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Articles 241 - 270 of 343
Full-Text Articles in Mathematics
On Mean Residence Times In Compartments, Jerome Eisenfeld
On Mean Residence Times In Compartments, Jerome Eisenfeld
Mathematics Technical Papers - Archive
This paper is concerned with a set of parameters which measure the mean time a random particle resides in individual compartments in response to a given load distribution. These parameters are related to other time parameters and to each other.
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.
Methodology For Testing Homogeneity Of Variances, Danny D. Dyer, Jerome P. Keating
Methodology For Testing Homogeneity Of Variances, Danny D. Dyer, Jerome P. Keating
Mathematics Technical Papers - Archive
Suppose random samples are drawn from each of n populations with unknown means and variances. Developing procedures to test the claim that the population variances are equal (homogeneity of variances) has frequently been a goal for statisticians. One widely used technique is due to Bartlett (1937) and is based on a slight modification of the generalized Neyman-Pearson likelihood ratio test. It is well known, however, that Bartlett's test is highly sensitive to the assumption that the underlying populations are normal (Box, 1953). If nonnormality is present, the use of Bartlett's test can often lead to the rejection of the claim …
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.
On The Comparison Of Estimators In A Rectangular Distribution, Danny D. Dyer
On The Comparison Of Estimators In A Rectangular Distribution, Danny D. Dyer
Mathematics Technical Papers - Archive
Given two estimators ^1 and ^2 of an unknown parameter ^, Pitman (1937) has suggested calling ^1 a "closer" estimator of ^ than is ^2 if [see pdf for notations] for all values of ^. Using this "closeness" criterion, Johnson (1950) compared several well known estimators of ^ based on a random sample from the rectangular distribution [see pdf for notations], otherwise. In addition, each estimator's mean squared error was given since Pitman's criterion does not take into account the degree of closeness. Unfortunately when two such estimators of ^ are compared, one of them is often preferred under the …
An Arithmetic Computer Approach To Gas Dynamical Modeling, Donald Greenspan, Aspi Rustom Wadia
An Arithmetic Computer Approach To Gas Dynamical Modeling, Donald Greenspan, Aspi Rustom Wadia
Mathematics Technical Papers - Archive
Unsteady, two dimensional internal and external flows are analyzed using an arithmetic n-body formulation. A Lagrangian approach is used to study the internal shock formation in a shock tube and the external flows over a circular cyclinder, a flat plate and an airfoil. Viable physical mechanisms of the shock and boundary layer formation and of flow separation are developed. This approach results in a computer simulation of a wind tunnel in which arbitrarily shaped bodies can be studied. Extensive computer examples are described for which agreement with experimental data is good for all cases in which the damping of the …
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 Results For A Class Of Volterra Integral Equations Of Sobolev Type, A. S. Vatsala, V. Lakshmikantham, Randy Vaughn
Existence And Comparison Results For A Class Of Volterra Integral Equations Of Sobolev Type, A. S. Vatsala, V. Lakshmikantham, Randy Vaughn
Mathematics Technical Papers - Archive
Recently [2] a class of new differential equations called Sobolev type differential equations was introduced and Picard type existence theorem for such equations was proved among other results like variation of constants formula and Gronwall type inequalities for such equations. However Peano's type existence result was open for such equations since it was not clear how to proceed. Special cases of such equations occur in imbedding method for solving Fredholm integral equations [5]. In this paper we consider Volterra integral equations of Sobolev type which include the foregoing class of differential equations as special cases. We consider Peano's type existence …
A Systems-Theory Approach To The Analysis Of Multiexponential Fluorescence Decay, Corey C. Ford, Jerome Eisenfeld
A Systems-Theory Approach To The Analysis Of Multiexponential Fluorescence Decay, Corey C. Ford, Jerome Eisenfeld
Mathematics Technical Papers - Archive
A mathematical model of the fluorescence decay experiment based on linear systems theory is presented. The model suggests an experimental technique which increases the probability of correctly determining the decay constants of a multicomponent system. Using moment methods for data analysis,accuracy is improved by combining information obtained from several discrete experiments. Examples are presented to show that the analysis of a three component system composed of known standards is improved as the number of experimental determinations is increased from 1 to 4. The discrete measurements are made by changing the excitation and emission wavelengths.
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.
On Existence Of Extremal Solutions Of Differential Equations In Banach Spaces, V. Lakshmikantham, K. Deimling
On Existence Of Extremal Solutions Of Differential Equations In Banach Spaces, V. Lakshmikantham, K. Deimling
Mathematics Technical Papers - Archive
Let X be a real Banach space, [see pdf for notation] a cone, [see pdf for notation] and [see pdf for notation] continuous. We look for conditions on X, K and f such that the IVP (1) [see pdf for notation] has a maximal solution [see pdf for notation] and a minimal solution u with respect to the partial ordering induced by K. Contrary to known results, [5,6], we shall not assume that K has interior points, since the standard cones of many infinite dimensional spaces have empty interior. The second essential new feature is that f is supposed to …
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.
On The Relative Behavior Of Estimators Of Reliability/Survivability, Danny D. Dyer, Onas L. Hensley, Jerome P. Keating
On The Relative Behavior Of Estimators Of Reliability/Survivability, Danny D. Dyer, Onas L. Hensley, Jerome P. Keating
Mathematics Technical Papers - Archive
Based on a decomposition of mean absolute error, a twofold technique is introduced whereby a pairwise comparison of point estimators of reliability/survivability can be made. Given two such estimators, the method examines (a) the "odds" in favor of one of the estimators being closer to the true value than is the other and (b) each estimator's average closeness to the true value not only when it is closer than is the other but also when it is not. Joint consideration of these concepts is shown to form a basis for determining which of the two estimators is preferred in a …
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.
Identification Of Linear Time-Invariant Systems, Jerome Eisenfeld
Identification Of Linear Time-Invariant Systems, Jerome Eisenfeld
Mathematics Technical Papers - Archive
A new method of identification for linear time-invariant systems with one input is presented. The method requires the estimation of weighted integrals over a finite time interval.
Non-Splitting Unitary Perfect Polynomials Over Gf(P), 7≤P≤19, Mickie Sue Harbin
Non-Splitting Unitary Perfect Polynomials Over Gf(P), 7≤P≤19, Mickie Sue Harbin
Mathematics Technical Papers - Archive
Examples are given of non-splitting unitary perfect polynomials over [see pdf for notation] for [see pdf for notation]. These, together with previous results, establish the existence of infinitely many such polynomials over [see pdf for notation] for each [see pdf for notation]. The given result further supports the conjecture that non-splitting unitary perfect polynomials exist over [see pdf for notation] for each, [see pdf for notation].
Parabolic Differential Inequalities In Cones, Randy Vaughn, V. Lakshmikantham
Parabolic Differential Inequalities In Cones, Randy Vaughn, V. Lakshmikantham
Mathematics Technical Papers - Archive
In this paper we investigate the theory of parabolic differential inequalities in arbitrary cones. After discussing the fundamental results concerning parabolic inequalities in cones, we prove a result on flow-invariance which is then used to obtain a comparison theorem. This comparison result is useful in deriving upper and lower bounds on solutions of parabolic differential equations in terms of the solutions of ordinary differential equations. We treat the Dirichlet problem in this paper since its theory follows the general pattern of ordinary differential equations and requires less restrictive assumptions. The treatment of Neumann problem, on the other hand, demands stronger …
A Further Look At The Comparison Of Normal Percentile Estimators, Danny D. Dyer
A Further Look At The Comparison Of Normal Percentile Estimators, Danny D. Dyer
Mathematics Technical Papers - Archive
For the purpose of making a pairwise comparison of point estimators of normal percentiles, a twofold technique is introduced which basically examines ,(a) the "odds" in favor of an estimator being closer to the true value than is a competing estimator and (b) an estimator's average closeness to the true value when it is closer (as well as when it is not) than is a competing estimator. Closeness to the true value is measured through an absolute error loss function. Joint consideration of these concepts is shown to form a basis for determining which of two estimators is preferred in …
On The Relative Behavior Of Point Estimators Based On A Decomposition Of Mean Absolute Error, Danny D. Dyer
On The Relative Behavior Of Point Estimators Based On A Decomposition Of Mean Absolute Error, Danny D. Dyer
Mathematics Technical Papers - Archive
Let [see pdf for notation] be a family of probability density functions indexed by the parameter [see pdf for notation]. We assume at least one of the [see pdf for notation] is unknown. Based on a random sample of size n from [see pdf for notation], let [see pdf for notation] be two point estimators of the real-valued function [see pdf for notation], where [see pdf for notation] are specified constants, if any. When comparing [see pdf for notation] and [see pdf for notation], it is quite common to examine the ratio of their respective average precisions usually measured by …
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 …
Attractivity Amp Hopf Bifurcation, L. Salvadori, P. Negrini
Attractivity Amp Hopf Bifurcation, L. Salvadori, P. Negrini
Mathematics Technical Papers - Archive
Consider the one-parameter family of differential equations [see pdf for notation] where [see pdf for notation] and [see pdf for notation]. Here [see pdf for notation] and [see pdf for notation]. Denoting by [see pdf for notation] the eigenvalues of [see pdf for notation] we shall suppose throughout the paper that [see pdf for notation] and [see pdf for notation]. We are concerned with the general problem of asymptotic stability of the periodic orbits arising in the Hopf bifurcation for (1.1). Such property is related to the asymptotic behaviour of the flow relative to 0 (the critical value of the …
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.