of the model. With these assumption violations, Ordinary Least Square Estimator</span><span style="font-family:""> </span><span style="font-family:""><span style="font-family:Verdana;">(OLS) will not give best linear unbiased, efficient and consistent estimator. In practice, there are several structures of heteroscedasticity and several methods of heteroscedasticity detection. For better estimation result, best heteroscedasticity detection methods must be determined for any structure of heteroscedasticity in the presence of multicollinearity between the explanatory variables of the model. In this paper we examine the effects of multicollinearity on type I error rates of some methods of heteroscedasticity detection in linear regression model in other to determine the best method of heteroscedasticity detection to use when both problems exist in the model. Nine heteroscedasticity detection methods were considered with seven heteroscedasticity structures. Simulation study was done via a Monte Carlo experiment on a multiple linear regression model with 3 explanatory variables. This experiment was conducted 1000 times with linear model parameters of </span><span style="white-space:nowrap;"><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">0</span></sub><span style="font-family:Verdana;"> = 4 , </span><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">1</span></sub><span style="font-family:Verdana;"> = 0.4 , </span><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;">= 1.5</span></span></span><span style="font-family:""><span style="font-family:Verdana;"> and </span><em style="font-family:""><span style="font-family:Verdana;">β</span><span style="font-family:Verdana;"><sub>3 </sub></span></em><span style="font-family:Verdana;">= 3.6</span><span style="font-family:Verdana;">. </span><span style="font-family:Verdana;">Five (5) </span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">levels of</span><span style="white-space:nowrap;font-family:Verdana;"> </span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">mulicollinearity </span></span><span style="font-family:Verdana;">are </span><span style="font-family:Verdana;">with seven</span><span style="font-family:""> </span><span style="font-family:Verdana;">(7) different sample sizes. The method’s performances were compared with the aids of set confidence interval (C.I</span><span style="font-family:Verdana;">.</span><span style="font-family:Verdana;">) criterion. Results showed that whenever multicollinearity exists in the model with any forms of heteroscedasticity structures, Breusch-Godfrey (BG) test is the best method to determine the existence of heteroscedasticity at all chosen levels of significance.
文摘When a statistical test of hypothesis for a population mean is performed, we are faced with the possibility of committing a Type II error by not rejecting the null hypothesis when in fact the population mean has changed. We consider this issue and quantify matters in a manner that differs a bit from what is commonly done. In particular, we define the probability distribution function for Type II errors. We then explore some interesting properties that we have not seen mentioned elsewhere for this probability distribution function. Finally, we discuss several Maple procedures that can be used to perform various calculations using the distribution.
文摘This study aimed to examine the performance of the Siegel-Tukey and Savage tests on data sets with heterogeneous variances. The analysis, considering Normal, Platykurtic, and Skewed distributions and a standard deviation ratio of 1, was conducted for both small and large sample sizes. For small sample sizes, two main categories were established: equal and different sample sizes. Analyses were performed using Monte Carlo simulations with 20,000 repetitions for each scenario, and the simulations were evaluated using SAS software. For small sample sizes, the I. type error rate of the Siegel-Tukey test generally ranged from 0.045 to 0.055, while the I. type error rate of the Savage test was observed to range from 0.016 to 0.041. Similar trends were observed for Platykurtic and Skewed distributions. In scenarios with different sample sizes, the Savage test generally exhibited lower I. type error rates. For large sample sizes, two main categories were established: equal and different sample sizes. For large sample sizes, the I. type error rate of the Siegel-Tukey test ranged from 0.047 to 0.052, while the I. type error rate of the Savage test ranged from 0.043 to 0.051. In cases of equal sample sizes, both tests generally had lower error rates, with the Savage test providing more consistent results for large sample sizes. In conclusion, it was determined that the Savage test provides lower I. type error rates for small sample sizes and that both tests have similar error rates for large sample sizes. These findings suggest that the Savage test could be a more reliable option when analyzing variance differences.
文摘In this simulation study, five correlation coefficients, namely, Pearson, Spearman, Kendal Tau, Permutation-based, and Winsorized were compared in terms of Type I error rate and power under different scenarios where the underlying distributions of the variables of interest, sample sizes and correlation patterns were varied. Simulation results showed that the Type I error rate and power of Pearson correlation coefficient were negatively affected by the distribution shapes especially for small sample sizes, which was much more pronounced for Spearman Rank and Kendal Tau correlation coefficients especially when sample sizes were small. In general, Permutation-based and Winsorized correlation coefficients are more robust to distribution shapes and correlation patterns, regardless of sample size. In conclusion, when assumptions of Pearson correlation coefficient are not satisfied, Permutation-based and Winsorized correlation coefficients seem to be better alternatives.
基金supported by the Fundamental Research Funds for the Central Universities in UIBE under Grant No.CXTD14-05。
文摘Smartphone-based electrocardiograms(ECGs)are increasingly utilized for monitoring atrial fibrillation(AF)recurrence after catheter ablation(CA),referred to as smartphone AF burden(SMURDEN).The SMURDEN data often exhibit complex patterns of zero AF episodes,which may arise from either true AF-free status(structural zeros)or missed AF episodes due to intermittent monitoring(random zeros).Such a mixture of AF-free and at-risk patients can lead to zero-inflation in the data.The authors propose a novel zero-inflation test for binomial regression models to identify recurrence-free AF populations.Unlike traditional approaches requiring fully specified zero-inflated models,the proposed test utilizes a weighted average of the discrepancies between observed and expected zero proportions,with weights determined by binomial sizes.A closed-form test statistic is developed,and its asymptotic distribution is derived using estimating equations.Simulations demonstrate superior performance over existing methods,and real-world AF monitoring data validate the practical utility of our proposed test.
文摘Error correction, in recent times, is seen as one of the important teaching processes in L2 （second language） learning, because comprehensible inputs alone is insufficient for acquisition of language. However, few L2 teachers know much about error analysis and how to correct errors in the L2 classroom. Error correction is a very complicated and a thorny issue in L2 teaching and learning. L2 teachers, therefore, need to be armed with ways in which errors can be treated to ensure maximum effect yet with less harm to learners. Identifying learners＇ errors is very important in L2 learning, but how to correct them to give the desired effect is equally important and very challenging to L2 teachers. It is therefore crucial to initiate a study in Ghana to find out how errors are corrected in the Ghanaian English language classroom. This case study used complete observation and semi-structured interview as data collection strategies to identify error correction strategies/types English teachers use in the Ghanaian JHS （Junior High School） classroom and how error correction/treatment can be improved to facilitate English language teaching and learning. The findings of the study showed that explicit error correction technique was the most commonly used followed by recast, elicitation, metalinguistic clues, clarification request, repetition, and cues. It was also found that the causes of the disparity in the use of the various error correction types were inadequate teacher preparation, incompetence in English language, limited knowledge in error correction, caliber of students, and insufficient teaching time. This study identified that the situation can be improved through effective teacher training, in-service training, learner involvement, and effective planning.
文摘English writing instruction plays an important role in foreign language education. This study aims to explore EFL learners' major writing problems by analyzing the nature and distribution of the writing errors of 98 second-year non-English majors of Xingtai College. The error analysis found that there were four major error types, they were: word choice, verb form, subject missing and verb tense. The author suggested four appropriate instructional strategies for English teachers to help to enhance students' writing proficiency.
文摘The comparison of dec1inations from the Preliminary Compilation of DS-Pr0grammeStar Positions (PCDS) with those contained in the catalogues observed with meridian circlesof several northern observatories (Belgrade, Kiev, Moscow l, Moscow 2, Kazan) shows thesystematic differences depending on the spectral type of stars involved. The effect canprobably be explained by the differences in the atmospheric refraction for different spectraltypes.
文摘The use of Statistical Hypothesis Testing procedure to determine type I and type II errors was linked to the measurement of sensitivity and specificity in clinical trial test and experimental pathogen detection techniques. A theoretical analysis of establishing these types of errors was made and compared to determination of False Positive, False Negative, True Positive and True Negative. Experimental laboratory detection methods used to detect Cryptosporidium spp. were used to highlight the relationship between hypothesis testing, sensitivity, specificity and predicted values. The study finds that, sensitivity and specificity for the two laboratory methods used for Cryptosporidium detection were low hence lowering the probability of detecting a “false null hypothesis” for the presence of cryptosporidium in the water samples using either Microscopic or PCR. Nevertheless, both procedures for cryptosporidium detection had higher “true negatives” increasing its probability of failing to reject a “true null hypothesis” with specificity of 1.00 for both Microscopic and PCR laboratory detection methods.
文摘Csiszar's strong coding theorem for discrete memoryless scarce is generalized to arbitrarily varying source.We also determine the asymptotic error exponent for arbitrarily wrying source.
文摘In the present paper, we study the polynomial approximation of analytic functions of several complex variables. The characterizations of generalized type of analytic functions of several complex variables have been obtained in terms of approximation and interpolation errors.
基金Project supported by the National Natural Science Foundation of China(Nos.11361035 and 11301258)the Natural Science Foundation of Inner Mongolia(Nos.2012MS0106 and 2012MS0108)
文摘The reduced-order finite element method （FEM） based on a proper orthogo- nal decomposition （POD） theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general FEM. It can significantly save mem- ory space and effectively relieve the computing load due to its reconstruction of POD basis functions. Furthermore, the reduced-order finite element （FE） scheme is shown to be un- conditionally stable, and error estimation is derived in detail. Two numerical examples are presented to show the feasibility and effectiveness of the method for time fractional differential equations （FDEs）.
