浅谈“平衡态”在数学游戏中的应用

数学游戏包含着许多数学理论，其中有一种是所谓的“平衡态”．比方说，甲乙二人进行数学游戏，甲先适当操作，创造出平衡态，乙接着不管怎样操作，得到的总是不平衡态，甲再设法(实际上也能够)恢复平衡态，……这样周而复始，最终甲获胜，下面举例说明．

Equilibrium Control Theory and Direct Method of Feedback Linearization for Nonlinear Time Varying Systems

Aim To present a simple and effective method for the design of nonlinear and time varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was pointed out that what is controlled directly by the input of a control system is the system's dynamic equilibrium rather than the states. Based on it, a new feedback linearization method for nonlinear system based on the Lyapunov direct method was given. Simulation studies were also carried out. Results The example and simulation show that by use of the method, the controller design becomes very simple and the control effect is quite satisfying. Conclusion The new method unifies the stabilizing problem(regulating problem) with the tracking problem. It is a very simple and effective method for the design of nonlinear and time varying control system.

Microstructural characteristics of Al-20Si-2Cu-0.4Mg-1Ni alloy formed by rheo-squeeze casting after ultrasonic vibration treatment

A swash plate for air conditioning compressor of cars was formed by rheo-squeeze casting with semi-solid Al-Si alloy slurry prepared by ultrasonic vibration process, and the microstructure of this alloy was investigated. Besides the microstructures of primary Si particles and α(Al)+β-Si eutectic phases, non-equilibrium α(Al) particles or dendrites are discovered in the microstructure of the Al-20Si-2Cu-0.4Mg-1Ni alloy. Rapid cooling generated by squeeze casting process rather than the pressure is considered as the main reason for the formation of non-equilibrium α(Al) phase. The sound pressurizing effect of ultrasonic vibration also enables the non-equilibrium α(Al) phases to form above eutectic temperature and grow into non-dendritic spheroids in the process of semi-solid slurry preparation. Non-equilibrium α(Al) phases formed in the hypereutectic Al-Si alloy with ultrasonic vibration treatment, consist of round α(Al) grains formed above the eutectic temperature and a small amount of fine α(Al) dendrites formed under the eutectic temperature. The volume fraction of primary Si particles is decreased significantly by the effect of ultrasonic vibration through increasing the solid solubility of Si atoms in α(Al) matrix and decreasing the forming temperature range of primary Si particles. The average particle diameter and the volume fraction of primary Si particles in microstructure of the swash-plate by rheo-squeeze casting are 24.3 μm and 11.1%, respectively.

Theoretical analysis of ultra-short pulsed laser ablation of SiO_2 material based on a Coulomb explosion model

Based on the kinetic theoretical Vlasov-Poisson equation, a surface Coulomb explosion model of SiO2 material induced by ultra-short pulsed laser radiation is established. The non-equilibrium free electron distribution resulting from the two mechanisms of multi-photon ionization and avalanche ionization is computed. A quantitative analysis is given to describe the Coulomb explosion induced by the self-consistent electric field, and the impact of the parameters of laser pulses on the surface ablation is also discussed. The results show that the electron relaxation time is not constant, but it is related to the microscopic state of the electrons, so the relaxation time approximation is not available on the femtosecond time scale. The ablation depths computed by the theoretical model are in good agreement with the experimental results in the range of pulse durations from 0 to 1 ps.

Progress in Studies on the Equilibrium Shape of Headland-bay Shoreline

Research on the laws controlling the shoreline equilibrium shape has been one important topic of studying the evolvement and stabilization of sandy coasts. After a brief review of the progress on the equilibrium shape laws research, five models are introduced in detail. Advantages and disadvantages of these models are then discussed, which leads to the conclusion that the empirical formula integrating with analysis of mechanism should be the future direction of study on the headland-bay equilibrium shape laws. Finally, the importance of the study on the equilibrium shape of headland-bay in China is also discussed.

Dynamic load balancing based on restricted multicast tree in triplet-based hierarchical interconnection network

To solve the load balancing problem in a triplet-based hierarchical interconnection network（THIN） system, a dynamic load balancing （DLB）algorithm--THINDLBA, which adopts multicast tree （MT）technology to improve the efficiency of interchanging load information, is presented. To support the algorithm, a complete set of DLB messages and a schema of maintaining DLB information in each processing node are designed. The load migration request messages from the heavily loaded node （HLN）are spread along an MT whose root is the HLN. And the lightly loaded nodes（LLNs） covered by the MT are the candidate destinations of load migration; the load information interchanged between the LLNs and the HLN can be transmitted along the MT. So the HLN can migrate excess loads out as many as possible during a one time execution of the THINDLBA, and its load state can be improved as quickly as possible. To avoid wrongly transmitted or redundant DLB messages due to MT overlapping, the MT construction is restricted in the design of the THINDLBA. Through experiments, the effectiveness of four DLB algorithms are compared, and the results show that the THINDLBA can effectively decrease the time costs of THIN systems in dealing with large scale computeintensive tasks more than others.

Precipitation responses to radiative processes of water- and ice-clouds: an equilibrium cloud-resolving modeling study

Cloud radiative processes are important in regulating weather and climate. Precipitation responses to radiative processes of water- and ice-clouds are investigated by analyzing mean equilibrium simulation data from a series of two-dimensional cloud-resolving model sensitivity experiments in this study. The model is imposed by zero vertical velocity.The exclusion of water radiative processes in the presence of ice radiative processes, as well as the removal of ice radiative processes, enhances tropospheric Iongwave radiative cooling and lowers air temperature and the saturation mixing ratio. The reduction in the saturation mixing ratio leads to an increase in vapor condensation and an associated release of latent heat, which increases rainfall. The elimination of water radiative processes strengthens local atmospheric warming Iongwave radiative cooling. The enhanced warming melting of graupel, which increases rainfa n the upper troposphere via a reduction in ncreases the rain source via an increase in the

Study on Hydrolysis of Methyl Acetate in a Catalytic Distillation Column

A nonequilibrium stage model was used to simulate countercurrent multicomponent catalytic distillation processes for methyl acetate hydrolysis. Computations of stage efficiencies or height equivalent to a theoretical plate (HETP) were entirely avoided by this model. The consistency of simulated results and experimental data in conversions and concentration of each component along a column indicates that the model predicts the actual process well. The influences of operating parameters on hydrolytic conversions, such as feed molar ratios, feed locations, feed and reflux rates, heights of reactive and stripping sections, were analyzed adequately by simulating calculations. A good operating mode was then obtained, which is helpful to the development of a new process.

Simulation of Suspension Catalytic Distillation for Synthesis of Linear Alkylbenzene

Suspension catalytic distillation (SCD) has been developed recently as an innovative technology in catalytic distillation. In this paper, a brief introduction to SCD is given and an equilibrium stage (EQ) modei is developed to simulate this new process for synthesis of linear alkylbenzene (LAB) from benzene and 1-dodecene. Since non-ideality of this reaction systern is not strong, EQ modei developed could be applied to it successfully. Simulation results agree well with experimental data, and indicate some characteristics of SCD process as an advanced technology for the production of LAB: 100% conversion of olefins, low temperature (90-100℃) and low benzene/olefin mole ratio.

Non-equilibrium State Salt-forming Phase Diagram：Utilization of Bittern Resource in High Efficiency

Salt-forming regions for a complex salt-water system in non-equilibrium state of evaporation process are usually different from those in solubility diagrams.To understand the solid-forming region of NaCl and improve the utilization of bittern resources,experiments were carried out to evaporate 20 representative mixture solution samples of Na ^＋,Mg ^2＋ //Cl^-, SO4^2--H2O system with an average evaporation intensity of（1.4±0.4） g·L^-1 ·min^-1（water） at boiling temperature 348 K,and determine the NaCl solid-forming regions in non-equilibrium state.Because of the complexity of salt-forming region,a maximal region and a minimal region were proposed to express the non-equilibrium state salt-forming region with different crystal seed,and a conditional salt-forming region was proposed to present the characteristic region of non-equilibrium salt-forming phase diagram.The areas of the maximal and minimal regions are 2.00 and 1.56 times those in solubility diagram,so it is possible to utilize bittern resources in high efficiency.The recovery rates of NaCl were 99.65%,93.14%,88.57%,72.76%,and 83.68%for six typical bittern sources from Tulantai Salt Lake（China）,Dongtai Salt Lake（China） ,Jilantai Salt Lake（China）,Qarun Salt Lake（Egypt） and seawater,respectively.It is testified that the non-equilibrium state salt-forming phase diagram can be used in industrial processes.

The Stepping Motion of Brownian Particle Derived by Nonequilibrium Fluctuation

The direct motion of Brownian particle is considered as a result of system derived by external nonequilibriumfluctuating. The cooperative effects caused by asymmetric ratchet potential, external rocking force and additive colorednoise drive a Brownian particle in the directed stepping motion. This provides this kind of motion of kinesin along amicrotubule observed in experiments with a reasonable explanation.

Analysis of Genetic Diversity and Differentiation of Seven Stocks of Litopenaeus vannamei Using Microsatellite Markers

Seven microsatellite markers were used to evaluate the genetic diversity and differentiation of seven stocks of Litopenaeus vannamei, which were introduced from Central and South America to China. All seven microsatellite loci were polymorphic, with polymorphism information content(PIC) values ranging from 0.593 to 0.952. Totally 92 alleles were identified, and the number of alleles(Na) and effective alleles(Ne) varied between 4 and 21 and 2.7 and 14.6, respectively. Observed heterozygosity(Ho) values were lower than the expected heterozygosity(He) values(0.526–0.754), which indicated that the seven stocks possessed a rich genetic diversity. Thirty-seven tests were detected for reasonable significant deviation from Hardy-Weinberg equilibrium. Fis values were positive at five loci, suggesting that there was a relatively high degree of inbreeding within stocks. Pairwise Fst values ranged from 0.0225 to 0.151, and most of the stock pairs were moderately differentiated. Genetic distance and cluster analysis using UPGMA revealed a close genetic relationship of L. vannamei between Pop2 and Pop3. AMOVA indicated that the genetic variation among stocks(11.3%) was much lower than that within stocks(88.7%). Although the seven stocks had a certain degree of genetic differentiation and a rich genetic diversity, there is an increasing risk of decreased performance due to inbreeding in subsequent generations.

Adsorption of Dye from Wastewater by Zeolites Synthesized from Fly Ash:Kinetic and Equilibrium Studies

The removal performance of a basic dye, methylene blue (MB), in aqueous solution was investigated by adsorption process on single-phase and high-crystalline zeolite A (FA-ZA) and X (FA-ZX). Both adsorbents FA-ZA and FA-ZX were synthesized from fly ash prepared aluminosilicate gel followed by the hydrothermal treatment at 100°C with the control of Si/Al molar ratio, respectively. The properties of the synthetic zeolites and commercial grade zeolites, such as thermal stability, elemental composition, and cation exchange capacity, were investigated for comparison. Batch method was used to study the influential parameters, such as initial pH value of the solution, temperatures, and adsorbents dosage, on the adsorption process. The experimental data were well fitted by Ho’ pseudo-second-order model and liquid film diffusion model. The suitability of Langmuir and Freundlich isotherms to the equilibrium data was investigated in the solid-liquid system while the Langmuir model produces the best re-sults. Thermodynamic data (△H, △S, and △G) corresponding to the MB uptake were evaluated from the Langmuir model. In all the adsorption experiments, the adsorption capacity followed the order as follows: FA-ZX > FA-ZA. In addition, attempts were also made to regenerate the adsorbents.

Thermal-environment characteristics and comfort of combined radiant-floor (Korean heating system ondol) and convective cooling system

The thermal-environment characteristics of the existing forced-convection cooling system were compared with those of the convective cooling system, which combined the radiant-floor cooling system using floor-heating panel typically applied to apartments in South Korea with the forced-convection cooling system using improved fan coil unit. The subjective warm/cool-feeling responses to the combined radiant-floor and convective cooling system in the questionnaire survey conducted among the test subjects were analyzed to establish the basic data for the combined cooling system. The results show that in the thermal-equilibrium condition, the vertical air temperature difference in the model living room is larger in the forced-convection-cooling condition. Most of the subjects feel a proper warm/cool feeling on their entire body, but they feel colder on the foot and lower body in the combined-cooling condition.

Isolation and characterization of 45 polymorphic microsatellite loci of turbot(Scophthalmus maximus)and cross-species amplification

Turbot （Scophthalmus maximus） is a flatfish species commercially important for aquaculture. In this study, we generated a microsatellite-enriched genomic DNA library for Scophthalmus rnaxirnus, and then isolated and characterized 45 microsateIIite loci by genotyping 30 individuals. The observed number of alleles ranged from 2 to 19 with an average of 6.24, while the effective number of alleles ranged from 1.30 to 11.11 with an average of 3.66. The expected heterozygosities varied from 0.235 to 0.9254 and polymorphic information content ranged from 0.204 4 to 0.903 3, with an average of 0.622. Twelve loci deviated significantly from Hardy-Weinberg equilibrium, and no significant linkage disequilibrium was observed between any pair of loci after Bonferroni correction. In cross-species amplification, five flatfish species （Paralichthys lethostigma, Verasper rnoseri, platichthys stellatus, Hippoglossoides dubius and Cynoglossus semilaevis） showed at least one polymorphic locus. These polymorphic microsatellite loci should prove useful for population analysis of turbot and other related species.

Salt-Water Dynamics in Soils: V. Salt Balance in Soil Profiles

Salt balance in simulated soil columns was calculated on the basis of a large amount of long termobservation data. The results showed that under the climate conditions of senii-arid region of the Hnaiig-Huai-Hai Plain, the soils in the columns were under salt accumulation conditions when the groundwater depthwas controlled at less than 2.0 m, and under desalinization conditions when at larger than 2.5 m. In the soilcolnmns with clay soil and silty loam soil intercalated with a clay layer, the aniount of salt accumulated wasfar less than that in the soil column with silty loain soil throughout the whole profile. Under no irrigationconditions crop planting niay increase groundwater evaporation and hence salt accumulation in soil, mforingthe soil colnmns under desalinization be under salt accumulation conditions.

Quantum Measurement of Single Electron State by a Mesoscopic Detector

A realistic measurement setup for a system such system measured by a mesoscopie detector,is theoretically as a charged two-state （qubit） or multi-state quantum studied. To properly describe the measurement-induced back-action,a detailed-balance preserved quantum master equation treatment is developed. The established framework is applicable for arbitrary voltages and temperatures.

Species-diversified plant cover enhances orchard ecosystem resistance to climatic stress and soil erosion in subtropical hillside

Naturally occurring plants in agroecosystem evidently play an important role in ecosystem stability. Field studies on the ecological effects of native plants conserved in orchard and their resistance to adverse climatic stress, and soil erosion were conducted from 1998 to 2001 in a newly developed Changshan-huyou (Citrus changshan-huyou Y.B. Chang) orchard. The experimental area covered 150 ha in typical red soil hilly region in southeastern China. The experimental design was a randomized complete block with six combinations of twelve plant species with four replications. All species used were native in the orchard. Plots were 15×8m^2 and separated by 2m buffer strips. Precipitation, soil erosion in rainstorm days and aboveground biomass of plant community when rainstorm days ended, soil temperature and moisture under various plant covers during seasonal megathermal drought period, antiscourability of soil with different root density under various simulated rainfalls were measured. Plant cover significantly decreased the daily highest and mean soil temperature and its daily variation in hot-drought season, but there was no significant difference of the alleviation among various plant covers. Plant covers significantly increased the soil moisture in seasonal megathermal drought period. Better moisture maintenance and soil erosion reduction was found when the plant species numbers in cover plant communities increased from one to eight. Higher root density in plant communities with higher species richness increased significantly the antiscourability of the soil. It was suggested that conserving plant communities with diversified native species could produce the best positive ecological effects on citrus orchard ecosystem stability.

Determination of a Reasonable Percentage for Ecological Water-Use in the Haihe River Basin, China

An investigation was conducted to study problems of determining a reasonable percentage for ecological water-use in the Haihe River Basin of China. Three key aspects for the ecological water requirement （EWR） were analyzed, involving i） the EWR for river system, ii） the EWR for wetlands and lakes, and iii） the EWR for discharge into the sea to maintain the estuary ecological balance of the Haihe River. The Montana method and related water level-flow relationships, and the statistic approach based on hydrological records were applied to estimate different components of EWR. The results showed that the total ecological water demand in the region, was about 3.47-14.56 billion m^3. Considering flow regime change and uncertainty, the ecological water demand could be estimated by the hydrological frequency approach. Preliminary analysis showed that for different annual runoff under the frequencies of 20%, 50%, 75% and 95%, the ecological water demand approached 12%-50%, 18%-74%, 24%-103%, 35%-148% and 16%-66%, respectively. By further analysis to balance ecological water-use and socioeconomic water-use, the rational percentage of ecological water-use was estimated as 35%-74%, that provides useful information to judge whether the allocation of water resources is reasonable, and was proved to be satisfactory by comparing with the practical condition.