The aim of this paper is to present a generalization of the Shapiro-Wilk W-test or Shapiro-Francia W'-test for application to two or more variables. It consists of calculating all the unweighted linear combination...The aim of this paper is to present a generalization of the Shapiro-Wilk W-test or Shapiro-Francia W'-test for application to two or more variables. It consists of calculating all the unweighted linear combinations of the variables and their W- or W'-statistics with the Royston’s log-transformation and standardization, z<sub>ln(1-W)</sub> or z<sub>ln(1-W</sub><sub>'</sub><sub>)</sub>. Because the calculation of the probability of z<sub>ln(1-W)</sub> or z<sub>ln(1-W</sub><sub>'</sub><sub>)</sub> is to the right tail, negative values are truncated to 0 before doing their sum of squares. Independence in the sequence of these half-normally distributed values is required for the test statistic to follow a chi-square distribution. This assumption is checked using the robust Ljung-Box test. One degree of freedom is lost for each cancelled value. Defined the new test with its two variants (Q-test or Q'-test), 50 random samples with 4 variables and 20 participants were generated, 20% following a multivariate normal distribution and 80% deviating from this distribution. The new test was compared with Mardia’s, runs, and Royston’s tests. Central tendency differences in type II error and statistical power were tested using the Friedman’s test and pairwise comparisons using the Wilcoxon’s test. Differences in the frequency of successes in statistical decision making were compared using the Cochran’s Q test and pairwise comparisons using the McNemar’s test. Sensitivity, specificity and efficiency proportions were compared using the McNemar’s Z test. The generated 50 samples were classified into five ordered categories of deviation from multivariate normality, the correlation between this variable and p-value of each test was calculated using the Spearman’s coefficient and these correlations were compared. Family-wise error rate corrections were applied. The new test and the Royston’s test were the best choices, with a very slight advantage Q-test over Q'-test. Based on these promising results, further study and use of this new sensitive, specific and effective test are suggested.展开更多
Background: Mental health has been impaired and at risk due to the worldwide COVID-19 pandemic. The consequences due to confinement impacted every scenario, which directly influenced the daily routine of nurse student...Background: Mental health has been impaired and at risk due to the worldwide COVID-19 pandemic. The consequences due to confinement impacted every scenario, which directly influenced the daily routine of nurse students;in each setting students faced stressors that trigger fear, anxiety and others, since being in confinement learning of topics moved to the home, laboratory practices in hospitals were cancelled leaving the room that is uncertain up to their return to in-person activities. It is important to highlight the need for innovation and strengthening of theoretical-pedagogic aspects centered at the student’s context as a human being with their own needs and problems, who will interact with others in the continuous process of health-illness. Objective: the aim was to identify the stressors in the nurse students’ formation in the new normality post-COVID-19. Methods: Qualitative and phenomenological research with 27 participants aged 20 - 25 years, nurse students of a public university. The information collection was through four focal groups of 6-7 members each, data analysis was done according to Miles & Huberman after signed informed consent of each participant, and authorized by the chairperson of the Nurse’ career. Results: Category 1, Cumulative stressors with sub-categories 1.1 Uncertainty, 1.2 Isolation, 1.3 Invisibility, 1.4 Mockery, 1.5 Exclusion. Category 2, Expectancy states with sub-categories 2.1 Low self-esteem, 2.2 Insecurity, 2.3 Anxiety, 2.4 Depression, 2.5 Temporary leave, 2.6 Search for authenticity. Category 3, Internalization processes with sub-categories 3.1 Social rejection, 3.2 Self-censorship, 3.3 Discrediting, 3.4 Disempowerment. Category 4, Academic aspects affected with sub-categories 4.1 Deficient studying habits, 4.2 Deficient assimilations of knowledge, 4.3 Archived knowledge in the computer, 4.4 Absence of practice in previous semesters. Conclusion: Once identified the stressors in nurse students in the new normality post-COVID-19, it will allow the creation of settings that help in getting confidence for students, i.e., a safe surrounding promotes the development of abilities and competencies during formation, as well as recommendations of teachers in the classroom and laboratories that contribute to filling space that students perceive as empty, and to intensifying the companionship in clinical settings where students perceive most aggressiveness.展开更多
This paper based on the essay [1]. studies in case that replicated observations are available in some experimental points, the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptoti...This paper based on the essay [1]. studies in case that replicated observations are available in some experimental points, the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptotic normality is established.展开更多
Let F be a family of functions meromorphic in a domain D, let m, n k , k be three positive integers and b be a finite nonzero complex number. Suppose that, (1) for eachf∈F, all zeros of f have multiplicities at least...Let F be a family of functions meromorphic in a domain D, let m, n k , k be three positive integers and b be a finite nonzero complex number. Suppose that, (1) for eachf∈F, all zeros of f have multiplicities at least k ; (2) for each pair of functions f, g ∈F,P(f)H(f) and P(g)H(g) share b, where P(f) and H(f) were defined as (1.1) and (1.2) and nk ≥ max 1≤i≤k-1 {n i }; (3) m ≥ 2 or nk ≥ 2, k ≥ 2, then F is normal in D.展开更多
In this study, to power comparison test, different univariate normality testing procedures are compared by using new algorithm. Different univariate and multivariate test are also analyzed here. And also review effici...In this study, to power comparison test, different univariate normality testing procedures are compared by using new algorithm. Different univariate and multivariate test are also analyzed here. And also review efficient algorithm for calculating the size corrected power of the test which can be used to compare the efficiency of the test. Also to test the randomness of generated random numbers. For this purpose, 1000 data sets with combinations of sample size n = 10, 20, 25, 30, 40, 50, 100, 200, 300 were generated from uniform distribution and tested by using different tests for randomness. The assessment of normality using statistical tests is sensitive to the sample size. Observed that with the increase of n, overall powers are increased but Shapiro Wilk (SW) test, Shapiro Francia (SF) test and Andeson Darling (AD) test are the most powerful test among other tests. Cramer-Von-Mises (CVM) test performs better than Pearson chi-square, Lilliefors test has better power than Jarque Bera (JB) Test. Jarque Bera (JB) Test is less powerful test among other tests.展开更多
The objective of this study is to propose the Parametric Seven-Number Summary (PSNS) as a significance test for normality and to verify its accuracy and power in comparison with two well-known tests, such as Royston’...The objective of this study is to propose the Parametric Seven-Number Summary (PSNS) as a significance test for normality and to verify its accuracy and power in comparison with two well-known tests, such as Royston’s W test and D’Agostino-Belanger-D’Agostino K-squared test. An experiment with 384 conditions was simulated. The conditions were generated by crossing 24 sample sizes and 16 types of continuous distributions: one normal and 15 non-normal. The percentage of success in maintaining the null hypothesis of normality against normal samples and in rejecting the null hypothesis against non-normal samples (accuracy) was calculated. In addition, the type II error against normal samples and the statistical power against normal samples were computed. Comparisons of percentage and means were performed using Cochran’s Q-test, Friedman’s test, and repeated measures analysis of variance. With sample sizes of 150 or greater, high accuracy and mean power or type II error (≥0.70 and ≥0.80, respectively) were achieved. All three normality tests were similarly accurate;however, the PSNS-based test showed lower mean power than K-squared and W tests, especially against non-normal samples of symmetrical-platykurtic distributions, such as the uniform, semicircle, and arcsine distributions. It is concluded that the PSNS-based omnibus test is accurate and powerful for testing normality with samples of at least 150 observations.展开更多
Based on the asymptotic spectral distribution of Wigner matrices,a new normality test method is proposed via reforming the white noise sequence.In this work,the asymptotic cumulative distribution function(CDF)of eigen...Based on the asymptotic spectral distribution of Wigner matrices,a new normality test method is proposed via reforming the white noise sequence.In this work,the asymptotic cumulative distribution function(CDF)of eigenvalues of the Wigner matrix is deduced.A numerical Kullback-Leibler divergence of the empirical spectral CDF based on test samples from the deduced asymptotic CDF is established,which is treated as the test statistic.For validating the superiority of our proposed normality test,we apply the method to weak 8PSK signal detection in the single-input single-output(SISO) system and the single-input multiple-output(SIMO)system.By comparing with other common normality tests and the existing signal detection methods,simulation results show that the proposed method is superior and robust.展开更多
In this article,two results concerning the periodic points and normality of meromorphic functions are obtained:(i)the exact lower bound for the numbers of periodic points of rational functions with multiple fixed poin...In this article,two results concerning the periodic points and normality of meromorphic functions are obtained:(i)the exact lower bound for the numbers of periodic points of rational functions with multiple fixed points and zeros is proven by let ting R(z)be a nonpolynomial rational function,and if all zeros and poles of R(z)—z are multiple,then Rk(z)has at least k+1 fixed points in the complex plane for each integer k≥2;(ii)a complete solution to the problem of normality of meromorphic functions with periodic points is given by let ting F be a family of meromorphic functions in a domain D,and let ting k≥2 be a positive integer.If,for each f∈F,all zeros and poles of f(z)-z are multiple,and its iteration fk has at most k distinct fixed points in D,then F is normal in D.Examples show that all of the conditions are the best possible.展开更多
The study of fuzzy sets is specifically designed to mathematically represent uncertainty and vagueness by assigning values of membership to objects that belong to a particular set. This notion has been broadly extende...The study of fuzzy sets is specifically designed to mathematically represent uncertainty and vagueness by assigning values of membership to objects that belong to a particular set. This notion has been broadly extended to other areas of topology where various topological concepts have been shown to hold on fuzzy topology. Some notions naturally extend to closure spaces without requiring a lot of modification of the underlying topological ideas. This work investigates the variants of normality on fuzzy isotone spaces.展开更多
This paper is to investigate the convergence rate of asymptotic normality of frequency polygon estimation for density function under mixing random fields, which include strongly mixing condition and some weaker mixing...This paper is to investigate the convergence rate of asymptotic normality of frequency polygon estimation for density function under mixing random fields, which include strongly mixing condition and some weaker mixing conditions. A Berry-Esseen bound of frequency polygon is established and the convergence rates of asymptotic normality are derived. In particularly, for the optimal bin width , it is showed that the convergence rate of asymptotic normality reaches to ?when mixing coefficient tends to zero exponentially fast.展开更多
Background: New normality is uncertain in every sense, specifically in education and for many health disciplines. Being immersed in COVID-19 pandemics brought serious consequences for mental health, and is very import...Background: New normality is uncertain in every sense, specifically in education and for many health disciplines. Being immersed in COVID-19 pandemics brought serious consequences for mental health, and is very important to handle emotions and stress coping strategies to obtain positive outcomes. Objective: To identify the most frequent emotions, as well as the adaptation strategies to the new normality faced by the students of nursing. Methods: Qualitative and phenomenological research, with the participation of 20 students from both genders in the middle term of nursing career at Faculty of Higher Studies Iztacala, National Autonomous University of Mexico, from August to November 2021. Information was collected from a focal group for ten sessions;analysis was according to De Souza Minayo, and there was a signed informed consent letter from participants. Results: Four categories emerged with sub-categories. Category I Maximized emotions. Sub-categories: 1) Frustration, anger, disappointment;2) Personal disappointment, hopelessness, uncertainty;3) Depression. Category II Support elements close to the new normality. Sub-categories: 1) Family communication;2) Education for mental and physical health. Category III Stressing situations that exceeded the student. Sub-category: Disease in lovely ones. Category IV Stress coping strategies. Sub-categories: 1) Friends and relatives that help to get better;2) Family values. Informers pointed out to have maximized emotion, and having no self-control on its negative outcomes occurred;in addition, the situation was not favorable at home with several losses of loved ones, as well as a poor economy that threatened students to give up studies. Conclusion: Emotions facing this new normality are very important and should be attended to, their proper handling will result in a new learning of socio-emotional abilities, stress coping strategies development, better adaptation and informed decisions taken.展开更多
The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper in...The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality;thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.展开更多
We studied the normality criterion for families of meromorphic functions which related to One-way sharing set, and obtain two normal criterions, which improve the previous results.
The normal direction to the normal direction to a line in Minkowski geometries generally does not give the original line. We show that in lp geometries with p>1?repeatedly finding the normal line through the origin...The normal direction to the normal direction to a line in Minkowski geometries generally does not give the original line. We show that in lp geometries with p>1?repeatedly finding the normal line through the origin gives sequences of lines that monotonically approach specific lines of symmetry of the unit circle. Which lines of symmetry that are approached depends upon the value of p and the slope of the initial line.展开更多
In this article,we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values,which improves some earlier related results.
Let κ be a positive integer and F be a family of meromorphic functions in a domain D such that for each f ∈ F, all poles of f are of multiplicity at least 2,and all zeros of f are of multiplicity at least κ + 1. L...Let κ be a positive integer and F be a family of meromorphic functions in a domain D such that for each f ∈ F, all poles of f are of multiplicity at least 2,and all zeros of f are of multiplicity at least κ + 1. Let α and b be two distinct finite complex numbers. If for each f ∈ F, all zeros of f^(κ)-α are of multiplicity at least 2,and for each pair of functions f, g ∈ F, f^(κ)and g^(κ) share b in D, then F is normal in D.展开更多
A bounded linear operator T on a complex Hilbert space H is called n-normal if T^(*)T^(n)=T^(n)T^(*).By Fuglede’s theorem T is n-normal if and only if T^(n)is normal.Let k,n∈N.Then a bounded linear operator T is sai...A bounded linear operator T on a complex Hilbert space H is called n-normal if T^(*)T^(n)=T^(n)T^(*).By Fuglede’s theorem T is n-normal if and only if T^(n)is normal.Let k,n∈N.Then a bounded linear operator T is said to be of typeⅠk-quasi-n-normal if T^(*k){T^(*)T^(n)-T^(n)T^(*)}T^(k)=0,and T is said to be of typeⅡk-quasi-n-normal if T^(*k){T^(*n)T^(n)-T^(n)T^(*n)}T^(k)=0.1-quasi-n-normal is called quasi-n-normal.We shall show that(1)typeⅠquasi-2-normal and typeⅡquasi-2-normal are different classes;(2)the intersection of the class of typeⅠquasi-2-normal and the class of typeⅡquasi-2-normal is equal to the class of 2-normal.We also give some examples of type I k-quasi-n-normal and typeⅡk-quasi-n-normal.We also show that Weyl’s theorem holds for this class of operators and every k-quasi-n-normal operator has a non trivial invariant subspace.展开更多
Currently,there is no solid criterion for judging the quality of the estimators in factor analysis.This paper presents a new evaluation method for exploratory factor analysis that pinpoints an appropriate number of fa...Currently,there is no solid criterion for judging the quality of the estimators in factor analysis.This paper presents a new evaluation method for exploratory factor analysis that pinpoints an appropriate number of factors along with the best method for factor extraction.The proposed technique consists of two steps:testing the normality of the residuals from the fitted model via the Shapiro-Wilk test and using an empirical quantified index to judge the quality of the factor model.Examples are presented to demonstrate how the method is implemented and to verify its effectiveness.展开更多
The M-estimate of parameters in the errors-in-variables (EV) model Y =xτβ0+∈,X =x+u ((∈,uτ)τ is a (p+1)-dimensional spherical error, Coy[(∈, uτ)τ] =σ2Ip+1)being considered. The M-estimate βn,, of β0 under ...The M-estimate of parameters in the errors-in-variables (EV) model Y =xτβ0+∈,X =x+u ((∈,uτ)τ is a (p+1)-dimensional spherical error, Coy[(∈, uτ)τ] =σ2Ip+1)being considered. The M-estimate βn,, of β0 under a general ρ(·) function and the estimateof σ2 are given, the strong consistency and asymptotic normality of βn as well as are obtained. The conditions for the ρ(·) function in this paper are similar to that of linearexpression of M-estimates in the linear regression model.展开更多
In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=...In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=1 ZiZ'i, the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.展开更多
文摘The aim of this paper is to present a generalization of the Shapiro-Wilk W-test or Shapiro-Francia W'-test for application to two or more variables. It consists of calculating all the unweighted linear combinations of the variables and their W- or W'-statistics with the Royston’s log-transformation and standardization, z<sub>ln(1-W)</sub> or z<sub>ln(1-W</sub><sub>'</sub><sub>)</sub>. Because the calculation of the probability of z<sub>ln(1-W)</sub> or z<sub>ln(1-W</sub><sub>'</sub><sub>)</sub> is to the right tail, negative values are truncated to 0 before doing their sum of squares. Independence in the sequence of these half-normally distributed values is required for the test statistic to follow a chi-square distribution. This assumption is checked using the robust Ljung-Box test. One degree of freedom is lost for each cancelled value. Defined the new test with its two variants (Q-test or Q'-test), 50 random samples with 4 variables and 20 participants were generated, 20% following a multivariate normal distribution and 80% deviating from this distribution. The new test was compared with Mardia’s, runs, and Royston’s tests. Central tendency differences in type II error and statistical power were tested using the Friedman’s test and pairwise comparisons using the Wilcoxon’s test. Differences in the frequency of successes in statistical decision making were compared using the Cochran’s Q test and pairwise comparisons using the McNemar’s test. Sensitivity, specificity and efficiency proportions were compared using the McNemar’s Z test. The generated 50 samples were classified into five ordered categories of deviation from multivariate normality, the correlation between this variable and p-value of each test was calculated using the Spearman’s coefficient and these correlations were compared. Family-wise error rate corrections were applied. The new test and the Royston’s test were the best choices, with a very slight advantage Q-test over Q'-test. Based on these promising results, further study and use of this new sensitive, specific and effective test are suggested.
文摘Background: Mental health has been impaired and at risk due to the worldwide COVID-19 pandemic. The consequences due to confinement impacted every scenario, which directly influenced the daily routine of nurse students;in each setting students faced stressors that trigger fear, anxiety and others, since being in confinement learning of topics moved to the home, laboratory practices in hospitals were cancelled leaving the room that is uncertain up to their return to in-person activities. It is important to highlight the need for innovation and strengthening of theoretical-pedagogic aspects centered at the student’s context as a human being with their own needs and problems, who will interact with others in the continuous process of health-illness. Objective: the aim was to identify the stressors in the nurse students’ formation in the new normality post-COVID-19. Methods: Qualitative and phenomenological research with 27 participants aged 20 - 25 years, nurse students of a public university. The information collection was through four focal groups of 6-7 members each, data analysis was done according to Miles & Huberman after signed informed consent of each participant, and authorized by the chairperson of the Nurse’ career. Results: Category 1, Cumulative stressors with sub-categories 1.1 Uncertainty, 1.2 Isolation, 1.3 Invisibility, 1.4 Mockery, 1.5 Exclusion. Category 2, Expectancy states with sub-categories 2.1 Low self-esteem, 2.2 Insecurity, 2.3 Anxiety, 2.4 Depression, 2.5 Temporary leave, 2.6 Search for authenticity. Category 3, Internalization processes with sub-categories 3.1 Social rejection, 3.2 Self-censorship, 3.3 Discrediting, 3.4 Disempowerment. Category 4, Academic aspects affected with sub-categories 4.1 Deficient studying habits, 4.2 Deficient assimilations of knowledge, 4.3 Archived knowledge in the computer, 4.4 Absence of practice in previous semesters. Conclusion: Once identified the stressors in nurse students in the new normality post-COVID-19, it will allow the creation of settings that help in getting confidence for students, i.e., a safe surrounding promotes the development of abilities and competencies during formation, as well as recommendations of teachers in the classroom and laboratories that contribute to filling space that students perceive as empty, and to intensifying the companionship in clinical settings where students perceive most aggressiveness.
基金the National Natural Science Foundation of China (Grant No. 19631040)
文摘This paper based on the essay [1]. studies in case that replicated observations are available in some experimental points, the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptotic normality is established.
基金Foundation item： Supported by the NNSF of China（11071083） Supported by the National Natural Science Foundation of Tianyuan Foundation（11126267）
文摘Let F be a family of functions meromorphic in a domain D, let m, n k , k be three positive integers and b be a finite nonzero complex number. Suppose that, (1) for eachf∈F, all zeros of f have multiplicities at least k ; (2) for each pair of functions f, g ∈F,P(f)H(f) and P(g)H(g) share b, where P(f) and H(f) were defined as (1.1) and (1.2) and nk ≥ max 1≤i≤k-1 {n i }; (3) m ≥ 2 or nk ≥ 2, k ≥ 2, then F is normal in D.
文摘In this study, to power comparison test, different univariate normality testing procedures are compared by using new algorithm. Different univariate and multivariate test are also analyzed here. And also review efficient algorithm for calculating the size corrected power of the test which can be used to compare the efficiency of the test. Also to test the randomness of generated random numbers. For this purpose, 1000 data sets with combinations of sample size n = 10, 20, 25, 30, 40, 50, 100, 200, 300 were generated from uniform distribution and tested by using different tests for randomness. The assessment of normality using statistical tests is sensitive to the sample size. Observed that with the increase of n, overall powers are increased but Shapiro Wilk (SW) test, Shapiro Francia (SF) test and Andeson Darling (AD) test are the most powerful test among other tests. Cramer-Von-Mises (CVM) test performs better than Pearson chi-square, Lilliefors test has better power than Jarque Bera (JB) Test. Jarque Bera (JB) Test is less powerful test among other tests.
文摘The objective of this study is to propose the Parametric Seven-Number Summary (PSNS) as a significance test for normality and to verify its accuracy and power in comparison with two well-known tests, such as Royston’s W test and D’Agostino-Belanger-D’Agostino K-squared test. An experiment with 384 conditions was simulated. The conditions were generated by crossing 24 sample sizes and 16 types of continuous distributions: one normal and 15 non-normal. The percentage of success in maintaining the null hypothesis of normality against normal samples and in rejecting the null hypothesis against non-normal samples (accuracy) was calculated. In addition, the type II error against normal samples and the statistical power against normal samples were computed. Comparisons of percentage and means were performed using Cochran’s Q-test, Friedman’s test, and repeated measures analysis of variance. With sample sizes of 150 or greater, high accuracy and mean power or type II error (≥0.70 and ≥0.80, respectively) were achieved. All three normality tests were similarly accurate;however, the PSNS-based test showed lower mean power than K-squared and W tests, especially against non-normal samples of symmetrical-platykurtic distributions, such as the uniform, semicircle, and arcsine distributions. It is concluded that the PSNS-based omnibus test is accurate and powerful for testing normality with samples of at least 150 observations.
基金Supported by the National Natural Science Foundation of China under Grant No 61371170the Fundamental Research Funds for the Central Universities under Grant Nos NP2015404 and NS2016038+1 种基金the Aeronautical Science Foundation of China under Grant No 20152052028the Funding of Jiangsu Innovation Program for Graduate Education under Grant No KYLX15_0282
文摘Based on the asymptotic spectral distribution of Wigner matrices,a new normality test method is proposed via reforming the white noise sequence.In this work,the asymptotic cumulative distribution function(CDF)of eigenvalues of the Wigner matrix is deduced.A numerical Kullback-Leibler divergence of the empirical spectral CDF based on test samples from the deduced asymptotic CDF is established,which is treated as the test statistic.For validating the superiority of our proposed normality test,we apply the method to weak 8PSK signal detection in the single-input single-output(SISO) system and the single-input multiple-output(SIMO)system.By comparing with other common normality tests and the existing signal detection methods,simulation results show that the proposed method is superior and robust.
基金supported by the NNSF of China(11901119,11701188)The third author was supported by the NNSF of China(11688101).
文摘In this article,two results concerning the periodic points and normality of meromorphic functions are obtained:(i)the exact lower bound for the numbers of periodic points of rational functions with multiple fixed points and zeros is proven by let ting R(z)be a nonpolynomial rational function,and if all zeros and poles of R(z)—z are multiple,then Rk(z)has at least k+1 fixed points in the complex plane for each integer k≥2;(ii)a complete solution to the problem of normality of meromorphic functions with periodic points is given by let ting F be a family of meromorphic functions in a domain D,and let ting k≥2 be a positive integer.If,for each f∈F,all zeros and poles of f(z)-z are multiple,and its iteration fk has at most k distinct fixed points in D,then F is normal in D.Examples show that all of the conditions are the best possible.
文摘The study of fuzzy sets is specifically designed to mathematically represent uncertainty and vagueness by assigning values of membership to objects that belong to a particular set. This notion has been broadly extended to other areas of topology where various topological concepts have been shown to hold on fuzzy topology. Some notions naturally extend to closure spaces without requiring a lot of modification of the underlying topological ideas. This work investigates the variants of normality on fuzzy isotone spaces.
文摘This paper is to investigate the convergence rate of asymptotic normality of frequency polygon estimation for density function under mixing random fields, which include strongly mixing condition and some weaker mixing conditions. A Berry-Esseen bound of frequency polygon is established and the convergence rates of asymptotic normality are derived. In particularly, for the optimal bin width , it is showed that the convergence rate of asymptotic normality reaches to ?when mixing coefficient tends to zero exponentially fast.
文摘Background: New normality is uncertain in every sense, specifically in education and for many health disciplines. Being immersed in COVID-19 pandemics brought serious consequences for mental health, and is very important to handle emotions and stress coping strategies to obtain positive outcomes. Objective: To identify the most frequent emotions, as well as the adaptation strategies to the new normality faced by the students of nursing. Methods: Qualitative and phenomenological research, with the participation of 20 students from both genders in the middle term of nursing career at Faculty of Higher Studies Iztacala, National Autonomous University of Mexico, from August to November 2021. Information was collected from a focal group for ten sessions;analysis was according to De Souza Minayo, and there was a signed informed consent letter from participants. Results: Four categories emerged with sub-categories. Category I Maximized emotions. Sub-categories: 1) Frustration, anger, disappointment;2) Personal disappointment, hopelessness, uncertainty;3) Depression. Category II Support elements close to the new normality. Sub-categories: 1) Family communication;2) Education for mental and physical health. Category III Stressing situations that exceeded the student. Sub-category: Disease in lovely ones. Category IV Stress coping strategies. Sub-categories: 1) Friends and relatives that help to get better;2) Family values. Informers pointed out to have maximized emotion, and having no self-control on its negative outcomes occurred;in addition, the situation was not favorable at home with several losses of loved ones, as well as a poor economy that threatened students to give up studies. Conclusion: Emotions facing this new normality are very important and should be attended to, their proper handling will result in a new learning of socio-emotional abilities, stress coping strategies development, better adaptation and informed decisions taken.
文摘The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality;thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.
文摘We studied the normality criterion for families of meromorphic functions which related to One-way sharing set, and obtain two normal criterions, which improve the previous results.
文摘The normal direction to the normal direction to a line in Minkowski geometries generally does not give the original line. We show that in lp geometries with p>1?repeatedly finding the normal line through the origin gives sequences of lines that monotonically approach specific lines of symmetry of the unit circle. Which lines of symmetry that are approached depends upon the value of p and the slope of the initial line.
文摘In this article,we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values,which improves some earlier related results.
基金The NSF(11301076)of Chinathe NSF(2014J01004) of Fujian Province
文摘Let κ be a positive integer and F be a family of meromorphic functions in a domain D such that for each f ∈ F, all poles of f are of multiplicity at least 2,and all zeros of f are of multiplicity at least κ + 1. Let α and b be two distinct finite complex numbers. If for each f ∈ F, all zeros of f^(κ)-α are of multiplicity at least 2,and for each pair of functions f, g ∈ F, f^(κ)and g^(κ) share b in D, then F is normal in D.
文摘A bounded linear operator T on a complex Hilbert space H is called n-normal if T^(*)T^(n)=T^(n)T^(*).By Fuglede’s theorem T is n-normal if and only if T^(n)is normal.Let k,n∈N.Then a bounded linear operator T is said to be of typeⅠk-quasi-n-normal if T^(*k){T^(*)T^(n)-T^(n)T^(*)}T^(k)=0,and T is said to be of typeⅡk-quasi-n-normal if T^(*k){T^(*n)T^(n)-T^(n)T^(*n)}T^(k)=0.1-quasi-n-normal is called quasi-n-normal.We shall show that(1)typeⅠquasi-2-normal and typeⅡquasi-2-normal are different classes;(2)the intersection of the class of typeⅠquasi-2-normal and the class of typeⅡquasi-2-normal is equal to the class of 2-normal.We also give some examples of type I k-quasi-n-normal and typeⅡk-quasi-n-normal.We also show that Weyl’s theorem holds for this class of operators and every k-quasi-n-normal operator has a non trivial invariant subspace.
基金Supported by the National Basic Research Program of China(2010CB126200)the National Natural Science Foundation of China(30370914)。
文摘Currently,there is no solid criterion for judging the quality of the estimators in factor analysis.This paper presents a new evaluation method for exploratory factor analysis that pinpoints an appropriate number of factors along with the best method for factor extraction.The proposed technique consists of two steps:testing the normality of the residuals from the fitted model via the Shapiro-Wilk test and using an empirical quantified index to judge the quality of the factor model.Examples are presented to demonstrate how the method is implemented and to verify its effectiveness.
文摘The M-estimate of parameters in the errors-in-variables (EV) model Y =xτβ0+∈,X =x+u ((∈,uτ)τ is a (p+1)-dimensional spherical error, Coy[(∈, uτ)τ] =σ2Ip+1)being considered. The M-estimate βn,, of β0 under a general ρ(·) function and the estimateof σ2 are given, the strong consistency and asymptotic normality of βn as well as are obtained. The conditions for the ρ(·) function in this paper are similar to that of linearexpression of M-estimates in the linear regression model.
基金supported by the National Natural Science Foundation of China(Grant No.10471136)Ph.D.Program Foundation of Ministry of Education of China and Special Foundation of the Chinese Academy of Science and USTC.
文摘In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=1 ZiZ'i, the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.
