We present old and new results about the size function of a set providing simple and complete proofs using basic tools of general topology. For instance, the decomposition of the size function is given and, under the ...We present old and new results about the size function of a set providing simple and complete proofs using basic tools of general topology. For instance, the decomposition of the size function is given and, under the calmness property of a set, the right continuity of the size function with respect to both arguments is established. Finally, a classification of its points of discontinuity is given.展开更多
In this paper,we develop an active set identification technique.By means of the active set technique,we present an active set adaptive monotone projected Barzilai-Borwein method(ASAMPBB)for solving nonnegative matrix ...In this paper,we develop an active set identification technique.By means of the active set technique,we present an active set adaptive monotone projected Barzilai-Borwein method(ASAMPBB)for solving nonnegative matrix factorization(NMF)based on the alternating nonnegative least squares framework,in which the Barzilai-Borwein(BB)step sizes can be adaptively picked to get meaningful convergence rate improvements.To get optimal step size,we take into account of the curvature information.In addition,the larger step size technique is exploited to accelerate convergence of the proposed method.The global convergence of the proposed method is analysed under mild assumption.Finally,the results of the numerical experiments on both synthetic and real-world datasets show that the proposed method is effective.展开更多
Decoy state method quantum key distribution (QKD) is one of the promising practical solutions for BB84QKD with coherent light pulses.The number of data-set size in practical QKD protocol is always finite,which will ca...Decoy state method quantum key distribution (QKD) is one of the promising practical solutions for BB84QKD with coherent light pulses.The number of data-set size in practical QKD protocol is always finite,which will causestatistical fluctuations.In this paper,we apply absolutely statistical fluctuation to amend the yield and error rate of thequantum state.The relationship between exchanged number of quantum signals and key generation rate is analyzed inour simulation,which offers a useful reference for experiment.展开更多
With photographing and experiments, this paper divides the cocoon layers into three categories according to their colors, establishes three-color membership function based on fuzzy mathematics, constructs fuzzy sets w...With photographing and experiments, this paper divides the cocoon layers into three categories according to their colors, establishes three-color membership function based on fuzzy mathematics, constructs fuzzy sets which satisfy the range of size control by using the ordinary set and attached frequency of threecolor cocoons combination, then achieves the ordinary sets of range of size control by choosing λ-cut. Under these ordinary sets, each end does duality relative level, then sets up relative matrix and overall sequence and finds the membership function to judge whether the size control is mormal.展开更多
The reproductive ability related to the population size of the endangered and endemic species Primula merrilliana Schltr. was investigated. In 26 populations observed, only four contain more than 500 flowering individ...The reproductive ability related to the population size of the endangered and endemic species Primula merrilliana Schltr. was investigated. In 26 populations observed, only four contain more than 500 flowering individuals, whereas most of them （53.8%） consist of less than 100 flowering individuals. Though the ratio of pin and thrum plants keeps its balance at 1：1 for all populations, the frequency of pin and thrum flowers was significantly biased in most small populations. Population size strongly affected reproductive success; plants in small populations produced significantly fewer flowers and fruits per plant and fewer seeds per fruit, and therefore fewer seeds per plant. The floral density was another important factor that influenced the reproductive success of P. merrilliana, because four main reproductive success parameters （fruits per plant, seeds per fruit, seeds per plant, and the proportion of flowers setting fruit） were all positively correlated with floral density. The size of plants and the number of leaves per plant （measure of habitat quality） were not influenced by the variation of population size, suggesting that the reduced fecundity in small populations may not be a consequence of lower habitat quality. Inbreeding depression and pollen limitation as a result of less attractiveness in small populations are therefore likely explanations for these patterns.展开更多
文摘We present old and new results about the size function of a set providing simple and complete proofs using basic tools of general topology. For instance, the decomposition of the size function is given and, under the calmness property of a set, the right continuity of the size function with respect to both arguments is established. Finally, a classification of its points of discontinuity is given.
基金the support from the National Natural Science Foundation of China(Nos.12171384,12201492,61976176)the National Science Foundation of Shaanxi(No.2021JM-323).
文摘In this paper,we develop an active set identification technique.By means of the active set technique,we present an active set adaptive monotone projected Barzilai-Borwein method(ASAMPBB)for solving nonnegative matrix factorization(NMF)based on the alternating nonnegative least squares framework,in which the Barzilai-Borwein(BB)step sizes can be adaptively picked to get meaningful convergence rate improvements.To get optimal step size,we take into account of the curvature information.In addition,the larger step size technique is exploited to accelerate convergence of the proposed method.The global convergence of the proposed method is analysed under mild assumption.Finally,the results of the numerical experiments on both synthetic and real-world datasets show that the proposed method is effective.
基金Supported by the National Basic Research Program (973) of China under Grant No.2010CB923200Chinese Universities Scientific Fund BUPT2009RC0709
文摘Decoy state method quantum key distribution (QKD) is one of the promising practical solutions for BB84QKD with coherent light pulses.The number of data-set size in practical QKD protocol is always finite,which will causestatistical fluctuations.In this paper,we apply absolutely statistical fluctuation to amend the yield and error rate of thequantum state.The relationship between exchanged number of quantum signals and key generation rate is analyzed inour simulation,which offers a useful reference for experiment.
文摘With photographing and experiments, this paper divides the cocoon layers into three categories according to their colors, establishes three-color membership function based on fuzzy mathematics, constructs fuzzy sets which satisfy the range of size control by using the ordinary set and attached frequency of threecolor cocoons combination, then achieves the ordinary sets of range of size control by choosing λ-cut. Under these ordinary sets, each end does duality relative level, then sets up relative matrix and overall sequence and finds the membership function to judge whether the size control is mormal.
基金National Natural Science Foundation of China General Projects (30500300)the Natural Science Foundation of Anhui Province (050430501)+1 种基金the Doctoral Subject Foundation of High College of Chinese Education Commission (20060370001) the Foundation for Junior Teacher of Anhui Education Department (2005jq1051)
文摘The reproductive ability related to the population size of the endangered and endemic species Primula merrilliana Schltr. was investigated. In 26 populations observed, only four contain more than 500 flowering individuals, whereas most of them （53.8%） consist of less than 100 flowering individuals. Though the ratio of pin and thrum plants keeps its balance at 1：1 for all populations, the frequency of pin and thrum flowers was significantly biased in most small populations. Population size strongly affected reproductive success; plants in small populations produced significantly fewer flowers and fruits per plant and fewer seeds per fruit, and therefore fewer seeds per plant. The floral density was another important factor that influenced the reproductive success of P. merrilliana, because four main reproductive success parameters （fruits per plant, seeds per fruit, seeds per plant, and the proportion of flowers setting fruit） were all positively correlated with floral density. The size of plants and the number of leaves per plant （measure of habitat quality） were not influenced by the variation of population size, suggesting that the reduced fecundity in small populations may not be a consequence of lower habitat quality. Inbreeding depression and pollen limitation as a result of less attractiveness in small populations are therefore likely explanations for these patterns.
