Now showing items 21-40 of 570

    • A New Approach to the Method of Nonlinear Variation of Parameters 

      Mitchell, A. Richard; Lord, M. E. (University of Texas at ArlingtonDepartment of Mathematics, 1975-01)
      **Please note that the full text is embargoed** ABSTRACT: As is well-known [3] the method of variation of parameters is a very useful tool in studying the properties of solutions of perturbed differential equations. Extending ...
    • On the Existence of Zeros of Lyapunov-Monotone Operators 

      Leela, S.; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1975-02)
      **Please note that the full text is embargoed** ABSTRACT: Consider a nonlinear operator T from a Banach space into itself. The study of the existence of zeros of T plays an important role in yielding fixed points of ...
    • Block Diagonalization and Eigenvalues 

      Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1975-03)
      **Please note that the full text is embargoed** ABSTRACT: Let A denote an Algebra with an identity element. Consider an [see pdf for notation] matrix [see pdf for notation] with a partitioning [see pdf for notation] where ...
    • Unitary Perfect Polynomials Over GF(q) 

      Beard, Jacob T. B., Jr. (University of Texas at ArlingtonDepartment of Mathematics, 1975-03)
      **Please note that the full text is embargoed** ABSTRACT: For monic polynomials A(x), B(x) e GF[q,x], call B(x) a unitary divisor of A(x) provided (B(x),A(x)/B(x)) = 1 . The polynomial A(x) is called unitary perfect over ...
    • Vector Lyapunov Functions and Perturbations of Nonlinear Systems 

      Moore, Marion E.; Mitchell, Roger W. (University of Texas at ArlingtonDepartment of Mathematics, 1975-03)
      **Please note that the full text is embargoed** ABSTRACT: Two recent papers [2,3] have combined the techniques of the Lyapunov method and the nonlinear variation of parameters to study the effects of perturbations of ...
    • Perfect Polynomials Over GF(q) 

      O'Connell, James R., Jr.; Beard, Jacob T. B., Jr.; West, Karen I. (University of Texas at ArlingtonDepartment of Mathematics, 1975-03)
      **Please note that the full text is embargoed** ABSTRACT: A monic polynomial [see pdf for notation] is called perfect over GF(q) if and only if the sum [see pdf for notation] of the distinct monic divisors in GF[q,x] of ...
    • Statistical Analysis of Fourier Coefficients in a Restricted Harmonic Dial 

      Dyer, Danny D. (University of Texas at ArlingtonDepartment of Mathematics, 1975-04)
      **Please note that the full text is embargoed** ABSTRACT: Due to the physical nature of certain periodic data, the harmonic dial points (the Fourier coefficients obtained from harmonic analysis of the data) are sometimes ...
    • On the Existence of Solutions of Differential Equations of Retarded Type in a Banach Space 

      Lakshmikantham, V.; Mitchell, Roger W.; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 1975-06)
      **Please note that the full text is embargoed** ABSTRACT: The existence and uniqueness of solutions of differential equations of retarded type in a Banach space are considered under a monotonicity type condition. The tools ...
    • Remarks on Nonlinear Contraction and Comparison Principle in Abstract Cones 

      Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1975-06)
      **Please note that the full text is embargoed** ABSTRACT: The contraction mapping principle and the Schauder principle can both be viewed as a comparison of maps. For the former one has a condition of the type [see pdf for ...
    • Maximal and Minimal Solutions and Comparison Principle for Differential Equations in Abstract Cones 

      Mitchell, Roger W.; Mitchell, A. Richard; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1975-06)
      **Please note that the full text is embargoed** ABSTRACT: Existence of maximal and minimal solutions for differential equations in abstract cones is established without requiring uniform continuity. Utilizing such a result ...
    • On a Measure of Nonconvexity and Applications 

      Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1975-06)
      **Please note that the full text is embargoed** ABSTRACT: The measure of noncompactness which was introduced by Kuratowski [8] (in 1930) has now become an important tool in nonlinear analysis (although its value in that ...
    • On the Convergence of Successive Approximations for Quasi-Nonexpansive Mappings Through Abstract Cones 

      Williams, B. B.; Bolen, J. C. (University of Texas at ArlingtonDepartment of Mathematics, 1975-07)
      **Please note that the full text is embargoed** ABSTRACT: In a recent paper, Petryshyn and Williamson [4] investigated the convergence of successive approximations of quasi- nonexpansive mappings in a Banach space. This ...
    • On the Zeros of Monotone Operators of Retarded Type in a Banach Space 

      Sutherland, Patrick; Lakshmikantham, V. (University of Texas at ArlingtonDepartment of Mathematics, 1975-09)
      **Please note that the full text is embargoed** ABSTRACT: Recent interest in the Cauchy problem for differential equations in a Banach space [9] has stimulated a similar interest for differential equations of a retarded ...
    • A Survey of Techniques for Determining Lower Confidence Bounds on Series System Reliability Based on Subsystem Test Data 

      Dyer, Danny D. (University of Texas at ArlingtonDepartment of Mathematics, 1975-09)
      **Please note that the full text is embargoed** ABSTRACT: A problem of considerable interest and for which a great deal of research has been expended is that of determining lower confidence bounds on series system ...
    • Structural Inference on Reliability in a Lognormal Model 

      Dyer, Danny D. (University of Texas at ArlingtonDepartment of Mathematics, 1975-12)
      **Please note that the full text is embargoed** ABSTRACT: The theory of structural inference, as developed by Fraser (1968), is based on a group-theoretic approach using invariant Haar measures to Fisher's fiducial theory. ...
    • The Extendability and Uniqueness of Solutions of Ordinary Differential Equations 

      Bernfeld, Stephen R. (University of Texas at ArlingtonDepartment of Mathematics, 1976)
      **Please note that the full text is embargoed** ABSTRACT: In a recent paper [1] the author obtained results on the extendability of solutions of perturbed differential equations. The question of the extendability of solutions ...
    • On the Construction of a Norm Associated with the Measure of Noncompactness 

      Bernfeld, Stephen R.; Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1976-02)
      **Please note that the full text is embargoed** ABSTRACT: It is shown that the bounded, nonempty subsets of a reflexive Banach space g can be imbedded in another Banach space B(E) in such a manner so that the measure of ...
    • A Nonlinear Variation of Constants Method for Integro-Differential and Integral Equations 

      Lord, M. E.; Bernfeld, Stephen R. (University of Texas at ArlingtonDepartment of Mathematics, 1976-02)
      **Please note that the full text is embargoed** ABSTRACT: It is well known that a very important technique in obtaining the asymptotic behavior of solutions of linear and nonlinear ordinary differential equations ...
    • The Method of Quasilinearization and Positivity of Solutions in Abstract Cones 

      Lakshmikantham, V.; Sety, Dolores D.; Mitchell, A. Richard (University of Texas at ArlingtonDepartment of Mathematics, 1976-03)
      **Please note that the full text is embargoed** ABSTRACT: The method of quasilinearization was first introduced by Bellman (Ref. 1) and was developed further by Kalaba (Ref. 2). More detailed information concerning the ...
    • Fixed Point Theorems on Closed Sets Through Abstract Cones 

      Lakshmikantham, V.; Eisenfeld, Jerome (University of Texas at ArlingtonDepartment of Mathematics, 1976-03)
      **Please note that the full text is embargoed** ABSTRACT: Let D be a closed subset of a complete metric space (X,p). We seek (i) conditions upon which a map T : D -> X has a fixed point in D and (ii) the construction of ...