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  system
This implies that a system is algebraically integrable (i.e., its eigenvalue problem is explicitly solvable in quadratures) if and only if the differential Galois group is commutative for generic eigenvalues.
      
We apply this criterion of algebraic integrability to two examples: finite-zone potentials and the elliptic Calogero-Moser system.
      
In the second example, we obtain a proof of the Chalyh-Veselov conjecture that the Calogero-Moser system with integer parameter is algebraically integrable, using the results of Felder and Varchenko.
      
The least upper bound for the degrees of elements in a system of generators turns out to be independent of the number of vector variables.
      
We consider 3-parametric polynomialsPμ*(x; q, t, s) which replace theAn-series interpolation Macdonald polynomialsPμ*(x; q, t) for theBCn-type root system.
      
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The purpose of this series is to make a thermodynamic analysis of the Fe-C system with a minimum of assumptions and to revise the equilibrium diagram of the same system in the light of the results of this investigation. In this paper, the first of the series, activities in liquid Fe-C alloys have been evaluated up to saturation, using Richardson and Dennis' data123 on dilute solutions of carbon in liquid iron and Darken and Smith's model~([1]) for carbon dissolved in austenite with certain modifications.A...

The purpose of this series is to make a thermodynamic analysis of the Fe-C system with a minimum of assumptions and to revise the equilibrium diagram of the same system in the light of the results of this investigation. In this paper, the first of the series, activities in liquid Fe-C alloys have been evaluated up to saturation, using Richardson and Dennis' data123 on dilute solutions of carbon in liquid iron and Darken and Smith's model~([1]) for carbon dissolved in austenite with certain modifications.A parameter α_c defined as logγc/N_Fe~2 with reference to graphite as the standard state is plotted against N_c for both austenite and Fe-C melt in order to facilitate the evaluation of α_(Fe) by graphical integration. Smith's data~([1]) on equilibrium between austenite and gaseous mixtures (CO_2/CO, CH_4/H_2) are re-treated to yield α_c~γ-N_c~γ curves for 800° and 1000℃ as shown in Fig. 1. On the assumption that L_c~γ the relative partial molal enthalpy of carbon in austenite, does not chan preciably with temperature, the α_c~γ-V_c~γ curve for 1153℃, the iron-graphite eutectic temperature, is obtained by extrapolation and found to lie above the graphite saturation point. This fact seems to indicate that the limit of application of Darken and Smith's model is reached somewhere around N_c~γ=0.0661 (1.50%) and a point of inflection should occur at this concentration. The above-mentioned assumption has been semi-quantitatively proved in this paper and will be discussed further in another paper of this series.In a similar manner, α_c~l-N_c~l curves for liquid Fe-C alloys are drawn through the experimental points of Richardson and Dennis on equilibrium between CO_2/CO mixed gases and dilute solutions of carbon in liquid iron at 1560° and 1660℃ as shown in Fig. 1. The curves are extended up to N_c~1=0.15 on the basis of Darken and Smith's model using 3600 cals. as the energy of interaction at 1560℃ between carbon atoms in the neighbouring interstitial sites as recommended by Richardson and Dens. Then, a suitable curve is drawn between N_c~l=0.15 and the graphite saturation point for 1560℃ to meet certain requirements, and a corresponding curve for 1660℃ is obtained by extrapolation, assuming that L_c~l, the relative partial molal enthalpy of carbon in liquid iron, does not change appreciably with temperature. Thus, α_c~l-N_c~l curves for 1560° and 1660℃ are completed from low carbon concentrations up to saturation. The activities of carbon in Fe-C melts at 1600℃ with reference to graphite as the standard state are readily obtained at different carbon concentrations by interpolation, from which the reversible electromotive forces of a concentration cell of the type Fe,C|slag, C_2~2|Fe,C(sat.) have been calculated and found to agree fairly well with the experimental values obtained by and as shown in Fig. 2. This agreement may be taken as partial confirmation of the choice of N_c~l=0.15 as the limit of application of Darken and Smith's model to liquid Fe-C alloys.From α_c~l-N_c~l curves for 160°and 1660℃, L_c~l is easily calculated to be 3930 cals., and by combining this value with certain other data, the following equation is obtained:C(gr.)=C[%]; AF°=3930-9.21 T,which differs considerably from Chipman's equation AF°=8900-12.10T given in the 1951 edition of the "Basic Open Hearth Steelmaking". It is believed that the present author's equation is more reliable than Chipman's in view of the uncertainties involved in the derivation of the latter especially regarding the evaluation of the enthalpy of solution of graphite in liquid iron.By graphical integration of the Gibbs-Duhem equation, the activities of iron in Fe-C melts with pure liquid iron as the standard state are obtained at different carbon concentrations and plotted against N_c~l in Fig. 3. The α_(Fe)~l-N_c~l curve thus obtained is independent of temperature. With the aid of Fig. 3 and certain other data, the activities of iron in an Fe-C melt and austenite both saturated with graphite at the eutectic temperature are evaluated with pure γ iron as the common standard state and found to be practically equal as required by the eutectic equilibrium. This fact renders additional support to the choice of N_c~l=0.15 as the inflection point of the α_c~l-N_c~l curves.The shape of the α_c~l-N_c~l curves is briefly discussed from a structural viewpoint.

作者在本文中综合分析了关於液态铁碳合金中碳活度测定的諸家研究结果並比较其优劣. 然后根据Richardson与Dennis用CO_2/CO平衡法的实验数据,用Darken与Smith的统计模型与最少假定,导出了液态鉄碳合金中α′_c与N′_c的关系(α′_c=logγ′_c,/(N_Fe′)~2,标准状态为石墨),并温度对此关系的影响.计算结果符合於(i)鉄液内石墨溶解度的实验数据;(ii)与用电动势法测定液态铁碳合金中碳活度的实验数据;及(iii)奥氏体、铁液、石墨共晶平衡的要求. 根据本文所导出的α′_c-N′_c曲綫,作者算得石墨在鉄液内的溶解热为3930卡;然后依此及其他必需数据,导出下列关系:C(石墨)=C[%],△F°=3930-9.21T. 最后作者从液态铁碳合金结构的观点讨论了图1中α′_c-N′_c曲綫的形状.

This is the first of a series of papers with a view to evaluation activities inliquid blast-furnace-type slags.The purpose of this paper is to present new results of calculation for activities of CaO and SiO_2 in liquid CaO-SiO_2,CaO-SiO_2-Al_2O_3 and CaO-MgO-SiO_2-Al_2O_3 systems from existing chemical and electrochemi-caldata with certain assumptions The activities of CaO in the above-mentionedsystems with reference to solid CaO as the standard state are plotted against(%CaO)/(%SiO_2).From a comparison...

This is the first of a series of papers with a view to evaluation activities inliquid blast-furnace-type slags.The purpose of this paper is to present new results of calculation for activities of CaO and SiO_2 in liquid CaO-SiO_2,CaO-SiO_2-Al_2O_3 and CaO-MgO-SiO_2-Al_2O_3 systems from existing chemical and electrochemi-caldata with certain assumptions The activities of CaO in the above-mentionedsystems with reference to solid CaO as the standard state are plotted against(%CaO)/(%SiO_2).From a comparison of these ~αCaO-(%CaO)/(%SiO_2)curves,a new expression for basicity has been proposed instead of the simple(%CaO)/(%SiO_2)ratio.The activities of CaO in the various systems concerned becomeapproximately equal at the same basicity when the latter is calculated accordingto the new formula.Alumina shows amphoteric behaviour in the new basicityformula in agreement with the general pattern of slag constitution.

在本文中,作者综合分析了关于CaO—SiO_2、CaO—SiO_2—Al_2O_3及CaO—MgO—SiO_2—Al_2O_3系统熔渣中α_(SiO_2)及α_(CaO)的测定结果,并加以比较。关于CaO—SiO_2二元系,作者综合了Fulton与Chipman,张禄经与Derge及坂上六郎的实验数据,导出了1600℃时液态渣在整个浓度范围内的α_(SiO_2)及α_(CaO),分别用β鳞石英及固态CaO为标准状态。根据这样算出的α_(SiO_2)及α_(CaO)以及坂上的CaO侧电动势数据,作者导出了一个经验公式,可以用来从已知的电动势数据与α_(SiO_2)计算α_(CaO)。将这个公式应用于CaO—SiO_2—Al_2O_3三元系,算出了三元系熔渣内当Al_2O_3=10、20%时的α_(CaO)。然后将二元系和三元系中的α_(CaO)加以比较,导出了一个新的碱度计算公式。在此式中A1_2O_3显示双性,当碱度较高时它属于酸性,因此可以分子比例与SiO_2相加;反之,当碱度较低时它属于碱性,因此须从SiO_2中扣去。如将MgO以重量百分率与CaO相加,这个碱度公式也可以适用于四元系。由于新的碱度公式所根...

在本文中,作者综合分析了关于CaO—SiO_2、CaO—SiO_2—Al_2O_3及CaO—MgO—SiO_2—Al_2O_3系统熔渣中α_(SiO_2)及α_(CaO)的测定结果,并加以比较。关于CaO—SiO_2二元系,作者综合了Fulton与Chipman,张禄经与Derge及坂上六郎的实验数据,导出了1600℃时液态渣在整个浓度范围内的α_(SiO_2)及α_(CaO),分别用β鳞石英及固态CaO为标准状态。根据这样算出的α_(SiO_2)及α_(CaO)以及坂上的CaO侧电动势数据,作者导出了一个经验公式,可以用来从已知的电动势数据与α_(SiO_2)计算α_(CaO)。将这个公式应用于CaO—SiO_2—Al_2O_3三元系,算出了三元系熔渣内当Al_2O_3=10、20%时的α_(CaO)。然后将二元系和三元系中的α_(CaO)加以比较,导出了一个新的碱度计算公式。在此式中A1_2O_3显示双性,当碱度较高时它属于酸性,因此可以分子比例与SiO_2相加;反之,当碱度较低时它属于碱性,因此须从SiO_2中扣去。如将MgO以重量百分率与CaO相加,这个碱度公式也可以适用于四元系。由于新的碱度公式所根据的实验数据并不充分,所以它的能否适用须视应用结果如何而定。Taylor与Stobo由脱硫平衡数据计算了三个熔渣内的α_(CaO),与作者的计算结果不能符合。本文初步分析了造成这个差异的原因。因为这个差异的存在,本文所计算的α_(CaO)只能认为相对的数值,同时图2的α_(SiO_2)曲线也有待将来研究复证或修正。

In order to determine the workability of cast iron with spheroidal graphite,the following tests have been conducted on this material in the as-cast and annealed condition:tensile tests,compression tests,Charpy impact tests,impacttensile tests,twisting tests,upsetting tests under the drop hammer and small-scaledrolling tests.Results from these tests show that the best hot-working temperature rangeof this material varies somewhat with the stress system applied and the speed ofworking,and in general lies...

In order to determine the workability of cast iron with spheroidal graphite,the following tests have been conducted on this material in the as-cast and annealed condition:tensile tests,compression tests,Charpy impact tests,impacttensile tests,twisting tests,upsetting tests under the drop hammer and small-scaledrolling tests.Results from these tests show that the best hot-working temperature rangeof this material varies somewhat with the stress system applied and the speed ofworking,and in general lies between 700° and 1100℃.Within this temperaturerange,the maximum amount of working permissible for a single working operationvaries considerably with the stress system applied.Under tensile stresses,thismaximum amount of working lies between 28 and 57.6%;under predominentlycompressive stresses,it lies between 58.5 and 72.9%;while in the small-scaledrolling tests,the maximum reduction in thickness permissible for a single passlies between 38.6 and 44.3%.The maximum amount of working permissible is alsoaffected by the speed of working,being greater at lower speeds.Tests on industrial scale show that the upsetting and small-scaled rollingtests give results nearest to those from industrial tests.Charpy impact tests,impacttensile tests,upsetting tests and small-scaled rolling tests show more prominentlythe best hot-working temperature range than the other tests conducted.Results of the present research also indicate that cast iron with spheroidal graphitehas a higher strength and workability when subjected to compressive stresses thanto tensile stresses,that a brittle temperature range has been recorded between200° and 650℃,which varies with the speed of test.Judging from the variationof the resistance to deformation with the change of temperature and the speedeffect,this phenomenon is associated with blue brittleness.

为了确定球墨铸铁的可塑性,曾进行了铸态和铸态经墨化热处理后的球墨铸铁在不同温度下的抗张试验、抗压试验、冲击弯曲试验、冲击抗张试验、撚扭试验、顶锻试验和小型压延试验庑┦匝橹赋?球墨铸铁的最好热加工温度范围随着应力体系和加工速度的不同而略有不同,但一般介于700℃和1100℃之间。在此温度范围内球墨铸铁能够耐受的最大加工量依所受的应力体系而有相当大的差別。在张应力作用下,此最大加工量介于28—57.6%之间,在主要为压应力作用下,介于58.5—72.9%之间;在小型压延试验中,其最大加工量则介于38.6—44.3%之间。最大加工量亦受速度的影响:实验室的试验指出,球墨铸铁在比较低速下加工有较高的塑性。在比较接近生产的条件下的试验结果指出:顶锻试验和小型压延试验给予最靠近生产试验结果的数值。冲击弯曲、冲击抗张、顶锻试验和小型压延试验给予比较明确的最好热加工温度范围,其他试验则不能给予很明确的结果。如果采用了测压仪、小型压延试验,还可以提供变形阻力的资料。试验结果指出:球墨铸铁在压应力作用下比在张应力作用下有较大的强度和塑性;其中温变脆温度依试验速度的变化而在200°—650℃之间变化,根据变形阻力和变脆温度范围的...

为了确定球墨铸铁的可塑性,曾进行了铸态和铸态经墨化热处理后的球墨铸铁在不同温度下的抗张试验、抗压试验、冲击弯曲试验、冲击抗张试验、撚扭试验、顶锻试验和小型压延试验庑┦匝橹赋?球墨铸铁的最好热加工温度范围随着应力体系和加工速度的不同而略有不同,但一般介于700℃和1100℃之间。在此温度范围内球墨铸铁能够耐受的最大加工量依所受的应力体系而有相当大的差別。在张应力作用下,此最大加工量介于28—57.6%之间,在主要为压应力作用下,介于58.5—72.9%之间;在小型压延试验中,其最大加工量则介于38.6—44.3%之间。最大加工量亦受速度的影响:实验室的试验指出,球墨铸铁在比较低速下加工有较高的塑性。在比较接近生产的条件下的试验结果指出:顶锻试验和小型压延试验给予最靠近生产试验结果的数值。冲击弯曲、冲击抗张、顶锻试验和小型压延试验给予比较明确的最好热加工温度范围,其他试验则不能给予很明确的结果。如果采用了测压仪、小型压延试验,还可以提供变形阻力的资料。试验结果指出:球墨铸铁在压应力作用下比在张应力作用下有较大的强度和塑性;其中温变脆温度依试验速度的变化而在200°—650℃之间变化,根据变形阻力和变脆温度范围的变化可以比较肯定地认为这是一种蓝脆的现象。

 
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