Probability Hypothesis Density (PHD) filtering approach has shown its advantages in tracking time varying number of targets even when there are noise,clutter and misdetection. For linear Gaussian Mixture (GM) system,P...Probability Hypothesis Density (PHD) filtering approach has shown its advantages in tracking time varying number of targets even when there are noise,clutter and misdetection. For linear Gaussian Mixture (GM) system,PHD filter has a closed form recursion (GMPHD). But PHD filter cannot estimate the trajectories of multi-target because it only provides identity-free estimate of target states. Existing data association methods still remain a big challenge mostly because they are com-putationally expensive. In this paper,we proposed a new data association algorithm using GMPHD filter,which significantly alleviated the heavy computing load and performed multi-target trajectory tracking effectively in the meantime.展开更多
Affective filter hypothesis is one of Krashen's five hypotheses on Second Language Acquisition (SLA), and it states that a number of affective variables play a very important role in Second Language Acquisition. B...Affective filter hypothesis is one of Krashen's five hypotheses on Second Language Acquisition (SLA), and it states that a number of affective variables play a very important role in Second Language Acquisition. Based on the introduction of affective filter hypothesis, this paper will analyze the significance and shortcomings of this hypothesis.展开更多
An important problem with null hypothesis significance testing, as it is normally performed, is that it is uninformative to reject a point null hypothesis [1]. A way around this problem is to use range null hypotheses...An important problem with null hypothesis significance testing, as it is normally performed, is that it is uninformative to reject a point null hypothesis [1]. A way around this problem is to use range null hypotheses [2]. But the use of range null hypotheses also is problematic. Aside from the usual issues of whether null hypothesis significance tests can be justified at all, there is an issue that is specific to range null hypotheses. It is not straightforward how to calculate the probability of the data given a range null hypothesis. The traditional way is to use the single point that maximizes the obtained p-value. The Bayesian alternative is to propose a prior probability distribution and integrate across it. Because frequentists and Bayesians disagree about a variety of issues, especially those pertaining to whether it is permissible to assign probabilities to hypotheses, and what gets lost in the shuffle is that the two camps actually come to different answers for the probability of the data given a range null hypothesis. Because the probability of the data given the hypothesis is a precursor for both camps, for drawing conclusions about hypotheses, different values for this probability for the different camps is crucial but seldom acknowledged. The goal of the present article is to bring out the problem in a manner accessible to researchers without strong mathematical or statistical backgrounds.展开更多
The particle Probability Hypotheses Density (particle-PHD) filter is a tractable approach for Random Finite Set (RFS) Bayes estimation, but the particle-PHD filter can not directly derive the target track. Most existi...The particle Probability Hypotheses Density (particle-PHD) filter is a tractable approach for Random Finite Set (RFS) Bayes estimation, but the particle-PHD filter can not directly derive the target track. Most existing approaches combine the data association step to solve this problem. This paper proposes an algorithm which does not need the association step. Our basic ideal is based on the clustering algorithm of Finite Mixture Models (FMM). The intensity distribution is first derived by the particle-PHD filter, and then the clustering algorithm is applied to estimate the multitarget states and tracks jointly. The clustering process includes two steps: the prediction and update. The key to the proposed algorithm is to use the prediction as the initial points and the convergent points as the es- timates. Besides, Expectation-Maximization (EM) and Markov Chain Monte Carlo (MCMC) ap- proaches are used for the FMM parameter estimation.展开更多
The Learning method of inductive logic programming evaluates the the quality of inductive hypotheses commonlyby how well the hypotheses cover training examples extensionally. Ths kind of evalution will be completely i...The Learning method of inductive logic programming evaluates the the quality of inductive hypotheses commonlyby how well the hypotheses cover training examples extensionally. Ths kind of evalution will be completely inapplica-ble to the situation where there are non-simple or noise examples. Based on Limited Negative semantics, This paperextends induction of simple examples to that of generalized ones and presents 3 criteria on accepting inductive hypothe-ses in order to fit for different goals of induction. The relation between inductive hypotheses and background knowledgeis also established in this Paper. The conclusions in this paper are helpful to implement learning algorithms and to ex-tend application fields of ILP.展开更多
Melanization is harmful to the lightness of galvanized steel surface and also reduces the bonding force between a paint coat and the steel sheet. Experimental results showed that the hypothesis of Zn-Pb codeposition d...Melanization is harmful to the lightness of galvanized steel surface and also reduces the bonding force between a paint coat and the steel sheet. Experimental results showed that the hypothesis of Zn-Pb codeposition does not hold true, while the fact that PbSO4 micelles in sulfate bath settle on the coating surface support the second hypothesis. The authors come to the conclusions that (1) Any measure to eliminate PbSO4 micelles before or after passivation of the coating will prevent melanization; (2) PbSO4 micelles adsorbed on the surface of passivated film promote the growth of oxygen-deficient Zn oxide and result in the generation of melanization.展开更多
In testing statistical hypotheses, as in other statistical problems, we may be confronted with fuzzy concepts. This paper deals with the problem of testing hypotheses, when the hypotheses are fuzzy and the data are cr...In testing statistical hypotheses, as in other statistical problems, we may be confronted with fuzzy concepts. This paper deals with the problem of testing hypotheses, when the hypotheses are fuzzy and the data are crisp. We first give new definitions for notion of mass (density) probability function with fuzzy parameter, probability of type I and type II errors and then state and prove the sequential probability ratio test, on the basis of these new errors, for testing fuzzy hypotheses. Numerical examples are also provided to illustrate the approach.展开更多
The original Probability Hypothesis Density (PHD) filter is a tractable algorithm for Multi-Target Tracking (MTT) in Random Finite Set (RFS) frameworks. In this paper,we introduce a novel Evidence PHD (E-PHD) filter w...The original Probability Hypothesis Density (PHD) filter is a tractable algorithm for Multi-Target Tracking (MTT) in Random Finite Set (RFS) frameworks. In this paper,we introduce a novel Evidence PHD (E-PHD) filter which combines the Dempster-Shafer (DS) evidence theory. The proposed filter can deal with the uncertain information,thus it forms target track. We mainly discusses the E-PHD filter under the condition of linear Gaussian. Research shows that the E-PHD filter has an analytic form of Evidence Gaussian Mixture PHD (E-GMPHD). The final experiment shows that the proposed E-GMPHD filter can derive the target identity,state,and number effectively.展开更多
This paper proposes a novel method based on statistical tests of hypotheses, such as F-ratio and Welch’s t-tests. The input query image is examined whether it is a textured or structured. If it is structured, the sha...This paper proposes a novel method based on statistical tests of hypotheses, such as F-ratio and Welch’s t-tests. The input query image is examined whether it is a textured or structured. If it is structured, the shapes are segregated into various regions according to its nature;otherwise, it is treated as textured image and considered the entire image as it is for the experiment. The aforesaid tests are applied regions-wise. First, the F-ratio test is applied, if the images pass the test, then it is proceeded to test the spectrum of energy, i.e. means of the two images. If the images pass both tests, then it is concluded that the two images are the same or similar. Otherwise, they differ. Since the proposed system is distribution-based, it is invariant for rotation and scaling. Also, the system facilitates the user to fix the number of images to be retrieved, because the user can fix the level of significance according to their requirements. These are the main advantages of the proposed system.展开更多
This paper we study a consistent criterion for checking Hypotheses. Given definition of consistent criterion for checking hypotheses for family probability measures which were defined by Z. Zerakidze （see 5）. We pro...This paper we study a consistent criterion for checking Hypotheses. Given definition of consistent criterion for checking hypotheses for family probability measures which were defined by Z. Zerakidze （see 5）. We prove the necessary and sufficient conditions are obtained for the existence of consistent criteria of hypotheses. For example we clearly build of a consistent criteria for checking hypotheses.展开更多
The paper discusses the generalization of constrained Bayesian method （CBM） for arbitrary loss functions and its application for testing the directional hypotheses. The problem is stated in terms of false and tru...The paper discusses the generalization of constrained Bayesian method （CBM） for arbitrary loss functions and its application for testing the directional hypotheses. The problem is stated in terms of false and true discovery rates. One more criterion of estimation of directional hypotheses tests quality, the Type III errors rate, is considered. The ratio among discovery rates and the Type III errors rate in CBM is considered. The advantage of CBM in comparison with Bayes and frequentist methods is theoretically proved and demonstrated by an example.展开更多
Hypotheses of humanity is the logical premise and foundation of institution design and perfect. ＂Political man＂ had boosted the sprout of ancient democracy polity, ＂economic man＂ has accelerated the development of...Hypotheses of humanity is the logical premise and foundation of institution design and perfect. ＂Political man＂ had boosted the sprout of ancient democracy polity, ＂economic man＂ has accelerated the development of market economy in immediate and modern times, ＂free man＂ described the blueprint of future society, and ＂harmonious man＂ will promote the construction of harmonious society and the development of management to conducting oneself so as to serve others. The article explains the theory headstream, abstract ways, basic intension and sustainability effect to the hypotheses of＂harmonious man＂.展开更多
The Krashen's second language acquisition theory have two important assumptions: input hypothesis and the affective filter hypothesis. They can guide and inspire vocational teaching, because they start from the st...The Krashen's second language acquisition theory have two important assumptions: input hypothesis and the affective filter hypothesis. They can guide and inspire vocational teaching, because they start from the student's learning situation, guide teachers to adjust their teaching methods, and provide better service for teaching and learning. This paper mainly analyzes the Krashen's input hypothesis and the affective filter hypothesis'enlightenment to the vocational English teaching.展开更多
Two hypotheses of modern warming are considered:natural and anthropogenic.The probabilities of each of them are compared.It is proved that the hypothesis of natural warming is much more likely than the hypothesi...Two hypotheses of modern warming are considered:natural and anthropogenic.The probabilities of each of them are compared.It is proved that the hypothesis of natural warming is much more likely than the hypothesis of anthropogenic warming.It is shown that the displacement of the Sun from the center of mass of the solar system directly affects the temperature of the surface atmosphere in the synoptic regions of Eurasia.This result corresponds to the model of E.P.Borysenkov with variations of the solar constant or,equivalently,with variations of the Bond albedo.展开更多
This article explores the association between salivary uric acid(UA)and periodontitis,systematically analyzing its dual roles and research progress.Studies indicate that UA acts as a primary antioxidant in saliva unde...This article explores the association between salivary uric acid(UA)and periodontitis,systematically analyzing its dual roles and research progress.Studies indicate that UA acts as a primary antioxidant in saliva under physiological conditions(accounting for 70%),protecting periodontal tissues by scavenging reactive oxygen species.However,when gum disease becomes severe,UA can switch roles and fuel inflammation,worsening tissue damage.Lorente et al’s research found an independent inverse correlation between salivary UA levels and periodontitis severity(odds ratio=6.14,P=0.001),establishing 111 nmol/mL as a diagnostic threshold(area under the curve=66%).Nevertheless,limitations include sample heterogeneity and failure to distinguish between gingivitis and periodontitis.Mechanistically,three hypotheses are proposed:The Antioxidant Depletion Hypothesis(UA oxidation consumption leading to feedback loops),the Microbial Metabolic Hijacking Hypothesis(pathogens utilizing UA as a carbon source to disrupt redox balance),and the Epithelial Barrier Dysfunction Hypothesis(UA deficiency causing downregulation of tight junction proteins).Future research should prioritize longitudinal cohorts to validate predictive value,integrate multi-omics to explore dysregulated signatures,and develop UA supplementation or targeted antioxidant therapies.This study provides novel insights into periodontitis diagnosis and mechanisms,advancing the application of salivary biomarkers in precision periodontics.展开更多
The conventional method for testing hypotheses is to find an exact or asymptotic distributionof a test statistic. But when the model is complex and the sample size is small, difficulty often arises. Thispaper aims to ...The conventional method for testing hypotheses is to find an exact or asymptotic distributionof a test statistic. But when the model is complex and the sample size is small, difficulty often arises. Thispaper aims to present a method for finding maximum probability with the help of EM algorithm. For any fixedsample size, this method can be used not only to obtain an accurate test but also to check the real level ofa test which is build by large sample theory. Especially, while doing this, one needs neither the accurate norasymptotic distribution of the test statistic. So the method is easily performed and is especially useful for small samples.展开更多
Suppose that X has density f(x,θ)=exp(θx-ψ(θ)} (with respect to some measure v),where θ∈(θ,θ),∞≤θ≤+∞.Consider the problem of testing the hypothesis θ≤θ0 against θ≥θ1 for some given θ0 and θ1 (θ&...Suppose that X has density f(x,θ)=exp(θx-ψ(θ)} (with respect to some measure v),where θ∈(θ,θ),∞≤θ≤+∞.Consider the problem of testing the hypothesis θ≤θ0 against θ≥θ1 for some given θ0 and θ1 (θ<θ0<θ1<θ).A class of truncated sequential tests is introduced with type Ⅰ and type Ⅱ error probabilities not exceeding a and β,respectively.The expected sample sizes of these tests are shown to be asymptotically minimal for all θ as α+β↓0展开更多
The thin fluid film was assumed to consist of a number of spherical fluid molecular groups and the attractive forces of molecular group pairs were calculated by the derived equation according to the three Hamaker homo...The thin fluid film was assumed to consist of a number of spherical fluid molecular groups and the attractive forces of molecular group pairs were calculated by the derived equation according to the three Hamaker homogeneous material hypotheses. Regarding each molecular group as a dynamics individual, the simulation method for the shearing motion of multilayer fluid molecular groups, which was initiated by two moving walls, was proposed based on the Verlet velocity iterative algorithm. The simulations reveal that the velocities of fluid molecular groups change about their respective mean velocities within a narrow range in steady state. It is also found that the velocity slips occur at the wall boundary and in a certain number of fluid film layers close to the wall. Because the dimension of molecular group and the number of group layers are not restricted, the hypothetical thickness of fluid film model can be enlarged from nanometer to micron by using the proposed simulation method.展开更多
基金Supported by the National Natural Science Foundation of China (No.60772154)the President Foundation of Graduate University of Chinese Academy of Sciences (No.085102GN00)
文摘Probability Hypothesis Density (PHD) filtering approach has shown its advantages in tracking time varying number of targets even when there are noise,clutter and misdetection. For linear Gaussian Mixture (GM) system,PHD filter has a closed form recursion (GMPHD). But PHD filter cannot estimate the trajectories of multi-target because it only provides identity-free estimate of target states. Existing data association methods still remain a big challenge mostly because they are com-putationally expensive. In this paper,we proposed a new data association algorithm using GMPHD filter,which significantly alleviated the heavy computing load and performed multi-target trajectory tracking effectively in the meantime.
文摘Affective filter hypothesis is one of Krashen's five hypotheses on Second Language Acquisition (SLA), and it states that a number of affective variables play a very important role in Second Language Acquisition. Based on the introduction of affective filter hypothesis, this paper will analyze the significance and shortcomings of this hypothesis.
文摘An important problem with null hypothesis significance testing, as it is normally performed, is that it is uninformative to reject a point null hypothesis [1]. A way around this problem is to use range null hypotheses [2]. But the use of range null hypotheses also is problematic. Aside from the usual issues of whether null hypothesis significance tests can be justified at all, there is an issue that is specific to range null hypotheses. It is not straightforward how to calculate the probability of the data given a range null hypothesis. The traditional way is to use the single point that maximizes the obtained p-value. The Bayesian alternative is to propose a prior probability distribution and integrate across it. Because frequentists and Bayesians disagree about a variety of issues, especially those pertaining to whether it is permissible to assign probabilities to hypotheses, and what gets lost in the shuffle is that the two camps actually come to different answers for the probability of the data given a range null hypothesis. Because the probability of the data given the hypothesis is a precursor for both camps, for drawing conclusions about hypotheses, different values for this probability for the different camps is crucial but seldom acknowledged. The goal of the present article is to bring out the problem in a manner accessible to researchers without strong mathematical or statistical backgrounds.
基金Supported by the National Key Fundamental Research & Development Program of China (2007CB11006)the Zhejiang Natural Science Foundation (R106745, Y1080422)
文摘The particle Probability Hypotheses Density (particle-PHD) filter is a tractable approach for Random Finite Set (RFS) Bayes estimation, but the particle-PHD filter can not directly derive the target track. Most existing approaches combine the data association step to solve this problem. This paper proposes an algorithm which does not need the association step. Our basic ideal is based on the clustering algorithm of Finite Mixture Models (FMM). The intensity distribution is first derived by the particle-PHD filter, and then the clustering algorithm is applied to estimate the multitarget states and tracks jointly. The clustering process includes two steps: the prediction and update. The key to the proposed algorithm is to use the prediction as the initial points and the convergent points as the es- timates. Besides, Expectation-Maximization (EM) and Markov Chain Monte Carlo (MCMC) ap- proaches are used for the FMM parameter estimation.
文摘The Learning method of inductive logic programming evaluates the the quality of inductive hypotheses commonlyby how well the hypotheses cover training examples extensionally. Ths kind of evalution will be completely inapplica-ble to the situation where there are non-simple or noise examples. Based on Limited Negative semantics, This paperextends induction of simple examples to that of generalized ones and presents 3 criteria on accepting inductive hypothe-ses in order to fit for different goals of induction. The relation between inductive hypotheses and background knowledgeis also established in this Paper. The conclusions in this paper are helpful to implement learning algorithms and to ex-tend application fields of ILP.
基金Tlle work was financially supported by ShanghaiBaoshan Steel Company.
文摘Melanization is harmful to the lightness of galvanized steel surface and also reduces the bonding force between a paint coat and the steel sheet. Experimental results showed that the hypothesis of Zn-Pb codeposition does not hold true, while the fact that PbSO4 micelles in sulfate bath settle on the coating surface support the second hypothesis. The authors come to the conclusions that (1) Any measure to eliminate PbSO4 micelles before or after passivation of the coating will prevent melanization; (2) PbSO4 micelles adsorbed on the surface of passivated film promote the growth of oxygen-deficient Zn oxide and result in the generation of melanization.
文摘In testing statistical hypotheses, as in other statistical problems, we may be confronted with fuzzy concepts. This paper deals with the problem of testing hypotheses, when the hypotheses are fuzzy and the data are crisp. We first give new definitions for notion of mass (density) probability function with fuzzy parameter, probability of type I and type II errors and then state and prove the sequential probability ratio test, on the basis of these new errors, for testing fuzzy hypotheses. Numerical examples are also provided to illustrate the approach.
基金Supports in part by the NSFC (No. 60772006, 60874105)the ZJNSF(Y1080422, R106745)NCET (08- 0345)
文摘The original Probability Hypothesis Density (PHD) filter is a tractable algorithm for Multi-Target Tracking (MTT) in Random Finite Set (RFS) frameworks. In this paper,we introduce a novel Evidence PHD (E-PHD) filter which combines the Dempster-Shafer (DS) evidence theory. The proposed filter can deal with the uncertain information,thus it forms target track. We mainly discusses the E-PHD filter under the condition of linear Gaussian. Research shows that the E-PHD filter has an analytic form of Evidence Gaussian Mixture PHD (E-GMPHD). The final experiment shows that the proposed E-GMPHD filter can derive the target identity,state,and number effectively.
文摘This paper proposes a novel method based on statistical tests of hypotheses, such as F-ratio and Welch’s t-tests. The input query image is examined whether it is a textured or structured. If it is structured, the shapes are segregated into various regions according to its nature;otherwise, it is treated as textured image and considered the entire image as it is for the experiment. The aforesaid tests are applied regions-wise. First, the F-ratio test is applied, if the images pass the test, then it is proceeded to test the spectrum of energy, i.e. means of the two images. If the images pass both tests, then it is concluded that the two images are the same or similar. Otherwise, they differ. Since the proposed system is distribution-based, it is invariant for rotation and scaling. Also, the system facilitates the user to fix the number of images to be retrieved, because the user can fix the level of significance according to their requirements. These are the main advantages of the proposed system.
文摘This paper we study a consistent criterion for checking Hypotheses. Given definition of consistent criterion for checking hypotheses for family probability measures which were defined by Z. Zerakidze （see 5）. We prove the necessary and sufficient conditions are obtained for the existence of consistent criteria of hypotheses. For example we clearly build of a consistent criteria for checking hypotheses.
文摘The paper discusses the generalization of constrained Bayesian method （CBM） for arbitrary loss functions and its application for testing the directional hypotheses. The problem is stated in terms of false and true discovery rates. One more criterion of estimation of directional hypotheses tests quality, the Type III errors rate, is considered. The ratio among discovery rates and the Type III errors rate in CBM is considered. The advantage of CBM in comparison with Bayes and frequentist methods is theoretically proved and demonstrated by an example.
文摘Hypotheses of humanity is the logical premise and foundation of institution design and perfect. ＂Political man＂ had boosted the sprout of ancient democracy polity, ＂economic man＂ has accelerated the development of market economy in immediate and modern times, ＂free man＂ described the blueprint of future society, and ＂harmonious man＂ will promote the construction of harmonious society and the development of management to conducting oneself so as to serve others. The article explains the theory headstream, abstract ways, basic intension and sustainability effect to the hypotheses of＂harmonious man＂.
文摘The Krashen's second language acquisition theory have two important assumptions: input hypothesis and the affective filter hypothesis. They can guide and inspire vocational teaching, because they start from the student's learning situation, guide teachers to adjust their teaching methods, and provide better service for teaching and learning. This paper mainly analyzes the Krashen's input hypothesis and the affective filter hypothesis'enlightenment to the vocational English teaching.
文摘Two hypotheses of modern warming are considered:natural and anthropogenic.The probabilities of each of them are compared.It is proved that the hypothesis of natural warming is much more likely than the hypothesis of anthropogenic warming.It is shown that the displacement of the Sun from the center of mass of the solar system directly affects the temperature of the surface atmosphere in the synoptic regions of Eurasia.This result corresponds to the model of E.P.Borysenkov with variations of the solar constant or,equivalently,with variations of the Bond albedo.
文摘This article explores the association between salivary uric acid(UA)and periodontitis,systematically analyzing its dual roles and research progress.Studies indicate that UA acts as a primary antioxidant in saliva under physiological conditions(accounting for 70%),protecting periodontal tissues by scavenging reactive oxygen species.However,when gum disease becomes severe,UA can switch roles and fuel inflammation,worsening tissue damage.Lorente et al’s research found an independent inverse correlation between salivary UA levels and periodontitis severity(odds ratio=6.14,P=0.001),establishing 111 nmol/mL as a diagnostic threshold(area under the curve=66%).Nevertheless,limitations include sample heterogeneity and failure to distinguish between gingivitis and periodontitis.Mechanistically,three hypotheses are proposed:The Antioxidant Depletion Hypothesis(UA oxidation consumption leading to feedback loops),the Microbial Metabolic Hijacking Hypothesis(pathogens utilizing UA as a carbon source to disrupt redox balance),and the Epithelial Barrier Dysfunction Hypothesis(UA deficiency causing downregulation of tight junction proteins).Future research should prioritize longitudinal cohorts to validate predictive value,integrate multi-omics to explore dysregulated signatures,and develop UA supplementation or targeted antioxidant therapies.This study provides novel insights into periodontitis diagnosis and mechanisms,advancing the application of salivary biomarkers in precision periodontics.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10071004).
文摘The conventional method for testing hypotheses is to find an exact or asymptotic distributionof a test statistic. But when the model is complex and the sample size is small, difficulty often arises. Thispaper aims to present a method for finding maximum probability with the help of EM algorithm. For any fixedsample size, this method can be used not only to obtain an accurate test but also to check the real level ofa test which is build by large sample theory. Especially, while doing this, one needs neither the accurate norasymptotic distribution of the test statistic. So the method is easily performed and is especially useful for small samples.
基金Project supported by the National Natural Science Foundation of China and a Hong Kong UPGC-RGC grant.
文摘Suppose that X has density f(x,θ)=exp(θx-ψ(θ)} (with respect to some measure v),where θ∈(θ,θ),∞≤θ≤+∞.Consider the problem of testing the hypothesis θ≤θ0 against θ≥θ1 for some given θ0 and θ1 (θ<θ0<θ1<θ).A class of truncated sequential tests is introduced with type Ⅰ and type Ⅱ error probabilities not exceeding a and β,respectively.The expected sample sizes of these tests are shown to be asymptotically minimal for all θ as α+β↓0
基金supported by the National Natural Science Foundation of China (Grant No. 10872088)the Doctoral Foundation of Ministry of Education of China (Grant Nos. 20070291004 and 20093221120009)the Academic Discipline Construction Fund of Nanjing University of Technology
文摘The thin fluid film was assumed to consist of a number of spherical fluid molecular groups and the attractive forces of molecular group pairs were calculated by the derived equation according to the three Hamaker homogeneous material hypotheses. Regarding each molecular group as a dynamics individual, the simulation method for the shearing motion of multilayer fluid molecular groups, which was initiated by two moving walls, was proposed based on the Verlet velocity iterative algorithm. The simulations reveal that the velocities of fluid molecular groups change about their respective mean velocities within a narrow range in steady state. It is also found that the velocity slips occur at the wall boundary and in a certain number of fluid film layers close to the wall. Because the dimension of molecular group and the number of group layers are not restricted, the hypothetical thickness of fluid film model can be enlarged from nanometer to micron by using the proposed simulation method.
