SIAM Journal Research Articles

Computer Aided Design-Drafting (CADD)- Engineering/Manufacturing Tool

Falb, P. L. and Wolovich, W. A., in the Design and Synthesis of Multivariable Control IEEE Transactions Automatic Vol. AC-12, No. 6, Dec. 1967. Gilbert, E. G., The Decoupling of Multivariable Systems by State Feedback, SIAM Journal Vol. 7, No. 1, Feb. 1969. Gilbert, E. G. and Pivnichny, J. R., Computer Program for the Synthesis of Decoupled Multivariable Feedback IEEE Transactions Automatic Vol. AC-14, No. 6, Dec. 1969. Wonham, W. M. and Morse, A. S., and Pole Assignment in Linear Multivariable Systems: A Geometric Approach, SIAM Journal on Vol. 8, Feb. 1970, pp. 1-18. Morse, A. S. and Wonham, W. M., and Pole Assignment by Dynamic Compensation, SIAM Journal on Vol. 8, Aug. 1970, pp. 317-337. Morse, A. S. and Wonham, W. M., Status of Noninteracting Control, IEEE Transactions Automatic Vol. AC-16, Dec. 1971, pp. 568-581. Cliff, E. M. and Lutze, F. H., Application of Geometric Decoupling Theory to Synthesis of Aircraft Lateral Control Journal of Aircraft, Vol. 9, No. 11, Nov. 1972, pp. 770-776. Nazar, S. and Rekasius, Z. V., of a Class of Nonlinear IEEE Transactions Automatic Vol. AC -16,1971, pp. 257-260. Singh, W. N. and Rugh, W. J., in a Class of Nonlinear Systems by State Variable Feedback, ASME Transactions Series G; Journal of Dynamic Systems, Measurement, and Control. Vol. 94G, No. 4G, Dec. 1972. ^Asseo, S. J. and Brodnicki, P. J., (C) Aircraft Control System Studies for Terrain Following/Terrain Avoidance (U), Rept. No. IH-2957-E-1, Cornell Aeronautical Lab., Buffalo, N.Y.

Inequalities for Special Functions (D. K. Ross)

Previous article Next article Inequalities for Special Functions (D. K. Ross)D. J. BordelonD. J. Bordelonhttps://doi.org/10.1137/1015083PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yudell L. Luke, The special functions and their approximations, Vol. I, Mathematics in Science and Engineering, Vol. 53, Academic Press, New York, 1969xx+349 MR0241700 0193.01701 Google Scholar[2] A. L. Jones, An extension of an inequality involving modified Bessel functions, J. Math. and Phys., 47 (1968), 220–221 MR0227483 0159.09603 CrossrefISIGoogle Scholar[3] D. K. Rosenthal, The shape and stability of a bubble at the axis of a rotating liquid, J. Fluid Mech., 12 (1962), 358–366 0107.19704 CrossrefISIGoogle Scholar[4] D. K. Ross, The stability of a column of liquid to torsional oscillations, Z. Angew. Math. Phys., 21 (1970), 137–140 10.1007/BF01594991 0185.55201 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Uniform Structural Stability of Hagen–Poiseuille Flows in a Pipe3 May 2022 | Communications in Mathematical Physics, Vol. 393, No. 3 Cross Ref Monotonicity and inequalities involving the modified Bessel functions of the second kindJournal of Mathematical Analysis and Applications, Vol. 508, No. 2 Cross Ref Bounds for modified Struve functions of the first kind and their ratiosJournal of Mathematical Analysis and Applications, Vol. 468, No. 1 Cross Ref Two-sided inequalities for the Struve and Lommel functions9 February 2018 | Quaestiones Mathematicae, Vol. 41, No. 7 Cross Ref On approximating the modified Bessel function of the second kind13 February 2017 | Journal of Inequalities and Applications, Vol. 2017, No. 1 Cross Ref ML Detection in Phase Noise Impaired SIMO Channels With Uplink TrainingIEEE Transactions on Communications, Vol. 64, No. 1 Cross Ref Bounds for modified Bessel functions of the first and second kinds5 August 2010 | Proceedings of the Edinburgh Mathematical Society, Vol. 53, No. 3 Cross Ref Log-convexity and log-concavity of hypergeometric-like functionsJournal of Mathematical Analysis and Applications, Vol. 364, No. 2 Cross Ref Inequalities involving Bessel and modified Bessel functionsJournal of Mathematical Analysis and Applications, Vol. 147, No. 1 Cross Ref An Inequality for the Bessel Function $J_\nu (\nu x)$R. B. Paris17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 15, No. 1AbstractPDF (177 KB)Inequalities for Ratios of Integrals Cross Ref Rational Bounds for Ratios of Modified Bessel FunctionsIngemar Nåsell17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 9, No. 1AbstractPDF (782 KB)Inequalities for hypergeometric functionsMathematics of Computation, Vol. 30, No. 134 Cross Ref Volume 15, Issue 3| 1973SIAM Review History Published online:18 July 2006 InformationCopyright © 1973 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1015083Article page range:pp. 665-670ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

Further Comments on the Paper “Optimal Control of Processes Described by Integral Equations. I” by V. R. Vinokurov

Previous article Next article Full AccessFurther Comments on the Paper “Optimal Control of Processes Described by Integral Equations. I” by V. R. VinokurovV. R. VinokurovV. R. Vinokurovhttps://doi.org/10.1137/0311015PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Further Comments on the Paper “Optimal Control of Processes Described by Integral Equations. I” by V. R. Vinokurov." SIAM Journal on Control, 11(1), p. 185[1] L. W. Neustadt and , J. Warga, Comments on the paper “Optimal control of processes described by integral equations. I” by V. R. Vinokurov, SIAM J. Control, 8 (1970), 572– 10.1137/0308041 MR0273489 0206.16503 LinkISIGoogle Scholar[2] V. R. Vinokurov, Optimal control of processes describable by integral equations. I, Izv. Vysš. Učebn. Zaved. Matematika, 1967 (1967), 21–33, (in Russian) MR0218951 Google Scholar[3] V. R. Vinokurov, Optimal control of processes described by integral equations. I, II, III, SIAM J. Control 7 (1969), 324–336; ibid. 7 (1969), 337–345; ibid., 7 (1969), 346–355, (English translation from the Russian) MR0247559 0182.20804 AbstractGoogle Scholar[4] V. R. Vinokurov, Erratum: “Optimal control of processes described by integral equations. I”, SIAM J. Control, 8 (1970), 440– 10.1137/0308031 MR0267441 0182.20804 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 11, Issue 1| 1973SIAM Journal on Control History Submitted:19 October 1971Published online:18 July 2006 InformationCopyright © 1973 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0311015Article page range:pp. 185-185ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics

Nondiscounted Continuous Time Markovian Decision Process with Countable State Space

Previous article Nondiscounted Continuous Time Markovian Decision Process with Countable State SpacePrasadarao KakumanuPrasadarao Kakumanuhttps://doi.org/10.1137/0310016PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Kai Lai Chung, Markov chains with stationary transition probabilities, Second edition. Die Grundlehren der mathematischen Wissenschaften, Band 104, Springer-Verlag New York, Inc., New York, 1967xi+301 MR0217872 0146.38401 Google Scholar[2] Cyrus Derman, Denumerable state Markovian decision processes—average cost criterion, Ann. Math. Statist., 37 (1966), 1545–1553 MR0207138 0144.43102 CrossrefISIGoogle Scholar[3] Ronald A. Howard, Dynamic programming and Markov processes, The Technology Press of M.I.T., Cambridge, Mass., 1960viii+136 MR0118514 0091.16001 Google Scholar[4] P. Kakumanu, Continuous time Markov decision models with applications to optimization problems, Tech. Rep., 63, Cornell University, Ithaca, N.Y., 1969 Google Scholar[5] Prasadarao Kakumanu, Continuously discounted Markov decision model with countable state and action space, Ann. Math. Statist., 42 (1971), 919–926 MR0282651 0234.93027 CrossrefISIGoogle Scholar[6] Bruce L. Miller, Finite state continuous time Markov decision processes with an infinite planning horizon, J. Math. Anal. Appl., 22 (1968), 552–569 10.1016/0022-247X(68)90194-7 MR0228251 0157.50301 CrossrefISIGoogle Scholar[7] Sheldon M. Ross, Non-discounted denumerable Markovian decision models, Ann. Math. Statist., 39 (1968), 412–423 MR0226933 0157.50504 CrossrefISIGoogle Scholar[8] Howard M. Taylor, III, Markovian sequential replacement processes, Ann. Math. Statist., 36 (1965), 1677–1694 MR0189839 0139.37802 CrossrefISIGoogle Scholar[9] D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, N.J., 1946 Google Scholar Previous article FiguresRelatedReferencesCited byDetails Ergodic BSDEs Driven by Markov ChainsSamuel N. Cohen and Ying Hu28 October 2013 | SIAM Journal on Control and Optimization, Vol. 51, No. 5AbstractPDF (350 KB)Linear Programming and Constrained Average Optimality for General Continuous-Time Markov Decision Processes in History-Dependent PoliciesXianping Guo, Yonghui Huang, and Xinyuan Song3 January 2012 | SIAM Journal on Control and Optimization, Vol. 50, No. 1AbstractPDF (300 KB)Optimal Control of Ergodic Continuous-Time Markov Chains with Average Sample-Path RewardsXianping Guo and Xi-Ren Cao26 July 2006 | SIAM Journal on Control and Optimization, Vol. 44, No. 1AbstractPDF (207 KB)On Homogeneous Markov Models with Continuous Time and Finite or Countable State SpaceA. A. Yushkevic and E. A. Fainberg17 July 2006 | Theory of Probability & Its Applications, Vol. 24, No. 1AbstractPDF (653 KB)Controlled Markov Models with Countable State Space and Continuous TimeA. A. Yushkevich17 July 2006 | Theory of Probability & Its Applications, Vol. 22, No. 2AbstractPDF (1900 KB) Volume 10, Issue 1| 1972SIAM Journal on Control History Submitted:26 May 1970Published online:18 July 2006 InformationCopyright © 1972 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0310016Article page range:pp. 210-220ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics

Errata: On the Evaluation of Certain Sums Involving the Natural Numbers Raised to an Arbitrary Power

Previous article Next article Full AccessErrata: On the Evaluation of Certain Sums Involving the Natural Numbers Raised to an Arbitrary PowerKeith B. OldhamKeith B. Oldhamhttps://doi.org/10.1137/0503008PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Errata: On the Evaluation of Certain Sums Involving the Natural Numbers Raised to an Arbitrary Power." SIAM Journal on Mathematical Analysis, 3(1), p. 71 Previous article Next article FiguresRelatedReferencesCited ByDetails Shapes of derivative neopolarogramsJournal of Electroanalytical Chemistry and Interfacial Electrochemistry, Vol. 85, No. 1 | 1 Dec 1977 Cross Ref Volume 3, Issue 1| 1972SIAM Journal on Mathematical Analysis History Submitted:10 April 1971Published online:17 February 2012 InformationCopyright © 1972 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0503008Article page range:pp. 71-71ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics

Lower and Upper Bounds for the Number of Lattice Points in a Simplex

Previous article Next article Lower and Upper Bounds for the Number of Lattice Points in a SimplexAharon Gavriel Beged-dovAharon Gavriel Beged-dovhttps://doi.org/10.1137/0122012PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. G. Beged-Dov, Some computational aspects of the P printers M paper mills trim problem, Business Administration, 2 (1970), 15–34 Google Scholar[2] P. C. Gilmore and , R. E. Gomory, A linear programming approach to the cutting-stock problem, Operations Res., 9 (1961), 849–859 MR0137589 0096.35501 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Homotopy techniques for solving sparse column support determinantal polynomial systemsJournal of Complexity, Vol. 66 Cross Ref Percolating sets in bootstrap percolation on the Hamming graphs and triangular graphsEuropean Journal of Combinatorics, Vol. 92 Cross Ref Polynomial Approximation of Anisotropic Analytic Functions of Several Variables16 July 2020 | Constructive Approximation, Vol. 51 Cross Ref Greedy approximations by signed harmonic sums and the Thue–Morse sequenceAdvances in Mathematics, Vol. 366 Cross Ref Sampling inequalities for anisotropic tensor product grids8 January 2019 | IMA Journal of Numerical Analysis, Vol. 107 Cross Ref Novel results for the anisotropic sparse grid quadratureJournal of Complexity, Vol. 47 Cross Ref On tensor product approximation of analytic functionsJournal of Approximation Theory, Vol. 207 Cross Ref Hyperbolic cross approximation in infinite dimensionsJournal of Complexity, Vol. 33 Cross Ref Rethinking the encounter probability for direct-to-target nuclear attacks for aviation security5 May 2011 | Journal of Transportation Security, Vol. 4, No. 3 Cross Ref Эффективные оценки производных обратной функцииИзвестия Российской академии наук. Серия математическая, Vol. 72, No. 4 Cross Ref Improved lower and upper bounds for the number of feasible solutions to a knapsaek problemOptimization, Vol. 19, No. 6 Cross Ref APPLICATION OF OPERATIONS RESEARCH IN PAPER PROCUREMENT Cross Ref The Number of Feasible Solutions to a Knapsack ProblemO. Achou12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 27, No. 4AbstractPDF (209 KB)Bounds on the Number of Feasible Solutions to a Knapsack ProblemThomas A. Lambe12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 26, No. 2AbstractPDF (229 KB)The Paper Trim Problem: A Variable Demand AnalysisA I I E Transactions, Vol. 6, No. 1 Cross Ref A Remark on “an Inequality for the Number of Lattice Points in a Simplex”Manfred W. Padberg12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 20, No. 4AbstractPDF (253 KB) Volume 22, Issue 1| 1972SIAM Journal on Applied Mathematics History Submitted:09 December 1969Published online:12 July 2006 InformationCopyright © 1972 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0122012Article page range:pp. 106-108ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics

Higher OrderG-Transformation

Higher Order<i>G</i>-Transformation

The Rate of Convergence for the Finite Element Method

The character of the proper refinement of the elements (mesh) around the boundary is studied. It is shown that it is possible to obtain the highest (optimal) rate of convergence by this refinement.

Multiple Stable Solutions of Nonlinear Boundary Value Problems Arising in Chemical Reactor Theory

This paper is concerned with the nonlinear boundary value problem (1) $\beta u''-u'+f(u)=0$, (2) $u'(0)-au(0)=0,u'(1)=0$, where $f(u)=b(c-u)\exp(-k/(1+u))$ and $\beta,a,b,c,k$ are constants. First a formal singular perturbation procedure is applied to reveal the possibility of multiple solutions of (1) and (2). Then an iteration procedure is introduced which yields sequences converging to the maximal solution from above and the minimal solution from below. A criterion for a unique solution of (1), (2) is given. It is mentioned that for certain values of the parameters multiple solutions have been found numerically. Finally, the stability of solutions of (1), (2) is discussed for certain values of the parameters. A solution $u(x)$ of (1), (2) is said to be stable if the first eigenvalue $\sigma$ of the variational equations $(1)' \beta v''-v'+[\sigma\beta+f'(u)]v=0$ and $(2)' v'(0)-av(0)=0, v'(1)=0$, is positive.

On the Nucleolus of a Characteristic Function Game

Introduction. The nucleolus is a solution concept for games in characteristic function form. It was introduced by D. Schmeidler in [1]. This paper is concerned with some of the properties of the nucleolus. Some of the results are new (Theorems 2, 4, 5) whereas others are known (Theorems l and 3), but the proofs given here are, in a sense, simpler than those in [1]. A characteristic function game is a pair (N, v) consisting of a set N = {1, 2, , n} of n players, and a characteristic function v, which maps each subset S of N, called a coalition, to a number v(S). In addition, it is assumed that v(N) _ 0, and that v(S) = 0 for all one-person coalitions, as well as for the empty coalition. A payoff vector is an n-tuple x = (x1, , xn) such that xi > 0 for all i = 1, , n, and x(N) = v(N), where for each coalition S, x(S) denotes Zi,eS Xi. X is the set of all payoff vectors. Of course, X depends on the particular game v. For any x in X, let q(x) be a vector in E2n, the components of which are the numbers v(S) x(S), arranged in order of decreasing magnitude, where S runs over all the coalitions of N. We shall say that x is at least as acceptable as y (with respect to v), and write x > y, if q(x) is not greater than q(y), in the lexicographical order on E2n. If q(x) is smaller than q(y), we shall say that x is more acceptable than y and write x >y. The nucleolus of the game is the set of those points in X which are "most acceptable," that is, {x E X :x > y for all y E X}. In [1], Schmeidler proved the basic result that every game possesses a nonempty nucleolus. He further showed that the nucleolus actually consists of just one point, and that-viewed as a point function of the game-it is continuous. Our aim is to give new proofs of the uniqueness and of the continuity of the nucleolus. To this end, we will have to introduce a few definitions and to prove an auxiliary theorem (Theorem 2), which may have some interest in its own right. DEFINITION. Let bo, b1, ... , bp be a sequence of sets whose elements are coalitions of N. This sequence is a coalition array whenever: (i) every coalition of N is contained in exactly one of the sets b1, bp, (ii) bo contains only one-element coalitions. For every game v and payoff vector x, let b1(x, v) be the set of those S c N for which max {v(S) x(S): S c N} is attained. Similarly, b2(x, v) is the set of those S c N where max {v(S) x(S) :S ? b1(x, v)} is attained, and so on. Finally, let bo(x) = {{i} : xi = 0}. It is obvious that bo(x), b1(x, v), . . , bp(x, v) is a coalition array. We shall say that it is the array that belongs to (v, x). DEFINITION 2. A coalition array bo, , bp has property I if for all k= 1,2,...,pandanyyinE n, (1) y(S) _ 0forall Sebo, (2) y(S) ? O for all Se b1 U U bk, and (3) y(N) = 0

On an Approach to the Solution of the Generalized Latent Value Problem for $\lambda $-Matrices

On an Approach to the Solution of the Generalized Latent Value Problem for $\lambda $-Matrices

Global Asymptotic Stability of a Generalized Liénard Equation

Previous article Global Asymptotic Stability of a Generalized Liénard EquationJ. W. HeidelJ. W. Heidelhttps://doi.org/10.1137/0119061PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] T. A. Burton, The generalized Lienard equation, J. Soc. Indust. Appl. Math. Ser. A Control, 3 (1965), 223–230 MR0190462 0135.30201 LinkGoogle Scholar[2] Philip Hartman, Ordinary differential equations, John Wiley & Sons Inc., New York, 1964xiv+612 MR0171038 0125.32102 Google Scholar[3] 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[4] D. W. Willett and , J. S. W. Wong, The boundedness of solutions of the equation $\ddot x+f(x,\dot x)+g(x)=0$, SIAM J. Appl. Math., 14 (1966), 1084–1098 10.1137/0114087 MR0208091 0173.34703 LinkISIGoogle Scholar[5] Philip Hartman, On an ordinary differential equation involving a convex function, Trans. Amer. Math. Soc., 146 (1969), 179–202 MR0276539 0196.10703 CrossrefISIGoogle Scholar Previous article FiguresRelatedReferencesCited byDetails Stability analysis and synthesis of stabilizing controls for a class of nonlinear mechanical systems5 June 2020 | Nonlinear Dynamics, Vol. 100, No. 4 Cross Ref Qualitative analysis for a variable delay system of differential equations of second order23 March 2019 | Journal of Taibah University for Science, Vol. 13, No. 1 Cross Ref Discrete Dynamics in Nature and Society, Vol. 2018 Cross Ref ALMOST AUTOMORPHIC DYNAMICS OF GENERALIZED LI&#201;NARD EQUATIONJournal of Applied Analysis & Computation, Vol. 7, No. 1 Cross Ref Boundedness of Solutions to a Certain System of Differential Equations with Multiple Delays29 January 2016 Cross Ref On the instability of solutions to a Liénard type equation with multiple deviating arguments15 June 2013 | Afrika Matematika, Vol. 25, No. 4 Cross Ref Stability to vector Liénard equation with constant deviating argument5 January 2013 | Nonlinear Dynamics, Vol. 73, No. 3 Cross Ref On the stability and boundedness of solutions of a class of nonautonomous differential equations of second order with multiple deviating arguments1 July 2011 | Afrika Matematika, Vol. 23, No. 2 Cross Ref New stability and boundedness results of Liénard type equations with multiple deviating arguments1 September 2010 | Journal of Contemporary Mathematical Analysis, Vol. 45, No. 4 Cross Ref Oscillations for Liénard type equationsJournal de Mathématiques Pures et Appliquées, Vol. 90, No. 1 Cross Ref Stability and boundedness properties of certain second-order differential equationsJournal of the Franklin Institute, Vol. 344, No. 5 Cross Ref On the asymptotic behavior of solutions of certain second-order differential equationsJournal of the Franklin Institute, Vol. 344, No. 5 Cross Ref Boundedness criteria for solutions of certain second order nonlinear differential equationsJournal of Mathematical Analysis and Applications, Vol. 123, No. 2 Cross Ref Comparison Theorems for Matrix Riccati EquationsRobert A. Jones12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 29, No. 1AbstractPDF (1020 KB)Stability Properties of a Second Order Damped and Forced Nonlinear Differential EquationJohn W. Baker12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 27, No. 1AbstractPDF (766 KB)On Global Asymptotic Stability of Certain Second Order Differential Equations with Integrable Forcing TermsLouis H. Thurston and James S. W. Wong17 February 2012 | SIAM Journal on Applied Mathematics, Vol. 24, No. 1AbstractPDF (975 KB)On the generalized Liénard equation with negative dampingJournal of Differential Equations, Vol. 12, No. 1 Cross Ref A Liapunov function for a generalized Liénard equationJournal of Mathematical Analysis and Applications, Vol. 39, No. 1 Cross Ref Oscillation of solutions of a generalized Liénard equation1 January 1972 | Proceedings of the American Mathematical Society, Vol. 33, No. 1 Cross Ref Structure of the solution set of some first order differential equations of comparison type1 January 1971 | Transactions of the American Mathematical Society, Vol. 160, No. 0 Cross Ref Volume 19, Issue 3| 1970SIAM Journal on Applied Mathematics History Submitted:21 October 1969Published online:12 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0119061Article page range:pp. 629-636ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics

Comments on the Paper “Optimal Control of Processes Described by Integral Equations. I” by V. R. Vinokurov

Previous article Next article Comments on the Paper “Optimal Control of Processes Described by Integral Equations. I” by V. R. VinokurovL. W. Neustadt and J. WargaL. W. Neustadt and J. Wargahttps://doi.org/10.1137/0308041PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Comments on the Paper “Optimal Control of Processes Described by Integral Equations. I” by V. R. Vinokurov." SIAM Journal on Control, 8(4), p. 572[1] V. R. Vinokurov, Optimal control of processes described by integral equations. I, SIAM J. Control 7 (1969), 324–336, 7 (1969), 346–355 MR0247559 0182.20901 LinkISIGoogle Scholar[2] E. Goursat, Cours d'analyse mathematiqueTime III, Gauthier-Villars, Paris, 1942 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails A Survey of the Maximum Principles for Optimal Control Problems with State Constraints17 February 2012 | SIAM Review, Vol. 37, No. 2AbstractPDF (4218 KB)Further Comments on the Paper “Optimal Control of Processes Described by Integral Equations. I” by V. R. Vinokurov18 July 2006 | SIAM Journal on Control, Vol. 11, No. 1PDF (110 KB) Volume 8, Issue 4| 1970SIAM Journal on Control History Submitted:15 May 1970Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0308041Article page range:pp. 572-572ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics

Nonlinear Controllability via Lie Theory

Previous article Next article Nonlinear Controllability via Lie TheoryG. W. Haynes and H. HermesG. W. Haynes and H. Hermeshttps://doi.org/10.1137/0308033PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Wei-Liang Chow, Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung, Math. Ann., 117 (1939), 98–105 10.1007/BF01450011 MR0001880 0022.02304 CrossrefGoogle Scholar[2] Robert Hermann, On the accessibility problem in control theoryInternat. Sympos. Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, 325–332 MR0149402 0142.36102 CrossrefGoogle Scholar[3] Robert Hermann, The differential geometry of foliations. II, J. Math. Mech., 11 (1962), 303–315 MR0142131 0152.20502 ISIGoogle Scholar[4] Robert Hermann, Some differential-geometric aspects of the Lagrange variational problem, Illinois J. Math., 6 (1962), 634–673 MR0145457 0196.54301 CrossrefGoogle Scholar[5] Jan Kučera, Solution in large of control problem $\dot x=(Au+Bv)x$, Czechoslovak Math. J., 17 (92) (1967), 91–96 MR0226103 0189.15701 ISIGoogle Scholar[6] Richard L. Bishop and , Richard J. Crittenden, Geometry of manifolds, Pure and Applied Mathematics, Vol. XV, Academic Press, New York, 1964ix+273 MR0169148 0132.16003 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Controllability of Poisson SystemsSIAM Journal on Control and Optimization, Vol. 43, No. 3 | 26 July 2006AbstractPDF (213 KB)Design of Homogeneous Time-Varying Stabilizing Control Laws for Driftless Controllable Systems Via Oscillatory Approximation of Lie Brackets in Closed LoopSIAM Journal on Control and Optimization, Vol. 38, No. 1 | 26 July 2006AbstractPDF (506 KB)An Approximation Algorithm for Nonholonomic SystemsSIAM Journal on Control and Optimization, Vol. 35, No. 4 | 26 July 2006AbstractPDF (642 KB)Linearized Control Systems and Applications to Smooth StabilizationSIAM Journal on Control and Optimization, Vol. 32, No. 2 | 14 July 2006AbstractPDF (2245 KB)The Realization Problem for a Class of Nonlinear SystemsSIAM Journal on Matrix Analysis and Applications, Vol. 11, No. 1 | 17 July 2006AbstractPDF (982 KB)Strong Controllability of Nonlinear SystemsSIAM Journal on Control and Optimization, Vol. 24, No. 2 | 17 February 2012AbstractPDF (1419 KB)Recent Developments and Future Perspectives in Nonlinear System TheorySIAM Review, Vol. 24, No. 3 | 10 July 2006AbstractPDF (3427 KB)Invertibility of Nonlinear Control SystemsSIAM Journal on Control and Optimization, Vol. 17, No. 2 | 18 July 2006AbstractPDF (924 KB)Local Controllability and Sufficient Conditions in Singular Problems. IISIAM Journal on Control and Optimization, Vol. 14, No. 6 | 18 July 2006AbstractPDF (1555 KB)Global Controllability of Nonlinear SystemsSIAM Journal on Control and Optimization, Vol. 14, No. 4 | 18 July 2006AbstractPDF (1166 KB)Global Bilinearization of Systems with Control Appearing LinearlySIAM Journal on Control, Vol. 13, No. 4 | 18 July 2006AbstractPDF (511 KB)A Generalization of Chow’s Theorem and the Bang-Bang Theorem to Nonlinear Control ProblemsSIAM Journal on Control, Vol. 12, No. 1 | 18 July 2006AbstractPDF (893 KB)Controllability of Nonlinear Systems on Compact ManifoldsSIAM Journal on Control, Vol. 12, No. 1 | 18 July 2006AbstractPDF (332 KB)On the Equivalence of Control Systems and the Linearization of Nonlinear SystemsSIAM Journal on Control, Vol. 11, No. 4 | 18 July 2006AbstractPDF (509 KB)Lie Theory and Control Systems Defined on SpheresSIAM Journal on Applied Mathematics, Vol. 25, No. 2 | 12 July 2006AbstractPDF (1172 KB)A Survey of Recent Results in Differential EquationsSIAM Review, Vol. 15, No. 2 | 2 August 2006AbstractPDF (1587 KB)The “Bang-Bang” Problem for Certain Control Systems in $GL(n,R)$SIAM Journal on Control, Vol. 10, No. 3 | 18 July 2006AbstractPDF (652 KB)System Theory on Group Manifolds and Coset SpacesSIAM Journal on Control, Vol. 10, No. 2 | 18 July 2006AbstractPDF (1759 KB)Global Controllability of Nonlinear SystemsSIAM Journal on Control, Vol. 10, No. 1 | 18 July 2006AbstractPDF (1137 KB)Contrôlabilité des Systèmes non LinéairesSIAM Journal on Control, Vol. 8, No. 4 | 18 July 2006AbstractPDF (64421 KB) Volume 8, Issue 4| 1970SIAM Journal on Control441-605 History Submitted:15 July 1969Accepted:15 March 1970Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0308033Article page range:pp. 450-460ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics

Perturbation Analysis of Diffusion-Coupled Biochemical Reaction Kinetics

Previous article Next article Perturbation Analysis of Diffusion-Coupled Biochemical Reaction KineticsL. W. RossL. W. Rosshttps://doi.org/10.1137/0119029PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] B. Atkinson, , E. L. Swilley, , A. W. Bush and , D. A. Williams, Kinetics, mass transfer and organism growth in a biological film reactor, Trans. Inst. Chem. Engrg., 45 (1967), T257–T264 Google Scholar[2] B. Atkinson and , I. S. Daoud, The analogy between micro-biological “reactions” and heterogeneous catalysis, Trans. Inst. Chem. Engrg., 46 (1968), T19–T24 Google Scholar[3] B. Atkinson, , I. S. Daoud and , D. A. Williams, A theory for the biological film reactor, Trans. Inst. Chem. Engrg., 46 (1968), T245–T250 Google Scholar[4] H. S. Carslaw and , J. C. Jaeger, Conduction of Heat in Solids, Oxford University Press, London, 1969, Chap. 2 Google Scholar[5] T. L. Miller and , M. J. Johnson, Utilization of normal alkanes by yeasts, Biotech. Bioengrg., 8 (1966), 549–565 10.1002/bit.260080408 CrossrefISIGoogle Scholar[6] L. S. Revelle, , W. R. Lynn and , M. A. Rivera, Bio-oxidation kinetics and a second-order equation describing the BOD reaction, J. Water Poll. Contr. Fed., 37 (1965), 1679–1692 Google Scholar[7] H. S. Tsien, The Poincaré-Lighthill-Kuo methodAdvances in applied mechanics, vol. IV, Academic Press Inc., New York, N.Y., 1956, 281–349 MR0079929 (18,167f) CrossrefGoogle Scholar[8] V. P. Vorotlin, , V. S. Krylov and , V. G. Levich, On the theory of extraction from a falling drop, Priklad. Mat. Mekh., 29 (1965), 386–394 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Numerical solution to a nonlinear McKendrick-Von Foerster equation with diffusion29 June 2022 | Numerical Algorithms, Vol. 41 Cross Ref Ground-state nodal solutions for superlinear perturbations of the Robin eigenvalue problem11 February 2022 | Zeitschrift für angewandte Mathematik und Physik, Vol. 73, No. 2 Cross Ref EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO ELLIPTIC PROBLEMS WITH SUBLINEAR MIXED BOUNDARY CONDITIONS20 November 2011 | Communications in Contemporary Mathematics, Vol. 11, No. 04 Cross Ref Numerical Methods for Quasi‐Linear Elliptic Equations with Nonlinear Boundary ConditionsC. V. Pao7 May 2007 | SIAM Journal on Numerical Analysis, Vol. 45, No. 3AbstractPDF (269 KB)Finite difference reaction diffusion equations with nonlinear boundary conditionsNumerical Methods for Partial Differential Equations, Vol. 11, No. 4 Cross Ref Existence of Quasi-Solutions of Systems of Nonlinear Elliptic BVP’s Suggested by Biochemical Reactions Cross Ref Optimal Control for a Class of Integral Equations Cross Ref Positive solutions of a nonlinear boundary-value problem of parabolic typeJournal of Differential Equations, Vol. 22, No. 1 Cross Ref Identification of dynamic zones in batch fermentationsBiotechnology and Bioengineering, Vol. 16, No. 4 Cross Ref Kinetics of diffusion-coupled fermentation processes: The conversion of cellulose to proteinBiotechnology and Bioengineering, Vol. 13, No. 1 Cross Ref Volume 19, Issue 2| 1970SIAM Journal on Applied Mathematics History Submitted:15 July 1969Published online:17 February 2012 InformationCopyright © 1970 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0119029Article page range:pp. 323-329ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics

Habit Formation and Dynamic Demand Functions

Most economists would agree that past consumption patterns are an important determinant of present consumption patterns, and that one ought to distinguish between long-run and short-run demand functions. But although the distinction between long-run and short-run behavior is traditional in the theory of the firm, it is seldom made in the theory of consumer behavior. If we regard demand theory as a theory of how a given amount of money (expenditure, called income) is allocated among goods, then-in a world without consumer durables-there are three reasons why longand shortrun demand functions might differ. (i) The consumer may have contractually fixed commitments which prevent him from adjusting some portion of his consumption (for example, housing) in response to changes in prices or income. When these fixed commitments lapse, he is able to adjust to his long-run equilibrium. (ii) The consumer may be ignorant of consumption possibilities or of his own tastes outside the range of his past consumption experience. In this case his adjustment to a new price-income situation will involve a time-consuming learning process. (iii) Finally, goods may be "habit forming" so that an individual's current preferences depend on his past consumption patterns. In this case a change in prices or income will cause a change-in consumption which will induce a change in tastes, which will cause a further change in consumption. In this paper I formulate a model of consumer behavior based on habit formation, beginning with a specific class of demand functions derived from the "modified Bergson family" of utility functions. The properties of these utility functions and the corresponding demand functions are briefly summarized in Section 1. I then postulate that the parameters

A Correction Concerning the Convergence Rate for the Conjugate Gradient Method

Previous article Next article A Correction Concerning the Convergence Rate for the Conjugate Gradient MethodJames W. DanielJames W. Danielhttps://doi.org/10.1137/0707020PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] James W. Daniel, The conjugate gradient method for linear and nonlinear operator equations, SIAM J. Numer. Anal., 4 (1967), 10–26 10.1137/0704002 MR0217987 0154.40302 LinkGoogle Scholar[2] James W. Daniel, Convergence of the conjugate gradient method with computationally convenient modifications, Numer. Math., 10 (1967), 125–131 10.1007/BF02174144 MR0219232 0178.18302 CrossrefISIGoogle Scholar[3] J. Ortega and , W. Rheinboldt, Private communication Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Krylov Solvability of Unbounded Inverse Linear Problems24 December 2020 | Integral Equations and Operator Theory, Vol. 93, No. 1 Cross Ref An improved unsharp masking model for intensive care unit chest radiograph enhancement Cross Ref Second-order adjoints for solving PDE-constrained optimization problemsOptimization Methods and Software, Vol. 27, No. 4-5 Cross Ref Discrete second order adjoints in atmospheric chemical transport modelingJournal of Computational Physics, Vol. 227, No. 12 Cross Ref 7 Mathematical programming — A computational perspective Cross Ref Some History of the Conjugate Gradient and Lanczos Algorithms: 1948–1976Gene H. Golub and Dianne P. O’Leary2 August 2006 | SIAM Review, Vol. 31, No. 1AbstractPDF (6558 KB)A derivative-based bracketing scheme for univariate minimization and the conjugate gradient methodComputers & Mathematics with Applications, Vol. 18, No. 9 Cross Ref Literatur Cross Ref Approximation methods for the unconstrained optimization of functions of several variablesJournal of Soviet Mathematics, Vol. 4, No. 6 Cross Ref Alternative proofs of the convergence properties of the conjugate-gradient methodJournal of Optimization Theory and Applications, Vol. 13, No. 5 Cross Ref Rate of Convergence of Several Conjugate Gradient AlgorithmsArthur I. Cohen3 August 2006 | SIAM Journal on Numerical Analysis, Vol. 9, No. 2AbstractPDF (773 KB)On the Convergence of the Conjugate Gradient Method for Singular Linear Operator EquationsW. J. Kammerer and M. Z. Nashed1 August 2006 | SIAM Journal on Numerical Analysis, Vol. 9, No. 1AbstractPDF (1764 KB) Volume 7, Issue 2| 1970SIAM Journal on Numerical Analysis History Submitted:24 December 1969Published online:14 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0707020Article page range:pp. 277-280ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics

Further Results on the Boundedness and the Stability of Solutions of Some Differential Equations of the Fourth Order

Previous article Next article Further Results on the Boundedness and the Stability of Solutions of Some Differential Equations of the Fourth OrderMartin HarrowMartin Harrowhttps://doi.org/10.1137/0501018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Martin Harrow, On the boundedness and the stability of solutions of some differential equations of the fourth order, SIAM J. Math. Anal., 1 (1970), 27–32 10.1137/0501002 MR0259264 0247.34038 LinkGoogle Scholar[2] E. A. Barbašin, On the theory of general dynamical systems, Učenye Zapiski Moskov. Gos. Univ., 135 (1948), 110–133 MR0033453 Google Scholar[3] H. A. Antosiewicz, On non-linear differential equations of the second order with integrable forcing term, J. London Math. Soc., 30 (1955), 64–67 MR0065752 0064.08404 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay9 June 2017 | Journal of Inequalities and Applications, Vol. 2017, No. 1 Cross Ref ON SOME QUALITATIVE BEHAVIORS OF CERTAIN DIFFERENTIAL EQUATIONS OF FOURTH ORDER WITH MULTIPLE RETARDATIONSJournal of Applied Analysis & Computation, Vol. 6, No. 2 Cross Ref On the boundedness and the stability results for the solution of certain fourth order differential equations via the intrinsic methodApplied Mathematics and Mechanics, Vol. 17, No. 11 Cross Ref On the boundedness and stability of a fourth order differential equationAnnali di Matematica Pura ed Applicata, Vol. 123, No. 1 Cross Ref On the Boundedness and Stability of Solutions of Some Differential Equations of the Fifth OrderE. N. Chukwu17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 7, No. 2AbstractPDF (1150 KB)On the boundedness and the stability properties of solutions of certain fourth order differential equationsAnnali di Matematica Pura ed Applicata, Vol. 95, No. 1 Cross Ref Further stability and boundedness results for the solutions of some differential equations of the fourth orderAnnali di Matematica Pura ed Applicata, Vol. 95, No. 1 Cross Ref A note on the asymptotic behavior of the solutions of $\ddot x + a\left( t \right)f\left( {\ddot x} \right)\ddot x + b\left( t \right)\phi \left( {\dot x,\ddot x} \right) + c\left( t \right)g\left( {\dot x} \right) + d\left( t \right)h\left( x \right) = p\left( {t,x,\dot x,\ddot x,\ddot x} \right)$Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 49, No. 5 Cross Ref On the stability of a nonhomogeneous differential equation of the fourth orderAnnali di Matematica Pura ed Applicata, Vol. 92, No. 1 Cross Ref A remark on the asymptotic behavior of the solution of $\ddddot x + f\left( {\ddot x} \right)\dddot x + \phi \left( {\dot x,\ddot x} \right) + g\left( {\dot x} \right) + h\left( x \right) = p\left( {t,x,\dot x,\ddot x,\dddot x} \right)$Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 48, No. 6 Cross Ref On the behavior of solutions of certain differential equations of the fourth orderAnnali di Matematica Pura ed Applicata, Vol. 89, No. 1 Cross Ref Some further stability and boundedness results of some differential equations of the fourth orderAnnali di Matematica Pura ed Applicata, Vol. 90, No. 1 Cross Ref On the Boundedness and the Stability of Some Differential Equations of the Fourth OrderB. S. Lalli and W. A. Skrapek17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 2, No. 2AbstractPDF (333 KB) Volume 1, Issue 2| 1970SIAM Journal on Mathematical Analysis History Submitted:22 July 1969Published online:17 February 2012 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0501018Article page range:pp. 189-194ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics

Singular Perturbation Theory and Geophysics

Singular Perturbation Theory and Geophysics

An Operator on Binary Sequences

Previous article Next article An Operator on Binary SequencesT. GokaT. Gokahttps://doi.org/10.1137/1012046PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout Previous article Next article FiguresRelatedReferencesCited byDetails Balanced de Bruijn Sequences Cross Ref BiEntropy, TriEntropy and Primality10 March 2020 | Entropy, Vol. 22, No. 3 Cross Ref On the depth distribution of linear codesIEEE Transactions on Information Theory, Vol. 46, No. 6 Cross Ref The depth distribution-a new characterization for linear codesIEEE Transactions on Information Theory, Vol. 43, No. 4 Cross Ref Rotating-table games and derivatives of wordsTheoretical Computer Science, Vol. 108, No. 2 Cross Ref Derivatives of Binary SequencesMelvyn B. Nathanson12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 21, No. 3AbstractPDF (495 KB) Volume 12, Issue 2| 1970SIAM Review History Submitted:27 May 1969Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1012046Article page range:pp. 264-266ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics