This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying tails.The moderate deviations of partial sums are first given.The results are the...This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying tails.The moderate deviations of partial sums are first given.The results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances.展开更多
A proper [h]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [h] ={1, 2,..., h}. Let w（u） denote the sum of the color on a vertex u and colors on all the edges incident to u. ...A proper [h]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [h] ={1, 2,..., h}. Let w（u） denote the sum of the color on a vertex u and colors on all the edges incident to u. For each edge uv ∈ E（G）, if w（u） ≠ w（v）, then we say the coloring c distinguishes adjacent vertices by sum and call it a neighbor sum distinguishing [h]-total coloring of G. By tndi∑ （G）, we denote the smallest value h in such a coloring of G. In this paper, we obtain that G is a graph with at least two vertices, if mad（G） 〈 3, then tndi∑ （G） ≤k ＋ 2 where k = max{△（G）, 5}. It partially confirms the conjecture proposed by Pilgniak and Wolniak.展开更多
A total [k]-coloring of a graph G is a mapping φ： V（G） U E（G） →{1, 2, ..., k} such that any two adjacent elements in V（G）UE（G） receive different colors. Let f（v） denote the sum of the colors of a vertex v...A total [k]-coloring of a graph G is a mapping φ： V（G） U E（G） →{1, 2, ..., k} such that any two adjacent elements in V（G）UE（G） receive different colors. Let f（v） denote the sum of the colors of a vertex v and the colors of all incident edges of v. A total [k]-neighbor sum distinguishing-coloring of G is a total [k]-coloring of G such that for each edge uv E E（G）, f（u） ≠ f（v）. By tt [G, Xsd（ J, we denote the smallest value k in such a coloring of G. Pilniak and Woniak conjectured X＇sd（G） 〈 A（G） ＋ 3 for any simple graph with maximum degree A（G）. This conjecture has been proved for complete graphs, cycles, bipartite graphs, and subcubic graphs. In this paper, we prove that it also holds for Ka-minor free graphs. Furthermore, we show that if G is a Ka-minor flee graph with A（G） 〉 4, then ＂ Xnsd（G） 〈 A（G） ＋ 2. The bound A（G） ＋ 2 is sharp.展开更多
In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash ...In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.展开更多
The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is...The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is employed in seismic stability analysis of a slope in this paper. Different from other conventional methods, the VSAM is proposed based on the vector characteristic of force and current stress state of the slope. The dynamic stress state of the slope at any moment under seismic load can he obtained by the DFEM, thus the factor of safety of the slope at any moment during earthquake can be easily obtained with the VSAM in consideration of the DFEM. Then, the global stability of the slope can be estimated on the basis of time-history curve of factor of safety and reliability theory. The VSAM is applied to a homogeneous slope under seismic load. The factor of safety of the slope is 1.30 under gravity only and the dynamic factor of safety under seismic load is 1.21. The calculating results show that the dynamic characteristics and stability state of the slope with input ground motion can be actually analyzed. It is believed that the VSAM is a feasible and practical approach to estimate the dynamic stability of slopes under seismic load.展开更多
This paper discusses the role of Hong Kong in China＇s grand scheme to build up the RMB as a global reserve currency. We highlight the economic importance of Hong Kong to China in terms of channeling foreign direct in...This paper discusses the role of Hong Kong in China＇s grand scheme to build up the RMB as a global reserve currency. We highlight the economic importance of Hong Kong to China in terms of channeling foreign direct investment into China, some of which, in the future, will be denominated in the RMB. We discuss the development of China＇s RMB currency swap and deposit markets in Hong Kong. These offshore markets enable the RMB to trade freely, setting the stage for the RMB to become fully convertible and allowing market forces to play a role in pricing the value of the RMB, and help in the development of the RMB-denominated bond （or dim sum bond） market in Hong Kong. Finally, we present evidence of the phenomenal growth of the dim sum bond market in Hong Kong, which can further enhance and strengthen the use of the RMB outside China.展开更多
A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of ...A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.展开更多
Parameters identification of rockfill materials is a crucial issue for high rockfill dams. Because of the scale effect, random sampling and sample disturbance, it is difficult to obtain the actual mechanical propertie...Parameters identification of rockfill materials is a crucial issue for high rockfill dams. Because of the scale effect, random sampling and sample disturbance, it is difficult to obtain the actual mechanical properties of rockfill from laboratory tests. Parameters inversion based on in situ monitoring data has been proven to be an efficient method for identifying the exact parameters of the rockfill. In this paper, we propose a modified genetic algorithm to solve the high-dimension multimodal and nonlinear optimal parameters inversion problem. A novel crossover operator based on the sum of differences in gene fragments(So DX) is proposed, inspired by the cloning of superior genes in genetic engineering. The crossover points are selected according to the difference in the gene fragments, defining the adaptive length. The crossover operator increases the speed and accuracy of algorithm convergence by reducing the inbreeding and enhancing the global search capability of the genetic algorithm. This algorithm is compared with two existing crossover operators. The modified genetic algorithm is then used in combination with radial basis function neural networks(RBFNN) to perform the parameters back analysis of a high central earth core rockfill dam. The settlements simulated using the identified parameters show good agreement with the monitoring data, illustrating that the back analysis is reasonable and accurate. The proposed genetic algorithm has considerable superiority for nonlinear multimodal parameter identification problems.展开更多
Suppose that f is transcendental meromorphic in the plane. Then (ⅰ) sum from ∈C=1 to δ(α,f^(k))≤1 holds for all k≥0 with at most four exceptions of k; (ⅱ) for n≥3,k≥0, (f^n)^(k) assumes all finite values (pos...Suppose that f is transcendental meromorphic in the plane. Then (ⅰ) sum from ∈C=1 to δ(α,f^(k))≤1 holds for all k≥0 with at most four exceptions of k; (ⅱ) for n≥3,k≥0, (f^n)^(k) assumes all finite values (possibly except zero) infinitely often. (ⅰ) affirms a conjecture of Mues for almost every positive integers. And (ⅱ) is a general Picard theorem. Some other results are also obtained.展开更多
The complexity of decoding the standard Reed-Solomon code is a well known open prob-lem in coding theory. The main problem is to compute the error distance of a received word. Using the Weil bound for character sum es...The complexity of decoding the standard Reed-Solomon code is a well known open prob-lem in coding theory. The main problem is to compute the error distance of a received word. Using the Weil bound for character sum estimate, we show that the error distance can be determined precisely when the degree of the received word is small. As an application of our method, we give a significant improvement of the recent bound of Cheng-Murray on non-existence of deep holes (words with maximal error distance).展开更多
Let f be a holomorphic cusp form of weight k for SL2(Z) and λf(n) its n-th Fourier coefficient.In this paper,the exponential sum X【n 2X λf(n)e(αnβ) twisted by Fourier coefficients λf(n) is proved toh ave a main ...Let f be a holomorphic cusp form of weight k for SL2(Z) and λf(n) its n-th Fourier coefficient.In this paper,the exponential sum X【n 2X λf(n)e(αnβ) twisted by Fourier coefficients λf(n) is proved toh ave a main term of size |λf(q)|X3/4 when β = 1/2 and α is close to ±2√q,q ∈ Z,and is smaller otherwise for β 【 3/4.This is a manifestation of the resonance spectrum of automorphic forms for SL2(Z).展开更多
A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to...A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to the zero point.展开更多
We discuss the relationship between the marginal tail risk probability and the innovation'stail risk probability for some stationary financial time series models.We first give the main results on the tail behavior...We discuss the relationship between the marginal tail risk probability and the innovation'stail risk probability for some stationary financial time series models.We first give the main results on the tail behavior of a class of infinite weighted sums of random variableswith heavy-tailed probabilities. And then, the main results are applied tothree important types of time series models:infinite order moving averages, the simple bilinear time series and the solutions of stochasticdifference equations. The explicit formulas are given to describe how the marginaltail probabilities come from the innovation's tail probabilities for these time series.Our results can be applied to the tail estimation of time series and are useful for risk analysis in finance.展开更多
This study examined the associations between dissolved organic matter（DOM） characteristics and potential nitrification occurrence in the presence of chloramine along a drinking water distribution system. High-perfor...This study examined the associations between dissolved organic matter（DOM） characteristics and potential nitrification occurrence in the presence of chloramine along a drinking water distribution system. High-performance size exclusion chromatography（HPSEC） coupled with a multiple wavelength detector（200–280 nm） was employed to characterise DOM by molecular weight distribution, bacterial activity was analysed using flow cytometry, and a package of simple analytical tools, such as dissolved organic carbon, absorbance at 254 nm, nitrate,nitrite, ammonia and total disinfectant residual were also applied and their applicability to indicate water quality changes in distribution systems were also evaluated. Results showed that multi-wavelength HPSEC analysis was useful to provide information about DOM character while changes in molecule weight profiles at wavelengths less than 230 nm were also able to be related to other water quality parameters. Correct selection of the UV wavelengths can be an important factor for providing appropriate indicators associated with different DOM compositions. DOM molecular weight in the range of 0.2–0.5 kDa measured at210 nm correlated positively with oxidised nitrogen concentration（r = 0.99）, and the concentrations of active bacterial cells in the distribution system（r = 0.85）. Our study also showed that the changes of DOM character and bacterial cells were significant in those sampling points that had decreases in total disinfectant residual. HPSEC-UV measured at210 nm and flow cytometry can detect the changes of low molecular weight of DOM and bacterial levels, respectively, when nitrification occurred within the chloraminated distribution system.展开更多
基金supported by National Natural Science Foundation of China(Grant No.10571139)the Research Foundation of Education Bureau of Hubei Province,China (Grant No.Q200710002)
文摘This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying tails.The moderate deviations of partial sums are first given.The results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances.
基金supported by National Natural Science Foundation of China(Grant No.11161035)the Research Fund for the Doctoral Program of Shandong Jiaotong University+2 种基金supported by National Natural Science Foundation of China(Grant No.11101243)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20100131120017)the Scientific Research Foundation for the Excellent Middle-Aged and Youth Scientists of Shandong Province of China(Grant No.BS2012SF016)
文摘A proper [h]-total coloring c of a graph G is a proper total coloring c of G using colors of the set [h] ={1, 2,..., h}. Let w（u） denote the sum of the color on a vertex u and colors on all the edges incident to u. For each edge uv ∈ E（G）, if w（u） ≠ w（v）, then we say the coloring c distinguishes adjacent vertices by sum and call it a neighbor sum distinguishing [h]-total coloring of G. By tndi∑ （G）, we denote the smallest value h in such a coloring of G. In this paper, we obtain that G is a graph with at least two vertices, if mad（G） 〈 3, then tndi∑ （G） ≤k ＋ 2 where k = max{△（G）, 5}. It partially confirms the conjecture proposed by Pilgniak and Wolniak.
文摘A total [k]-coloring of a graph G is a mapping φ： V（G） U E（G） →{1, 2, ..., k} such that any two adjacent elements in V（G）UE（G） receive different colors. Let f（v） denote the sum of the colors of a vertex v and the colors of all incident edges of v. A total [k]-neighbor sum distinguishing-coloring of G is a total [k]-coloring of G such that for each edge uv E E（G）, f（u） ≠ f（v）. By tt [G, Xsd（ J, we denote the smallest value k in such a coloring of G. Pilniak and Woniak conjectured X＇sd（G） 〈 A（G） ＋ 3 for any simple graph with maximum degree A（G）. This conjecture has been proved for complete graphs, cycles, bipartite graphs, and subcubic graphs. In this paper, we prove that it also holds for Ka-minor free graphs. Furthermore, we show that if G is a Ka-minor flee graph with A（G） 〉 4, then ＂ Xnsd（G） 〈 A（G） ＋ 2. The bound A（G） ＋ 2 is sharp.
基金This work is supported by the National Natural Science Foundation (Grant No.10371067)the Youth Teacher Foundation of Fok Ying Tung Education Foundation, the Excellent Young Teachers Program and the Doctoral Program Foundation of MOE and Shandong Province, China.
文摘In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.
基金Supported by the Program of Yunnan Provincial Institute of Communications Planning,Design and Research (2011(D)11-b)
文摘The vibration characteristics and dynamic responses of rock and soil under seismic load can be estimated with dynamic finite element method （DFEM）. Combining with the DFEM, the vector sum analysis method （VSAM） is employed in seismic stability analysis of a slope in this paper. Different from other conventional methods, the VSAM is proposed based on the vector characteristic of force and current stress state of the slope. The dynamic stress state of the slope at any moment under seismic load can he obtained by the DFEM, thus the factor of safety of the slope at any moment during earthquake can be easily obtained with the VSAM in consideration of the DFEM. Then, the global stability of the slope can be estimated on the basis of time-history curve of factor of safety and reliability theory. The VSAM is applied to a homogeneous slope under seismic load. The factor of safety of the slope is 1.30 under gravity only and the dynamic factor of safety under seismic load is 1.21. The calculating results show that the dynamic characteristics and stability state of the slope with input ground motion can be actually analyzed. It is believed that the VSAM is a feasible and practical approach to estimate the dynamic stability of slopes under seismic load.
文摘This paper discusses the role of Hong Kong in China＇s grand scheme to build up the RMB as a global reserve currency. We highlight the economic importance of Hong Kong to China in terms of channeling foreign direct investment into China, some of which, in the future, will be denominated in the RMB. We discuss the development of China＇s RMB currency swap and deposit markets in Hong Kong. These offshore markets enable the RMB to trade freely, setting the stage for the RMB to become fully convertible and allowing market forces to play a role in pricing the value of the RMB, and help in the development of the RMB-denominated bond （or dim sum bond） market in Hong Kong. Finally, we present evidence of the phenomenal growth of the dim sum bond market in Hong Kong, which can further enhance and strengthen the use of the RMB outside China.
基金National Natural Science Foundation of China (60572023)
文摘A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.
基金supported by the National Natural Science Foundation of China(Grant Nos.51379161&51509190)China Postdoctoral Science Foundation(Grant No.2015M572195)the Fundamental Research Funds for the Central Universities
文摘Parameters identification of rockfill materials is a crucial issue for high rockfill dams. Because of the scale effect, random sampling and sample disturbance, it is difficult to obtain the actual mechanical properties of rockfill from laboratory tests. Parameters inversion based on in situ monitoring data has been proven to be an efficient method for identifying the exact parameters of the rockfill. In this paper, we propose a modified genetic algorithm to solve the high-dimension multimodal and nonlinear optimal parameters inversion problem. A novel crossover operator based on the sum of differences in gene fragments(So DX) is proposed, inspired by the cloning of superior genes in genetic engineering. The crossover points are selected according to the difference in the gene fragments, defining the adaptive length. The crossover operator increases the speed and accuracy of algorithm convergence by reducing the inbreeding and enhancing the global search capability of the genetic algorithm. This algorithm is compared with two existing crossover operators. The modified genetic algorithm is then used in combination with radial basis function neural networks(RBFNN) to perform the parameters back analysis of a high central earth core rockfill dam. The settlements simulated using the identified parameters show good agreement with the monitoring data, illustrating that the back analysis is reasonable and accurate. The proposed genetic algorithm has considerable superiority for nonlinear multimodal parameter identification problems.
文摘Suppose that f is transcendental meromorphic in the plane. Then (ⅰ) sum from ∈C=1 to δ(α,f^(k))≤1 holds for all k≥0 with at most four exceptions of k; (ⅱ) for n≥3,k≥0, (f^n)^(k) assumes all finite values (possibly except zero) infinitely often. (ⅰ) affirms a conjecture of Mues for almost every positive integers. And (ⅱ) is a general Picard theorem. Some other results are also obtained.
文摘The complexity of decoding the standard Reed-Solomon code is a well known open prob-lem in coding theory. The main problem is to compute the error distance of a received word. Using the Weil bound for character sum estimate, we show that the error distance can be determined precisely when the degree of the received word is small. As an application of our method, we give a significant improvement of the recent bound of Cheng-Murray on non-existence of deep holes (words with maximal error distance).
基金supported in part by National Basic Research Program of China (973-Program) (Grant No.)National Natural Science Foundation of China (Grant No.10971119)
文摘Let f be a holomorphic cusp form of weight k for SL2(Z) and λf(n) its n-th Fourier coefficient.In this paper,the exponential sum X【n 2X λf(n)e(αnβ) twisted by Fourier coefficients λf(n) is proved toh ave a main term of size |λf(q)|X3/4 when β = 1/2 and α is close to ±2√q,q ∈ Z,and is smaller otherwise for β 【 3/4.This is a manifestation of the resonance spectrum of automorphic forms for SL2(Z).
基金This work is partially supported by D.G.E.S. PB 96-1338-CO2-01 and the Junta de Andalucla.
文摘A sufficient condition is given to assert that a continuous mapping between Rm and Rn has a zero. The constructive proof of the result is based upon continuation methods and supplies the existence of a path leading to the zero point.
基金This work was supported by the National Natural Science Foundation of China (Grant No.10071003).
文摘We discuss the relationship between the marginal tail risk probability and the innovation'stail risk probability for some stationary financial time series models.We first give the main results on the tail behavior of a class of infinite weighted sums of random variableswith heavy-tailed probabilities. And then, the main results are applied tothree important types of time series models:infinite order moving averages, the simple bilinear time series and the solutions of stochasticdifference equations. The explicit formulas are given to describe how the marginaltail probabilities come from the innovation's tail probabilities for these time series.Our results can be applied to the tail estimation of time series and are useful for risk analysis in finance.
基金the Australian Research Council (ARC) for financial support of the Linkage Project 110100459 - Multi-scale Strategy to Manage Chloramine Decay and Nitrification in Water Distribution Systems
文摘This study examined the associations between dissolved organic matter（DOM） characteristics and potential nitrification occurrence in the presence of chloramine along a drinking water distribution system. High-performance size exclusion chromatography（HPSEC） coupled with a multiple wavelength detector（200–280 nm） was employed to characterise DOM by molecular weight distribution, bacterial activity was analysed using flow cytometry, and a package of simple analytical tools, such as dissolved organic carbon, absorbance at 254 nm, nitrate,nitrite, ammonia and total disinfectant residual were also applied and their applicability to indicate water quality changes in distribution systems were also evaluated. Results showed that multi-wavelength HPSEC analysis was useful to provide information about DOM character while changes in molecule weight profiles at wavelengths less than 230 nm were also able to be related to other water quality parameters. Correct selection of the UV wavelengths can be an important factor for providing appropriate indicators associated with different DOM compositions. DOM molecular weight in the range of 0.2–0.5 kDa measured at210 nm correlated positively with oxidised nitrogen concentration（r = 0.99）, and the concentrations of active bacterial cells in the distribution system（r = 0.85）. Our study also showed that the changes of DOM character and bacterial cells were significant in those sampling points that had decreases in total disinfectant residual. HPSEC-UV measured at210 nm and flow cytometry can detect the changes of low molecular weight of DOM and bacterial levels, respectively, when nitrification occurred within the chloraminated distribution system.
