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The essential dimension is a numerical invariant of the group; it is often equal to the minimal number of independent parameters required to describe all algebraic objects of a certain type.


We show that the structure of a block outside the critical hyperplanes of category O over a symmetrizable KacMoody algebra depends only on the corresponding integral Weyl group and its action on the parameters of the Verma modules.


Quantitative parameters in an analog of the BeurlingPollard theorem differ from those for A.


Quantitative parameters in an analog of the BeurlingPollard theorem differ from those for A.


In this article we consider the question when one can generate a Weyl Heisenberg frame for l2(?) with shift parameters N, M1 (integer N, M) by sampling a WeylHeisenberg frame for L2(?) with the same shift parameters at the integers.

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 The purpose of this series is to make a thermodynamic analysis of the FeC 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 FeC 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... The purpose of this series is to make a thermodynamic analysis of the FeC 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 FeC 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 FeC 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 retreated to yield α_c~γN_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~γV_c~γ curve for 1153℃, the irongraphite 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 abovementioned assumption has been semiquantitatively proved in this paper and will be discussed further in another paper of this series.In a similar manner, α_c~lN_c~l curves for liquid FeC 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~lN_c~l curves for 1560° and 1660℃ are completed from low carbon concentrations up to saturation. The activities of carbon in FeC 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,Cslag, C_2~2Fe,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 FeC alloys.From α_c~lN_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°=39309.21 T,which differs considerably from Chipman's equation AF°=890012.10T 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 GibbsDuhem equation, the activities of iron in FeC 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)~lN_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 FeC 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~lN_c~l curves.The shape of the α_c~lN_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′_cN′_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°=39309.21T. 最后作者从液态铁碳合金结构的观点讨论了图1中α′_cN′_c曲綫的形状.  The key to successful cross rolling is to understand fully the distribution of deformation and the mechanism of crack formation at the centre of the rolled material as well as the optimum parameters for the technological process. With these points in mind, the authors carried out investigations by means of microscopic examinations and hardness tests on the distribution of deformation and the mechanism of crack formation at the centre of certain steel specimens at various temperatures, various rates of... The key to successful cross rolling is to understand fully the distribution of deformation and the mechanism of crack formation at the centre of the rolled material as well as the optimum parameters for the technological process. With these points in mind, the authors carried out investigations by means of microscopic examinations and hardness tests on the distribution of deformation and the mechanism of crack formation at the centre of certain steel specimens at various temperatures, various rates of deformation, different ratios between the length of the plastic zone and the specimen diameters as well as at different lengths of material at both ends of the plastic zone.As the deformation of metals in cross rolling is in many ways similar to that in cross forging, the authors carried out experiments on the cross forging of aluminium and lead which had been marked with concentric circles at the ends in a 35ton mechanical press at room temperatures, and then compared the results thus obtained with those in the cross rolling of carbon and alloy steels.The results of these experiments show that:(1) With only one strike of the press in cross forging, the deformation is greatest at the surface and diminishes towards the centre of the specimen. When reduction is small, only elastic deformation occurs at the centre.(2) With several strikes of the press on rotating specimens, the deformation at the surface and in the centre is greater than that in the intermediate zone. When reduction is very small, plastic deformation also does not penetrate into the centre.(3) Similar to cross forging, the deformation of metal in cross rolling is also greatest at the surface, less at the centre and least in the intermediate zone. This distribution of deformation remains practically unchanged in different metals and various rolling temperatures as well as under other testing conditions mentioned above. Under conditions of the present experiments, when reduction is small, the deformation at the centre may be only elastic. In this case, the distribution of deformation is similar to that with only one strike of the press in cross forging.In cross rolling, the greater the reduction, the higher the rolling temperature, the higher the rate of deformation, the greater the ratio between the length of the plastic zone and the specimen diameter, and the shorter the length of the material on either side of the plastic zone, the greater is the tendency for crack formation at the centre. Alloy steels seem less liable to crack formation than carbon steels.  在200—300毫米輥径的横軋机上于不同溫度、速度、变形程度、变形区长度与直径之比以及外端等条件下,用金相法和硬度法对各鋼种的圓棒的变形分布和中心破裂进行了研究。在冲床上用端面画有同心圓的鋁棒和鉛棒进行了常溫的旋轉橫鍛試驗,以了解横鍛横軋时金属的变形分布。試驗結果表明: 1.一次横鍛时,表面层的变形最大,越靠中心变形愈小。当压縮率不大时,中心处可能只发生弹性变形。2.旋轉橫鍛时,表面层和中心区的塑性变形較大,过渡区的变形最小。当变形率很小时,塑性变形亦可能不致于深入到中心区。3.横軋时金属的变形規律与旋轉橫鍛时相似,但在压縮很小时,断面中心只发生弹性变形。4.横軋时,軋制溫度、軋制速度增高,压縮率及变形长度与直径比越大,外端越小,中心破裂愈易产生。  A new concept, the "energetic parameter of solution", is suggested for molten salt solutions. For the A_n B_m—A_n' C_m' system (valency of A ion is Z):f(r)=(Z~2nn')/(m(r_A+r_B))+(Z~2n'~2)/(m'(r_A+r_C))(2Z~2nn')/(2r_A+r_B+r_C)(n'/nm'+1/m)n>n'. For A_nB_m—C_n'D_m' system (valency of C ion is Z'): f(r)=(n'Z'Z((n+nZ)/(n'Z')m'))/(m'(r_A+r_D))+nZZ'(m+nZ/Z')/(m(r_B+r_C))(nZ~3(n+m))/(m(r_A+r_B))(n'Z'Z(n'+m'))/(m'(r_C+r_D)). The "energetic parameter of solution" is an approximate function of electrostatic... A new concept, the "energetic parameter of solution", is suggested for molten salt solutions. For the A_n B_m—A_n' C_m' system (valency of A ion is Z):f(r)=(Z~2nn')/(m(r_A+r_B))+(Z~2n'~2)/(m'(r_A+r_C))(2Z~2nn')/(2r_A+r_B+r_C)(n'/nm'+1/m)n>n'. For A_nB_m—C_n'D_m' system (valency of C ion is Z'): f(r)=(n'Z'Z((n+nZ)/(n'Z')m'))/(m'(r_A+r_D))+nZZ'(m+nZ/Z')/(m(r_B+r_C))(nZ~3(n+m))/(m(r_A+r_B))(n'Z'Z(n'+m'))/(m'(r_C+r_D)). The "energetic parameter of solution" is an approximate function of electrostatic energy of mixing of molten salts. When f(r) is positive, the solution exhibits negative deviation; when f(r) is negative, the solution shows positive deviation. The function f(r) may be used as an approximate method to estimate the thermodynamic properties of molten salt solutions, as well as phase diagrams of binary salt systems.  提出了熔盐溶液的溶解能参数的概念,熔盐系A_nB_mA_(n′)C_(m′)(A离子之价数为Z)的溶解能参数为: f(r)=Z~2nn′/m(r_A+r_B)+Z~2n′~2/m′(r_A+r_C)2Z~2nn′/(2r_A+r_B+r_C)(n′/nm′+1/m) 熔盐系A_nB_mC_(n′)D_(m′)(C离子之价数为Z′)的溶解能参数为: f(r)=n′Z′Z(n+(nZ/n′Z′)m′/m′(r_A+r_D)+nZZ′(m+nZ/Z′)/m(r_B+r_C)nZ~2(n+m)/m(r_A+r_B)n′Z′Z(n′+m′)/m′(r_C+r_D)。溶解能参数是熔盐静电混合能的近似函数,当f(r)为正值时,溶液呈现负偏差,当f(r)为负值时,溶液呈现正偏差,f(r)可作为估计熔盐溶液的热力学性质和二元熔盐相图的近似方法。   << 更多相关文摘 
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