Journal of The Society for Industrial and Applied Mathematics

A tournament is a finite set whose elements are called players, together with a binary relation called beating which is complete and asymmetric. A ranking of the players is an order-relation on the set of players. A ranking method is a function from the set of tournaments to the set of possible rankings. The ranking method commonly known as the “points system” is characterized by a set of axioms.

In an early paper with H. Bolza and Max Born, von Kármán examined the relation between the "collision-dominated" and "collision-free" regimes in the simple case of steady flow or steady heat conduction through a porous medium. Von Kármán also formulated the boundary condition at a gas-solid interface, and showed that the temperature "jump" arises quite naturally from the two-sidedness of the velocity distribution function, independently of any statements about the thermal accommodation coefficient. We reexamine this question of the transition between gas-kinetics and gasdynamics with the aid of the Maxwell moment method, utilizing a two-sided Maxwellian-type distribution as weighting function. The main features deduced from this approach are illustrated by considering two simple examples: (1) steady heat conduction between two concentric cylinders, and between two concentric spheres; (2) the "signaling problem" generated by the sudden motion and heating of an infinite flat plate.

Previous article Next article Nonsymmetric Difference EquationsPaul GordonPaul Gordonhttps://doi.org/10.1137/0113044PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. C. Du Fort and , S. P. Frankel, Stability conditions in the numerical treatment of parabolic differential equations, Math. Tables and Other Aids to Computation, 7 (1953), 135–152 MR0059077 0053.26401 CrossrefGoogle Scholar[2] Bert K. Larkin, Some stable explicit difference approximations to the diffusion equation, Math. Comp., 18 (1964), 196–202 MR0164450 0121.11501 CrossrefISIGoogle Scholar[3] D. W. Peaceman and , H. H. Rachford, Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl. Math., 3 (1955), 28–41 10.1137/0103003 MR0071874 0067.35801 LinkISIGoogle Scholar[4] Robert D. Richtmyer, Difference methods for initial-value problems, Interscience tracts in pure and applied mathematics. Iract 4, Interscience Publishers, Inc., New. York, 1957xii+238 MR0093918 0079.33702 Google Scholar[5] J. V. Uspensky, Theory of Equations, McGraw-Hill, New York, 1948 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Volume 13, Issue 3| 1965Journal of the Society for Industrial and Applied Mathematics603-912 History Submitted:30 April 1964Accepted:18 January 1965Published online:13 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113044Article page range:pp. 667-673ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

Previous article Next article Turbulent Boundary Layer and Mixing CoefficientLuigi CroccoLuigi Croccohttps://doi.org/10.1137/0113013PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] F. Clauser, Turbulent boundary layers in adverse pressure gradients, J. Aero. Sci., 21 (1954), 91–108 CrossrefISIGoogle Scholar[2] C. Millikan, A critical discussion of turbulent flows in channels and circular tubes, Proc. 5th International Congress Appl. Mech., Cambridge, 1938, 386–392 Google Scholar[3] D. E. Coles, The turbulent boundary layer in a compressible fluid, Report, R-403-PR, RAND Corporation, 1962 Google Scholar[4] Donald Coles, The law of the wake in the turbulent boundary layer, J. Fluid Mech., 1 (1956), 191–226 MR0081115 0070.42903 CrossrefISIGoogle Scholar[5] L. Crocco and , L. Lees, A mixing theory for the interaction between dissipative flows and nearly isentropic streams., J. Aero. Sci., 19 (1952), 649–676 0047.18502 CrossrefISIGoogle Scholar[6] Hans Wolfgang Liepmann and , John Laufer, Investigations of free turbulent mixing, Tech. Notes Nat. Adv. Comm. Aeronaut.,, 1947 (1947), 38 pp. (21 plates) MR0021815 Google Scholar[7] D. E. Coles, Remarks on the equilibrium turbulent boundary layer, California Institute of Technology, Pasadena, 1956 0078.17702 Google Scholar[8] D. E. Coles, The law of the wall in turbulent shear flow50 Jahre Grenzschichtforschung, Vieweg and Sohn, Braunschweig, 1955, 153–163 0067.43102 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 13, Issue 1| 1965Journal of the Society for Industrial and Applied Mathematics History Submitted:03 June 1964Published online:17 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113013Article page range:pp. 206-215ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

In this paper the entropy of a point process is defined. This entropy can be expressed as a sum of two terms: (a) the numerical entropy, associated with the number of events in a fixed interval, and (b) the locational entropy, associated with the locations of those events in the interval. For point processes describable as a generalized birth process, with fixed intensity function, the rate of change of entropy at a given time is a maximum for the inhomogeneous Poisson process. For the mixed Poisson process with fixed intensity, the locational entropy for a given interval is a maximum for the Poisson process. Other properties of the numerical and locational entropies are also discussed.

Previous article Next article The Existence of Periodic Solutions of Nonlinear OscillatorsJ. H. Heinbockel and R. A. StrubleJ. H. Heinbockel and R. A. Strublehttps://doi.org/10.1137/0113002PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] W. S. Loud, Periodic solutions of $x''+cx'+g(x)=\varepsilon f(t)$, Mem. Amer. Math. Soc. no., 31 (1959), 58 pp. (1959) MR0107058 0085.30701 Google Scholar[2] K. W. Blair and , W. S. Loud, Periodic solutions of $x\sp{\prime\prime}+cx\sp{\prime} +g(x)=Ef(t)$ under variation of certain parameters, J. Soc. Indust. Appl. Math., 8 (1960), 74–101 10.1137/0108006 MR0111900 0101.06904 LinkISIGoogle Scholar[3] C. A. Harvey, Periodic solutions of the differential equation $\ddot x+g(x)=p(t)$, Contributions to Differential Equations, 1 (1963), 425–451 MR0149011 0126.30202 Google Scholar[4] Hans-Wilhelm Knobloch, Eine neue Methode zur Approximation periodischer Lösungen nicht-linearer Differentialgleichungen zweiter Ordnung, Math. Z., 82 (1963), 177–197 10.1007/BF01111422 MR0158124 0117.05404 CrossrefGoogle Scholar[5] Raimond A. Struble, Nonlinear differential equations, International Series in Pure and applied Mathematics, McGraw-Hill Book Co., Inc., New York, 1961x+267 MR0130408 0124.04904 Google Scholar[6] Solomon Lefschetz, Differential equations: geometric theory, Pure and Applied Mathematics. Vol. VI, Interscience Publishers, Inc., New York, 1957, 283–288 MR0094488 0080.06401 Google Scholar[7] Raimond A. Struble, A note on periodic solutions of the Duffing equation, J. Math. Anal. Appl., 9 (1964), 498–501 10.1016/0022-247X(64)90033-2 MR0168860 0135.14203 CrossrefISIGoogle Scholar[8] J. H. Heinbockel, Ph.D. Thesis, The construction of periodic solutions of nonlinear oscillators, North Carolina State of the University of North Carolina at Raleigh, 1964 Google Scholar[9] Paul F. Byrd and , Morris D. Friedman, Handbook of elliptic integrals for engineers and physicists, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete. Bd LXVII, Springer-Verlag, Berlin, 1954xiii+355 MR0060642 0055.11905 CrossrefGoogle Scholar[10] George Seifert, A note on periodic solutions of second order differential equations without damping, Proc. Amer. Math. Soc., 10 (1959), 396–398; errata, 1000 MR0107057 0091.26601 Google Scholar[11] Choy-Tak Taam, The solutions of nonlinear differential equations III, J. Math. Mech., 6 (1957), 511–519 0080.07402 Google Scholar[12] G. R. Morris, A differential equation for undamped forced non-linear oscillations. I, Proc. Cambridge Philos. Soc., 51 (1955), 297–312 MR0069362 0065.07403 CrossrefGoogle Scholar[13] Leon Kotin, Solutions of systems of periodic differential equations, J. Math. Anal. Appl., 8 (1964), 52–56 10.1016/0022-247X(64)90082-4 MR0158125 0124.30002 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails High Order Resonance for Duffing’s Differential EquationL. P. Meissner12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 17, No. 2AbstractPDF (861 KB)Periodic Solutions of Second Order Nonlinear Differential Equations Without DampingJ. A. Marlin and D. F. Ullrich28 July 2006 | SIAM Journal on Applied Mathematics, Vol. 16, No. 5AbstractPDF (1100 KB)Periodic Solutions for Differential Systems with SymmetriesJ. H. Heinbockel and R. A. Struble13 July 2006 | Journal of the Society for Industrial and Applied Mathematics, Vol. 13, No. 2AbstractPDF (1377 KB) Volume 13, Issue 1| 1965Journal of the Society for Industrial and Applied Mathematics History Submitted:06 March 1964Published online:17 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113002Article page range:pp. 6-36ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

Previous article Next article Domains of Attraction for Absolute Values of Random VariablesJesse M. ShapiroJesse M. Shapirohttps://doi.org/10.1137/0113009PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout Previous article Next article FiguresRelatedReferencesCited ByDetails Volume 13, Issue 1| 1965Journal of the Society for Industrial and Applied Mathematics1-352 History Submitted:29 April 1964Published online:17 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113009Article page range:pp. 129-135ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

Previous article Next article On the Lyapunov Stability CriteriaJohn Jones, Jr.John Jones, Jr.https://doi.org/10.1137/0113061PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Richard Bellman, Introduction to matrix analysis, McGraw-Hill Book Co., Inc., New York, 1960xx+328 MR0122820 0124.01001 Google Scholar[2] David H. Carlson and , Hans Schneider, Inertia theorems for matrices: the semidefinite case, J. Math. Anal. Appl., 6 (1963), 430–446 10.1016/0022-247X(63)90023-4 MR0148678 0192.13402 CrossrefGoogle Scholar[3] Wolfgang Hahn, Eine Bemerkung zur zweiten Methode von Ljapunov, Math. Nachr., 14 (1955), 349–354 (1956) MR0082013 0071.30701 CrossrefGoogle Scholar[4] John Jones, Jr., A Diophantine matrix equation, Amer. Math. Monthly, 62 (1955), 244–247 MR0068511 0065.24804 CrossrefGoogle Scholar[5A] R. E. Kalman and , J. E. Bertram, Control system analysis and design via the “second method” of Lyapunov. I. Continuous-time systems, Trans. ASME Ser. D. J. Basic Engrg., 82 (1960), 371–393 MR0157810 CrossrefGoogle Scholar[5B] R. E. Kalman and , J. E. Bertram, Control system analysis and design via the “second method” of Lyapunov. II. Discrete-time systems, Trans. ASME Ser. D. J. Basic Engrg., 82 (1960), 394–400 MR0157811 CrossrefGoogle Scholar[6] Joseph LaSalle and , Solomon Lefschetz, Stability by Liapunov's direct method, with applications, Mathematics in Science and Engineering, Vol. 4, Academic Press, New York, 1961vi+134 MR0132876 0098.06102 Google Scholar[7] Solomon Lefschetz, Some mathematical considerations on nonlinear automatic controls, Contributions to Differential Equations, 1 (1963), 1–28 MR0155068 0126.30502 Google Scholar[8] A. M. Lyapunov, Problem général de la stabilité du mouvementAnnals of Matheimatics Study No. 17, Princeton University Press, Princeton, 1947 Google Scholar[9] Alexander Ostrowski and , Hans Schneider, Some theorems on the inertia of general matrices, J. Math. Anal. Appl., 4 (1962), 72–84 10.1016/0022-247X(62)90030-6 MR0142555 0112.01401 CrossrefGoogle Scholar[10] P. C. Parks, A new proof of the Routh-Hurwitz stability criterion using the second method of Liapunov, Proc. Cambridge Philos. Soc., 58 (1962), 694–702 MR0144032 0111.28303 CrossrefISIGoogle Scholar[11] R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc., 51 (1955), 406–413 MR0069793 0065.24603 CrossrefGoogle Scholar[12] William E. Roth, The equations $AX-YB=C$ and $AX-XB=C$ in matrices, Proc. Amer. Math. Soc., 3 (1952), 392–396 MR0047598 0047.01901 ISIGoogle Scholar[13] Olga Taussky, A remark on a theorem of Lyapunov, J. Math. Anal. Appl., 2 (1961), 105–107 10.1016/0022-247X(61)90048-8 MR0124335 0158.28203 CrossrefGoogle Scholar[14] O. Taussky and , H. Wielandt, On the matrix function $AX+X\sp{\prime} A\sp{\prime}$, Arch. Rational Mech. Anal., 9 (1962), 93–96 10.1007/BF00253335 MR0132751 0101.25402 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 13, Issue 4| 1965Journal of the Society for Industrial and Applied Mathematics History Submitted:14 August 1964Published online:13 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113061Article page range:pp. 941-945ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

Previous article Next article Some Multiple Sums and Binomial IdentitiesL. CarlitzL. Carlitzhttps://doi.org/10.1137/0113029PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] , Problem 60-2, SIAM Rev., 4 (1962), 396–398 LinkISIGoogle Scholar[2] Robert M. Baer and , Paul Brock, Natural sorting, J. Soc. Indust. Appl. Math., 10 (1962), 284–304 10.1137/0110021 MR0154448 0111.15404 LinkISIGoogle Scholar[3] W. N. Bailey, Generalized Hypergeometric Series, Cambridge, 1935 0011.02303 Google Scholar[4] L. Carlitz, A binomial identity arising from a sorting problem, SIAM Rev., 6 (1964), 20–30 10.1137/1006003 MR0167435 0128.01601 LinkISIGoogle Scholar[5] G. H. Hardy and , E. M. Wright, An introduction to the Theory of Numbers, Oxford, 1938 0020.29201 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Iterative Formulas Associated with Generalized Third Order Recurrence RelationsA. G. Shannon12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 23, No. 3AbstractPDF (264 KB)A Binomial Identity18 July 2006 | SIAM Review, Vol. 9, No. 2AbstractPDF (145 KB) Volume 13, Issue 2| 1965Journal of the Society for Industrial and Applied Mathematics History Submitted:06 July 1964Published online:13 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113029Article page range:pp. 469-486ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

Previous article Next article Estimation of Signals Containing Unknown Parameters: Comparison of Linear and Arbitrary Unbiased EstimatesDavid J. SakrisonDavid J. Sakrisonhttps://doi.org/10.1137/0113046PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. W. Barankin, Locally best unbiased estimates, Ann. Math. Statistics, 20 (1949), 477–501 MR0034003 0034.23002 CrossrefISIGoogle Scholar[2] Frigyes Riesz and , Béla Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955xii+468 MR0071727 0070.10902 Google Scholar[3] Paul R. Halmos, Finite-dimensional vector spaces, The University Series in Undergraduate Mathematics, D. Van Nostrand Co., Inc., Princeton-Toronto-New York-London, 1958viii+200 MR0089819 0107.01404 Google Scholar[4] Samuel S. Wilks, Mathematical statistics, A Wiley Publication in Mathematical Statistics, John Wiley & Sons Inc., New York, 1962xvi+644 MR0144404 0173.45805 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Volume 13, Issue 3| 1965Journal of the Society for Industrial and Applied Mathematics603-912 History Submitted:17 October 1963Published online:13 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113046Article page range:pp. 706-719ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

Previous article Next article Irreducible Realizations and the Degree of a Rational MatrixR. E. KalmanR. E. Kalmanhttps://doi.org/10.1137/0113034PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. E. Kalman, Mathematical description of linear dynamical systems, J. SIAM Control Ser. A, 1 (1963), 152–192 (1963) MR0152167 0145.34301 Google Scholar[2A] Brockway McMillan, Introduction to formal realizability theory. I, Bell System Tech. J., 31 (1952), 217–279 MR0049079 CrossrefISIGoogle Scholar[2B] Brockway McMillan, Introduction to formal realizability theory. II, Bell System Tech. J., 31 (1952), 541–600 MR0049080 CrossrefISIGoogle Scholar[3] Elmer G. Gilbert, Controllability and observability in multivariable control systems, J. SIAM Control Ser. A, 1 (1963), 128–151 (1963) MR0153505 0143.12401 Google Scholar[4] B. D. H. Tellegen, Synthesis of $2n$-poles by networks containing the minimum number of elements, J. Math. Physics, 32 (1953), 1–18 MR0058459 0051.19301 CrossrefISIGoogle Scholar[5] R. J. Duffin and , D. Hazony, The degree of a rational matrix function, J. Soc. Indust. Appl. Math., 11 (1963), 645–658 10.1137/0111049 MR0157590 0152.01502 LinkISIGoogle Scholar[6] D. Hazony, Elements of Network Synthesis, Reinhold, 1963 Google Scholar[7] L. A. Zadeh and , C. A. Desoer, Linear System Theory, McGraw-Hill, New York, 1963 Google Scholar[8] J. R. Ragazzini and , G. F. Franklin, Sampled-Data Control Systems, McGraw-Hill, New York, 1958 0198.19803 Google Scholar[9] B. Friedland, Linear modular sequential circuits, Trans. IRE PGCT, 6 (1959), 61–68 Google Scholar[10] R. E. Kalman, On a new characterization of linear passive systems, Proc. First Allerton Conference on Circuit and System Theory, University of Illinois, 1963 Google Scholar[11] R. E. Kalman, Structure of linear dynamical systems, (to appear in Arch. Rational Mech. Anal.) Google Scholar[12] Rudolf Zurmuhl, Matrizen und ihre technischen Anwendungen, 3te neubearbeitete Aufl, Springer-Verlag, Berlin, 1961xvi+459, 3rd ed. MR0135707 Google Scholar[13] F. R. Gantmakher, The Theory of Matrices, vol. 1, Chelsea, New York, 1959 Google Scholar[14] Maxims Bôcher, Introduction to Higher Algebra, Macmillan, New York, 1907 Google Scholar[15] J. H. M. Wedderburn, Lectures on Matrices, American Mathematical Society, 1934 0010.09904 CrossrefGoogle Scholar[16] E. Bodewig, Matrix calculus, North-Holland Publishing Company, Amsterdam, 1956xii+334, 1st ed. MR0080363 0086.32501 Google Scholar[17] B. L. van der Waerden, Modern Algebra, vol. 2, Ungar, New York, 1950 Google Scholar[18] I. W. Sandberg, On the theory of linear multi-loop feedback systems, Bell System Tech. J., 42 (1963), 355–382 MR0149988 0129.11706 CrossrefISIGoogle Scholar[19] R. E. Kalman, When is a linear control system optimal?, Trans. ASME Ser D. J. Basic Engrg., 86 (1964), 51–60 CrossrefGoogle Scholar[20] V. Belevitch, On the algebraic structure of formal realizability theory, Revue HF, 4 (1959), Google Scholar[21] V. Belevitch, S. R. Deards, On network analysis by polynomial matriceRecent Developments in Network Theory, Macmillan, New York, 1963, 19–30 CrossrefGoogle Scholar[22] R. E. Kalman, Algebraic structure of linear dynamical systems. I. The module of $\sum$, Proc. Nat. Acad. Sci. U.S.A., 54 (1965), 1503–1508 MR0199025 0144.11604 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Systems over a Principal Ideal Domain. A Polynomial Model ApproachSIAM Journal on Control and Optimization, Vol. 20, No. 1 | 17 February 2012AbstractPDF (1621 KB)Control of Linear Systems through Specified Input ChannelsSIAM Journal on Control and Optimization, Vol. 14, No. 1 | 3 August 2006AbstractPDF (1331 KB)Equivalence Relations for the Algebraic Riccati EquationSIAM Journal on Control, Vol. 11, No. 2 | 18 July 2006AbstractPDF (1122 KB)The Prime Structure of Linear Dynamical SystemsSIAM Journal on Control, Vol. 10, No. 3 | 18 July 2006AbstractPDF (840 KB)Transfer Equivalence of Linear Dynamical SystemsSIAM Journal on Control, Vol. 8, No. 1 | 18 July 2006AbstractPDF (1868 KB)Equivalent Realizations of Linear SystemsL. M. Silverman and H. E. MeadowsSIAM Journal on Applied Mathematics, Vol. 17, No. 2 | 12 July 2006AbstractPDF (1627 KB)A System Theory Criterion for Positive Real MatricesSIAM Journal on Control, Vol. 5, No. 2 | 18 July 2006AbstractPDF (1040 KB)The Synthesis of Linear Dynamical Systems from Prescribed Weighting PatternsD. C. YoulaSIAM Journal on Applied Mathematics, Vol. 14, No. 3 | 28 July 2006AbstractPDF (1537 KB) Volume 13, Issue 2| 1965Journal of the Society for Industrial and Applied Mathematics353-602 History Submitted:20 January 1964Published online:13 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113034Article page range:pp. 520-544ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

Previous article Next article Langenhop’s Stabilization TheoremM. F. SmileyM. F. Smileyhttps://doi.org/10.1137/0113036PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] C. E. Langenhop, On the stabilization of linear systems, Proc. Amer. Math. Soc., 15 (1964), 735–742 MR0168408 0129.06303 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 13, Issue 2| 1965Journal of the Society for Industrial and Applied Mathematics History Submitted:05 November 1964Published online:13 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113036Article page range:pp. 555-557ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics

The concept of a "module", i.e., a package of components of a system which can be removed and replaced as a whole, has been long in use in systems design and analysis. In this paper a formal definition of this concept is given and its properties are studied. Most of the results are obtained for "coherent" systems, i.e., for systems whose performance improves as the performance of their components improves. For such systems the relationship between modules and minimal paths can be fully clarified, and the results obtained lead to a criterion for deciding whether or not a given set of components constitutes a module of a given system. It is shown that a coherent system always has uniquely determined maximal modules which have the property that either all are disjoint or no two of them are disjoint. These maximal modules determine uniquely a decomposition of the system into disjoint modular factors. Furthermore, a theorem on the union of modules (the "three modules theorem"), which has been previously known for general systems, is obtained by a rather simple argument for coherent systems.

The nonlinear deflections of a thin elastic simply-supported rectangular plate are studied. The plate is deformed by a compressive thrust applied along the short edges. For the boundary value problem considered we prove that the platecannot buckle for thrusts less than or equal to the lowest eigenvalue of the linearized buckling problem. For larger thrusts approximate solutions of the von Kármán equations are obtained by an accelerated iteration method. Each iterate is numerically evaluated by a finite difference procedure. Using this method approximate solutions are obtained for thrusts considerably larger than the lowest eigenvalue. These solutions bifurcate from the eigenvalues of the linearized problem. In addition, an asymmetric solution is found which appears to branch from a previously bifurcated solution. The extensive numerical results are used to study the formation of boundary layers and the related problem of the plate’s ultimate load. On the basis of the numerical results, an energy mechanism is proposed to explain a “mode-jumping” phenomenon which has been previously observed in experiments.

Previous article Next article On a Problem of Optimum Priority ClassificationRobert M. Oliver and Gerold PestalozziRobert M. Oliver and Gerold Pestalozzihttps://doi.org/10.1137/0113057PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. Cobham, Priority assignment in waiting line problems, Operations Res., 2 (1954), 70–76 CrossrefISIGoogle Scholar[2] D. R. Cox and , Walter L. Smith, Queues, Methuen's Monographs on Statistical Subjects, Methuen & Co. Ltd., London, 1961xii+180 MR0133178 Google Scholar[3A] H. Kesten and , J. Th. Runnenburg, Priority in waiting line problems. I, Nederl. Akad. Wetensch. Proc. Ser. A. 60 = Indag. Math., 19 (1957), 312–324 MR0089775 0085.34801 CrossrefGoogle Scholar[3B] H. Kesten and , J. Th. Runnenburg, Priority in waiting line problems. II, Nederl. Akad. Wetensch. Proc. Ser. A. 60 = Indag. Math., 19 (1957), 325–336 MR0089776 0085.34801 CrossrefGoogle Scholar[4] T. E. Phipps, Machine repair as a priority waiting line problem, Operations Res., 4 (1956), 76–85 CrossrefISIGoogle Scholar[5] Richard Bellman, Dynamic programming, Princeton Univeristy Press, Princeton, N. J., 1957xxv+342 MR0090477 Google Scholar[6] J. Koerts, On mean waiting times and their reduction by priority procedures: An expository survey and some tables, Statistica Neerlandica, 17 (1963), 267–283 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Optimal Strategies for Priority Queues with Nonlinear Costs of DelayRasoul Haji and G. F. NewellSIAM Journal on Applied Mathematics, Vol. 20, No. 2 | 12 July 2006AbstractPDF (1708 KB) Volume 13, Issue 3| 1965Journal of the Society for Industrial and Applied Mathematics603-912 History Submitted:19 August 1963Accepted:04 December 1964Published online:13 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113057Article page range:pp. 890-901ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics