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Articles 271 - 300 of 343
Full-Text Articles in Mathematics
Competitive-Cooperative Processes And Stability Of Diffusion Systems, V. Lakshmikantham, G. S. Ladde
Competitive-Cooperative Processes And Stability Of Diffusion Systems, V. Lakshmikantham, G. S. Ladde
Mathematics Technical Papers - Archive
Very recently, the stability analysis of deterministic [12], random [12,13] competitive-cooperative process has been made in a systematic and unified way. It is well recognized that the probabilistic models in biological [7,9,19,20,30], physical [7,20,21,30], and social [31] sciences are more realistic than the deterministic models. In this paper, we extend the stability analysis of random competitive-cooperative processes [11] to the stability analysis of competitive processes of the diffusion type. The stability results presented includes the stability analysis of multispecies community models [16,17] under white-noise excitations. All our results are in the frame-work of the earlier results [11-13, 16-18]. The paper …
A Direct Computational Method For Estimating The Parameters Of A Nonlinear Model, Jerome Eisenfeld, Stephen W. Cheng
A Direct Computational Method For Estimating The Parameters Of A Nonlinear Model, Jerome Eisenfeld, Stephen W. Cheng
Mathematics Technical Papers - Archive
We consider the system identification problem which deals with determining information about the unknown constant matrices A, B, and C or the linear dynamical system: [see pdf for notation], where u(t) and y(t) are given discretely on the interval [0,T]. This leads to a nonlinear estimation problem, or a so-called deconvolution problem, which deals with estimating the number of components [see pdf for notation], the decay rates [see pdf for notation], and the corresponding amplitudes [see pdf for notation] in the model: [see pdf for notation] from the given discrete data [see pdf for notation]. Deconvolution problems are important in …
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.
Fixed Point Theorem For Non-Expansive Mappings On Banach Spaces With Unifformly Normal Structure, B. B. Williams, A. A. Gillespie
Fixed Point Theorem For Non-Expansive Mappings On Banach Spaces With Unifformly Normal Structure, B. B. Williams, A. A. Gillespie
Mathematics Technical Papers - Archive
In [1] Kirk proved that if D is a bounded, closed, and convex subset of a reflexive Banach space that has normal structure, then every non-expansive mapping of D into D has a fixed point. This was also proved for a uniformly convex space by Browder [2]. In this paper we replace uniformly convex, or reflexive and normal structure, by uniformly normal structure to obtain this result. Let S be a bounded subset of the Banach space X and [see pdf for notation] (1) [see pdf for notation] (2) [see pdf for notation] (3) [see pdf for notation] A space …
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 …
Comparison Of Point Estimators Of Normal Percentiles, Danny D. Dyer, Onas L. Hensley, Jerome P. Keating
Comparison Of Point Estimators Of Normal Percentiles, Danny D. Dyer, Onas L. Hensley, Jerome P. Keating
Mathematics Technical Papers - Archive
There are available several point estimators of the percentiles of a normal distribution with both mean and variance unknown. Consequently, it would seam appropriate to make a comparison among the estimators through sums "closeness to the true value" criteria. Along these lines, the concept of Pitman-closeness efficiency is introduced. Essentially, when comparing two estimators, the Pitman-closeness efficiency gives "odds" in favor of one of the estimators being closer to the true value than is the other in a given situation. Through the use of Pitman-closeness efficiency, this paper compares (a) the maximum likelihood estimator, (b) the minimum variance unbissed estimator, …
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.
The Method Of Nonlinear Variation Of Constants For Difference Equations, M. E. Lord
The Method Of Nonlinear Variation Of Constants For Difference Equations, M. E. Lord
Mathematics Technical Papers - Archive
A method of nonlinear variation of constants for discrete difference equations is developed, which generalizes a well-known linear variation of constants formula. The method is shown to be useful in studying asymptotic behavior of perturbed nonlinear difference equations.
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 …
Efficiency In Estimation Of Mean Time To Failure In A Two-Parameter Exponential Failure Model, Danny D. Dyer
Efficiency In Estimation Of Mean Time To Failure In A Two-Parameter Exponential Failure Model, Danny D. Dyer
Mathematics Technical Papers - Archive
When comparing two point estimators of some parametric function, Pitman-closeness efficiency gives the "odds" in favor of one of the estimators being closer to the true value than is the other in a given situation. Through this measure of efficiency, we compare (i) the maximum likelihood estimator, (ii) the minimum variance unbiased estimator, (iii) the best invariant estimator, and (iv) the median unbiased estimator of the mean time to failure in a two-parameter exponential failure model. Mean squared efficiency is also discussed.
Efficiency Contours For Estimators Of Reliability In A 2-Parameter Exponential Failure Model, I-Le Lu, Danny D. Dyer
Efficiency Contours For Estimators Of Reliability In A 2-Parameter Exponential Failure Model, I-Le Lu, Danny D. Dyer
Mathematics Technical Papers - Archive
When there are available several point estimators of some parametric function, it would seem desirable to make a comparison among the estimators based on some measure of closeness to the true value. Along these lines, the concept of Pitman-closeness (PC) efficiency is introduced. Essentially, when comparing two estimators, PC efficiency gives the odds in favor of one of the estimators being closer to the true value in a given situation than is the other. The traditional method of comparison, i.e., mean squared (MS) efficiency is also considered. This paper presents graphical results based on simulation techniques which depict PC efficiencies …
Differential Inequalities And Flow-Invariance Via Linear Functionals, V. Lakshmikantham, Jerome Eisenfeld
Differential Inequalities And Flow-Invariance Via Linear Functionals, V. Lakshmikantham, Jerome Eisenfeld
Mathematics Technical Papers - Archive
This paper deals with flow-invariance properties with respect to [see pdf for notation] and resulting comparison inequalities. Both the order relation He and the regularity conditions on x are defined, in a general manner, in terms of a specified set of linear functionals, S. This permits greater flexibility for applications e.g., a proper choice of S gives the PDE operators of the form [see pdf for notation] where [see pdf for notation], an appropriate quasimonotonicity property.
Infinitely Many Perfect And Unitary Perfect Polynomials Over Some Gf(Q), Mickie Sue Harbin, A.T. Bullock, Jacob T. B. Beard Jr.
Infinitely Many Perfect And Unitary Perfect Polynomials Over Some Gf(Q), Mickie Sue Harbin, A.T. Bullock, Jacob T. B. Beard Jr.
Mathematics Technical Papers - Archive
The existence is shown of infinitely many non-splitting perfect polynomials over GF(2d), GF(3d), GF(5d) for each odd integer d > 1, and over GF(2d) for each (even) integer d 1 0 (mod 3). Stronger results show that each unitary perfect polynomial over GF(q) determines an infinite equivalence class of unitary perfect polynomials over GF(q). The number SUP(q) of distinct equivalence classes of splitting unitary perfect polynomials over GF(q) is calculated for q = p and shown to be infinite for q # p. The number NSUP(q) of distinct equivalence classes of non-splitting unitary perfect polynomials over GF(q) remains undetermined, but is …
System Identification Problems And The Method Of Moments, Jerome Eisenfeld, S. W. Cheng, Stephen R. Bernfeld
System Identification Problems And The Method Of Moments, Jerome Eisenfeld, S. W. Cheng, Stephen R. Bernfeld
Mathematics Technical Papers - Archive
Let X(t) and W(t) be vectors of dimension N > 0. We are concerned with the problem of computing an N x N matrix A such that [see pdf for notation](1.1) where X'(t) is the rate of change of X(t) with respect to time t. Such problems frequently arise in the biosciences although it is not always immediately evident that they may be posed in the form of Eq. (1.1). In applications the data for X(t) and W(t) is obtained from experiments and the collection of such data is not always performed over equal time intervals nor is it always the …
Linear Algebraic Computational Procedures For System Identification Problems, Jerome Eisenfeld, B. Soni
Linear Algebraic Computational Procedures For System Identification Problems, Jerome Eisenfeld, B. Soni
Mathematics Technical Papers - Archive
An algorithm is presented for identifying exponentials sums [see pdf for notation] from discrete data [see pdf for notation] The algorithm determines the number of components, [see pdf for notation] the rate constants [see pdf for notation] and the amplitudes [see pdf for notation]. The method is based on the method of moments as it is applied to analyze fluorescence decay experiments. However the present method is more general. It permits greater flexibility in weighting the data and, in particular, alleviates the "cut-off error" incurred when integration is required to infinite time.
Existence And Comparison Results For Nonlinear Volterra Integral Equations In A Banach Space, Randy Vaughn
Existence And Comparison Results For Nonlinear Volterra Integral Equations In A Banach Space, Randy Vaughn
Mathematics Technical Papers - Archive
In this paper we prove the existence of solutions to nonlinear Volterra integral equations in a Banach Space. A comparison theorem and the existence of maximal solutions are also obtained using the notion of ordering with respect to a cone. As is known, in infinite dimensional Banach spaces compactness-type conditions are needed to prove existence, whereas in finite dimensional cases these assumptions are not necessary. The results of the paper generalize the corresponding results of Nohel [6]. See also Miller [5] and Lakshmikantham and Leela [2]. Throughout this paper, E will denote a Banach space, and [to,to + a] = …
Existence And Uniqueness Of Solutions Of Delay Differential Equations On A Closed Subset Of A Banach Space, V. Moauro, S. Leela, V. Lakshmikantham
Existence And Uniqueness Of Solutions Of Delay Differential Equations On A Closed Subset Of A Banach Space, V. Moauro, S. Leela, V. Lakshmikantham
Mathematics Technical Papers - Archive
In an earlier work [5], sufficient conditions for the existence of solutions in a closed subset F of a Banach space E for the Cauchy problem (1.1) [see pdf for notation] where [see pdf for notation], are obtained by requiring f to satisfy (i) a compactness-type condition in terms of the Kuratowski measure of noncompactness and (ii) a boundary condition, namely, (1.2) [see pdf for notation] for every [see pdf for notation]. In this paper, we wish to explore the other direction followed in the study of the Cauchy problem for differential equations in a Banach space [4,6,7], that is, …
Existence Of Solutions Of Boundary Value Problems For Nonlinear Second Order Systems In A Banach Space, A. Richard Mitchell, V. Chandra
Existence Of Solutions Of Boundary Value Problems For Nonlinear Second Order Systems In A Banach Space, A. Richard Mitchell, V. Chandra
Mathematics Technical Papers - Archive
This paper is concerned with the existence of solutions of boundary value problems (BVP, for short) for nonlinear second order ordinary differential equations of the type (1.1) [see pdf for notation] (1.2) [see pdf for notation] where [see pdf for notation] is a real Banach space. In case [see pdf for notation], existence was proved by first obtaining a priori bounds for [see pdf for notation] of a solution of (1.1) and (1.2) and then employing a theorem of Scorza-Dragoni [3,7,16]. The methods involve assuming inequalities in terms of the second derivative of Lyapunov-like functions relative to H, using comparison …
On The Existence Of Weak Solutions Of Differential Equations In Nonreflexive Banach Spaces, V. Lakshmikantham, Evin Bronson, A. Richard Mitchell
On The Existence Of Weak Solutions Of Differential Equations In Nonreflexive Banach Spaces, V. Lakshmikantham, Evin Bronson, A. Richard Mitchell
Mathematics Technical Papers - Archive
The study of the Cauchy problem for differential equations in a Banach space relative to the strong topology has attracted much attention in recent years [2,4,5,7]. This study has taken two different directions. One direction is to impose compactness type conditions that guarantee only existence and the corresponding results are extensions of the classical Peano's Theorem. The other approach is to utilize dissipative type conditions that assure existence and uniqueness of solutions, and the corresponding results are extensions of the classical Picard's Theorem. However, a similar study of the Cauchy problem in a Banach space relative to the weak topology …
Mathematical Analysis Of Stress Relaxation In Articular Cartilage During Compression, Jerome Eisenfeld, Harold Lipshitz, Van C. Mow
Mathematical Analysis Of Stress Relaxation In Articular Cartilage During Compression, Jerome Eisenfeld, Harold Lipshitz, Van C. Mow
Mathematics Technical Papers - Archive
Articular cartilage is the avascular bearing material covering the articulating ends of the mating bony segments of synovial joints. Functionally articular cartilage provides a near frictionless surface, whose coefficient of friction 0.002, which is tough and wear resistant. These biomechanical functions of the tissue are preserved so long as the tissue is maintained in a normal physiological state. The destruction and subsequent loss of articular cartilage as a result of degenerative joint diseases would lead to joint stiffness, pain and deformities. An abnormal state of mechanical stress exerted upon the tissue is an initiating factor or at least a precursor …
Interval Estimation Of Reliability Characteristics Of A K-Identical Unit Standby Redundant System, Danny D. Dyer
Interval Estimation Of Reliability Characteristics Of A K-Identical Unit Standby Redundant System, Danny D. Dyer
Mathematics Technical Papers - Archive
Standby redundancy is a method for increasing the reliability of a system through the use of additional "backup" units. Assuming perfect failure-sensing and switch-over, we consider such a system when the units are identical, non-repairable, and their lifetimes follow a two-parameter exponential distrubution. Based on unit Type II censored data, interval estimates of the system threshold parameter, mean time to failure, and reliability at time [see pdf for notation], are made through structural inference (a group theoretic approach to fiducial theory). A discussion of n-content structural tolerance intervals for the distribution of the lifetime of the system is also given. …
Estimation Of The Guarantee Time In A Two-Parameter Exponential Failure Model, Danny D. Dyer
Estimation Of The Guarantee Time In A Two-Parameter Exponential Failure Model, Danny D. Dyer
Mathematics Technical Papers - Archive
There are available several classical point estimators of the guarantee time (location parameter) in a two-parameter exponential failure model. For the purpose of making a pairwise comparison of the estimators, a two-fold technique is introduced which essentially 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 given that it is closer to the true value as well as given that it is not. Closeness to the true value is measured through an absolute error loss function. Joint consideration of these concepts is discussed …
Existence Of Solutions In A Closed Set For Delay Differential Equations In Banach Spaces, V. Moauro, S. Leela
Existence Of Solutions In A Closed Set For Delay Differential Equations In Banach Spaces, V. Moauro, S. Leela
Mathematics Technical Papers - Archive
The study of the Cauchy problem for ordinary differential equations in a Banach space has been extensive [1,3-7,9-12]. The two main directions that are followed in such a study are (i) finding monotonicity type conditions which guarantee the existence as well as uniqueness of solutions and (ii) finding compactness type conditions which assure only the existence of solutions [3,4]. It is also known [10,12] that in order to prove the existence of solutions in a closed subset F of the Banach space, a boundary condition of the type [see pdf for notation] is required.
Asymptotic Properties Of A Nonlinear Diffusion Process Arising In Articular Cartilage, Van C. Mow, Jerome Eisenfeld
Asymptotic Properties Of A Nonlinear Diffusion Process Arising In Articular Cartilage, Van C. Mow, Jerome Eisenfeld
Mathematics Technical Papers - Archive
There has been considerable effort put forth to analyse degenerative Joint diseases in terms of the principles of mechanics and hydrodynamics [8]. This effort has led to mathematical models which are systems of nonlinear partial differential equations (see e.g., [6] and [7]). The mathematical models are based on assumptions concerning the nature of the physical system which are not a priori known. Therefore laboratory experiments are performed with an eye towards validating the mathematical models. This paper deals with a particular mathematical model, a nonlinear diffusion equation, which has been proposed by Mow and Monsour [4], [5] to describe the …
General Moment Methods For A Class Of Nonlinear Models, Stephen W. Cheng, Jerome Eisenfeld
General Moment Methods For A Class Of Nonlinear Models, Stephen W. Cheng, Jerome Eisenfeld
Mathematics Technical Papers - Archive
This paper deals with the following problems: (i) the development of a general theory which incorporates several methods as special cases; (ii) the applicability of moment methods to a class of nonlinear problems, (iii) the specification of the class of admissible weighting functions; (iv) the estimation of the number of parameters; (v) the elimination of the cut-off error in the analysis of fluorescence decay data.
Stability Of Differential Systems With Impulsive Perturbations In Terms Of Two Measures, S. Leela
Stability Of Differential Systems With Impulsive Perturbations In Terms Of Two Measures, S. Leela
Mathematics Technical Papers - Archive
The study of differential systems of the form (1.1) [see pdf for notation] where [see pdf for notation] denotes the distributional derivative of [see pdf for notation], a function of bounded variation (that is, differential systems with impulsive perturbations, also called measure differential equations), is both interesting and important because most models for biological neural nets,pulse frequency modulation systems, automatic control problems with impulsive inputs and many physical processes are best described by such equations [1-3,8,10,12,13]. Since the solutions of (1.1) are discontinuous (that is, functions of bounded variation), the investigation of the stability properties of (1.1) by the usual …
Mathematical Modeling In Medicine, Jerome Eisenfeld
Mathematical Modeling In Medicine, Jerome Eisenfeld
Mathematics Technical Papers - Archive
Although the involvement of mathematics in medicine is still relatively recent, the discipline has become attractive to the mathematics community, and in fact, medically oriented articles presently appear in several mathematics journals. We call the reader's attention to the following journals: Bulletin of Mathematical Biology (continues The Bulletin of Mathematical Biophysics), Biomathematics (also called Revue de Bio-Mathematique), SIAM Journal in Applied Mathematics (a new series devoted to biomathematics will appear shortly), Math Biosciences, Biomedical Engineering, IEEE Transactions in Biomedical Engineering, Journal of Biomechanics, Biological Cybernetics, Computers in Biology and Medicine, Journal of Theoretical Biology, and Biometrics. Each year there are …
Cone-Valued Lyapunov Functions, S. Leela, V. Lakshmikantham
Cone-Valued Lyapunov Functions, S. Leela, V. Lakshmikantham
Mathematics Technical Papers - Archive
It is very well known that employing a single Lyapunov function and the theory of scalar differential inequality offers a useful mechanism to study a variety of qualitative problems of differential equations in a unified way [10]. Nevertheless, when using this powerful technique for concrete problems, the main difficulty we face is the lack of general method of constructing a Lyapunov function. This naturally beads to the development of the method of vector Lyapunov functions which utilizes several Lyapunov-like functions and the theory of vector differential inequalities in a fruitful manner [5,8-12]. This method offers a more flexible mechanism to …
A Monotone Method For Infinite System Of Nonlinear Boundary Value Problems, V. Lakshmikantham, Jagdish Chandra, S. Leela
A Monotone Method For Infinite System Of Nonlinear Boundary Value Problems, V. Lakshmikantham, Jagdish Chandra, S. Leela
Mathematics Technical Papers - Archive
Monotone iterative methods have been successfully used to generate improvable two-sided point-wise bounds on solutions of nonlinear boundary value problems for both ordinary and partial differential equations. While such procedures take a simple form when the nonlinearities are independent of gradient terms [6,9], the extension of such techniques to fully nonlinear problems has been quite formidable. In the case of scalar ordinary differential equations of the type (1.1) [see PDF for equation] such results have been obtained making use of either a linear maximum principle (3,1] or a nonlinear maximum principle [4]. In either case an essential use is made …