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Articles 151 - 180 of 343
Full-Text Articles in Mathematics
Fortran Program Is For Single States Of Para Helium Singlets, Donald Greenspan
Fortran Program Is For Single States Of Para Helium Singlets, Donald Greenspan
Mathematics Technical Papers - Archive
No abstract provided.
A New Computer Approach To The Modeling Of Close Binary Stars, Donald Greenspan
A New Computer Approach To The Modeling Of Close Binary Stars, Donald Greenspan
Mathematics Technical Papers - Archive
A new, n-body approach is developed for the modeling of close binary systems, the most commonly occurring star systemsknown. Both local and long range forces are included. Computer examples of streaming, mass loss, and self-reorganization processes are described and discussed.
Computer-Oriented, N-Body Modelling Of Minimal Surfaces, Donald Greenspan
Computer-Oriented, N-Body Modelling Of Minimal Surfaces, Donald Greenspan
Mathematics Technical Papers - Archive
In this paper a new approach to the modeling of minimal surfaces is described and applied. Rather than use a continuous model, we develop a discrete n-body model with basic tensile interactions derived from classical molecular force formulas. Computer results area described and discussed.
A Monte Carlo Study Of Robustness Of Preliminary Test Estimators In Pooling Means, Chien-Pai Han, T. A. Bancroft
A Monte Carlo Study Of Robustness Of Preliminary Test Estimators In Pooling Means, Chien-Pai Han, T. A. Bancroft
Mathematics Technical Papers - Archive
Pooling data, when justified, for estimating the target mean is advantageous when the sample size is small from the target population. In case it is doubtful whether two sets of data have the same mean, a normal test or a t test can be used for testing the equality of the two means depending on variance known or unknown. A preliminary test estimator is then constructed for estimating the population mean. We study the robustness of the preliminary test estimators when certain populations are not normal. The result of a Monte Carlo study is given, when the populations are either …
On The Existence Of Periodic Quasi Solutions For First Order Systems, A. S. Vatsala
On The Existence Of Periodic Quasi Solutions For First Order Systems, A. S. Vatsala
Mathematics Technical Papers - Archive
Recently the method of upper and lower solutions and Lyapunov-Schmitt method have been fruitfully employed to prove the existence of periodic solutions for scalar first and second order equations in [2,4]. In this paper we shall use this technique to prove the existence of periodic solutions for first order systems which is the generalisation of Müller's result [3] for periodic case. We shall also develop monotone iterative technique to obtain coupled minimal and maximal periodic quasisoltions for system of first order equations. Further, under a uniqueness assumption, our results yield a unique periodic solution for the first order system.
Comparison Results For Parabolic Differential Equations At Resonance, A. S. Vatsala, G. R. Shendge
Comparison Results For Parabolic Differential Equations At Resonance, A. S. Vatsala, G. R. Shendge
Mathematics Technical Papers - Archive
It is very well known that comparison principles for initial and boundary value problems for nonresonance cases have been very much used in the existence of solutions and the development of the monotone method [1,2,3,4,5,9]. These comparison techniques do not cover the resonance cases. Hence it is of practical interest to look at such results for resonance cases. With this view, different comparison results were recently developed for first and second order periodic boundary value problems [10]. Some special cases of these have been used in [6,7] and in developing the monotone method for first order periodic systems in [11]. …
Computer Simulation Of A Dynamical Model Of The Water Molecule, Donald Greenspan
Computer Simulation Of A Dynamical Model Of The Water Molecule, Donald Greenspan
Mathematics Technical Papers - Archive
A new computer-orlented theory for molecular dynamics is applied to modeling the water molecule. The dynamical equations are derived from molecular stability properties and from aspects of modern particle theory, especially as it relates to the structure of the electron. Computer studies are described and discussed.
Monotone Technique For Periodic Solutions Of Differential Equations, S. Leela
Monotone Technique For Periodic Solutions Of Differential Equations, S. Leela
Mathematics Technical Papers - Archive
The existence of periodic solutions has received a great deal of attention in recent years [1,7-11,14]. In [8,11] the existence of solutions of first and second order PBVP (periodic boundary value problem) has been studied successfully by combining the two basic techniques, namely, the method of lower and upper solutions and the Lyapunov-Schmidt method. In [6,11-13] monotone methods are developed for obtaining extremal solutions of BVP as limits of monotone iterates. In the first order PBVP [11] the monotone method has a greater significance since each member of the sequence is a periodic solution of a first order linear equation …
Monotone Method For Second Order Periodic Boundary Value Problems, S. Leela
Monotone Method For Second Order Periodic Boundary Value Problems, S. Leela
Mathematics Technical Papers - Archive
In recent years, there has been an extensive study of the existence of periodic solutions [1,8-11,14,15]. In, [8,11], the existence of solutions of first and second order PBVP (periodic boundary value problems) has been obtained by a novel approach of combining the classical method of lower and upper solutions and the method of alternative problems (Lyapunov-Schmidt method), which provide conditions that are easily verifiable and which covers previous known results of other authors. As a constructive method for obtaining extremal solutions of initial and boundary value problems, the monotone iterative procedure has been employed by several researchers [5-7,11-13,15]. The objective …
The Most Conservative Beta Prior Distribution For Binomial Sampling, Paul Chiou, Danny D. Dyer
The Most Conservative Beta Prior Distribution For Binomial Sampling, Paul Chiou, Danny D. Dyer
Mathematics Technical Papers - Archive
The incorporation of prior information about a parameter into a statistical procedure is an essential feature of Bayesian statistics. However, the manner in which this is done is often arbitrary. In order to reduce such arbitrariness, methodology based on information theoretic concepts is introduced which (a) quantifies the amount of information provided by the sample data relative to that provided by the prior distribution and (b) allows for a ranking of prior distributions with respect to conservativeness, where conservatism refers to restraint of extraneous information which is embedded in any prior distribution of the parameter. To illustrate the implementation of …
Discrete Modeling Of Minimal Surfaces, C. Coppin, Donald Greenspan
Discrete Modeling Of Minimal Surfaces, C. Coppin, Donald Greenspan
Mathematics Technical Papers - Archive
A new computer approach to the modeling of minimal surfaces is described and implemented. Quasi-molecular particles and forces are used to simulate actual molecular structure and forces. Detailed formulas and computer techniques are given. As an example, the approximation of the unique minimal surface through a skew quadrilateral is constructed and displayed.
Remarks On First And Second Order Periodic Boundary Value Problems, V. Lakshmikantham
Remarks On First And Second Order Periodic Boundary Value Problems, V. Lakshmikantham
Mathematics Technical Papers - Archive
We consider the first and second order periodic boundary value problems (PBVP for brevity)[see pdf for notation] and [see pdf for notation]and obtain the existence of extremal solutions as limits of monotone iterates. In [2] and [3], the monotone method was employed for the problems (1.1) and (1.2) when the corresponding lower and upper solutions a(t),B(t) satisfy [see pdf for notation] in addition to other conditions. Furthermore, when f is increasing, it is shown [2,3] that the conditions (1.3) and (1.4) are tantamount to assuming the existence of a periodic solution. Accordingly, the problem of proving the existence of periodic …
Comparison Results For First And Second Order Boundary Value Problems At Resonance, A. S. Vatsala, G. R. Shendge
Comparison Results For First And Second Order Boundary Value Problems At Resonance, A. S. Vatsala, G. R. Shendge
Mathematics Technical Papers - Archive
It is well known that the comparison principle for the initial value problems has been very useful in the theory of differential equations [1, 2,5]. Recently, such types of comparison results were developed for boundary value problems [3,4] and were used in proving the existence of solutions. It is natural to expect that comparison results for problems at resonance will he useful in proving, for example, existence results for periodic boundary value problems. Recently, existence of periodic solutions for first and second order differential equations have been considered by utilizing the method of upper and lower solutions and Lyapunov-Schmidt method, …
A Topological Method For Vector-Valued And Nth Order Nonlinear Boundary Value Problems, P. K. Palamides, Stephen R. Bernfeld
A Topological Method For Vector-Valued And Nth Order Nonlinear Boundary Value Problems, P. K. Palamides, Stephen R. Bernfeld
Mathematics Technical Papers - Archive
The use of topological methods in the analysts of second order nonlinear boundary value problems (BVP for short) in Rn of the form (E) [see pdf for notation] (C) [see pdf for notation] has recently attracted the interest of many authors (e.g. [1], [4], [5],[8],[11]) for the case in which n = 1. The prevalent approaches have been the topological method of Wazewski [1,8], the shooting method via the maximum principle, and the Kneser-Hukuhara continuum theorem [1]. A common ingredient in these approaches is the use of upper and lower solutions to obtain bounds on the solutions.
Structural Identification Of Large Systems By Reduction To Subsystems: Vldl Triglycerides, S. M. Grundy, Jerome Eisenfeld
Structural Identification Of Large Systems By Reduction To Subsystems: Vldl Triglycerides, S. M. Grundy, Jerome Eisenfeld
Mathematics Technical Papers - Archive
Experiments are performed for identification purposes, i.e. to identify the values of unknown paprameters from data. In the event that one or more parameters can not be identified, the cause could be the result of a variety of problems: insuffcient or infrequent sampling, random or nonrandom disturbances, numerical ill-conditioning and etc. The input-output configuration may also be the cause of non-identifiability. In other words, evenif the sampling and numerical procedure could be carried out under the most ideal conditions, certain parameters may not be identifiable because these parameters are not uniquely contained in the transfer function, in which case these …
Existence Of Periodic Solutions Of Semilinear Parabolic Equations And The Method Of Upper And Lower Solutions, V. Lakshmikantham, R. Kannan
Existence Of Periodic Solutions Of Semilinear Parabolic Equations And The Method Of Upper And Lower Solutions, V. Lakshmikantham, R. Kannan
Mathematics Technical Papers - Archive
The existence of periodic solutions of semilinear parabolic equations has been investigated by several authors [1-10,15-18] by different methods such as the method of Poincare operator and the theory of monotone operators. In a recent paper [1] Amann also obtains multiplicity results. Recently, an attempt was made successfully in [11,12,16] to combine the two basic techniques, namely the method of upper and lower solutions and the method of Lyapunov-Schmidt to investigate existence of periodic solutions of first and second order equations. In this paper we continue this fruitful approach to study existence of periodic solutions of semilinear parabolic equations with …
Probability Of Selecting The "Correct" Model And Determination Of Sample Size In Regression, Chien-Pai Han, Wendell C. Smith
Probability Of Selecting The "Correct" Model And Determination Of Sample Size In Regression, Chien-Pai Han, Wendell C. Smith
Mathematics Technical Papers - Archive
Selection of variables in multiple linear regression is a common problem in model building. Let the "correct" model be the model which includes all variables that influence the dependent variable and excludes all others. This paper derives the probability of selecting the correct model for the sequential deletion procedure. A concept of least favorable selection is given. Based on this concept, the sample size is determined for given probability of selecting the correct model. The procedure is illustrated by considering the polynomial regression.
Problems At Resonance For First And Second Order Differential Equations Via Lyapunov-Like Functions, J. J. Nieto
Problems At Resonance For First And Second Order Differential Equations Via Lyapunov-Like Functions, J. J. Nieto
Mathematics Technical Papers - Archive
Recently [7,8,10] an attempt is made successfully to combine the two basic techniques namely, Lyapunov-Schmidt method and the method of upper and lower solutions, to investigate the existence of periodic solutions of differential equations. When we wish to extend such results for systems of differential equations there are two possibilities to follow. One is to generalize the method of upper and lower solutions using a suitable cone, and the other is to utilize the concept of tyapunov-like functions and the theory of differential inequalities. In the paper, we shall discuss the existence of problems at resonance for first and second …
Monotone Iterative Technique For Delay Differantial Equations In Abstract Cones, Sen-Wo Du
Monotone Iterative Technique For Delay Differantial Equations In Abstract Cones, Sen-Wo Du
Mathematics Technical Papers - Archive
Monotone iterative technique is developed for delay differential equations in a Banach space by utilizing the method of upper and lower solutions.
An Algorithm For Finding The Generalized Nucleolus Of A Finite Set And The Multiobjective Discrete Programming Problems, Irinel C. Dragan
An Algorithm For Finding The Generalized Nucleolus Of A Finite Set And The Multiobjective Discrete Programming Problems, Irinel C. Dragan
Mathematics Technical Papers - Archive
No abstract provided.
A New Computer-Oriented Approach To Molecular Mechanics, Donald Greenspan
A New Computer-Oriented Approach To Molecular Mechanics, Donald Greenspan
Mathematics Technical Papers - Archive
A new dynamical theory for atomic and molecular dynamics is formulated and discussed. The associated nonlinear differential system is derived from general atomic and molecular stability properties and from aspects of modern particle theory, especially as it relates to the structure of the electron. Computer experiments are described for developing a new model of the water molecule.
General Uniqueness Criteria For Ordinary Differential Equations, V. Lakshmikantham, Mansour Samimi
General Uniqueness Criteria For Ordinary Differential Equations, V. Lakshmikantham, Mansour Samimi
Mathematics Technical Papers - Archive
This paper generalizes various uniqueness results and offers very general uniqueness criteria which include different types of results considered so far.
Shape Parameters For The Parametric Cubic Curve, J. A. Conly, R. L. Tennison
Shape Parameters For The Parametric Cubic Curve, J. A. Conly, R. L. Tennison
Mathematics Technical Papers - Archive
No abstract provided.
A New Approach To The Stability Theory Of Functional Differential Systems, G. R. Shendge
A New Approach To The Stability Theory Of Functional Differential Systems, G. R. Shendge
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 [see pdf for notation] is estimated [3]. This approach has recently been recognized [3] as a very natural method in the study of the qualitative behavior of delay differential equations.
Bifurcation And Total Stability, V. Moauro, M. L. Bertotti
Bifurcation And Total Stability, V. Moauro, M. L. Bertotti
Mathematics Technical Papers - Archive
In this paper we are concerned with the problem of bifurcation of invariant sets from an invariant set with respect to a family of flows. In particular, we will suppose that such flows are defined by a one-parameter family of ordinary differential equations: [see pdf for notation] where [see pdf for notation], f is locally Lipschitzian with respect to x, f(µ,0) = 0. As is well known, bifurcation phenomenon is often associated with a drastic change of suitable stability properties. For example, let suppose that the origin 0 of Rn be, with respect to (1), asymptotically stable for µ = …
Existence Of Periodic Solutions Of Nonlinear Boundary Value Problems And The Method Of Upper And Lower Solutions, V. Lakshmikantham, R. Kannan
Existence Of Periodic Solutions Of Nonlinear Boundary Value Problems And The Method Of Upper And Lower Solutions, V. Lakshmikantham, R. Kannan
Mathematics Technical Papers - Archive
We study the existence of periodic solutions of second order nonlinear differential equations by combining the method of upper and lower solutions and the method of Alternative problems. Besides including previous results of other authors, we obtain criteria which are easily verifiable. These criteria are in a form that they can be adapted for partial differential equations of parabolic and elliptic type.
Nonuniqueness Criteria For Ordinary Differential Equations, Mansour Samimi
Nonuniqueness Criteria For Ordinary Differential Equations, Mansour Samimi
Mathematics Technical Papers - Archive
We consider an initial value problem (1.1) [see pdf for notation] where [see pdf for notation]. Several uniqueness results weaker than a Lipschitz condition are known, see [1,4]. However, results concerning with nonuniqueness criteria are rare. For the case n = 1, a nonuniqueness result was given in [5,6], see also [4]. Very recently the general case was also investigated in [3]. In this paper, we consider nonuniqueness problem from a very general point of view. Our first nonuniqueness result deals with the scalar case which extends the results of [5,6]. It also shows that when the conditions of general …
Existence And Monotone Method For Periodic Solutions Of First Order Differential Equations, S. Leela, V. Lakshmikantham
Existence And Monotone Method For Periodic Solutions Of First Order Differential Equations, S. Leela, V. Lakshmikantham
Mathematics Technical Papers - Archive
An attempt was made recently in [3] to combine fruitfully the two basic techniques, namely the method of upper and lower solutions and the Lyapunov-Schmitt method to investigate the existence of periodic solutions of second order nonlinear boundary value problems. in this paper, we utilize this fruitful approach to study existence of periodic solutions of first order nonlinear differential equations. We also develope monotone iterative technique for obtaining multiple periodic solutions which are obtained as limits of monotone sequences. Since each member of these sequences is a periodic solution of a linear differential equation of first order which can explicitly …
Error Estimates Of Solutions And Mean Of Solutions Of Stochastic Differential Systems, M. Sambandham, G. S. Ladde
Error Estimates Of Solutions And Mean Of Solutions Of Stochastic Differential Systems, M. Sambandham, G. S. Ladde
Mathematics Technical Papers - Archive
Stochastic differential equations are considered. Estimates in terms of statistical properties are given for the difference between the solutions and solutions of the mean of stochastic differential systems. For this purpose necessary theorems are developed and sufficient conditions are given to obtain error estimates. A few examples are worked out to demonstrate the usefulness of the results.
A New Computer Approach To Atomic And Molecular Dynamics With Application To The Water Molecule, Donald Greenspan
A New Computer Approach To Atomic And Molecular Dynamics With Application To The Water Molecule, Donald Greenspan
Mathematics Technical Papers - Archive
A new computer oriented theory for atomic and molecular dynamics is developed. In it are incorporated modifications of classical ideas which are motivated by modern particle theory, especially as it relates to the structure of the electron and to the existence of fractional charge. Computer results of a dynamical water molecule model, which are consistent with the bond angle and bond length vibrations of H2O, are described and discussed.