Classroom Notes

An algorithm is developed that will select a hospital's charge structure to maximize reimbursements. Although the algorithm relies on the Kuhn–Tucker theory of nonlinear programming, it may be implemented using elementary sorting techniques.

[1]  H. Cramér.  Mathematical Methods of Statistics (PMS-9), Volume 9 , 1946 .

[2]  I. Bihari.  A generalization of a lemma of bellman and its application to uniqueness problems of differential equations , 1956 .

[3]  Another look at centroids of quadrilaterals , 1992 .

[4]  H. O. Lancaster.  Pairwise Statistical Independence , 1965 .

[5]  Willard Van Orman Quine,et al.  Methods of Logic , 1951 .

[6]  R. Baer.  Inverses and zero-divisors , 1942 .

[7]  W. Cheney,et al.  Proximity maps for convex sets , 1959 .

[8]  W. Krull.  Idealtheorie in Ringen ohne Endlichkeitsbedingung , 1929 .

[9]  Mitio Nagumo.  Eine hinreichende Bedingung für die Unität der Lösung von Differentialgleichungen erster Ordnung , 1926 .

[10]  P. F. Brandwein.  The Culturing of Fresh-Water Protozoa and Other Small Invertebrates , 1935, The American Naturalist.

[11]  H. Hotelling.  Some New Methods in Matrix Calculation , 1943 .

[12]  S. Wylie,et al.  Homology Theory by P. J. Hilton , 1960 .

[13]  F. D. Parker.  When is a Loop a Group , 1965 .

[14]  Charles B. Morrey,et al.  College Calculus with Analytic Geometry , 1970 .

[15]  THE FUNDAMENTAL GROUP OF TWO SPACES WITH A COMMON POINT , 1954 .

[16]  M. Dwass.  A FLUCTUATION THEOREM FOR CYCLIC RANDOM VARIABLES , 1962 .

[17]  Harold S. Shapiro,et al.  The Taylor coefficients of inner functions. , 1962 .

[18]  Nathan Jacobson.  Introduction: Concepts from Set Theory the System of Natural Numbers , 1951 .

[19]  R. Courant,et al.  What Is Mathematics , 1943 .

[20]  Edwin Hewitt,et al.  Real And Abstract Analysis , 1967 .

[21]  J. L. Brenner,et al.  Matrices of quaternions. , 1951 .

[22]  Counterexamples in Haar Measure , 1966 .

[23]  C. I. Bliss,et al.  FITTING THE NEGATIVE BINOMIAL DISTRIBUTION TO BIOLOGICAL DATA AND NOTE ON THE EFFICIENT FITTING OF THE NEGATIVE BINOMIAL , 1953 .

[24]  B. A. Bernstein.  A set of four independent postulates for Boolean algebras , 1916 .

[25]  Louis Sucheston,et al.  On existence of finite invariant measures , 1964 .

[26]  Dieter Puppe,et al.  Korrespondenzen in abelschen Kategorien , 1962 .

[27]  R. Bellman.  The stability of solutions of linear differential equations , 1943 .

[28]  A. D. Wallace.  A substitute for the axiom of choice , 1944 .

[29]  R. Redheffer.  Maximum principles and duality , 1958 .

[30]  B. Burrows,et al.  Random distributions of points in n‐dimensional spheres , 1988 .

[31]  Sums of Powers of the Natural Numbers , 1957 .

[32]  Arthur M. Johnson,et al.  Made in New York : case studies in metropolitan manufacturing , 1959 .

[33]  E. J. McShane.  Partial Orderings and Moore-Smith Limits , 1952 .

[34]  E. C. Titchmarsh.  The Zeros of Certain Integral Functions , 1926 .

[35]  R. Penrose.  On best approximate solutions of linear matrix equations , 1956, Mathematical Proceedings of the Cambridge Philosophical Society.

[36]  W. Leavitt.  The module type of a ring , 1962 .

[37]  S. Gordon.  INTRODUCING TAYLOR POLYNOMIAL APPROXIMATIONS IN INTRODUCTORY CALCULUS , 1991 .

[38]  Patrick Suppes,et al.  Introduction To Logic , 1958 .

[39]  T. Motzkin.  Approximation by curves of a unisolvent family , 1949 .

[40]  R. Langer.  On the zeros of exponential sums and integrals , 1931 .

[41]  W. Rheinboldt.  A unified convergence theory for a class of iterative processes. , 1968 .

[42]  H. Spohn.  Kinetic equations from Hamiltonian dynamics: Markovian limits , 1980 .

[43]  C. Chevalley,et al.  Theory of Lie Groups (PMS-8) , 1946 .

[44]  R. Rado,et al.  Note on generalized inverses of matrices , 1956, Mathematical Proceedings of the Cambridge Philosophical Society.

[45]  N. J. Lennes.  Theorems on the Simple Finite Polygon and Polyhedron , 1911 .

[46]  O. Perron.  Zur Theorie der Matrices , 1907 .

[47]  I. Schur.  Über die charakteristischen Wurzeln einer linearen Substitution mit einer Anwendung auf die Theorie der Integralgleichungen , 1909 .

[48]  L. Rosenberg.  Nonnormality of Linear Combinations of Normally Distributed Random Variables , 1965 .

[49]  R. C. Yates,et al.  The Probability Integral , 1950 .

[50]  T. H. Gronwall.  Note on the Derivatives with Respect to a Parameter of the Solutions of a System of Differential Equations , 1919 .

[51]  Garrett Birkhoff,et al.  A survey of modern algebra , 1942 .

[52]  Ralph P. Boas,et al.  A Primer of Real Functions , 1961, The Mathematical Gazette.

[53]  Walter Feit,et al.  The representation theory of finite groups , 1982, North-Holland mathematical library.

[54]  R. Selfridge.  Approximations with least maximum error , 1953 .

[55]  N. Rosenauer.  Some Fundamentals of Space Mechanisms , 1956 .

[56]  P. Sansgiry,et al.  B(m,n) = G(m)G(n)/G(m + n) and volume of an n‐dimensional sphere , 1991 .

[57]  A. Spitzbart,et al.  Inverses of Vandermonde Matrices , 1958 .

[58]  A. F. Horadam,et al.  A Search for Solutions of a Functional Equation , 1996 .

[59]  A. Cohn,et al.  Über die Anzahl der Wurzeln einer algebraischen Gleichung in einem Kreise , 1922 .

[60]  A. Sutcliffe.  Complete Solution of the Ladder Problem in Integers , 1963, The Mathematical Gazette.

[61]  Z. Opial,et al.  Sur une inégalité , 1960 .

[62]  M. Nagata.  Some remarks on prime divisors. , 1960 .

[63]  J. Dettman.  The Solution of a Second Order Linear Differential Equation Near a Regular Singular Point , 1964 .

[64]  G. Di Antonio,et al.  Problems for Solution: 4977-4982 , 1961 .

[65]  S. Wylie,et al.  Homology Theory: HOMOLOGY THEORY OF POLYHEDRA , 1960 .

[66]  T. Greville,et al.  Some Applications of the Pseudoinverse of a Matrix , 1960 .

[67]  George G. Lorentz,et al.  A contribution to the theory of divergent sequences , 1948 .

[68]  J. Venn,et al.  . On the diagrammatic and mechanical representation of propositions and reasonings , 2022 .

[69]  Leonard Eugene Dickson,et al.  Linear algebras with associativity not assumed , 1935 .

[70]  R. A. Fisher,et al.  123: The Mathematical Distributions Used in the Common Tests of Significance. , 1935 .

[71]  Orrin Frink,et al.  A new class of orthogonal polynomials: The Bessel polynomials , 1949 .

[72]  E. Palmes,et al.  Personal sampler for nitrogen dioxide. , 1976, American Industrial Hygiene Association journal.

[73]  Akira Kuwagaki.  Sur l’équation fonctionnelle: $f(x+y)=R\{f(x), f(y)\}$ , 1950 .

[74]  Almost γ-continuous functions , 1992 .

[75]  H. S. M. Coxeter,et al.  Non-Euclidean Geometry: Fifth Edition , 1965 .

[76]  John Milnor,et al.  Some Consequences of a Theorem of Bott , 1958 .

[77]  Wilfried Imrich.  Zehnpunktige Kubische Graphen , 1970 .

[78]  K. Knopp.  Theorie und Anwendung der Unendlichen Reihen , 1924 .

[79]  Rory A. Fisher,et al.  THE NEGATIVE BINOMIAL DISTRIBUTION , 1941 .

[80]  Robert D. Silverman,et al.  Tables of Fibonacci and Lucas factorizations , 1988 .

[81]  Iain T. Adamson.  A New Approach to Limits , 1958 .

[82]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[83]  Solution of Equations by Interpolation , 1948 .

[84]  R. Moroney.  Note on a theorem of Nehari , 1962 .

[85]  H. Behnke,et al.  Analysis der komplexen Zahlen , 1955 .

[86]  A. Dinghas,et al.  Vorlesungen über Funktionentheorie , 1961 .

[87]  J. Aczél.  Vorlesungen über Funktionalgleichungen und ihre Anwendungen , 1960 .

[88]  J. Adams,et al.  On the Non-Existence of Elements of Hopf Invariant One , 1960 .

[89]  D. Jordan,et al.  Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers , 1979 .

[90]  A. C. Aitken.  On Interpolation by Iteration of Proportional Parts, without the Use of Differences , 1932 .

[91]  D. Goldberg.  Problem solving in small groups , 1981 .

[92]  Alfred Tarski,et al.  Relational selves as self-affirmational resources , 2008 .

[93]  John B. Moore.  A Convergent Algorithm for Solving Polynomial Algorithms , 1967, JACM.

[94]  R. Ernst,et al.  KINETICS OF HEAT ACTIVATION AND OF THERMAL DEATH OF BACTERIAL SPORES. , 1963, Applied microbiology.

[95]  G. Thomas.  Calculus and Analytic Geometry , 1953 .

[96]  Ronald L. Graham.  A COMBINATORIAL THEOREM FOR PARTIAL SUMS , 1963 .

[97]  F. B. Wright.  Absolute Valued Algebras. , 1960, Proceedings of the National Academy of Sciences of the United States of America.

[98]  Z. Nehari.  On a class of nonlinear second-order differential equations , 1960 .

[99]  F. Harary.  A Parity Relation Partitions its Field Distinctly , 1961 .

[100]  R. Penrose.  A Generalized inverse for matrices , 1955 .

[101]  A. F. Horadam.  Generating functions for powers of a certain generalised sequence of numbers , 1965 .

[102]  M. P. Manning,et al.  Transient response of diffusion dosimeters. , 1980, American Industrial Hygiene Association journal.

[103]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[104]  Alan A. Desrochers,et al.  State Variables for Engineers , 1997 .

[105]  M. Hestenes.  Inversion of Matrices by Biorthogonalization and Related Results , 1958 .

[106]  Meyer Jerison,et al.  The Set of all Generalized Limits of Bounded Sequences , 1957, Canadian Journal of Mathematics.

[107]  N. E. Nörlund.  Vorlesungen über Differenzenrechnung , 1924 .

[108]  M. Rosenlicht,et al.  Integration in Finite Terms , 1972 .

[109]  Joseph Liouville.  Mémoire sur l'intégration d'une classe de fonctions transcendantes. , 1835 .

[110]  E. Wright,et al.  An Introduction to the Theory of Numbers , 1939 .

[111]  B. Elspas,et al.  The Theory of Autonomous Linear Sequential Networks , 1959 .

[112]  A. Denjoy.  Sur les fonctions dérivées sommables , 1915 .

[113]  G. S. Rogers.  A Note on the Stochastic Independence of Functions of Order Statistics , 1959 .

[114]  J. E. Kelley.  An Application of Linear Programming to Curve Fitting , 1958 .

[115]  E. Kobald.  Notiz, betreffend die Berechnung der Wurzeln numerischer Gleichungen , 1891 .

[116]  John von Neumann,et al.  On Regular Rings. , 1936 .

[117]  S. Geisser,et al.  Pairwise Independence of Jointly Dependent Variables , 1962 .

[118]  D. Owens,et al.  Radioactive labelled insulin kinetics , 1995 .

[119]  Bronisław Knaster,et al.  Ein Beweis des Fixpunktsatzes für n-dimensionale Simplexe , 1929 .

[120]  H. O. Lancaster.  ZERO CORRELATION AND INDEPENDENCE , 1959 .

[121]  T. Rado.  On non-computable functions , 1962 .

[122]  John S. Chipman,et al.  On Least Squares with Insufficient Observations , 1964 .

[123]  F. B. Jones.  Connected and disconnected plane sets and the functional equation $f\left( x \right) + f\left( y \right) = f\left( {x + y} \right)$ , 1942 .

[124]  J. Ritt,et al.  Integration in finite terms : Liouville's theory of elementary methods , 1948 .

[125]  A. Giordana,et al.  Modelling Production Systems by means of Predicate-Transitions Networks , 1985, Inf. Sci..

[126]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .

[127]  Cayley.  Desiderata and Suggestions: No. 3.The Newton-Fourier Imaginary Problem , 1879 .

[128]  L. Chambadal,et al.  Fonctions d'une variable rèelle , 1972 .

[129]  R. Plackett.  A historical note on the method of least squares. , 1949, Biometrika.

[130]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[131]  A. D. Wallace.  The structure of topological semigroups , 1955 .

[132]  A. Wintner.  (L 2 )-Connections Between the Potential and Kinetic Energies of Linear Systems , 1947 .

[133]  E. Albert,et al.  Analgesic Properties of Derivatives of Diphenylethylamine , 1946, Nature.

[134]  I. J. Schoenberg,et al.  An extremum problem for polynomials , 1960 .

[135]  Paul Bachmann.  Zur Theorie der complexen Zahlen. , 1867 .

[136]  Jack W. Rotman.  Language Approaches to Beginning Algebra. , 1990 .

[137]  Roger Fletcher,et al.  Practical methods of optimization; (2nd ed.) , 1987 .

[138]  J. Riordan.  Derivatives of composite functions , 1946 .

[139]  I. Vekua.  Generalized Analytic Functions , 1962 .

[140]  A. F. Horadam,et al.  Generalized Fibonacci and Lucas Factorizations , 1991 .