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Microbial community structure and functional metabolic diversity are associated with organic carbon availability in an agricultural soil 被引量:5
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作者 LI Juan LI Yan-ting +3 位作者 YANG Xiang-dong ZHANG Jian-jun LIN Zhi-an ZHAO Bing-qiang 《Journal of Integrative Agriculture》 SCIE CAS CSCD 2015年第12期2500-2511,共12页
Exploration of soil environmental characteristics governing soil microbial community structure and activity may improve our understanding of biogeochemical processes and soil quality. The impact of soil environmental ... Exploration of soil environmental characteristics governing soil microbial community structure and activity may improve our understanding of biogeochemical processes and soil quality. The impact of soil environmental characteristics especially organic carbon availability after 15-yr different organic and inorganic fertilizer inputs on soil bacterial community structure and functional metabolic diversity of soil microbial communities were evaluated in a 15-yr fertilizer experiment in Changping County, Beijing, China. The experiment was a wheat-maize rotation system which was established in 1991 including four different fertilizer treatments. These treatments included: a non-amended control(CK), a commonly used application rate of inorganic fertilizer treatment(NPK); a commonly used application rate of inorganic fertilizer with swine manure incorporated treatment(NPKM), and a commonly used application rate of inorganic fertilizer with maize straw incorporated treatment(NPKS). Denaturing gradient gel electrophoresis(DGGE) of the 16 S r RNA gene was used to determine the bacterial community structure and single carbon source utilization profiles were determined to characterize the microbial community functional metabolic diversity of different fertilizer treatments using Biolog Eco plates. The results indicated that long-term fertilized treatments significantly increased soil bacterial community structure compared to CK. The use of inorganic fertilizer with organic amendments incorporated for long term(NPKM, NPKS) significantly promoted soil bacterial structure than the application of inorganic fertilizer only(NPK), and NPKM treatment was the most important driver for increases in the soil microbial community richness(S) and structural diversity(H). Overall utilization of carbon sources by soil microbial communities(average well color development, AWCD) and microbial substrate utilization diversity and evenness indices(H' and E) indicated that long-term inorganic fertilizer with organic amendments incorporated(NPKM, NPKS) could significantly stimulate soil microbial metabolic activity and functional diversity relative to CK, while no differences of them were found between NPKS and NPK treatments. Principal component analysis(PCA) based on carbon source utilization profiles also showed significant separation of soil microbial community under long-term fertilization regimes and NPKM treatment was significantly separated from the other three treatments primarily according to the higher microbial utilization of carbohydrates, carboxylic acids, polymers, phenolic compounds, and amino acid, while higher utilization of amines/amides differed soil microbial community in NPKS treatment from those in the other three treatments. Redundancy analysis(RDA) indicated that soil organic carbon(SOC) availability, especially soil microbial biomass carbon(Cmic) and Cmic/SOC ratio are the key factors of soil environmental characteristics contributing to the increase of both soil microbial community structure and functional metabolic diversity in the long-term fertilization trial. Our results showed that long-term inorganic fertilizer and swine manure application could significantly improve soil bacterial community structure and soil microbial metabolic activity through the increases in SOC availability, which could provide insights into the sustainable management of China's soil resource. 展开更多
关键词 long-term fertilization regimes organic amendment soil microbial community structure microbial functional metabolic activity carbon substrate utilization
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Optimal Quota-Share and Excess-of-Loss Reinsurance and Investment with Heston’s Stochastic Volatility Model 被引量:2
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作者 伊浩然 舒慧生 单元闯 《Journal of Donghua University(English Edition)》 CAS 2023年第1期59-67,共9页
An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is... An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided. 展开更多
关键词 optimal reinsurance optimal investment quota-share and excess-of-loss reinsurance stochastic volatility(SV)model exponential utility function
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An RVT-based power allocation method for dynamic LEO-MEO links
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作者 潘坤贝 ZHOU Bin +1 位作者 ZHAO Yu BU Zhiyong 《High Technology Letters》 EI CAS 2023年第1期1-11,共11页
Optimizing the power resources allocation method of low earth orbit(LEO)satellites to medium earth orbit(MEO)satellite'links is a significant way to construct efficient satellite constellations for satellite commu... Optimizing the power resources allocation method of low earth orbit(LEO)satellites to medium earth orbit(MEO)satellite'links is a significant way to construct efficient satellite constellations for satellite communication.A game theory power allocation method based on remaining visible time(RVT)of LEO-MEO satellites is proposed.Firstly,one LEO-MEO satellite network is classified as a cluster in which the RVT of LEO satellites is modeled.Secondly,the cost function of RVT concerning the character of orbit and throughput in each LEO satellite is mainly designed,which gives greater punishment of utility value to LEO satellites with less RVT and is an essential part of the reasonable utility function applied in diverse motion scenes.Meanwhile,the existence of Nash equilibrium for the proposed utility function in game theory area is proved.Thirdly,an off-cluster scheme for LEO satellites through the proposed threshold is raised to ensure the overall utility value of the whole LEO satellites in cluster.Finally,the performance improvement of the proposed algorithm to the baseline algorithm is verified through simulations in different scenarios. 展开更多
关键词 inter-satellite link power allocation remaining visible time(RVT) utility function motion trajectory(MT) game theory
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Entrepreneur Education Level and Its Utility Maximization
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作者 Baozhu Liu Mingxia Lyu Yirong Ying 《Intelligent Information Management》 2023年第3期160-168,共9页
The education level of entrepreneurs plays an important role in the decision-making process of loan financing. In this paper, the research method of optimization theory is used to study the problem of the education le... The education level of entrepreneurs plays an important role in the decision-making process of loan financing. In this paper, the research method of optimization theory is used to study the problem of the education level and maximizing utility of entrepreneurs, and the optimal analytic solution is obtained. On this basis, the influence of the change of bank loan interest rate, the marginal effect of entrepreneur’s effort, the marginal effect of entrepreneur’s investment, the elastic coefficient of entrepreneur’s effort and the elastic coefficient of entrepreneur’s investment on the optimal solution of entrepreneur’s effort and investment amount is discussed. 展开更多
关键词 Educational Background Utility Function Enterprise Performance
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Curb parking pricing method based on parking choice behavior 被引量:3
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作者 梅振宇 陈峻 王炜 《Journal of Southeast University(English Edition)》 EI CAS 2006年第4期559-563,共5页
In order to improve the use efficiency of curb parking, a reasonable curb parking pricing is evaluated by considering individual parking choice behavior. The parking choice behavior is analyzed from micro-aspects, and... In order to improve the use efficiency of curb parking, a reasonable curb parking pricing is evaluated by considering individual parking choice behavior. The parking choice behavior is analyzed from micro-aspects, and the choice behavior utility function is established combining trip time, search time, waiting time, access time and parking fee. By the utility function, a probit-based parking choice behavior model is constructed. On the basis of these, the curb parking pricing model is deduced by considering the constrained conditions, and an incremental assignment algorithm of the model is also designed. Finally, the model is applied to the parking planning of Tongling city. It is pointed out that the average parking time of curb parking decreases 34%, and the average turnover rate increases 67% under the computed parking price system. The results show that the model can optimize the utilization of static traffic facilities. 展开更多
关键词 curb parking parking choice behavior utility function incremental assignment
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Rapid design of secondary deformation-aging parameters for ultra-low Co content Cu-Ni-Co-Si-X alloy via Bayesian optimization machine learning 被引量:6
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作者 Hongtao Zhang Huadong Fu +1 位作者 Yuheng Shen Jianxin Xie 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 2022年第6期1197-1205,共9页
It is difficult to rapidly design the process parameters of copper alloys by using the traditional trial-and-error method and simultaneously improve the conflicting mechanical and electrical properties.The purpose of ... It is difficult to rapidly design the process parameters of copper alloys by using the traditional trial-and-error method and simultaneously improve the conflicting mechanical and electrical properties.The purpose of this work is to develop a new type of Cu-Ni-Co-Si alloy saving scarce and expensive Co element,in which the Co content is less than half of the lower limit in ASTM standard C70350 alloy,while the properties are as the same level as C70350 alloy.Here we adopted a strategy combining Bayesian optimization machine learning and experimental iteration and quickly designed the secondary deformation-aging parameters(cold rolling deformation 90%,aging temperature 450℃,and aging time 1.25 h)of the new copper alloy with only 32 experiments(27 basic sample data acquisition experiments and 5 iteration experiments),which broke through the barrier of low efficiency and high cost of trial-and-error design of deformation-aging parameters in precipitation strengthened copper alloy.The experimental hardness,tensile strength,and electrical conductivity of the new copper alloy are HV(285±4),(872±3)MPa,and(44.2±0.7)%IACS(international annealed copper standard),reaching the property level of the commercial lead frame C70350 alloy.This work provides a new idea for the rapid design of material process parameters and the simultaneous improvement of mechanical and electrical properties. 展开更多
关键词 copper alloy process design machine learning Bayesian optimization utility function
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Power Control Algorithm of Cognitive Radio Based on Non-Cooperative Game Theory 被引量:4
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作者 赵军辉 杨涛 +2 位作者 贡毅 王娇 付雷 《China Communications》 SCIE CSCD 2013年第11期143-154,共12页
This paper addresses the power con- trol problems of Cognitive Radio (CR) trader transmission power and interference tempera- ture constraints. First, we propose the interfer- ence constraint which ensures that the ... This paper addresses the power con- trol problems of Cognitive Radio (CR) trader transmission power and interference tempera- ture constraints. First, we propose the interfer- ence constraint which ensures that the Quality of Service (QoS) standards for primary users is considered and a non-cooperative game power control model. Based on the proposed model, we developed a logical utility function based on the Signal-to-Interference-Noise Ratio (S/NR) and a novel algorithm network power control. that is suitable for CR Then, the existence and uniqueness of the Nash Equilibrium (NE) in our utility function are proved by the principle of game theory and the corresponding optimi- zations. Compared to traditional algorithms, the proposed one could converge to an NE in 3-5 iterative operations by setting an appropriate pricing factor. Finally, simulation results ver- ified the stability and superiority of the novel algorithm in flat-fading channel environments. 展开更多
关键词 cognitive radio non-cooperativepower control game theory utility function Na-sh equilibrium target power
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Utility function based fair data scheduling algorithm for OFDM wireless network 被引量:3
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作者 Guo Kunqi Sun Lixin Jia Shilou 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2007年第4期731-738,共8页
A system model is formulated as the maximization of a total utility function to achieve fair downlink data scheduling in multiuser orthogonal frequency division multiplexing (OFDM) wireless networks. A dynamic subca... A system model is formulated as the maximization of a total utility function to achieve fair downlink data scheduling in multiuser orthogonal frequency division multiplexing (OFDM) wireless networks. A dynamic subcarrier allocation algorithm (DSAA) is proposed, to optimize the system model. The subcarrier allocation decision is made by the proposed DSAA according to the maximum value of total utility function with respect to the queue mean waiting time. Simulation results demonstrate that compared to the conventional algorithms, the proposed algorithm has better delay performance and can provide fairness under different loads by using different utility functions. 展开更多
关键词 OFDM SCHEDULING ALGORITHM utility function.
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Attractive Model and Marketing Implications of Theme Shopping Tourism Destination 被引量:2
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作者 LIU Jiaming WANG Run 《Chinese Geographical Science》 SCIE CSCD 2010年第6期562-567,共6页
This paper discusses the definition and connotation of Theme Shopping Tourism(TST) destination,and reveals the attractive distance of TST destination based on the utility function derived from the supposed demand func... This paper discusses the definition and connotation of Theme Shopping Tourism(TST) destination,and reveals the attractive distance of TST destination based on the utility function derived from the supposed demand function.An attractive model is deduced.According to this attractive model,it is can be known that the attractive distance is related to the price difference of the theme commodities between TST destination and tourist origin place,the average expenditure of transport,the demand elasticity of price,the actual price of sightseeing spot,the critical price that a tourist will afford,the number of nights that a tourist stays on the TST destination and the price level of accommodation in the TST destination.The change mechanism of attractive distance of TST destinations is revealed in this paper,and implications on TST marketing are put forward.First,theme commodities should be luxuries.Second,lower price is the primary pulling factor of theme shopping tourism.Third,the route combining with sightseeing spots is beneficial to shopping tourism.At last,TST development is one way of rejuvenating the falling destinations. 展开更多
关键词 theme shopping tourism destination attractive model utility function tourism marketing
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Optimization of the Dressing Parameters in Cylindrical Grinding Based on a Generalized Utility Function 被引量:2
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作者 ALEKSANDROVA Irina 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2016年第1期63-73,共11页
The existing studies, concerning the dressing process, focus on the major influence of the dressing conditions on the grinding response variables. However, the choice of the dressing conditions is often made, based on... The existing studies, concerning the dressing process, focus on the major influence of the dressing conditions on the grinding response variables. However, the choice of the dressing conditions is often made, based on the experience of the qualified staff or using data from reference books. The optimal dressing parameters, which are only valid for the particular methods and dressing and grinding conditions, are also used. The paper presents a methodology for optimization of the dressing parameters in cylindrical grinding. The generalized utility function has been chosen as an optimization parameter. It is a complex indicator determining the economic, dynamic and manufacturing characteristics of the grinding process. The developed methodology is implemented for the dressing of aluminium oxide grinding wheels by using experimental diamond roller dressers with different grit sizes made of medium- and high-strength synthetic diamonds type AC32 and AC80. To solve the optimization problem, a model of the generalized utility function is created which reflects the complex impact of dressing parameters. The model is built based on the results from the conducted complex study and modeling of the grinding wheel lifetime, cutting ability, production rate and cutting forces during grinding. They are closely related to the dressing conditions (dressing speed ratio, radial in-feed of the diamond roller dresser and dress-out time), the diamond roller dresser grit size/grinding wheel grit size ratio, the type of synthetic diamonds and the direction of dressing. Some dressing parameters are determined for which the generalized utility fimction has a maximum and which guarantee an optimum combination of the following: the lifetime and cutting ability of the abrasive wheels, the tangential cutting force magnitude and the production rate of the grinding process. The results obtained prove the possibility of control and optimization of grinding by selecting particular dressing parameters. 展开更多
关键词 dressing conditions cylindrical grinding diamond roller dresser generalized utility function based optimization
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Analysis of Optimal Portfolio with Different Utility Function 被引量:2
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作者 YAO Yuan SHI Ben-shan 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第1期124-128,共5页
The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probabili... The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure (martingale measure) if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function. 展开更多
关键词 expected utility function OPTIMIZATION PORTFOLIO risk neutral probability
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Measuring the social performance of forest management 被引量:1
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作者 Timo Pukkala 《Journal of Forestry Research》 SCIE CAS CSCD 2021年第5期1803-1818,共16页
Forests produce several types of benefits to both forest landowners and society.The social benefit of private forestry is equal to private benefit plus positive externalities minus negative externalities.This study de... Forests produce several types of benefits to both forest landowners and society.The social benefit of private forestry is equal to private benefit plus positive externalities minus negative externalities.This study developed alternative metrics for the evaluation of the social benefit of forest management.Forest management was assessed in terms of five criteria:economic,socio-cultural,environmental and ecological performance and the resilience of the forest ecosystem.Each criterion was described with three numerical indicators.Alternative performance indices were calculated from the indicator values using methods developed for multi-criteria decision making.It was concluded that indices based on the multiplicative Cobb-Douglas utility function might be the most recommendable when forestry should produce a balanced combination of different ecosystem services.When the indices were used to compare alternative silvicultural systems in terms of their social performance,continuous cover management was ranked better than even-aged management.The performance of even-aged management improved when it aimed at increasing the share of mixed stands and broadleaf species.Maximizing net present value(NPV) with a 1 % discount rate led to better social performance than maximizing NPV with a 4% discount rate. 展开更多
关键词 Efficiency analysis ACCEPTABILITY Sustainable forestry Performance index Utility function Multi-criteria analysis Continuous cover forestry Evenaged forestry RESILIENCE
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Characteristic Properties of Perspective Sets for Finite Stochastic Decision 被引量:1
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作者 Zhang Mingshan & Guo Yaohuang (College of Econonlics and Management, Southwest Jiaotong University, Chengdu 610031, P. R. China ) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1998年第3期8-15,共8页
For a perspective set that is derived by finite consequences with probabilities, this paper introduces the conception of basis that is proved and the uniqueness of basis over a perspective set holds. These give the ch... For a perspective set that is derived by finite consequences with probabilities, this paper introduces the conception of basis that is proved and the uniqueness of basis over a perspective set holds. These give the characteristic properties of perspective sets and finite consequences with probabilities. These properties are applied to the utility defined by the consequences. 展开更多
关键词 Perspective set BASIS Characteristic properties Utility functions
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FOREIGN CURRENCY OPTION PRICING WITH PROPORTIONAL TRANSACTION COSTS 被引量:1
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作者 Li Shujin Li Shenghong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第4期383-396,共14页
The purpose of present work is to examine the financial problem of finding the universal reservation prices of a European call option written on exchange rate when there is proportional transaction costs of trading fo... The purpose of present work is to examine the financial problem of finding the universal reservation prices of a European call option written on exchange rate when there is proportional transaction costs of trading foreign currency in the market. An approach is suggested to compute the reservation bid-ask price of foreign currency call option based on maximizing the investor's expected utility. Option prices are determined from the investor's basic portfolio selection problem, without the need to solve a more complex optimization problem involving the insertion of the option payoffs into the terminal value function. Option prices are computed numerically in a Markov chain approximation for the case of exponential utility. Numerical results show that the option price bounds are almost independent of the alternative risk aversion parameter, but the bounds of NT region becomes narrower and the range of values of the initial holding for which the fair price lies within the bid-ask spread is shifted to a lower value when the risk aversion parameter increases. 展开更多
关键词 exchange rate proportional transaction costs utility function optimal strategy.
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Sensitivity analysis method for increasing the passenger demands of parking and riding 被引量:1
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作者 邓卫 潘艳荣 郭唐仪 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2009年第6期859-862,共4页
Focused on finding out the relationship between passenger demands of P&R and its influencing factors, a nested-logit mode choice model was developed based on the characteristic of different modes and transfer rule... Focused on finding out the relationship between passenger demands of P&R and its influencing factors, a nested-logit mode choice model was developed based on the characteristic of different modes and transfer rules. The utility functions were given respectively according to the characteristic of each alternative. Passenger demands of different modes between O-D pairs were obtained by making use of the binary logit model. Then an equilibrium model for different modes was proposed. Under this condition, the approximate relationship between passenger demands of different modes and their characteristic indexes was modeled by the sensitivity analysis method. Shift volume among different modes was achieved by utilizing this model when their characteristic indexes were changed. A case study indicates that the model and algorithm presented in this paper are effective. 展开更多
关键词 nested-logit model parking and riding (P&R) sensitivity analysis utility function passenger demands
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Study on information utility 被引量:1
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作者 张东戈 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2005年第3期579-582,644,共5页
Information has two aspects. One aspect is the objective one; another aspect is the subjective one. Shannon has discussed the objective aspect of information in information theory. But the subjective aspect of informa... Information has two aspects. One aspect is the objective one; another aspect is the subjective one. Shannon has discussed the objective aspect of information in information theory. But the subjective aspect of information has not been fully discussed. Someone use “Bayesian approaches” to evaluate the value of information. But in some cases it does not meet the information user's need. This paper is focus on the subjective aspect of objectively measurable information and gives formal definitions for information, information utility, and marginal information utility, normalized calculation of information utility. The information discussed in the paper has interdisciplinary nature. This work can be the foundation of many application areas. 展开更多
关键词 analysis definition of information analysis definition of information utility analysis definition of marginal information utility normalized calculation of information utility mic^nomics analysis expression of information utility information utility functions C^4ISR system evaluation.
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Proportional rate scheduling based on QoS in mobile WiMAX networks
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作者 Fang Lintang Zhang Xiaolin 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第6期1332-1335,共4页
A new scheduling scheme based on users' quality of service(QoS) in mobile WiMAX networks is presented.The proposed scheme tracks each user's average rate and adjusts the corresponding scheduling weight adaptively ... A new scheduling scheme based on users' quality of service(QoS) in mobile WiMAX networks is presented.The proposed scheme tracks each user's average rate and adjusts the corresponding scheduling weight adaptively to result in:(a) each user's average rate is proportional to the corresponding QoS level;(b) the constraints of the minimal and/or maximal rates required by QoS can be satisfied;(c) the utility function of system is maximal under the constraints(a) and(b).Theoretical analysis based on utility function and simulation results indicates the system throughput can be improved dramatically in the proposed scheme. 展开更多
关键词 mobile WiMAX QUALITY-OF-SERVICE SCHEDULING utility function.
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QoS awared power and admission controls based on non-cooperative game theory in wireless networks
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作者 张阳 朱世华 李峰 《Journal of Pharmaceutical Analysis》 SCIE CAS 2008年第3期149-154,共6页
In order to better accommodate heterogeneous quality of service (QoS) in wireless networks, an algorithm called QoS-aware power and admission controls (QAPAC) is proposed. The system is modeled as a non-cooperative ga... In order to better accommodate heterogeneous quality of service (QoS) in wireless networks, an algorithm called QoS-aware power and admission controls (QAPAC) is proposed. The system is modeled as a non-cooperative game where the users adjust their transmit powers to maximize the utility, thus restraining the interferences. By using adaptive utility functions and tunable pricing parameters according to QoS levels, this algorithm can well meet different QoS requirements and improve system capacity compared with those that ignore the QoS differences. 展开更多
关键词 power and admission control non-cooperative game utility function PRICING heterogeneous QoS
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Exploring multiple equilibria for symmetric 2×2 CES/LES pure exchange economies
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作者 SHI Xiao-jun ZHANG Shun-ming 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第2期137-154,共18页
This paper explores the existence of 3 equilibria for symmetric 2-individual 2-good CES/LES pure exchange economies. For certain parameterizations in the economies, we show analytically that there are no more than 3 e... This paper explores the existence of 3 equilibria for symmetric 2-individual 2-good CES/LES pure exchange economies. For certain parameterizations in the economies, we show analytically that there are no more than 3 equilibria. We generalize our analytical results of existence of 3 equilibria for a wide range of parameterizations. Then we provide examples of 3 equilibria and parameter zones of 3 equilibria for CES and CES/LES economies. 展开更多
关键词 Multiple equilibria Cobb-Douglas utility function CES/LES utility function.
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Optimal investment with transaction costs based on exponential utility function:a parabolic double obstacle problem
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作者 BAO Qun-fang YANG Jing-yang +1 位作者 SUN Chao LI Sheng-hong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第4期483-492,共10页
This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the prob... This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method. 展开更多
关键词 Optimal investment transaction costs double obstacle problem stochastic control exponential utility function.
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