01982nam 2200553 450 991081727140332120170821170715.00-8218-9914-7(CKB)3360000000464031(EBL)3113560(SSID)ssj0000973499(PQKBManifestationID)11552374(PQKBTitleCode)TC0000973499(PQKBWorkID)10960298(PQKB)11265733(MiAaPQ)EBC3113560(RPAM)3609083(PPN)195410017(EXLCZ)99336000000046403120720503d1972 uy| 0engur|n|---|||||txtccrExtensions of positive-definite functions /by John R. McMullenProvidence, Rhode Island :American Mathematical Society,1972.1 online resource (79 p.)Memoirs of the American Mathematical Society ;number 117Description based upon print version of record.0-8218-1817-1 Includes bibliographical references.""CONTENTS""; ""1. INTRODUCTION""; ""2. EXTENSION OF AN ALMOST PERIODIC POSITIVE-DEFINITE CONTINUOUS FUNCTION""; ""3. MISCELLANEOUS EXTENSION THEOREMS""; ""4. EXTENSION OF ELEMENTS OF THE FOURIER ALGEBRA""; ""5. EXTENSION FROM ABELIAN NORMAL SUBGROUPS""; ""BIBLIOGRAPHY""Memoirs of the American Mathematical Society ;number 117.Locally compact groupsPositive-definite functionsHarmonic analysisLocally compact groups.Positive-definite functions.Harmonic analysis.515/.253McMullen John R.1714663MiAaPQMiAaPQMiAaPQBOOK9910817271403321Extensions of positive-definite functions4108682UNINA04240nam 22006975 450 991029955570332120200703223553.03-319-04010-310.1007/978-3-319-04010-3(CKB)3710000000089127(EBL)1698333(OCoLC)881161831(SSID)ssj0001161072(PQKBManifestationID)11624886(PQKBTitleCode)TC0001161072(PQKBWorkID)11122245(PQKB)10982578(MiAaPQ)EBC1698333(DE-He213)978-3-319-04010-3(PPN)176750568(EXLCZ)99371000000008912720140219d2014 u| 0engur|n|---|||||txtccrIntroduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems /by William G. Gray, Cass T. Miller1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (609 p.)Advances in Geophysical and Environmental Mechanics and Mathematics,1866-8348Description based upon print version of record.3-319-04009-X Includes bibliographical references and index.Chapter 1 Elements of Thermodynamically Constrained Averaging Theory -- Chapter 2 Microscale Conservation Principles -- Chapter 3 Microscale Thermodynamics -- Chapter 4 Microscale Equilibrium Conditions -- Chapter 5 Microscale Closure for a Fluid Phase -- Chapter 6 Macroscale Conservation Principles -- Chapter 7 Macroscale Thermodynamics -- Chapter 8 Evolution Equations -- Chapter 9 Single-Fluid-Phase Flow -- Chapter 10 Single-Fluid-Phase Species Transport -- Chapter 11 Two-Phase Flow -- Chapter 12 Modeling Approach and Extensions -- Appendix A Considerations on Calculus of Variations -- Appendix B Derivations of Averaging Theorems -- Appendix C Constrained Entropy Inequality Derivations -- Index.Thermodynamically constrained averaging theory provides a consistent method for upscaling conservation and thermodynamic equations for application in the study of porous medium systems.  The method provides dynamic equations for phases, interfaces, and common curves that are closely based on insights from the entropy inequality. All larger scale variables in the equations are explicitly defined in terms of their microscale precursors, facilitating the determination of important parameters and macroscale state equations based on microscale experimental and computational analysis. The method requires that all assumptions that lead to a particular equation form be explicitly indicated, a restriction which is useful in ascertaining the range of applicability of a model as well as potential sources of error and opportunities to improve the analysis.Advances in Geophysical and Environmental Mechanics and Mathematics,1866-8348GeophysicsGeology—Statistical methodsMineralogyThermodynamicsGeophysics/Geodesyhttps://scigraph.springernature.com/ontologies/product-market-codes/G18009Quantitative Geologyhttps://scigraph.springernature.com/ontologies/product-market-codes/G17030Mineralogyhttps://scigraph.springernature.com/ontologies/product-market-codes/G38000Thermodynamicshttps://scigraph.springernature.com/ontologies/product-market-codes/P21050Geophysics.Geology—Statistical methods.Mineralogy.Thermodynamics.Geophysics/Geodesy.Quantitative Geology.Mineralogy.Thermodynamics.620.116015118Gray William Gauthttp://id.loc.gov/vocabulary/relators/aut447822Miller Cass Tauthttp://id.loc.gov/vocabulary/relators/autBOOK9910299555703321Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems2501963UNINA