Abstract
The equations for the sum of Poincaré indices of the singular points in the tie-line vector field are written in new forms for various two-dimensional complexes. The equations are applied to systems at phase and chemical equilibria.
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References
Gurikov, Yu.V., Liquid-Vapor Diagrams for Ternary Homogeneous Solutions,Zh. Fiz. Khim., 1958, vol. 32, no. 9, p. 1980.
Zharov, V.T. and Serafimov, L.A.,Fiziko-khimicheskie osnovy distillyatsii i rektifikatsii (Physicochemical Foundations of Distillation and Rectification), Moscow: Khimiya, 1975.
Serafimov, L.A., Theoretical Principles of Distillation Flowsheet Synthesis for Nonideal Multicomponent Mixtures,Doctoral (Eng.) Dissertation, Moscow: Mosk. Inst. Tonkoi Khim. Tekhnol. im. M.V. Lomonosova, 1968.
Serafimov, L.A., The Azeotropic Relationships and Classification of Multicomponent Mixtures. III. Arrangement of Singular Points on Liquid-Vapor Diagrams of Quaternary Mixtures,Zh. Fiz. Khim., 1968, vol. 42, no. 1, p. 252.
Serafimov, L.A., The Azeotropic Relationships and Classification of Multicomponent Mixtures. VI.n-Component Mixtures,Zh. Fiz. Khim., 1969, vol. 43, no. 7, p. 1753.
Zharov, V.T., Nonlocal Properties of Liquid-Vapor Diagrams of Multicomponent Mixtures,Zh. Fiz. Khim., 1969, vol. 43, no. 11, p. 2785.
Zharov, V.T., On Liquid-Vapor Diagrams of Multicomponent Mixtures,Vestn. Leningr. Univ., Ser. 4: Fiz. Khim., 1969, vol. 10, no 2, p. 155.
Serafimov, L.A., The Azeotropic Relationships and Classification of Multicomponent Mixtures. XII. Different Forms of the Generalized Azeotropic Relationships),Zh. Fiz. Khim., 1971, vol. 45, no. 12, p. 3022.
Serafimov, L.A., Thermodynamic-Topological Analysis and Problems in the Separation of Multicomponent Polyazeotropic Mixtures),Teor. Osn. Khim. Tekhnol., 1987, vol. 21, no. 1, p. 74.
Serafimov, L.A. and Babich, S.V., New Forms of the Azeotropic Relationships,Teor. Osn. Khim. Tekhnol., 1996, vol. 30, no. 2, p. 140.
Arnol’d, V.I.,Obyknovennye differentsial’nye uravneniya (Ordinary Differential Equations), Moscow: Nauka, 1975.
Seifert, H. and Threlfall, W.,Lehrbuch der Topologie, Leipzig: Teubner, 1934. Translated under the titleTopologiya, Moscow: Gos. Izd. Nauchn. Tekh. Lit., 1938.
Aleksandrov, P.S. and Efremovich, V.A.,Ocherk osnovnykh ponyatii topologii (Basic Concepts in Topology), Moscow: Gos. Izd. Nauchn. Tekh. Lit., 1936.
Efremovich, V.A.,Osnovnye topologicheskie ponyatiya. Entsiklopediya elementarnoi matematiki (Enciclopedia of Elementary Mathematics: Basic Concepts in Topology), Moscow: Nauka, 1966, vol. 5, p. 476.
Milnor, J.W. and Wallace, A.H.,Topology from the Differentiable Viewpoint, Charlottesville: Univ. of Virginia Press, 1965. Translated under the titleDifferentsial’naya topologiya), Moscow: Mir, 1972.
Hopf, H., Vektorfelder inn-dimensionalen Mannifaligk,Math. Ann., 1926, vol. 96, p. 225.
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Serafimov, L.A., Blagov, S.A. & Solokhin, A.V. New forms of the azeotropic relationships for two-dimensional concentration complexes. Theor Found Chem Eng 34, 157–161 (2000). https://doi.org/10.1007/BF02757834
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DOI: https://doi.org/10.1007/BF02757834