Geostatistics of extreme values makes it possible to model the asymptotic behavior of random phenomena that depend on time or space. In this paper, we propose new models of the extremal coefficient of a stationary ran...Geostatistics of extreme values makes it possible to model the asymptotic behavior of random phenomena that depend on time or space. In this paper, we propose new models of the extremal coefficient of a stationary random field where the cumulative distribution is associated with a multivariate copula. More precisely, some models of extensions of the extremogram and these derivatives are built in a spatial framework. Moreover, both these two geostatistical tools are modeled using the extremal variogram which characterizes the asymptotic stochastic behavior of the phenomena.展开更多
In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common h...In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.展开更多
Metal oxide cluster(MOC)photoresists are highly promising materials for the next generation of extreme ultraviolet lithography(EUVL).The consecutive exploration of novel MOC materials and their structural irradiation ...Metal oxide cluster(MOC)photoresists are highly promising materials for the next generation of extreme ultraviolet lithography(EUVL).The consecutive exploration of novel MOC materials and their structural irradiation chemistry are the major concerns associated with EUVL.Herein,we report two bicoordinated tin-oxo clusters(TOCs),the organic ligands of which contain both adamantane carboxylic acids and alkyl groups(methyl:Sn_(4)–Me–C10;butyl:Sn_(4)–Bu–C10).We explore the correlation between the structures of the TOCs and their patterning properties by adjusting the alkyl groups coordinated to the Sn atom.The structural variation causes different irradiation chemistry,with Sn_(4)–Me–C10 exhibiting improved resolution and Sn_(4)–Bu–C10 demonstrating higher sensitivity.These differences are attributed to the bonding energies of the Sn-methyl and Sn-butyl groups,the size of the resulting alkyl radicals,and their reaction probabilities.Both clusters occur in the reactions of Sn–C bond cleavage and the decarboxylation of adamantane carboxylic acids upon irradiation.However,the entire process exhibits distinct characteristics.Based on the electron-beam lithography and other experiments,we proposed irradiationinduced reaction mechanisms for both clusters.The Sn_(4)–Bu–C10 cluster predominantly undergoes alkane chain linkage,whereas the Sn_(4)–Me–C10 cluster mainly follows the adamantanes linkage pathway.展开更多
This paper presents mathematics models that describe and optimize the passenger flow at the airport security checkpoints by applying the queuing theory. Firstly, a Poisson process is used to estimate the flow of passe...This paper presents mathematics models that describe and optimize the passenger flow at the airport security checkpoints by applying the queuing theory. Firstly, a Poisson process is used to estimate the flow of passengers waiting for going through the security. Then, the Poisson distribution is combined with a multiple M/M/s model. Following that, an arrival model (passengers’ arriving at the checkpoints preparing for security examination and departure) with Gumbel extreme value estimation is described that predicts the busiest time in the busiest airport. Real case data collected from several major airports worldwide is used for creating a hybrid Poisson model to generate the simulation of passenger volume. At last, Markov Chain theory is applied to the analysis to randomly simulate the flow of enplaned passengers again, and the results of these two simulations are compared and discussed, revealing that the hybrid Poisson model is the more accurate one. After successfully characterizing the passenger flow mathematically, two methods for optimizing the passenger flow are then provided in two different respects: one is bypassing passengers and creating an express pass;while the other one promotes Pre-Check service application.展开更多
文摘Geostatistics of extreme values makes it possible to model the asymptotic behavior of random phenomena that depend on time or space. In this paper, we propose new models of the extremal coefficient of a stationary random field where the cumulative distribution is associated with a multivariate copula. More precisely, some models of extensions of the extremogram and these derivatives are built in a spatial framework. Moreover, both these two geostatistical tools are modeled using the extremal variogram which characterizes the asymptotic stochastic behavior of the phenomena.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10071081) .
文摘In this paper we consider the large deviations for random sums $S(t) = \sum _{i = t}^{N(t)} X_i ,t \geqslant 0$ , whereX n,n?1 are independent, identically distributed and non-negative random variables with a common heavy-tailed distribution function F, andN(t), t?0 is a process of non-negative integer-valued random variables, independent ofX n,n?1. Under the assumption that the tail of F is of Pareto’s type (regularly or extended regularly varying), we investigate what reasonable condition can be given onN(t), t?0 under which precise large deviation for S( t) holds. In particular, the condition we obtain is satisfied for renewal counting processes.
基金supported by the National Natural Science Foundation of China(grant nos.22090011 and 22378052)the Fundamental Research Funds for China Central Universities(grant nos.DUT22LAB608 and DUT20RC(3)030)Key R&D Program of Shandong Province(grant no.2021CXGC010308).
文摘Metal oxide cluster(MOC)photoresists are highly promising materials for the next generation of extreme ultraviolet lithography(EUVL).The consecutive exploration of novel MOC materials and their structural irradiation chemistry are the major concerns associated with EUVL.Herein,we report two bicoordinated tin-oxo clusters(TOCs),the organic ligands of which contain both adamantane carboxylic acids and alkyl groups(methyl:Sn_(4)–Me–C10;butyl:Sn_(4)–Bu–C10).We explore the correlation between the structures of the TOCs and their patterning properties by adjusting the alkyl groups coordinated to the Sn atom.The structural variation causes different irradiation chemistry,with Sn_(4)–Me–C10 exhibiting improved resolution and Sn_(4)–Bu–C10 demonstrating higher sensitivity.These differences are attributed to the bonding energies of the Sn-methyl and Sn-butyl groups,the size of the resulting alkyl radicals,and their reaction probabilities.Both clusters occur in the reactions of Sn–C bond cleavage and the decarboxylation of adamantane carboxylic acids upon irradiation.However,the entire process exhibits distinct characteristics.Based on the electron-beam lithography and other experiments,we proposed irradiationinduced reaction mechanisms for both clusters.The Sn_(4)–Bu–C10 cluster predominantly undergoes alkane chain linkage,whereas the Sn_(4)–Me–C10 cluster mainly follows the adamantanes linkage pathway.
文摘This paper presents mathematics models that describe and optimize the passenger flow at the airport security checkpoints by applying the queuing theory. Firstly, a Poisson process is used to estimate the flow of passengers waiting for going through the security. Then, the Poisson distribution is combined with a multiple M/M/s model. Following that, an arrival model (passengers’ arriving at the checkpoints preparing for security examination and departure) with Gumbel extreme value estimation is described that predicts the busiest time in the busiest airport. Real case data collected from several major airports worldwide is used for creating a hybrid Poisson model to generate the simulation of passenger volume. At last, Markov Chain theory is applied to the analysis to randomly simulate the flow of enplaned passengers again, and the results of these two simulations are compared and discussed, revealing that the hybrid Poisson model is the more accurate one. After successfully characterizing the passenger flow mathematically, two methods for optimizing the passenger flow are then provided in two different respects: one is bypassing passengers and creating an express pass;while the other one promotes Pre-Check service application.
