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CATALOGUE","human_readable_type_tesim":["Document"],"read_access_group_ssim":["public"],"edit_access_group_ssim":["admin"],"edit_access_person_ssim":["thoma2mr@ucmail.uc.edu"],"nesting_collection__pathnames_ssim":["z316q2560"],"nesting_collection__deepest_nested_depth_isi":1,"_version_":1697074971380023296,"timestamp":"2021-04-15T03:20:13.221Z","score":0.00049999997},{"system_create_dtsi":"2019-03-21T15:12:56Z","system_modified_dtsi":"2019-03-21T15:22:11Z","has_model_ssim":["Document"],"id":"2f75r8986","accessControl_ssim":["f963369f-9983-44de-85c1-cb7dac2ade80"],"hasRelatedMediaFragment_ssim":["jq085m116"],"hasRelatedImage_ssim":["jq085m116"],"depositor_ssim":["chalklr@ucmail.uc.edu"],"depositor_tesim":["chalklr@ucmail.uc.edu"],"title_tesim":["The Research about Invariants of Ordinary Differential Equations"],"date_uploaded_dtsi":"2019-03-21T15:12:55Z","date_modified_dtsi":"2019-03-21T15:22:02Z","isPartOf_ssim":["admin_set/default"],"genre_tesim":["Book"],"required_software_tesim":["Adobe Acrobat Reader"],"college_tesim":["Arts and Sciences"],"department_tesim":["Mathematical Sciences Emeritus"],"creator_tesim":["Chalkley, Roger"],"publisher_tesim":["(available through Amazon.com and other retail outlets)","Roger Chalkley  "],"subject_tesim":["Differential Equations","Mathematics"],"language_tesim":["English"],"description_tesim":["Abstract. Several basic relative invariants for homogeneous linear differential\r\nequations were discovered during the years shortly after 1878. Also, a basic\r\nrelative invariant was found by Paul Appell in 1889 for a type of nonlinear\r\ndifferential equation. There was little progress during the years 1892--1988 as\r\nresearchers who worked with homogeneous linear differential equations were\r\nunknowingly handicapped by the standard practice of introducing binomial\r\ncoefficients in the writing of their equations. They thereby failed to develop\r\nadequate formulas for the coefficients of equations resulting from a change of\r\nthe independent variable. Consequently, for relative invariants as the most\r\nimportant kind of invariant, progress was stymied.\r\nThe notation was simplified in 1989, adequate transformation formulas\r\nwere developed, and explicit expressions were deduced in 2002 for all of the\r\nbasic relative invariants of homogeneous linear differential equations. In 2007,\r\nexplicit formulas were obtained for all of the basic relative invariants of a\r\ntype of ordinary differential equation involving two parameters m and n that\r\nrepresent positive integers. When n = 1 and m \u003e= 3, the formulas specialize to\r\nprovide all of the basic relative invariants for homogeneous linear differential\r\nequations of order m; and, when m = n = 2, they yield all three of the basic\r\nrelative invariants for the equations of Paul Appell.\r\nA general method developed in 2014 combines two relative invariants of\r\nweights p and q for the same type of equation to explicitly obtain a relative\r\ninvariant of weight p+q +r, for any r \u003e= 0. With that, the principal problems\r\nabout relative invariants have now been solved.\r\nThis monograph provides clear perspective about the reformulation begun\r\nafter 1988 and recently completed. 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