Aris and Amundson studied a chemical reactor and obtained the two equationsDaoud showed that at most one limit cycle may exist in the region of interest. Itis showed in this paper that other singular points exist and ...Aris and Amundson studied a chemical reactor and obtained the two equationsDaoud showed that at most one limit cycle may exist in the region of interest. Itis showed in this paper that other singular points exist and that a stable limitt cycle existsaround the singularity (1/2, 2) when K∈(9-δ, 9).展开更多
For a finite group G, let S（G） be the set of minimal subgroups of odd order,which are complemented in G. It is proved that if every minimal subgroup X of odd orderof G which does not belong to S（G）, CG（X） is eit...For a finite group G, let S（G） be the set of minimal subgroups of odd order,which are complemented in G. It is proved that if every minimal subgroup X of odd orderof G which does not belong to S（G）, CG（X） is either subnormal or abnormal in G. Then Gsolvable.展开更多
Evolutionary game dynamics in finite size populations can be described by a fitness-dependent Wright- Fisher process. We consider symmetric 2×2 games in a well-mixed population. In our model, two parameters to de...Evolutionary game dynamics in finite size populations can be described by a fitness-dependent Wright- Fisher process. We consider symmetric 2×2 games in a well-mixed population. In our model, two parameters to describe the level of player＇s rationality and noise intensity in environment are introduced. In contrast with the fixation probability method that used in a noiseless case, the introducing of the noise intensity parameter makes the process an ergodic Markov process and based on the limit distribution of the process, we can analysis the evolutionary stable strategy （ESS） of the games. We illustrate the effects of the two parameters on the ESS of games using the Prisoner＇s dilemma games （PDG） and the snowdrift games （SG）. We also compare the ESS of our model with that of the replicator dynamics in infinite size populations. The results are determined by simulation experiments.展开更多
A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (...A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (0 < α ≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d < 2α, the limiting process is Brownian motion.展开更多
Let X_1, X_2,... be a sequence of independent random variables and S_n=sum X_1 from i=1 to n and V_n^2=sum X_1~2 from i=1 to n . When the elements of the sequence are i.i.d., it is known that the self-normalized sum S...Let X_1, X_2,... be a sequence of independent random variables and S_n=sum X_1 from i=1 to n and V_n^2=sum X_1~2 from i=1 to n . When the elements of the sequence are i.i.d., it is known that the self-normalized sum S_n/V_n converges to a standard normal distribution if and only if max1≤i≤n|X_i|/V_n → 0 in probability and the mean of X_1 is zero. In this paper, sufficient conditions for the self-normalized central limit theorem are obtained for general independent random variables. It is also shown that if max1≤i≤n|X_i|/V_n → 0 in probability, then these sufficient conditions are necessary.展开更多
This paper presents limit theorems for realized power variation of processes of the form Xt=t0φsdGs+ξt as the sampling frequency within a fixed interval increases to infinity.Here G is a Gaussian process with statio...This paper presents limit theorems for realized power variation of processes of the form Xt=t0φsdGs+ξt as the sampling frequency within a fixed interval increases to infinity.Here G is a Gaussian process with stationary increments,ξis a purely non-Gaussian L′evy process independent from G,andφis a stochastic process ensuring that the integral is well defined as a pathwise Riemann-Stieltjes integral.We obtain the central limit theorems for the case that both the continuous term and the jump term are presented simultaneously in the law of large numbers.展开更多
The finite element analysis(FEA) technology by hydraulic-mechanical-chemical-damage(HMCD) coupling is proposed in this paper for inclined wellbore stability analysis of water-sensitive and laminated rock, developed ba...The finite element analysis(FEA) technology by hydraulic-mechanical-chemical-damage(HMCD) coupling is proposed in this paper for inclined wellbore stability analysis of water-sensitive and laminated rock, developed basing on the recently established FEA technology for transversely isotropic rock with hydraulic-mechanical-damage(HMD) coupling. The chemical activity of the drilling fluid is considered as phenomenological hydration behavior, the moisture content and parameters of rock considering hydration could be determined with time. The finite element(FE) solutions of numerical wellbore model considering the chemical activity of drilling fluid, damage tensor calculation and weak plane strength criterion for transversely isotropic rock are developed for researching the wellbore failure characteristics and computing the time-dependent collapse and fracture pressure of laminated rock as shale reservoirs. A three-dimensional FE model and elastic solid deformation and seepage flow coupled equations are developed, and the damage tensor calculation technology for transversely isotropic rock are realized by introducing effect of the hydration and the stress state under the current load. The proposed method utilizing weak plane strength criterion fully reflects the strength parameters in rock matrix and weak plane. To the end, an effective and reliable numerically three-step FEA strategy is well established for wellbore stability analysis. Numerical examples are given to show that the proposed method can establish efficient and applicable FE model and be suitable for analyzing the timedependsolutions of pore pressure and stresses, and the evolution region considering the hydration surrounding wellbore,furthermore to compute the collapse cycling time and the safe mud weight for collapse and fracture pressure of transversely isotropic rock.展开更多
Platinum-based material is the most efficient and durable electrocatalyst for motivating the hydrogen evolution reaction(HER)in an acidic electrolyte;however,its low abundance and high cost limit its further applicati...Platinum-based material is the most efficient and durable electrocatalyst for motivating the hydrogen evolution reaction(HER)in an acidic electrolyte;however,its low abundance and high cost limit its further application in proton-exchange membrane water electrolysis(PEMWE)technology.Therefore,minimizing the Pt amount while retaining high activity would be desirable.Herein,we use defect-rich W_(18)O_(49)nanowires to anchor well-dispersed,ultrafine Pt species(Pt-W_(18)O_(49))via a freeze-drying method to avoid aggregation,further mediating an efficient and durable HER in acidic water.Density functional theory analyses also demonstrate that the strong electronic interaction between the Pt species and W_(18)O_(49)support greatly improves the HER performance.With a 1/10 Pt loading amount of the commercial 20 wt%Pt/C,the Pt-W_(18)O_(49)catalyst requires the overpotentials of 116 and 743 mV to achieve high current densities of 100 and 1000 mA cm^(−2)in 0.5 mol L^(−1)H_(2)SO_(4),outperforming those of the 20 wt%Pt/C benchmark.More importantly,the Pt-W_(18)O_(49)catalyst can sustain a high-currentdensity HER at 500 mA cm^(−2)for more than 38 h without obvious degradation.This work paves a new avenue for synergistically reducing the Pt amount and retaining high activity for real-world PEMWE.展开更多
文摘Aris and Amundson studied a chemical reactor and obtained the two equationsDaoud showed that at most one limit cycle may exist in the region of interest. Itis showed in this paper that other singular points exist and that a stable limitt cycle existsaround the singularity (1/2, 2) when K∈(9-δ, 9).
基金Supported by the Natural Science Foundation of Guangxi Autonomous Region（0249001）
文摘For a finite group G, let S（G） be the set of minimal subgroups of odd order,which are complemented in G. It is proved that if every minimal subgroup X of odd orderof G which does not belong to S（G）, CG（X） is either subnormal or abnormal in G. Then Gsolvable.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 71071119 and 60574071
文摘Evolutionary game dynamics in finite size populations can be described by a fitness-dependent Wright- Fisher process. We consider symmetric 2×2 games in a well-mixed population. In our model, two parameters to describe the level of player＇s rationality and noise intensity in environment are introduced. In contrast with the fixation probability method that used in a noiseless case, the introducing of the noise intensity parameter makes the process an ergodic Markov process and based on the limit distribution of the process, we can analysis the evolutionary stable strategy （ESS） of the games. We illustrate the effects of the two parameters on the ESS of games using the Prisoner＇s dilemma games （PDG） and the snowdrift games （SG）. We also compare the ESS of our model with that of the replicator dynamics in infinite size populations. The results are determined by simulation experiments.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.10101005 and 10121101)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry.
文摘A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (0 < α ≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d < 2α, the limiting process is Brownian motion.
基金supported by Hong Kong Research Grants Council General Research Fund(Grant Nos.14302515 and 14304917)
文摘Let X_1, X_2,... be a sequence of independent random variables and S_n=sum X_1 from i=1 to n and V_n^2=sum X_1~2 from i=1 to n . When the elements of the sequence are i.i.d., it is known that the self-normalized sum S_n/V_n converges to a standard normal distribution if and only if max1≤i≤n|X_i|/V_n → 0 in probability and the mean of X_1 is zero. In this paper, sufficient conditions for the self-normalized central limit theorem are obtained for general independent random variables. It is also shown that if max1≤i≤n|X_i|/V_n → 0 in probability, then these sufficient conditions are necessary.
基金supported by National Natural Science Foundation of China(Grant Nos.11071045 and 11226201)Natural Science Foundation of Jiangsu Province of China(Grant No.BK20131340)+1 种基金Social Science Foundation of Chinese Ministry of Education(Grant No.12YJCZH128)QingLan Project ofthe Priority Academic Program Development of Jiangsu Higher Education Institutions(Auditing Science and Technology)
文摘This paper presents limit theorems for realized power variation of processes of the form Xt=t0φsdGs+ξt as the sampling frequency within a fixed interval increases to infinity.Here G is a Gaussian process with stationary increments,ξis a purely non-Gaussian L′evy process independent from G,andφis a stochastic process ensuring that the integral is well defined as a pathwise Riemann-Stieltjes integral.We obtain the central limit theorems for the case that both the continuous term and the jump term are presented simultaneously in the law of large numbers.
基金supported by the National Natural Science Foundation of China(Grant Nos.11372157,11302115&51608301)the Doctoral Fund of Ministry of Education of China(Grant No.20120002110075)+1 种基金the Foundation for the Author of National Excellent Doctoral Dissertation of China(Grant No.201326)the China Postdoctoral Science Foundation(Grant No.2015M571030)
文摘The finite element analysis(FEA) technology by hydraulic-mechanical-chemical-damage(HMCD) coupling is proposed in this paper for inclined wellbore stability analysis of water-sensitive and laminated rock, developed basing on the recently established FEA technology for transversely isotropic rock with hydraulic-mechanical-damage(HMD) coupling. The chemical activity of the drilling fluid is considered as phenomenological hydration behavior, the moisture content and parameters of rock considering hydration could be determined with time. The finite element(FE) solutions of numerical wellbore model considering the chemical activity of drilling fluid, damage tensor calculation and weak plane strength criterion for transversely isotropic rock are developed for researching the wellbore failure characteristics and computing the time-dependent collapse and fracture pressure of laminated rock as shale reservoirs. A three-dimensional FE model and elastic solid deformation and seepage flow coupled equations are developed, and the damage tensor calculation technology for transversely isotropic rock are realized by introducing effect of the hydration and the stress state under the current load. The proposed method utilizing weak plane strength criterion fully reflects the strength parameters in rock matrix and weak plane. To the end, an effective and reliable numerically three-step FEA strategy is well established for wellbore stability analysis. Numerical examples are given to show that the proposed method can establish efficient and applicable FE model and be suitable for analyzing the timedependsolutions of pore pressure and stresses, and the evolution region considering the hydration surrounding wellbore,furthermore to compute the collapse cycling time and the safe mud weight for collapse and fracture pressure of transversely isotropic rock.
基金the National Natural Science Foundation of China(21866028)the Development and Innovation Program of Bingtuan(2012QY13)+1 种基金the Program of Science and Technology Innovation Team in Bingtuan(2020CB006)the Achievement Transformation and Technique Popularization Project of Shihezi University(CGZH201910).
文摘Platinum-based material is the most efficient and durable electrocatalyst for motivating the hydrogen evolution reaction(HER)in an acidic electrolyte;however,its low abundance and high cost limit its further application in proton-exchange membrane water electrolysis(PEMWE)technology.Therefore,minimizing the Pt amount while retaining high activity would be desirable.Herein,we use defect-rich W_(18)O_(49)nanowires to anchor well-dispersed,ultrafine Pt species(Pt-W_(18)O_(49))via a freeze-drying method to avoid aggregation,further mediating an efficient and durable HER in acidic water.Density functional theory analyses also demonstrate that the strong electronic interaction between the Pt species and W_(18)O_(49)support greatly improves the HER performance.With a 1/10 Pt loading amount of the commercial 20 wt%Pt/C,the Pt-W_(18)O_(49)catalyst requires the overpotentials of 116 and 743 mV to achieve high current densities of 100 and 1000 mA cm^(−2)in 0.5 mol L^(−1)H_(2)SO_(4),outperforming those of the 20 wt%Pt/C benchmark.More importantly,the Pt-W_(18)O_(49)catalyst can sustain a high-currentdensity HER at 500 mA cm^(−2)for more than 38 h without obvious degradation.This work paves a new avenue for synergistically reducing the Pt amount and retaining high activity for real-world PEMWE.
