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Full-Text Articles in Mathematics
Quasi-Solutions And Monotone Method For Systems Of Nonlinear Boundary Value Problems, A. S. Vatsala, V. Lakshmikantham
Quasi-Solutions And Monotone Method For Systems Of Nonlinear Boundary Value Problems, A. S. Vatsala, V. Lakshmikantham
Mathematics Technical Papers - Archive
In the study of comparison theorems, existence of extremal solutions and monotone iterative techniques for initial and boundary value problems of ordinary differential systems, it becomes necessary to impose a condition generally known as quasi-monotone property [1,3,5]. In systems which represent physical situations such as a model governing the combustion of a material, quasi-monotonicity is not satisfied, see [4]. However a kind of mixed monotone property holds. To deal with such situations the notion of quasi-solutions was systematically developed in [4]. In this paper, we investigate monotone iterative method for systems of nonlinear boundary value problems when the system possesses …
Some Theorems On Fixed Points In Lipschitz And Kannan Type Mappings, B. B. Williams, A. A. Gillespie
Some Theorems On Fixed Points In Lipschitz And Kannan Type Mappings, B. B. Williams, A. A. Gillespie
Mathematics Technical Papers - Archive
No abstract provided.
On The Existence Of Positive Solutions For Non-Linear Elliptic Equations, Giovanni Vidossich
On The Existence Of Positive Solutions For Non-Linear Elliptic Equations, Giovanni Vidossich
Mathematics Technical Papers - Archive
No abstract provided.
Generalized Hopf Bifurcation And H-Asymptotic Stability, L. Salvadori, Stephen R. Bernfeld
Generalized Hopf Bifurcation And H-Asymptotic Stability, L. Salvadori, Stephen R. Bernfeld
Mathematics Technical Papers - Archive
The prevalent approach to the Hopf bifurcation problem is to prove directly the existence of the bifurcating periodic orbits by using such standard procedures as the implicit function theorem, the LiapunovSchmidt method and its known variants, and topological degree arguments (see [7]). The phenomenon of Hopf bifurcation often occurs because of exchange of stability properties of the equilibrium under perturbations (see for instance, Chafee in [7] p. 85-88,Andronov et. al. [1], Marchetti et. al. [6] and Negrini and Salvadori [8]). This connection between the exchange of stability of the equilibrium and the appearance of bifurcating periodic orbits can be carefully …
Generalized Hopf Bifurcation In Rn And H-Asymptotic Stability, L. Salvadori, Stephen R. Bernfeld
Generalized Hopf Bifurcation In Rn And H-Asymptotic Stability, L. Salvadori, Stephen R. Bernfeld
Mathematics Technical Papers - Archive
No abstract provided.
A New Computer Approach To Atomic Electron Configuartions With Application To The Elements From Helium Through Oxygen, Donald Greenspan
A New Computer Approach To Atomic Electron Configuartions With Application To The Elements From Helium Through Oxygen, Donald Greenspan
Mathematics Technical Papers - Archive
In this paper a new, computer approach is developed for atomic and molecular dynamics. Though classical in nature, it includes all electron-electron interactions. Experimental ionization energies are used to determine average radial distances and velocities for atoms. Computer examples for symmetric and nonsymmetric electron motions are described and discussed. Auto-ionization results fix the nonadmissibility of a significant class of electron configurations.
Quasi-Solutions And Their Role In The Qualitative Theory Of Differential Equations, V. Lakshmikantham, K. Deimling
Quasi-Solutions And Their Role In The Qualitative Theory Of Differential Equations, V. Lakshmikantham, K. Deimling
Mathematics Technical Papers - Archive
In the study of comparison theorems and extremal solutions for systems of ordinary differential equations [5], one usually imposes a condition on the right hand side known as quasi-monotone nondecreasing property. This property. is also needed in proving comparison theorems for second order, boundary value problems [9] as well as for the initial boundary value problem for parabolic systems [5, 6]. Also, it is well known that in the .method of vector Lyapunov functions which provides an effective tool to investigate the stability of Large Scale Systems [1-4], an unpleasant drawback is the requirement of the quasi-monotone property for the …
Equations With Unbounded Delay: A Survey, V. Lakshmikantham, C. Corduneanu
Equations With Unbounded Delay: A Survey, V. Lakshmikantham, C. Corduneanu
Mathematics Technical Papers - Archive
The theory of equations with delay has been considerably developed during the past 30 years. The first book dedicated to this subject has been published by A. D. Myshkis [180], in 1951, and has been subsequently translated into German (1955) and English (1966). A second Russian edition, that came out in 1972, contains a good deal of references and points out interesting features of the theory of linear equations with delayed argument, including also examples of equations with unbounded delay.
Comparison Results For Reaction-Diffusion Equations In A Banach Space, V. Lakshmikantham
Comparison Results For Reaction-Diffusion Equations In A Banach Space, V. Lakshmikantham
Mathematics Technical Papers - Archive
Let T be the temperature and n the concentration of a combustible substance. A simple model governing the combustion of the material is given by [see pdf for notations] (1.1) where the constant Q is the heat of reaction; the constants Kl , K2 are thermal, material diffusion coefficients; the term exp(-E/RT) is the Arrenhius rate factor; E is the activation energy; and R is the univeral gas constant. Equations (1.1) are considered on a bounded domain ^ with the boundary conditions [see pdf for notations] (1.2) together with initial conditions [see pdf for notations] (1.3) under the assumption T0(x) …
On Numerical Treatment Of Free Surfaces For Incompressible Fluid-Flow Problems, Vincenzo Casulli
On Numerical Treatment Of Free Surfaces For Incompressible Fluid-Flow Problems, Vincenzo Casulli
Mathematics Technical Papers - Archive
In this paper a detailed analysis of numerical schemes for treatment of free surfaces is presented. The kinematic free surface condition is solved by a new numerical scheme that, using the proper boundary conditions, conserves the total fluid volume. Some comparisons are given on a sample test problem.
Existence/Uniqueness And Validation Of Parameter Imbedding Equations For Nonlinear Fredholm Integral Equations, M. E. Lord
Mathematics Technical Papers - Archive
A parameter imbedding method for nonlinear Fredholm integral equations produces a Cauchy system involving the solution of the integral equation and an associated resolvent kernel. For such Cauchy systems sufficient conditions are given to guarantee local existence and uniqueness of solutions. A Picard type theorem utilizing a Lipschitz condition is obtained. This result then yields the validation of the Cauchy system.
On Identifiability Of Impulse-Response In Compartmental Systems, Jerome Eisenfeld
On Identifiability Of Impulse-Response In Compartmental Systems, Jerome Eisenfeld
Mathematics Technical Papers - Archive
Structural identifiability in compartmental systems deals with the map from impulse-response parameters to model parameters. If the data is analyzed in terms of integral transforms sk (Fourier, moments, etc) then we may study also the map from the sk to impulse-response parameters. This paper is mainly concerned with the latter correspondence. In other words we discuss the possibility of removing (inadvertently or intentionally) decay terms in the process of forming integral transforms.
Parameter Estimation In Illness-Death Processes: Preinfaractional Angina, Jerome Eisenfeld, B. Canada
Parameter Estimation In Illness-Death Processes: Preinfaractional Angina, Jerome Eisenfeld, B. Canada
Mathematics Technical Papers - Archive
An illness-death process is an absorbing Markov process where the illness states from the transient states of the process. This paper deals with the estimation of illness-death parameters from survivor data. The parameters of interest include the probabilities of recovery, relapse and death and mean residence times. The estimation problem is considered from the point of view of the theory of structural identifiability in compartmental analysis. As a prototypical example, we consider published data on preinfarctional angina.
Existence And Comparison Results For Differential Equations Of Sobolev Type, Randy Vaughn, A. S. Vatsala
Existence And Comparison Results For Differential Equations Of Sobolev Type, Randy Vaughn, A. S. Vatsala
Mathematics Technical Papers - Archive
Recently a new class of differential equations, called differential equations of Sobolev type was studied in [4] in which an existence theorem of Picards type was investigated as well as a variation of constants formula. In [5], existence and comparison results for a class of Volterra integral equation of Sobolev-type were discussed. In this paper we recall the Peano type existence result from [5] for Sobolev-differential equations and show that solutions can be extended to the entire square under consideration. This result extends results found in [1] for nonlinear Volterra integral equations. Our results include a comparison result in addition …
Note On Special Relativistic Calculations With Identical Laboratory And Rocket Frame Computers, Donald Greenspan
Note On Special Relativistic Calculations With Identical Laboratory And Rocket Frame Computers, Donald Greenspan
Mathematics Technical Papers - Archive
Dynamical relativistic problems invariably require the solution of nonlinear differential equations. These equations are rarely solvable in closed form and are now being solved numerically on modern digital computers. In this paper, a numerical method is developed which has the special property that computations on identical computers in both the laboratory and rocket frames yield numerical results which continue to be related by the Lorentz transformation.
N-Body Modeling Of Nonlinear, Free Surface Liquid Flow, Donald Greenspan
N-Body Modeling Of Nonlinear, Free Surface Liquid Flow, Donald Greenspan
Mathematics Technical Papers - Archive
In this paper a new, n-body approach is developed for the modeling of liquid phenomena. Both long and short range forces are included. Computer examples of several prototype, nonlinear, free surface problems are described and discussed.
Non-Splitting Unitary Perfect Polynomials Over Gf(Q)T, Mickie Sue Harbin, Jacob T. B. Beard Jr.
Non-Splitting Unitary Perfect Polynomials Over Gf(Q)T, Mickie Sue Harbin, Jacob T. B. Beard Jr.
Mathematics Technical Papers - Archive
It has been conjectured that there are infinitely many distinct pd-equivalence classes of non-splitting unitary perfect polynomials over GF(pd) for each prime p and each odd integer d > 1. The conjecture is proved in the affirmative in the cases i) p < 97, ii) 2 ^ GF(p) is not a square, iii) 2 ^ GF(p) is a square and all of the positive integer intervals determined by distinct odd powers of ^t contain a square, where GF*(p) = (^). In addition, it has been determined that iii) is satisfied by 314 primes p > 97.2
Mathematical Models Of Porous Flow, Donald Greenspan
Mathematical Models Of Porous Flow, Donald Greenspan
Mathematics Technical Papers - Archive
In this paper a new, viable mathematical approach to the analysis of porous flow is developed. Liquids and solids are modeled as sets of particles which interact in accordance with both long range (gravity) and short range (molecular type) forces. The resulting nonlinear, n-body problem is resolved numerically on a digital computer. A variety of fundamental porous flow type problems, solved on the University of Texas at Arlington IBM 370-155, are described and analyzed.
Existence And Comparison Theorems For Differential Equations In Banach Spaces, V. Lakshmikantham, K. Deimling
Existence And Comparison Theorems For Differential Equations In Banach Spaces, V. Lakshmikantham, K. Deimling
Mathematics Technical Papers - Archive
In our recent paper [3] we have studied the existence of maximal and minimal solutions to the IVP in a Banach space [see pdf for notation]. (1) [see pdf for notation] where [see pdf for notation] maps [see pdf for notation] into [see pdf for notation], with [see pdf for notation] and [see pdf for notation] a cone. The essential hypotheses have been that [see pdf for notation]f is quasimonotone with respect to [see pdf for notation] and that [see pdf for notation] and [see pdf for notation] have some natural properties. If such extremal solutions exist then it is …
Stochastic Differential Inequalities Of Ito Type, V. Lakshmikantham, G. S. Ladde
Stochastic Differential Inequalities Of Ito Type, V. Lakshmikantham, G. S. Ladde
Mathematics Technical Papers - Archive
It is well known [3] that the method of differential inequalities plays an important role in the qualitative theory of differential equations. It is therefore natural to expect that a similar theory would be equally important in the study of Stochastic differential systems of Ito type. As will be seen that this investigation is not straightforward extension of the deterministic situation and needs special techniques to be utilized. In this paper, we develop the theory of stochastic differential inequality of Ito type, consider the nonnegativity of solutions, prove existence of extremal solutions and derive a comparison result.
Separation And Monotonicity Results For The Roots Of The Moment Problem, Jerome Eisenfeld, James Hallmark
Separation And Monotonicity Results For The Roots Of The Moment Problem, Jerome Eisenfeld, James Hallmark
Mathematics Technical Papers - Archive
Consider the system identification problem [see pdf for notation] [see pdf for notation] where u(t) and y(t) are given discretely on the interval [see pdf for notation] and we wish to determine information about the unknown constant matrices A, B, and C. Many techniques are available for approaching this problem. Several of these methods lead to what is known as the moment problem, [1]-[6]. This paper pertains to the moment problem which will now be introduced.
A Technique In Stability Theory Of Delay-Differential Equations, S. Leela, V. Lakshmikantham
A Technique In Stability Theory Of Delay-Differential Equations, S. Leela, V. Lakshmikantham
Mathematics Technical Papers - Archive
In the study of stability theory for delay-differential equations using Lyapunov functions and the theory of differential inequalities, it becomes necessary to choose an appropriate minimal class of functions relative to which the derivative of the Lyapunov function is estimated. This approach has recently been recognized as a very natural method in the study of the qualitative behavior of delay equations.
Reaction-Diffusion Inequalities In Cones, Randy Vaughn, V. Lakshmikantham
Reaction-Diffusion Inequalities In Cones, Randy Vaughn, V. Lakshmikantham
Mathematics Technical Papers - Archive
Recently there has been a growing interest in the study of nonlinear reaction-diffusion equations [2,3,4,7] because of the fact examples of such equations occur in population genetics [2,5,12,13], nuclear and chemical reactors [2,7,8], conduction of nerve impulses [1,7,15], and several other biological models [1,6,15]. As is the case of ordinary differential equations [9,10], it is natural to expect that the theory of reaction-diffusion inequalities and comparison theorems will play a prominent role in this study. In this paper, we consider reaction-diffusion equations which are weakly coupled relative to an arbitrary cone. We prove a result on flow-invariance which is then …
System Identification Of Models Exhibiting Exponential, Harmonic And Resonant Modes, B. Soni, Jerome Eisenfeld
System Identification Of Models Exhibiting Exponential, Harmonic And Resonant Modes, B. Soni, Jerome Eisenfeld
Mathematics Technical Papers - Archive
A classical problem arising in compartmental analysis is the so called identification problem or the inverse problem. One is presented with the linear time invariant compartmental model [see pdf for notation] [see pdf for notation] Where A is a square matrix and the dimensions of B and C are consistent with that of A. The problem is to estimate a certain subset of the matrix elements [see pdf for notation], [see pdf for notation] and [see pdf for notation] from discrete observations of the input vector u(t) and the output vector y(t). When instantaneous mixing is assumed the analogous equations …
Relationship Between Stochastic And Differential Models Of Compartmental Systems, Jerome Eisenfeld
Relationship Between Stochastic And Differential Models Of Compartmental Systems, Jerome Eisenfeld
Mathematics Technical Papers - Archive
This paper shows that the differential equations model for compartmental systems is consistent with a stochastic description. Consequently, we may employ either a differential equations or a stochastic formulation for either parameter identification, or for physical interpretation, as best suits the purpose. The differential equations parameters, the so-called fractional transfer coefficients, may be determined from the corresponding set of stochastic parameters and vice versa.
Monotone Methods For Nonlinear Boundary Value Problems In Banach Spaces, Stephen R. Bernfeld, V. Lakshmikantham
Monotone Methods For Nonlinear Boundary Value Problems In Banach Spaces, Stephen R. Bernfeld, V. Lakshmikantham
Mathematics Technical Papers - Archive
Monotone methods have been used to generate multiple solutions of nonlinear boundary value problems for both ordinary and partial differential equations. Keller [10] and Sattinger [13], extending the chord method, considered nonlinear partial differential equations containing no gradient term. The inclusion of the gradient term was first introduced by Chandra and Davis [6] who considered the ordinary boundary value problem (1.1) [see pdf for notation] (1.2) [see pdf for notation] Here [see pdf for notation]. They assumed that f depends linearly on [see pdf for notation]; and this restriction on [see pdf for notation]' was eliminated by Bernfeld and Chandra …
Remarks On Numerical Computations Using The Alternative Method, R. Kannan, Jerome Eisenfeld, Stephen R. Bernfeld
Remarks On Numerical Computations Using The Alternative Method, R. Kannan, Jerome Eisenfeld, Stephen R. Bernfeld
Mathematics Technical Papers - Archive
Recently Cesari and Bowman [1] have demonstrated the applicability of the alternative method to obtain approximate solutions of nonlinear equations. They provided numerical approximations of solutions of two point nonlinear boundary value problems. Our purpose here is to point out how these approximations may be improved upon without much additional effort. For illustrative purposes we discuss one of their examples.
Pitman-Closeness Efficiency Of Estimators Of Reliability With Application To The Exponent/Al Failure Model, Jerome P. Keating, Danny D. Dyer
Pitman-Closeness Efficiency Of Estimators Of Reliability With Application To The Exponent/Al Failure Model, Jerome P. Keating, Danny D. Dyer
Mathematics Technical Papers - Archive
When there are available several point estimators of component or system reliability, it would be of interest to compare such estimators through some "closeness to the true value of reliability" criteria. Along these lines, the concept of Pitman-closeness efficiency is introduced. Essentially, when comparing two estimators of reliability for a given situation, Pitman-closeness efficiency gives the odds in favor of one of the estimators being closer to the true value of reliability than is the other. Theory is developed which provides a straightforward way to evaluate this measure of efficiency under fairly general conditions on the estimators. Based on this …
Existence And Uniqueness Of Sobolev Type Integrodifferential Equations, M. E. Lord
Existence And Uniqueness Of Sobolev Type Integrodifferential Equations, M. E. Lord
Mathematics Technical Papers - Archive
An imbedding method for nonlinear Fredholm integral equations gives rise to a Sobolev type integrodifferential equation. For such equations, sufficient conditions are given to guarantee local existence and uniqueness of solutions. A Picard type theorem utilizing a Lipschitz condition is obtained.
Sobolev Type Differential Equations, M. E. Lord, V. Lakshmikantham
Sobolev Type Differential Equations, M. E. Lord, V. Lakshmikantham
Mathematics Technical Papers - Archive
An imbedding method for solving linear Fredholm integral equations was introduced by Sobolev [3] which involves the solution of the following differential equation with initial value for the resolvent kernel [see pdf for notation]. The differential equation in (1.1) is unusual in that the solution K(t,y,x) is evaluated at different combinations of the independent variables (t,y,x) . We will refer to any differential equation with this property as a Sobolev type differential equation. We introduce a Sobolev type differential equation which generalizes (1.1) and consider conditions for existence and uniqueness. A Picard type theorem is obtained, which by way of …