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Articles 211 - 240 of 343
Full-Text Articles in Mathematics
Existence And Asymptotic Behavior Of Reaction-Diffusion Systems Via Coupled Quasi-Solutions, G. S. Ladde, A. S. Vatsala, V. Lakshmikantham
Existence And Asymptotic Behavior Of Reaction-Diffusion Systems Via Coupled Quasi-Solutions, G. S. Ladde, A. S. Vatsala, V. Lakshmikantham
Mathematics Technical Papers - Archive
In the study of comparison theorems, existence of extremal solutions and monotone iterative techniques for differential systems a property called quasimonotone property is necessary [2,7,10]. However, there are several physical situations wherein such a property is not satisfied [1]. This difficulty has been overcome by introducing the notion of quasi-solutions [3,8,9]. In this paper we consider the reaction-diffusion system in which quasi-monotone property is not satisfied but a mixed quasimonotone property holds. By utilizing fruitfully the notion of quasi-solutions we prove the existence of coupled maximal and minimal solutions. For this purpose we exploit the monotone iterative technique. We then …
Fixed Point Theorems For Ppf Mappings Satisfying Inwardness Conditions, Stephen R. Bernfeld, Y. M. Reddy, V. Lakshmikantham
Fixed Point Theorems For Ppf Mappings Satisfying Inwardness Conditions, Stephen R. Bernfeld, Y. M. Reddy, V. Lakshmikantham
Mathematics Technical Papers - Archive
In this paper we continue our recent development [1] of the theory of fixed point theorems of nonlinear operators whose domain and range are different Banach spaces. In particular we consider the analogues of recent results of Caristi and Kirk [5,6,8] where "inwardness conditions" are used to obtain fixed points. More precisely "inwardness conditions" on a mapping T whose domain K is a proper subspace of its range have been imposed to ensure that T maps points x of K "towards" K. Caristi and Kirk, for example, have considered two different conditions, metrically inward and weakly inward (this is the …
The Riccati Equation Arising In The Control Theory, G. Da Prato
The Riccati Equation Arising In The Control Theory, G. Da Prato
Mathematics Technical Papers - Archive
No abstract provided.
A New Mathematical Approach To Biological Cell Rearrangement With Applications To The Inversion Of Volvox, Donald Greenspan
A New Mathematical Approach To Biological Cell Rearrangement With Applications To The Inversion Of Volvox, Donald Greenspan
Mathematics Technical Papers - Archive
This paper develops a new method for modeling cell rearrangement in both two and three dimensions. The method uses classical molecular type forces and is computer oriented, recursively explicit, and economical. As yet, the approach is simplistic in that switching processes are not related deterministically to chemical, neurological, or genetic precursors. Illustrative computer examples of the inversion of volvox are described and discussed.
On The Discrimination Between The Lognormal And The Weibull Distributions With Applications To Offshore Oil/Gas Lease Bids, Danny D. Dyer
On The Discrimination Between The Lognormal And The Weibull Distributions With Applications To Offshore Oil/Gas Lease Bids, Danny D. Dyer
Mathematics Technical Papers - Archive
The competitive sealed bids on an individual offshore oil and gas lease are often assumed to follow a lognormal distribution (Brown, 1969). However, under the lognormality assumption there are known discrepancies between observed and theoretical results. Accordingly, alternative lease bid distributions have been studied. In particular, Dyer (1980) has shown that one would not reject the hypothesis that the bids on certain groups of leases follow Weibull distributions. In this paper, we discuss test procedures for discriminating between a lognormal distribution and a Weibull distribution. The procedure is then applied to the group of 12-, 13-, 14-, 15-, and 16-bid …
A Classical Molecular Approach To Computer Simulation Of Biological Sorting, Donald Greenspan
A Classical Molecular Approach To Computer Simulation Of Biological Sorting, Donald Greenspan
Mathematics Technical Papers - Archive
Steinberg's theory of sorting is modified by replacing the free energy minimization principle with dynamical equations of a molecular nature. Correct cellular sorting then follows in all cases where the mixture is in a liquid or a near-liquid state. Computer examples are described and discussed, primarily for two dimensional, but also for three dimensional, interactions.
Stochastic Parameters In Compartmental Systems, Jerome Eisenfeld
Stochastic Parameters In Compartmental Systems, Jerome Eisenfeld
Mathematics Technical Papers - Archive
Let [see pdf for notation] denote the probability that a particle in compartment j will reach (or enter) compartment i. We present several formulas for obtaining the [see pdf for notation] in terms of the fractional transfer coefficients. The parameter are interesting for their own sake and they are also useful for obtaining qualitative properties of compartmental systems and for interpreting results already obtained. The reachability parameters also play a role in structural identification since they give us a new method for expressing the transfer function.
Variation Of Constants, Vector Lyapunov Functions And Comparison Theorem, A. R. Aftabizadeh
Variation Of Constants, Vector Lyapunov Functions And Comparison Theorem, A. R. Aftabizadeh
Mathematics Technical Papers - Archive
In this paper we combine the above ideas to obtain a new comparison result and discuss its relation to known results. A simple application to stability theory is also given to indicate the usefulness of the comparison result. Our result is expected to play a prominent role in the qualitative study of differential equations.
Periodic Solutions Of Nonlinear Boundary Value Problems, V. Lakshmikantham, R. Kannan
Periodic Solutions Of Nonlinear Boundary Value Problems, V. Lakshmikantham, R. Kannan
Mathematics Technical Papers - Archive
One of the well known techniques in the theory of nonlinear boundary value problems (BVP) is the method of differential inequalities or the method of upper and lower solutions. The method of "Alternative Problems", a global variant of the Lyapunov-Schmidt method, has been used in the study of problems at resonance. The investigation of periodic BVP's forms an important subclass of problems at resonance. Our aim is to combine the two approaches to discuss nonlinear problems at resonance. We restrict ourselves in this paper to the discussion of periodic boundary value problems. In Section 1, we shall indicate the method …
Computer Studies Of The Classical Oxygen Molecule, Donald Greenspan
Computer Studies Of The Classical Oxygen Molecule, Donald Greenspan
Mathematics Technical Papers - Archive
A classical, simplistic model of the molecular dynamics of 02 is developed for interactions which are not readily amenable to quantum mechanical analysis. All electron-electron interactions are included. Extensive computer examples are described and the reasonableness of the Born-Oppenheimer approximation is explored.
Offshore Oil/Gas Lease Bidding And The Weibull Distributions, Danny D. Dyer
Offshore Oil/Gas Lease Bidding And The Weibull Distributions, Danny D. Dyer
Mathematics Technical Papers - Archive
It is the purpose of this paper to study the use of the Weibull distribution as an acceptable model for the distribution of the bids on a lease. A multi-sample test procedure of the Weibull-bids hypothesis will be given and implemented to show that the Weibull distribution provides a better statistical fit than does the lognormal distribution for the group of 13-, 14-, 15-, and 16-bid leases.
Quasi-Solutions, Vector Lyapunov Functions And Monotone Method, S. Leela, V. Lakshmikantham, M. N. Oguztoreli
Quasi-Solutions, Vector Lyapunov Functions And Monotone Method, S. Leela, V. Lakshmikantham, M. N. Oguztoreli
Mathematics Technical Papers - Archive
It is now well known that the method of vector Lyapunov functions provides an effective tool to investigate the properties of large scale interconnected dynamical and control systems. [3,4,5,11-15]. Several Lyapunov functions result in a natural way in the study of such systems by the decomposition and aggregation method [1-4,12-14]. However an unpleasant fact in this approach is the requirement of quasi-monotone property on the comparison system since comparison systems with a desired property like stability exist without satisfying quasi-monotone property. Also in the study of comparison theorems and extremal solutions for differential systems one usually imposes this quasi-monotone property. …
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.
A Monte Carlo Power Study Of K-Sample Tests For Exponentiality, Mickie Sue Harbin, Danny D. Dyer
A Monte Carlo Power Study Of K-Sample Tests For Exponentiality, Mickie Sue Harbin, Danny D. Dyer
Mathematics Technical Papers - Archive
Suppose one has a collection of k independent samples where the ith sample size is [see pdf for notation]. Let [see pdf for notation] denote the ordered observations in the ith sample. A number of test procedures are available to jointly test for exponentiality of the collection of independent samples, that is [see pdf for notation] is the probability density function (pdf) of the ith population. These include the k-sample Durbin (1975) test, the k-sample Shapiro-Wilk (1972) W-exponential test, the k-sample Tiku (1974) test, and a test procedure derived by Dyer (1979) which is based on a characterization of the …
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 …
Practical Stability And Lyapunov Functions, V. Lakshmikantham, Stephen R. Bernfeld
Practical Stability And Lyapunov Functions, V. Lakshmikantham, Stephen R. Bernfeld
Mathematics Technical Papers - Archive
The notion of "practical stability" was discussed in the monograph by LaSalle and Lefschetz [6] in which they point out that stability investigations may not assure "practical stability" and vice versa. For example an aircraft may oscillate around a mathematically unstable path, yet its performance may be acceptable. Motivated by this, Weiss and Infante introduced the concept of finite time stability [7]. They were interested in the behavior of systems contained within specified bounds during a fixed time interval. Many problems fall into this category including the travel of a space vehicle between two points and the problem, in a …
On The Existence And Uniqueness Of Periodic Solutions Of Second Order Ordinary Differential Equations, Giovanni Vidossich
On The Existence And Uniqueness Of Periodic Solutions Of Second Order Ordinary Differential Equations, Giovanni Vidossich
Mathematics Technical Papers - Archive
No abstract provided.
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.
Comparison, Existence, Uniqueness And Successive Approximations For The Dirichlet Problem Of Elliptic Equations, Giovanni Vidossich
Comparison, Existence, Uniqueness And Successive Approximations For The Dirichlet Problem Of Elliptic Equations, Giovanni Vidossich
Mathematics Technical Papers - Archive
No abstract provided.
Existence Of Extremal Solutions And Comparison Results For Delay Differential Equations In Abstract Cones, R. L. Laughn, A. S. Vatsala
Existence Of Extremal Solutions And Comparison Results For Delay Differential Equations In Abstract Cones, R. L. Laughn, A. S. Vatsala
Mathematics Technical Papers - Archive
The study of Cauchy problem for ordinary differential equations in a Banach space has been extensive [2,4,10]. It is of interest to look at the corresponding problem for delay differential equations since such equations occur in many physical problems. Existence of solutions of such equations are considered in [6,8,9] using monotonicity conditions and dissipative conditions.In this paper our objective is to prove the existence of extremal solutions for the delay differential equation [see pdf for notation] (1.1) relative to a cone k of the Banach space E. For this purpose, we begin by proving an existence result under a simple …
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.
A Survey Of Certain K-Sample Test Procedures With Applications To Lpr-5 Data, Danny D. Dyer
A Survey Of Certain K-Sample Test Procedures With Applications To Lpr-5 Data, Danny D. Dyer
Mathematics Technical Papers - Archive
When dealing with k independent samples, it is frequently of interest to jointly assess the underlying population distributions. Usually such an assessment is carried out by performing k independent tests; that is, we test the null hypothesis [see pdf for notation] that the population from which the [see pdf for notaion] sample was drawn has some specified distribution. Combining the results of such independent tests may then be carried out by Fisher's method (1950, pp. 99-101). Specifically, let Ti be the test statistic associated with the [see pdf for notaion] sample. Suppose large values of Ti are considered critical for …
Stochastic Parameters In Compartmental Systems And Structural Identification, Jerome Eisenfeld
Stochastic Parameters In Compartmental Systems And Structural Identification, Jerome Eisenfeld
Mathematics Technical Papers - Archive
Let [see pdf for notation] denote the mean time a particle resides in i having started in j and let [see pdf for notation] denote the probability that a particle reaches i from j. These parameters, expressed in terms of the fractional transfer coefficients, provide an interpretation and a representation of the transfer function which are useful for determining the identifiable parameters in an input-output experiment. In particular the transfer function is expressed in terms of other transfer functions which represent smaller subsystems along the flow.
On The Determination Of Critical Values For Bartlett's Test, Jerome P. Keating, Danny D. Dyer
On The Determination Of Critical Values For Bartlett's Test, Jerome P. Keating, Danny D. Dyer
Mathematics Technical Papers - Archive
The exact critical values for Bartlett's test for homogeneity of variances based on equal sample sizes from several normal populations are tabulated. It is also shown how these values may be used to obtain highly accurate approximations to the critical values for unequal sample sizes.
A New Approach To Computer Oriented, Quasi-Quantum Mechanical Dynamics, Donald Greenspan
A New Approach To Computer Oriented, Quasi-Quantum Mechanical Dynamics, Donald Greenspan
Mathematics Technical Papers - Archive
A new approach to atomic and molecular dynamics is developed which combines both quantum and classical concepts. Applications are made to the hydrogen atom, the hydrogen ion, and the hydrogen molecule. An accurate computer technique for the approximation of bond lengths is developed and illustrative examples of electron motions are described and discussed. Uncertainty results naturally from a mathematical statement of total system energy, which is always quantized. Angular momentum can be zero and need not be quantized, thereby avoiding inconsistencies of Bohr-Sommerfeld type models.
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) …