Urban green innovation(UGI)is essential to environmental protection,ecological conservation,and high quality economic growth.Using green patents,our study assessed the level of UGI of 287 Chinese cities at and above t...Urban green innovation(UGI)is essential to environmental protection,ecological conservation,and high quality economic growth.Using green patents,our study assessed the level of UGI of 287 Chinese cities at and above the prefecture level.Then,using the Dagum Gini coefficient,kernel density estimation(KDE),and con‐vergence models,we examined regional differences,distribution dynamics,and convergence of UGI across China.The study’s findings are as follows:(1)Overall,regional differences in UGI tended to narrow,and the main contributor to these differences was the difference between economic zones.(2)KDE showed that the level of UGI was rising,which was polarized within each economic zone.(3)The national UGI in economic zones other than the Northeast and Middle Yellow River Economic Zones featured significantσconvergence,while each economic zone showed absolute and conditionalβconvergence.展开更多
In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order ...In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.展开更多
Random variables and uncertain variables are respectively used to model randomness and uncertainty. While randomness and uncertainty always coexist in a same complex system. As an evolution of random variables and unc...Random variables and uncertain variables are respectively used to model randomness and uncertainty. While randomness and uncertainty always coexist in a same complex system. As an evolution of random variables and uncertain variables, uncertain random variable is introduced as a tool to deal with complex phenomena including randomness and uncertainty simultaneously. For uncertain random variables, a basic and important topic is to discuss the convergence of its sequence.Specifically, this paper focuses on studying the convergence in distribution for a sequence of uncertain random sequences with different chance distributions where random variables are not independent.And the result of this paper is a generalization of the existing literature. Relations among convergence theorems are studied. Furthermore, the theorems are explained by several examples.展开更多
Considering the time-sequence characteristic and randomness of load and natural resources, ?this paper studies on the distributed generation (DG) impacts on voltage limit violation probability of distribution lines. T...Considering the time-sequence characteristic and randomness of load and natural resources, ?this paper studies on the distributed generation (DG) impacts on voltage limit violation probability of distribution lines. The time-sequence characteristic and randomness of load, wind and photovoltaic (PV) generation are analyzed;the indices and risk levels of voltage limit violation probability of node and distribution line are proposed. By using probabilistic load flow based on semi-invariant method, the impact degrees of voltage limit violation are calculated with different distributed power penetration levels, different seasons, different time periods, different allocation ratio between the wind power and PV power. Voltage limit violation laws of distribution line, which are concluded by IEEE33 bus system simulation, are very helpful to guide the voltage?regulation of distribution line including distributed generation.展开更多
We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in ...We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.展开更多
We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it f...We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it for synchronized or randomly activated implementation,which may create deadlocks in practice.In sharp contrast,we propose a fully asynchronous push-pull gradient(APPG) algorithm,where each node updates without waiting for any other node by using possibly delayed information from neighbors.Then,we construct two novel augmented networks to analyze asynchrony and delays,and quantify its convergence rate from the worst-case point of view.Particularly,all nodes of APPG converge to the same optimal solution at a linear rate of O(λ^(k)) if local functions have Lipschitz-continuous gradients and their sum satisfies the Polyak-?ojasiewicz condition(convexity is not required),where λ ∈(0,1) is explicitly given and the virtual counter k increases by one when any node updates.Finally,the advantage of APPG over the synchronous counterpart and its linear speedup efficiency are numerically validated via a logistic regression problem.展开更多
Recently, Kyriakoussis and Vamvakari [1] have established a q-analogue of the Stirling type for q-constant which have lead them to the proof of the pointwise convergence of the q-binomial distribution to a Stieltjes-W...Recently, Kyriakoussis and Vamvakari [1] have established a q-analogue of the Stirling type for q-constant which have lead them to the proof of the pointwise convergence of the q-binomial distribution to a Stieltjes-Wigert continuous distribution. In the present article, assuming a sequence q(n) of n with q(n)→1 as n→∞, the study of the affect of this assumption to the q(n)-analogue of the Stirling type and to the asymptotic behaviour of the q(n)-Binomial distribution is presented. Specifically, a q(n) analogue of the Stirling type is provided which leads to the proof of deformed Gaussian limiting behaviour for the q(n)-Binomial distribution. Further, figures using the program MAPLE are presented, indicating the accuracy of the established distribution convergence even for moderate values of n.展开更多
In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of nor...In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).展开更多
Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hilde...Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hildebrand's work in [1], the authors investigate the a.s. convergence of Sigma (infinity)(n=1) X-n under a hypothesis that Sigma (infinity)(n=1) rho (X-n, c(n)) = infinity whener Sigma (infinity)(n=1) c(n) diverges, where the notation rho (X,c) denotes the Levy distance between the random variable X and the constant c. The principal result of this paper shows that the hypothesis is the condition under which the convergence of F-n(x(0)) with the limit value 0 < L-0 < 1, together with the essential convergence of Sigma (infinity)(n=1) X-n, is both sufficient and necessary in order for the series Sigma (infinity)(n=1) X-n to a.s. coverage. Moreover, if the essential convergence of Sigma (infinity)(n=1) X-n is strengthened to limsup(n=infinity) P(\S-n\ < K) = 1 for some K > 0, the hypothesis is already equivalent to the a.s. convergence of Sigma (infinity)(n=1) X-n. Here they have not only founded a very general limit theorem, but improved the related result in Hildebrand([1]) as well.展开更多
Analytical method for the distributions of axial-load and stress is based on elastic assumption, but the threaded connections are often in plastic deformation stage in practice. Meanwhile the strain in the threaded co...Analytical method for the distributions of axial-load and stress is based on elastic assumption, but the threaded connections are often in plastic deformation stage in practice. Meanwhile the strain in the threaded connection is difficult to measure. So it is necessary to study the reliable numerical method. At present neither the convergence analysis of the computational results nor the elastic-plastic analysis in the loading-unloading process are studied. In this paper, von Mises plasticity and kinematic hardening model is used to describe the material response. A new convergence criterion for nonlinear finite element analysis of the loading-unloading process is proposed. An axisymmetric finite element model according to the proposed convergence criterion is developed and used to analyze the distributions of axial-load and stress. It can be conclude that the stress distribution analysis is more dependent on the mesh density than the axial-load distribution analysis. The stress distribution result indicates that with increasing of applied load, the engaged threads close to the nut-bearing surface become plastic firstly. The axial-load distribution result reveals that the load percentage carried by single thread depends on the position of thread and load intensity. When the load is relatively small, the applied load is mainly carried by the engaged threads near the nut-bearing surface, when the load is larger, the differences of percentages for all threads become small. The proposed convergence analyzing procedure is applicable for other nonlinear analyses. The obtained distributions of axial-load and stress can be a reference of engineering application.展开更多
In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is as...In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.展开更多
With the widespread application of distributed systems, many problems need to be solved urgently. How to design distributed optimization strategies has become a research hotspot. This article focuses on the solution r...With the widespread application of distributed systems, many problems need to be solved urgently. How to design distributed optimization strategies has become a research hotspot. This article focuses on the solution rate of the distributed convex optimization algorithm. Each agent in the network has its own convex cost function. We consider a gradient-based distributed method and use a push-pull gradient algorithm to minimize the total cost function. Inspired by the current multi-agent consensus cooperation protocol for distributed convex optimization algorithm, a distributed convex optimization algorithm with finite time convergence is proposed and studied. In the end, based on a fixed undirected distributed network topology, a fast convergent distributed cooperative learning method based on a linear parameterized neural network is proposed, which is different from the existing distributed convex optimization algorithms that can achieve exponential convergence. The algorithm can achieve finite-time convergence. The convergence of the algorithm can be guaranteed by the Lyapunov method. The corresponding simulation examples also show the effectiveness of the algorithm intuitively. Compared with other algorithms, this algorithm is competitive.展开更多
Background:To assess the influence of different spectral energy distribution on accommodation,vergence and reading performance.Methods:A Randomized experimental study was conducted after getting the approval of the Et...Background:To assess the influence of different spectral energy distribution on accommodation,vergence and reading performance.Methods:A Randomized experimental study was conducted after getting the approval of the Ethical Committee of University of Hyderabad.Forty participants with an age group of 18-21 years was integrated,out of which 50%was male and 50%was female.Subjects with emmetropia and no history of ocular pathology were included in the study.Near point of accommodation(NPA)&near point of convergence(NPC)was measured with the help of royal air force(RAF)ruler followed by near visual task of a readability passage.Results:A statistically significant result was obtained when reading rate,reading speed and NPC was compared among different spectral distribution of light(P<0.001)except NPA(P=0.43).Post hoc analysis showed a significant difference(P<0.001)when tungsten was compared with fluorescent light(FLOU),compact fluorescent light(CFL),and light emitting diode(LED)for reading rate,reading speed and NPC.But there is no noteworthy difference exist when fluorescent was compared with CFL for reading rate(P=0.530)&reading speed(P=0.595).Similarly,LED also showed no considerable difference when compared with CFL(P=0.682)and fluorescent(P=0.490)for NPC.When NPA was assessed within the group LED showed insignificant difference with CFL(P=0.205)and fluorescent(P=0.275)similar like fluorescent and tungsten(P=0.482).Conclusions:This study concluded that reading performance(reading rate and reading speed)and NPC has a significance change if we use inappropriate lighting during visual tasks.It will cause visual fatigue and strain after sustained near work.In addition,tungsten spectral energy influences the convergence which can also show an impact on reading and near visual tasks because of its brightness and miosis.Prolonged reading and working under this lighting can cause convergence disorders and visual fatigue.展开更多
Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = （ai1,…, aiM） be random vectors with {aij} being i.i.d, random variables. Define XN =（x1,…, xk） and SN =XNXN^T,where xi=ai...Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = （ai1,…, aiM） be random vectors with {aij} being i.i.d, random variables. Define XN =（x1,…, xk） and SN =XNXN^T,where xi=ai×si and si=1/√N（v1i,…, vN,i）^T. The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.展开更多
In this paper, we give a necessary and sufficient condition of sequence of nodes, such that, the error of trigonometric interpolation for analytic function converges to 0.
The Boltzmann equilibrium distribution is an important rigorous tool for determining entropy, since this function cannot be measured, but only calculated in accordance with Boltzmann＇s law. On the basis of the commen...The Boltzmann equilibrium distribution is an important rigorous tool for determining entropy, since this function cannot be measured, but only calculated in accordance with Boltzmann＇s law. On the basis of the commensuration coefficient of discrete and continuous similarly-named distributions developed by the authors, the article analyses the statistical sum in the Boltzmann distribution to the commensuration with the improper integral of the similarly-named function in the full range of the term of series of the statistical sum at the different combination of the temperature and the step of variation （quantum） of the particle energy. The convergence of series based on the Cauchy, Maclaurin criteria and the equal commensuration of series and improper integral of the similarly-named function in each unit interval of variation of series and similarly-named function were estab- lished. The obtained formulas for the commensuration coefficient and statistical sum were analyzed, and a general expres- sion for the total and residual statistical sums, which can be calculated with any given accuracy, is found. Given a direct calculation formula for the Boltzmann distribution, taking into account the values of the improper integral and commensuration coefficient. To determine the entropy from the new expression for the Boltzmann distribution in the form of a series, the conver- gence of the similarly-named improper integral is established. However, the commensuration coefficient of integral and series in each unit interval turns out to be dependent on the number of the term of series and therefore cannot be used to determine the sum of series through the improper integral. In this case, the entropy can be calculated with a given accuracy with a corresponding quantity of the term of series n at a fixed value of the statistical sum. The given accuracy of the statistical sum turns out to be mathematically identical to the fraction of particles with an energy exceeding a given level of the energy barrier equal to the activation energy in the Arrhenius equation. The prospect of development of the proposed method for expressing the Boltzmann distribution and entropy is to establish the relationship between the magnitude of the energy quantum Ae and the properties of the system-forming particles.展开更多
Due to the development of digital transformation,intelligent algorithms are getting more and more attention.The whale optimization algorithm(WOA)is one of swarm intelligence optimization algorithms and is widely used ...Due to the development of digital transformation,intelligent algorithms are getting more and more attention.The whale optimization algorithm(WOA)is one of swarm intelligence optimization algorithms and is widely used to solve practical engineering optimization problems.However,with the increased dimensions,higher requirements are put forward for algorithm performance.The double population whale optimization algorithm with distributed collaboration and reverse learning ability(DCRWOA)is proposed to solve the slow convergence speed and unstable search accuracy of the WOA algorithm in optimization problems.In the DCRWOA algorithm,the novel double population search strategy is constructed.Meanwhile,the reverse learning strategy is adopted in the population search process to help individuals quickly jump out of the non-ideal search area.Numerical experi-ments are carried out using standard test functions with different dimensions(10,50,100,200).The optimization case of shield construction parameters is also used to test the practical application performance of the proposed algo-rithm.The results show that the DCRWOA algorithm has higher optimization accuracy and stability,and the convergence speed is significantly improved.Therefore,the proposed DCRWOA algorithm provides a better method for solving practical optimization problems.展开更多
The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbe...The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.展开更多
基金supported by the National Natural Science Foun‐dation of China[Grant No.72004124,72373084]Shandong Provin‐cial Education Department,China[Grant No.2022RW-064]+1 种基金Depart‐ment of Science and Technology of Shandong Province,China[Grant No.2022RKY04002]Humanities and Social Sciences Project of Shan‐dong Province,China[Grant No.2022-YYJJ-32].
文摘Urban green innovation(UGI)is essential to environmental protection,ecological conservation,and high quality economic growth.Using green patents,our study assessed the level of UGI of 287 Chinese cities at and above the prefecture level.Then,using the Dagum Gini coefficient,kernel density estimation(KDE),and con‐vergence models,we examined regional differences,distribution dynamics,and convergence of UGI across China.The study’s findings are as follows:(1)Overall,regional differences in UGI tended to narrow,and the main contributor to these differences was the difference between economic zones.(2)KDE showed that the level of UGI was rising,which was polarized within each economic zone.(3)The national UGI in economic zones other than the Northeast and Middle Yellow River Economic Zones featured significantσconvergence,while each economic zone showed absolute and conditionalβconvergence.
文摘In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.
基金the Natural Science Foundation of Hebei Province under Grant No.F2020202056Key Project of Hebei Education Department under Grant No. ZD2020125。
文摘Random variables and uncertain variables are respectively used to model randomness and uncertainty. While randomness and uncertainty always coexist in a same complex system. As an evolution of random variables and uncertain variables, uncertain random variable is introduced as a tool to deal with complex phenomena including randomness and uncertainty simultaneously. For uncertain random variables, a basic and important topic is to discuss the convergence of its sequence.Specifically, this paper focuses on studying the convergence in distribution for a sequence of uncertain random sequences with different chance distributions where random variables are not independent.And the result of this paper is a generalization of the existing literature. Relations among convergence theorems are studied. Furthermore, the theorems are explained by several examples.
文摘Considering the time-sequence characteristic and randomness of load and natural resources, ?this paper studies on the distributed generation (DG) impacts on voltage limit violation probability of distribution lines. The time-sequence characteristic and randomness of load, wind and photovoltaic (PV) generation are analyzed;the indices and risk levels of voltage limit violation probability of node and distribution line are proposed. By using probabilistic load flow based on semi-invariant method, the impact degrees of voltage limit violation are calculated with different distributed power penetration levels, different seasons, different time periods, different allocation ratio between the wind power and PV power. Voltage limit violation laws of distribution line, which are concluded by IEEE33 bus system simulation, are very helpful to guide the voltage?regulation of distribution line including distributed generation.
基金supported by the National Natural Science Foundation of China(11571052,11731012)the Hunan Provincial Natural Science Foundation of China(2018JJ2417)the Open Fund of Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(2018MMAEZD02)。
文摘We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.
基金Supported by National Natural Science Foundation of China(62033006,62203254)。
文摘We study distributed optimization problems over a directed network,where nodes aim to minimize the sum of local objective functions via directed communications with neighbors.Many algorithms are designed to solve it for synchronized or randomly activated implementation,which may create deadlocks in practice.In sharp contrast,we propose a fully asynchronous push-pull gradient(APPG) algorithm,where each node updates without waiting for any other node by using possibly delayed information from neighbors.Then,we construct two novel augmented networks to analyze asynchrony and delays,and quantify its convergence rate from the worst-case point of view.Particularly,all nodes of APPG converge to the same optimal solution at a linear rate of O(λ^(k)) if local functions have Lipschitz-continuous gradients and their sum satisfies the Polyak-?ojasiewicz condition(convexity is not required),where λ ∈(0,1) is explicitly given and the virtual counter k increases by one when any node updates.Finally,the advantage of APPG over the synchronous counterpart and its linear speedup efficiency are numerically validated via a logistic regression problem.
文摘Recently, Kyriakoussis and Vamvakari [1] have established a q-analogue of the Stirling type for q-constant which have lead them to the proof of the pointwise convergence of the q-binomial distribution to a Stieltjes-Wigert continuous distribution. In the present article, assuming a sequence q(n) of n with q(n)→1 as n→∞, the study of the affect of this assumption to the q(n)-analogue of the Stirling type and to the asymptotic behaviour of the q(n)-Binomial distribution is presented. Specifically, a q(n) analogue of the Stirling type is provided which leads to the proof of deformed Gaussian limiting behaviour for the q(n)-Binomial distribution. Further, figures using the program MAPLE are presented, indicating the accuracy of the established distribution convergence even for moderate values of n.
文摘In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).
文摘Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hildebrand's work in [1], the authors investigate the a.s. convergence of Sigma (infinity)(n=1) X-n under a hypothesis that Sigma (infinity)(n=1) rho (X-n, c(n)) = infinity whener Sigma (infinity)(n=1) c(n) diverges, where the notation rho (X,c) denotes the Levy distance between the random variable X and the constant c. The principal result of this paper shows that the hypothesis is the condition under which the convergence of F-n(x(0)) with the limit value 0 < L-0 < 1, together with the essential convergence of Sigma (infinity)(n=1) X-n, is both sufficient and necessary in order for the series Sigma (infinity)(n=1) X-n to a.s. coverage. Moreover, if the essential convergence of Sigma (infinity)(n=1) X-n is strengthened to limsup(n=infinity) P(\S-n\ < K) = 1 for some K > 0, the hypothesis is already equivalent to the a.s. convergence of Sigma (infinity)(n=1) X-n. Here they have not only founded a very general limit theorem, but improved the related result in Hildebrand([1]) as well.
基金supported by Vehicular Diesel Engine Development Program of China (Grant No. DEDP0202)
文摘Analytical method for the distributions of axial-load and stress is based on elastic assumption, but the threaded connections are often in plastic deformation stage in practice. Meanwhile the strain in the threaded connection is difficult to measure. So it is necessary to study the reliable numerical method. At present neither the convergence analysis of the computational results nor the elastic-plastic analysis in the loading-unloading process are studied. In this paper, von Mises plasticity and kinematic hardening model is used to describe the material response. A new convergence criterion for nonlinear finite element analysis of the loading-unloading process is proposed. An axisymmetric finite element model according to the proposed convergence criterion is developed and used to analyze the distributions of axial-load and stress. It can be conclude that the stress distribution analysis is more dependent on the mesh density than the axial-load distribution analysis. The stress distribution result indicates that with increasing of applied load, the engaged threads close to the nut-bearing surface become plastic firstly. The axial-load distribution result reveals that the load percentage carried by single thread depends on the position of thread and load intensity. When the load is relatively small, the applied load is mainly carried by the engaged threads near the nut-bearing surface, when the load is larger, the differences of percentages for all threads become small. The proposed convergence analyzing procedure is applicable for other nonlinear analyses. The obtained distributions of axial-load and stress can be a reference of engineering application.
基金Supported by the National Natural Science Foundation of China(11671375 and 11471303)Natural Science Foundation of Anhui Provincial Education Department(KJ2017A171)
文摘In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.
文摘With the widespread application of distributed systems, many problems need to be solved urgently. How to design distributed optimization strategies has become a research hotspot. This article focuses on the solution rate of the distributed convex optimization algorithm. Each agent in the network has its own convex cost function. We consider a gradient-based distributed method and use a push-pull gradient algorithm to minimize the total cost function. Inspired by the current multi-agent consensus cooperation protocol for distributed convex optimization algorithm, a distributed convex optimization algorithm with finite time convergence is proposed and studied. In the end, based on a fixed undirected distributed network topology, a fast convergent distributed cooperative learning method based on a linear parameterized neural network is proposed, which is different from the existing distributed convex optimization algorithms that can achieve exponential convergence. The algorithm can achieve finite-time convergence. The convergence of the algorithm can be guaranteed by the Lyapunov method. The corresponding simulation examples also show the effectiveness of the algorithm intuitively. Compared with other algorithms, this algorithm is competitive.
文摘Background:To assess the influence of different spectral energy distribution on accommodation,vergence and reading performance.Methods:A Randomized experimental study was conducted after getting the approval of the Ethical Committee of University of Hyderabad.Forty participants with an age group of 18-21 years was integrated,out of which 50%was male and 50%was female.Subjects with emmetropia and no history of ocular pathology were included in the study.Near point of accommodation(NPA)&near point of convergence(NPC)was measured with the help of royal air force(RAF)ruler followed by near visual task of a readability passage.Results:A statistically significant result was obtained when reading rate,reading speed and NPC was compared among different spectral distribution of light(P<0.001)except NPA(P=0.43).Post hoc analysis showed a significant difference(P<0.001)when tungsten was compared with fluorescent light(FLOU),compact fluorescent light(CFL),and light emitting diode(LED)for reading rate,reading speed and NPC.But there is no noteworthy difference exist when fluorescent was compared with CFL for reading rate(P=0.530)&reading speed(P=0.595).Similarly,LED also showed no considerable difference when compared with CFL(P=0.682)and fluorescent(P=0.490)for NPC.When NPA was assessed within the group LED showed insignificant difference with CFL(P=0.205)and fluorescent(P=0.275)similar like fluorescent and tungsten(P=0.482).Conclusions:This study concluded that reading performance(reading rate and reading speed)and NPC has a significance change if we use inappropriate lighting during visual tasks.It will cause visual fatigue and strain after sustained near work.In addition,tungsten spectral energy influences the convergence which can also show an impact on reading and near visual tasks because of its brightness and miosis.Prolonged reading and working under this lighting can cause convergence disorders and visual fatigue.
文摘Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = （ai1,…, aiM） be random vectors with {aij} being i.i.d, random variables. Define XN =（x1,…, xk） and SN =XNXN^T,where xi=ai×si and si=1/√N（v1i,…, vN,i）^T. The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.
文摘In this paper, we give a necessary and sufficient condition of sequence of nodes, such that, the error of trigonometric interpolation for analytic function converges to 0.
文摘The Boltzmann equilibrium distribution is an important rigorous tool for determining entropy, since this function cannot be measured, but only calculated in accordance with Boltzmann＇s law. On the basis of the commensuration coefficient of discrete and continuous similarly-named distributions developed by the authors, the article analyses the statistical sum in the Boltzmann distribution to the commensuration with the improper integral of the similarly-named function in the full range of the term of series of the statistical sum at the different combination of the temperature and the step of variation （quantum） of the particle energy. The convergence of series based on the Cauchy, Maclaurin criteria and the equal commensuration of series and improper integral of the similarly-named function in each unit interval of variation of series and similarly-named function were estab- lished. The obtained formulas for the commensuration coefficient and statistical sum were analyzed, and a general expres- sion for the total and residual statistical sums, which can be calculated with any given accuracy, is found. Given a direct calculation formula for the Boltzmann distribution, taking into account the values of the improper integral and commensuration coefficient. To determine the entropy from the new expression for the Boltzmann distribution in the form of a series, the conver- gence of the similarly-named improper integral is established. However, the commensuration coefficient of integral and series in each unit interval turns out to be dependent on the number of the term of series and therefore cannot be used to determine the sum of series through the improper integral. In this case, the entropy can be calculated with a given accuracy with a corresponding quantity of the term of series n at a fixed value of the statistical sum. The given accuracy of the statistical sum turns out to be mathematically identical to the fraction of particles with an energy exceeding a given level of the energy barrier equal to the activation energy in the Arrhenius equation. The prospect of development of the proposed method for expressing the Boltzmann distribution and entropy is to establish the relationship between the magnitude of the energy quantum Ae and the properties of the system-forming particles.
基金supported by National Natural Science Foundation of China(NSFC)Key Program(61573094)the Fundamental Research Funds for the Central Universities(N140402001)
基金supported by Anhui Polytechnic University Introduced Talents Research Fund(No.2021YQQ064)Anhui Polytechnic University ScientificResearch Project(No.Xjky2022168).
文摘Due to the development of digital transformation,intelligent algorithms are getting more and more attention.The whale optimization algorithm(WOA)is one of swarm intelligence optimization algorithms and is widely used to solve practical engineering optimization problems.However,with the increased dimensions,higher requirements are put forward for algorithm performance.The double population whale optimization algorithm with distributed collaboration and reverse learning ability(DCRWOA)is proposed to solve the slow convergence speed and unstable search accuracy of the WOA algorithm in optimization problems.In the DCRWOA algorithm,the novel double population search strategy is constructed.Meanwhile,the reverse learning strategy is adopted in the population search process to help individuals quickly jump out of the non-ideal search area.Numerical experi-ments are carried out using standard test functions with different dimensions(10,50,100,200).The optimization case of shield construction parameters is also used to test the practical application performance of the proposed algo-rithm.The results show that the DCRWOA algorithm has higher optimization accuracy and stability,and the convergence speed is significantly improved.Therefore,the proposed DCRWOA algorithm provides a better method for solving practical optimization problems.
文摘The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.
