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Articles 181 - 210 of 343
Full-Text Articles in Mathematics
An Estimate For The Roots Of Random Algebraic Polynomial With Application, M. Sambandham, G. S. Ladde
An Estimate For The Roots Of Random Algebraic Polynomial With Application, M. Sambandham, G. S. Ladde
Mathematics Technical Papers - Archive
An algebraic polynomial with dependent random coefficients is considered. The difference between the sample roots of random algebraic equation and the roots of the mean equation is estimated. As an application the difference between the sample solution of a random difference equation and the solution of the mean difference equation is also obtained.
Existence Theorems For A Class Of Functional Differential Systems, B. G. Pachpatte, G. S. Ladde
Existence Theorems For A Class Of Functional Differential Systems, B. G. Pachpatte, G. S. Ladde
Mathematics Technical Papers - Archive
In recent papers [2,6], the authors have established existence and comparison theorems for the well known Cauchy problem for ordinary differential equations without using the monotone property on the given system. These results are obtained under the conditions of the type which have been considered in the classical paper of Müller [8]. The interesting feature of the results established in [2,6], is the fact that the solutions of the Cauchy problem remain in the given sector. In this paper, we shall first establish existence and comparison theorems for a class of more general functional differential systems without using monotone property. …
Monotone Method For Equations Describing Transport Phenomena In A Banach Space, A. S. Vatsala, B. G. Pachpatte
Monotone Method For Equations Describing Transport Phenomena In A Banach Space, A. S. Vatsala, B. G. Pachpatte
Mathematics Technical Papers - Archive
Existence of extremal solutions of initial and boundary value problems (B.V.P. for short) of differential equations in a Banach space has been recently considered in [2,7] by utilizing monotone iterative method. A special type of B.V.P. of the form [see pdf for notation] in finite dimensional spaces have been recently investigated in [6]. It is of interest to investigate (1.1) in a Banach space since special forms of them occur in transport processes [1,8,9]. In order to develop monotone technique for (1.1) it becomes necessary to develop a comparison Theorem (see Theorem 2.1) which is of interest in itself. The …
Method Of Quasi-Upper And Lower Solutions In Abstract Cones, V. Lakshmikantham, A. S. Vatsala, S. Leela
Method Of Quasi-Upper And Lower Solutions In Abstract Cones, V. Lakshmikantham, A. S. Vatsala, S. Leela
Mathematics Technical Papers - Archive
Let E be a real Banach space with ||•|| and let E* denote the dual of E. Let K C E be a cone, that is, a closed convex subset such that ^K C K for every ^ ≥ 0 and K ^ {-K} = {O}, By means of K a partial order ≤ is defined as v ≤ u if u - v E K. We let K* =[φ E E*: φ(u) ≥ 0 for all u E K]. A cone K is said to be normal if there exists a real number N > 0 such that 0 ≤ …
Linear Monotone Method For Nonlinear Boundary Value Problems In Banach Spaces, V. Lakshmikantham, Stephen R. Bernfeld
Linear Monotone Method For Nonlinear Boundary Value Problems In Banach Spaces, V. Lakshmikantham, Stephen R. Bernfeld
Mathematics Technical Papers - Archive
One of the most useful techniques in proving the existence of multiple solutions of nonlinear boundary value problems (BVP for short) is the monotone iterative method, which yields monotone sequences that converge to extremal solutions of the problem. Recently, because of applications, this technique has attracted much attention, see [1,3-7,11,12,14,15]. To explain this method, let us consider the scalar BVP (1.1) [see pdf for notation] where [see pdf for notation] and [see pdf for notation], I being the interval [0,1]. Suppose that [see pdf for notation] with [see pdf for notation] on I and (1.2) [see pdf for notation] Then …
Periodic Solution For Nonlinear Delay Equation In Higher Order, Sen-Wo Du
Periodic Solution For Nonlinear Delay Equation In Higher Order, Sen-Wo Du
Mathematics Technical Papers - Archive
In recent years, the existence and uniqueness of 2n-period solution for (1.1) [see pdf for notation] where x E Rn, and e(t,u,v) is a given function with 2^-period in t, have been discussed in several papers [1],[2],[3],[4] by using the Fourier expansion and fixed point method. The delay case is first discussed by W. Layton [5]. Applying similar ideas, we extend the study of (1.1) for any positive integer j.
Bounded Solutions For Some Gradient Type Systems, A. R. Aftabizadeh
Bounded Solutions For Some Gradient Type Systems, A. R. Aftabizadeh
Mathematics Technical Papers - Archive
C. Corduneanu in [3,TH.1] investigated the existence of a unique bounded solution of the system [see pdf for notation] (1.1) with [see pdf for notation] continuous and of class c(2) in u. In this paper we shall prove the existence of a unique bounded solution of (1.1), stated in [3,TR.1], under weaker conditions, and also we shall discuss the asymptotic behavior of bounded solution of (1.1) on a half-line. We wish to mention that M. M. Belova [1] had similar ideas, but she did consider only a special case (space L2), and without concern for existence. Before we proceed further, …
On Washout In Nonlinear Compartmental Systems, Jerome Eisenfeld
On Washout In Nonlinear Compartmental Systems, Jerome Eisenfeld
Mathematics Technical Papers - Archive
Let x(t) be a solution of a compartmental system. If, for some compartment j, x (t) -> 0 as t -> °°, then we say that compartment j washes out. We show that a compartment washes out if it always reaches (along a fixed path) either the environment or another compartment for which there is no return path. Additional criteria, particularly regarding exponential convergence, are also presented. Examples are drawn from tracer kinetics, enzyme reactions, and epidemic models.
On None Approach To Equilibrium In Compartmental Systems, Jerome Eisenfeld
On None Approach To Equilibrium In Compartmental Systems, Jerome Eisenfeld
Mathematics Technical Papers - Archive
The question of convergence of a solution of a compartmental system to an equilibrium point, as t -> °°, is of considerable interest [1-6]. Although it was not explicitly stated, the remarks in [1] seem to suggest that in the case of closed systems, of the type specified below, every solution approaches an equilibrium point. These remarks prompted the construction of counter examples, to be presented below, to show that a closed compartmental system may admit periodic solutions as well as aperiodic solutions that do not approach a constant vector.
Monotone Method For Nonlinear Boundary Value Problems Arising In Transport Process, B. G. Pachpatte, V. Lakshmikantham
Monotone Method For Nonlinear Boundary Value Problems Arising In Transport Process, B. G. Pachpatte, V. Lakshmikantham
Mathematics Technical Papers - Archive
Recently, monotone iterative methods have been successfully employed to prove existence of multiple solutions and point-wise bounds on solutions of nonlinear boundary value problems for both ordinary and partial differential equations (see, [1], [3]-[6], [9]). In the transport process [10] of n different types of particles in a finite rod of length (b-a) the equation governing the particle's density is given by the following linear system of equations [see pdf for notation] where Ai, Bi (i = 0,1,2) are n x n matrices and x,y,p,q are n-vectors. The components x1,...,xn of the vector x represent the n distinct type of …
The Threshold Problem For Fitzhugh-Nagumo Equations, C. Corduneanu
The Threshold Problem For Fitzhugh-Nagumo Equations, C. Corduneanu
Mathematics Technical Papers - Archive
No abstract provided.
Quasi-Invariant Manifolds, Stability, And Generalized Hopf Bifurcation, L. Salvadori, Stephen R. Bernfeld
Quasi-Invariant Manifolds, Stability, And Generalized Hopf Bifurcation, L. Salvadori, Stephen R. Bernfeld
Mathematics Technical Papers - Archive
We are interested in obtaining an analysis of the bifurcating periodic orbits arising in the generalized Hopf bifurcation problems in Rn. The existence of these periodic orbits has often been obtained by using such techniques as the Lyapunov-Schmidt method or topological degree arguments (see Marsden and McCracken [8] and Hale [6] and their references). Our approach, on the other bend, is based upon stability properties of the equilibrium point of the unperturbed system. Andronov et. al. [1] showed the fruitfulness of this approach in studying bifurcation problems in R2 (for more recent papers see Negrini and Salvadori [9] and Bernfeld …
Fixed Point Theorems For Expanding Maps, B. B. Williams, A. A. Gillespie
Fixed Point Theorems For Expanding Maps, B. B. Williams, A. A. Gillespie
Mathematics Technical Papers - Archive
Suppose (X,d) is a metric space, h > 0 and T: X -> X. We shall use the notation T E E(h) to mean [see pdf for notation] for each x,y E X. If h > 1, then T will be called an expanding map. Clearly T E E(h) implies T is a 1-1 function and [see pdf for notation] for each x,y E T(X). In this paper some conditions are found to insure that an expanding map will have a fixed point. It is shown that each finite dimensional Banach space X has the following property: each continuous and expanding map …
Generalized Transversality, Exchange Of Stability And Hopf Bifurcation, Stephen R. Bernfeld
Generalized Transversality, Exchange Of Stability And Hopf Bifurcation, Stephen R. Bernfeld
Mathematics Technical Papers - Archive
In Hopf bifurcation theory often an exchange of stability of an equilibrium gives rise to the creation of periodic orbits for a one parameter family of differential equations. In particular, let us consider the system in Rn given by [see pdf for notation] where µ E [0,^) for µ sufficiently small, a(µ), ß(µ) and Aµ are C°° in µ with a(0) = 0 and ß(0) = 1. Assume [see pdf for notation] where [see pdf for notation] and for each µ, X, Y, Z are of order greater than one at the origin. Finally, the eigenvalues [see pdf for notation] …
On Approach To Equilibrium In Nonlinear Compartmental Systems, Jerome Eisenfeld
On Approach To Equilibrium In Nonlinear Compartmental Systems, Jerome Eisenfeld
Mathematics Technical Papers - Archive
A closed compartmental system is a set of nonnegative interdependent functions, [see pdf for notation] such that their sum is constant. The functions can represent populations, masses or concentrations, depending on the particular application. It is convenient to normalize so that [see pdf for notation] in which case the functions are proportions. It is assumed that the (nonnegative) flow rate from j to i has the form fjjxj. Thus, the rate of change, [see pdf for notation] The first term is the inflow to i from the other "compartments" and the second term is the outflow from i to the …
Monotone Iterative Technique For Differential Equations In A Banach Space, V. Lakshmikantham, Sen-Wo Du
Monotone Iterative Technique For Differential Equations In A Banach Space, V. Lakshmikantham, Sen-Wo Du
Mathematics Technical Papers - Archive
Let E be a real Banach space with norm [see pdf for notation]. Consider the initial value problem (1.1) [see pdf for notation], where [see pdf for notation]. Generally speaking of approximate solutions of (1.1) consist of three steps, namely, (i) constructing a sequence of approximate solutions of some kinds for (1.1); (ii) showing the convergence of the constructed sequence; (iii) proving that the limit function is a solution. If f is continous, steps (i) and (iii) are standard and straight forward. It is a step (ii) that deserves attention. This in turn leads to three possibilities; namely to show …
On The Theory Of Terminal Value Problems For Ordinary Differential Equations, V. Lakshmikantham, A. R. Aftabizadeh
On The Theory Of Terminal Value Problems For Ordinary Differential Equations, V. Lakshmikantham, A. R. Aftabizadeh
Mathematics Technical Papers - Archive
It is well known [2] that the comparison principle for initial value problems of ordinary differential equations is a very useful tool in the study of qualitative and quantitative theory. Recently, attempts have been made to study the corresponding comparison principle for terminal value problems (TVP for short), [1,3,4]. Since the theory related to TVP's is much more complicated than that of initial value problems, the development of the theory corresponding to these problems has met with difficulties. For example, one of the difficulties arises because the existence of a solution of the TVP [see pdf for notation] need not …
On The Method Of Upper And Lower Solutions In Abstract Cones, S. Leela, V. Lakshmikantham
On The Method Of Upper And Lower Solutions In Abstract Cones, S. Leela, V. Lakshmikantham
Mathematics Technical Papers - Archive
No abstract provided.
Numerical Simulation Of Miscible And Immiscible Fluid Flows In Porous Media, Donald Greenspan, Vincenzo Casulli
Numerical Simulation Of Miscible And Immiscible Fluid Flows In Porous Media, Donald Greenspan, Vincenzo Casulli
Mathematics Technical Papers - Archive
Fast, economical, and accurate finite difference numerical methods are developed for approximating continuum models of both miscible and immiscible fluid flows in porous media. The methods apply to very general systems of equations and boundary configurations. Computer examples are described and discussed.
The Convolution Of Generialized-F Distributions, Danny D. Dyer
The Convolution Of Generialized-F Distributions, Danny D. Dyer
Mathematics Technical Papers - Archive
The generalized-F variate is the ratio of two independent gamma variates, and its distribution includes as special cases such distributions as the inverted beta, Lomax, and Snedecor's-F. Based on convolution, the distribution function of the sum of two independent generalized-F variates is derived in terms of a Lauricella-Saran hypergeometric function of three variables. The results are applied with numerical examples given to (a) a Bayesian analysis of the availability of a two-component series system and (b) a test of hypothesis on the multinormal mean vector whenever the covariance matrix has the intraclass correlation pattern.
Numerical Solution Of Free Surface, Porous Flow Problems, Donald Greenspan, Vincenzo Casulli
Numerical Solution Of Free Surface, Porous Flow Problems, Donald Greenspan, Vincenzo Casulli
Mathematics Technical Papers - Archive
In this paper an inexpensive, fast numerical method is developed for the approximate solution of general, free surface, porous flow problems. The method is so designed that the required numerical boundary conditions coincide exactly with the required physical boundary conditions. Numerical examples of a prototype problem are described and discussed.
Stochastic Analysis Of Compressible Gas Lubrication Slider Bearing Problem, Jagdish Chandra, V. Lakshmikantham, G. S. Ladde
Stochastic Analysis Of Compressible Gas Lubrication Slider Bearing Problem, Jagdish Chandra, V. Lakshmikantham, G. S. Ladde
Mathematics Technical Papers - Archive
By employing the theory of stochastic differential inequalities and a comparison result for the stochastic boundary value problem, the effects of roughness for nonlinear gas lubricated problem is analyzed. In particular, by summarizing analytic techniques, estimates on the absolute mean and root-mean-square deviations of a normalized load carrying capacity from the smooth case is obtained for a general nonlinear one-dimensional problem.
Systems By The Method Of Quasisolutions, A. S. Vatsala, V. Lakshmikantham
Systems By The Method Of Quasisolutions, A. S. Vatsala, V. Lakshmikantham
Mathematics Technical Papers - Archive
Recently [10] the method of lower and upper solutions has been extended to systems of reaction diffusion equations which has become very useful in dealing with applications. This extension depends crucially on a certain property known as quasimonotone nondecreasing property [8] without which the results fail under natural definition of lower and upper solutions. When the quasimonotone property does not hold but a certain mixed quasimonotone property is satisfied, which is the case in several applications [7], the method of quasisolutions is more suitable [2,4,6,9]. All these results utilize monotone iterative technique. When no monotone condition holds one can also …
On The Fundamental Theory Of Nonlinear Second Order Stochastic Boundary Value Problems, G. S. Ladde, Jagdish Chandra, V. Lakshmikantham
On The Fundamental Theory Of Nonlinear Second Order Stochastic Boundary Value Problems, G. S. Ladde, Jagdish Chandra, V. Lakshmikantham
Mathematics Technical Papers - Archive
A Study of nonlinear second order stochastic boundary value problems (SBVP for short) is initiated through sample calculus approach. A basic existence result for bounded nonlinearities is established. The method of upper and lower solution processes and a general existence theorem are established. After proving the stochastic version of the needed maximum principle, the monotone iterative technique is developed which yields existence of multiple solution processes of SBVP. Finally, by developing a stochastic comparison result, the important problem of finding error estimates between the sample solutions of SBVP and the solutions of corresponding mean BVP, is considered.
The Method Of Upper, Lower Solutions And Volterra Integral Equations, G. S. Ladde, B. G. Pachpatte, V. Lakshmikantham
The Method Of Upper, Lower Solutions And Volterra Integral Equations, G. S. Ladde, B. G. Pachpatte, V. Lakshmikantham
Mathematics Technical Papers - Archive
In employing the method of upper and lower solutions to dynamical systems, one is required to impose a certain monotone property on the given system [5,6,11] When the given system does not possess such a monotonic property, stronger forms of upper and lower solutions have to be assumed in order to obtain similar results [4,6,9]. Furthermore, if the system enjoys a mixed monotone property the method of quasi-upper and lower solutions, which is recently introduced, is most useful [7]. In this paper we shall extend these ideas to Volterra integral equations. We want to note that Volterra integral equations and …
An Analysis Of Stress Wave Propagation In Slender Bars Using A Discrete Particle Approach, Donald Greenspan, W. R. Reeves
An Analysis Of Stress Wave Propagation In Slender Bars Using A Discrete Particle Approach, Donald Greenspan, W. R. Reeves
Mathematics Technical Papers - Archive
In this paper, a discrete particle approach is developed for the quantitative analysis of stress wave propagation in metal bars. Though linear forces are emphasized, nonlinear forces are also considered. Cylindrical, tapered, homogeneous, and nonhomogeneous bars are studied. Computer results show most favorable agreement with available theoretical and experimental results.
Numerical Simulation Of Free Surface Thermally-Influenced Flows For Nonhomogeneous Fluids, Vincenzo Casulli
Numerical Simulation Of Free Surface Thermally-Influenced Flows For Nonhomogeneous Fluids, Vincenzo Casulli
Mathematics Technical Papers - Archive
In this paper a finite difference technique is presented to simulate the behavior of natural water bodies under the influence of pollutants and temperature differences. The mathematical model which has been discretized is the closed system obtained by combining the Navier-Stokes equations, the heat transfer equation, the diffusion equations, and an equation relating fluid density to both the chemical concentration and the temperature. The numerical method is based on the Marker-and-Cell method which has been extended to consider the volume expansion due to heat transfer and the density variations.
Stability And Generalized Hopf Bifurcation Through A Reduction Principle, Stephen R. Bernfeld, L. Salvadori, P. Negrini
Stability And Generalized Hopf Bifurcation Through A Reduction Principle, Stephen R. Bernfeld, L. Salvadori, P. Negrini
Mathematics Technical Papers - Archive
We are interested in obtaining an analysis of the bifurcating periodic orbits arising in the generalized Hopf bifurcation problems in Rn. The existence of these periodic orbits has often been obtained by using such techniques as the Liapunov-Schmidt method or topological degree arguments (see [5] and its references). Our approach, on the other hand, is based upon stability properties of the equilibrium point of the unperturbed system. Andronov et. al. [1] showed the fruitfulness of this approach in studying bifurcation problems in R2 (for more recent papers see Negrini and Salvadori 161 and Bernfeld and Salvadori [2]). In the case …
Numerical Studies Of Double-Layer Circularization And Gastrulation, Donald Greenspan
Numerical Studies Of Double-Layer Circularization And Gastrulation, Donald Greenspan
Mathematics Technical Papers - Archive
In this paper, certain types of biological cell rearrangements are modeled from a computer point of view. All forces are of a local nature and are patterned on classical atomic and molecular interactions. It is first shown how to induce a double-layered flat tissue to fold into a double-layered circular tissue. Then, it is shown how to induce a section of the circular tissue to pull inward, or gastrulate.
Stability And Asymptotic Equivalence Of Perturbations Of Nonlinear Systems Of Differential Equations, M. E. Lord
Stability And Asymptotic Equivalence Of Perturbations Of Nonlinear Systems Of Differential Equations, M. E. Lord
Mathematics Technical Papers - Archive
A nonlinear variation of constants method was introduced by Alekseev [1] and applications of this formula to questions of stability and asymptotic equivalence of differential systems was demonstrated by Brauer [2,3,4]. In [6] a different approach to the nonlinear variation of constants method is given. This new approach involves determining the solution of the perturbed system by variation of the starting vector in the unperturbed system. Conceptually this is the method used in obtaining the classical variation of constants formula for perturbations of linear systems. In [6] the method yields two different formulas, one of which is equivalent to the …