Actions,finite state sets and applications to trees

Let M be a monoid acting on a set X; for any x?X and A?X we put x ^?1 A = {m?M/xm?A}. Call A?X finite state if card {x ^?1 A/x?X} <∞.

The finite state subsets of T _Σvia the action T _Σ × P _Σ→T _Σare the recognizable forests (P _Σis the monoid of all Σ-trees with just one leaf labeled by a variable x).

Next we prove that the recognizability of forests is equivalent to the finiteness of a certain “syntactic” monoid A Mezei's-like theorem for trees is established: the finite state subsets of T _Σ × T_г are exactly the finite unions of sets of sets of the form B × C B?Rec(T _Σ) and C?Rec(T _г) Another characterization of such relations is given using bimorphisms.     

隧道通风过程中空气湿热状态变化研究

隧道及巷道等地下工程在施工及运营阶段需要以自然或机械通风设施等方式进行通风,以保持充足的新鲜空气量,并维持其内人员的舒适感。当前大多研究集中在隧道通风过程中的空气质量以及烟雾透过率,而较少关注通风过程中空气的湿热状态的变化。以热力学及流体力学的基本理论为基础,研究地下隧道长距离、大规模地下输送新鲜空气过程中,隧道内空气湿热状态的变化。通过论证,在经过隧道长距离输送后,空气湿热状态参数发生较大变化。这说明,空气在地下输送过程中,尽管有风机做功以及摩擦生热过程,但在恒温层的保温作用下,温度只会略有上升;而湿度则会升至饱和状态。这将对地下储库、地下采矿等地下工程的空气调节系统设计研究工作有一定指导意义。     

某型发动机高温转速不足分析

文章分析了某型发动机在外场点火试车试验中,发动机到达一定的转速后,发动机转速增加缓慢,伺服阀可能产生的原因.重点从系统油压波动、油液温度、液流流态等方面对伺服阀进行了分析.     

Zipf,Gibrat and geography: Evidence from China,India and Brazil

We investigate Zipf's Law on the size distribution and Gibrat's Law on the growth of sub‐national populations in China, India and Brazil. We reject Zipf's Law for India, but not for China and Brazil; a log normal distribution also fits Brazil well, but not China and India. Gibrat's Law holds for Brazil; that is, lagged population is the best predictor of current population in Brazil. In China, market potential is an important predictor of population growth, while in India both crop area and market potential are important. Our results show that there is a diversity of experiences across countries, and we speculate that this diversity maybe caused by differences in the characteristics of the three countries.     

Addition of malodorants to lighter gas – The phase equilibrium properties of mixtures of lighter gas and selected substances

Relevant thermodynamic and phase behavior of mixtures created by adding malodorants to lighter gas to discourage its abuse have been studied. The influence of physical factors such as temperature, pressure and concentration of the selected substances with lighter gas is studied. This work represents one component in a larger study examining the feasibility of adding malodorants to lighter gas and focuses on the physical chemistry or chemical engineering aspects of the problem. An initial set of 27 compounds was selected based on deterrent effect (odor) in order to find suitable additives to lighter gas components. The aim is to find substances that not only have the correct physiological effect (discourage abuse) but also the correct physical behavior upon addition to lighter gas (solubility, phase behavior). Specifically the way the malodorant partitions between the vapor and liquid phase is modeled. Furthermore, addition of the malodorants should not affect the normal use of the lighter. Thus of the 27 initial components chosen, nine were found that could be suitable additives. In this work we used the thermodynamic models COSMOtherm – an activity coefficient model – and Cubic-Plus-Association (CPA) – an equation of state – to model the fluid phase and solubility behavior of the mixtures formed by the various additives with butane.     

High-pressure phase equilibrium measurements and thermodynamic modeling for the systems involving CO2, ethyl esters (oleate,stearate, palmitate) and acetone

The aim of this work was to study the phase behavior of systems involving carbon dioxide (CO₂), fatty acid ethyl esters (ethyl oleate, ethyl stearate and ethyl palmitate) and acetone at high pressures. The phase behavior involving these components is an important step regarding the design and optimization of industrial processes based on supercritical conditions, such as biodiesel production and fatty esters fractionation involving supercritical and/or pressurized solvents. In addition, supercritical CO₂ can offer an interesting alternative for glycerol separation in water-free biodiesel purification processes. The binary systems investigated in this work were CO₂ + ethyl oleate, and CO₂ + ethyl stearate and these were compared with the CO₂ + ethyl palmitate system. The ternary CO₂ + ethyl palmitate + acetone was also investigated at two different ethyl palmitate to acetone molar ratios of (1:1) and (1:3). The static synthetic method using a variable-volume view cell was employed to obtain the experimental data in the temperature range of 303.15–353.15 K. Vapor–liquid (VL), liquid–liquid (LL) and vapor–liquid–liquid (VLL) phase transitions were observed in these systems. In the binary systems, the solubility increased with the presence of unsaturation and decreased with the number of carbon atoms in the fatty ester chain. Addition of acetone as well as ethanol eliminated the liquid–liquid immiscibility and reduced the pressure transitions, therefore increasing the solubility of the ester in supercritical CO₂. The experimental data sets for the binary and ternary systems were successfully modeled using the Peng–Robinson equation of state with the classical van der Waals quadratic mixing rule (PR-vdW2) and Wong-Sandler (PR-WS) mixing rule. Both models showed good performance in the phase equilibrium correlations and in predictions for the binary and ternary systems.     

Investigation for the amorphous state of ER-34122, a dual 5-lipoxygenase/cyclooxygenase inhibitor with poor aqueous solubility,in HPMC solid dispersion prepared by the solvent evaporation method

ER-34122, a poorly water-soluble dual 5-lipoxygenase/cyclooxygenase inhibitor, exists as a crystalline form. According to an Oak Ridge thermal ellipsoid plot drawing, carbonyl oxygen O (5) makes an intermolecular hydrogen bond with the hydrogen bonded to N (3) in the crystal structure. The FTIR and the solid-state ¹³C NMR spectra suggest that the network is spread out in the amorphous state and the hydrogen bonding gets weaker than that in the crystalline phase, because the carbonyl signals significantly shift in both spectra. When amorphous ER-34122 was heated, crystallization occurred at around 140°C. Similar crystallization happened in the solid dispersion; however, the degree of crystallization was much lower than that observed in the pure amorphous material. Also, the DSC thermogram of the solid dispersion did not show any exothermic peaks implying crystallization. The heat of fusion (ΔH_f) determined in the pure amorphous material was nearly equal to that for the crystalline form, whereas the ΔH_f value obtained in the solid dispersion was less than a third of them. These data prove that crystallization of the amorphous form is dramatically restrained in the solid dispersion system. The carbonyl wavenumber shifts in the FTIR spectra indicate that the average hydrogen bond in the solid dispersion is lower than that in the pure amorphous material. Therefore, HPMC will suppress formation of the intermolecular network observed in ER-34122 crystal and preserve the amorphous state, which is thermodynamically less stable, in the solid dispersed system.     

Computing point estimates from a non-Gaussian posterior distribution using a probabilistic k-means clustering approach

The Kalman filter algorithm gives an analytical expression for the point estimates of the state estimates, which is the mean of their posterior distribution. Conventional Bayesian state estimators have been developed under the assumption that the mean of the posterior of the states is the ‘best estimate’. While this may hold true in cases where the posterior can be adequately approximated as a Gaussian distribution, in general it may not hold true when the posterior is non-Gaussian. The posterior distribution, however, contains far more information about the states, regardless of its Gaussian or non-Gaussian nature. In this study, the information contained in the posterior distribution is explored and extracted to come up with meaningful estimates of the states. The need for combining Bayesian state estimation with extracting information from the distribution is demonstrated in this work.     

Modelling the compaction curve of fine-grained soils

A theoretical model for the compaction curve of fine-grained soils at various compaction efforts for the entire range of water content is presented in this study. The prediction method is based on the assumption that the compaction curve represents the state surface at the yield state in an unsaturated condition. Thus, for each applied compaction effort, the compaction curve relates to one yielding point on the saturated normal consolidation line (NCL). For a given soil, the model requires the NCL, S_rc, and one point from any compaction curve to predict the compaction curves for different compaction efforts. Moreover, the lines of equal suctions on the compaction curves can be determined if the SWCC, the wetting path, is known. The model introduced here provides additional theoretical understanding of the soil׳s volume change behavior of the compaction curve. The model was verified in two ways: first it was verified quantitatively, by experimental results, and second it was verified qualitatively, by examining the relationships from other models in the literature. The model was further applied to experimental data reported in the literature on previous static and dynamic compaction tests. The results show that the model fits the experimental data very well. Finally, a simple chart, based on this model and using only liquid limits, is presented to estimate γ_dmax and OMC quickly.