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Existence Of Periodic Solutions Of Nonlinear Boundary Value Problems And The Method Of Upper And Lower Solutions, V. Lakshmikantham, R. Kannan Nov 1981

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.

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The History Of The Study And Teaching Of American Literature, Erma P. Whittington Nov 1981

The History Of The Study And Teaching Of American Literature, Erma P. Whittington

Covers, Titles, and Tables: The Formations of American Literary Canons in Anthologies - Archive

American Literature Extra Essays

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Nonuniqueness Criteria For Ordinary Differential Equations, Mansour Samimi Oct 1981

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 …

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Existence And Monotone Method For Periodic Solutions Of First Order Differential Equations, S. Leela, V. Lakshmikantham Sep 1981

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 …

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Error Estimates Of Solutions And Mean Of Solutions Of Stochastic Differential Systems, M. Sambandham, G. S. Ladde Aug 1981

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.

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Transportation In Texas : Past, Present, And Future, Texas Transportation Institute, Texas A & M University System Aug 1981

Transportation In Texas : Past, Present, And Future, Texas Transportation Institute, Texas A & M University System

Documents from the State of Texas-Archive

Transportation is seldom of value in and of itself. It generally is a means rather than an end, and for this reason the importance of transportation is often unnoticed. In fact, a smoothlyworking, well-ordered transportation system may likely be taken for granted in much the same sense as the air we breathe is taken for granted. But if a disruption occurs in this efficient system, the results are immediate, often dramatic, and potentially destructive. A traffic accident can instantly block the flow of an entire freeway resulting in huge losses of valuable travel time and the waste of hundreds of …

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Alluvial Fan Deposits Of The Todos Santos Formation Of Central Chiapas, Mexico, Terence Cletus Blair Jul 1981

Alluvial Fan Deposits Of The Todos Santos Formation Of Central Chiapas, Mexico, Terence Cletus Blair

Earth & Environmental Sciences Theses - Archive

The Todos Santos Formation at Jerico was deposited as an alluvial fan system by high gradient, short duration ephemeral streams which transported gravel, sand, and mud northeastward through a feeder canyon which opened out onto an alluvial plain. This alluvial fan system is composed of streamflood, debris flow, and braided stream deposits. Three distinct alluvial fan environments were distinguished at Jerico: proximal fan facies, mid-fan facies, and distal fan facies. Analysis of the vertical succession of these depositional facies reveals two proximal to distal alluvial fan transitions separated by a distal to proximal transition. This suggests that a period of …

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A New Computer Approach To Atomic And Molecular Dynamics With Application To The Water Molecule, Donald Greenspan Jul 1981

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.

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Computer Use In Social Services Network Newsletter, Dick Schoech Jul 1981

Computer Use In Social Services Network Newsletter, Dick Schoech

Computer Use in Social Services Network

No abstract provided.

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Test Excavations At The Tankersley Creek Site, A Multicomponent Campsite In Titus County, Texas, Wayne C. Young Jul 1981

Test Excavations At The Tankersley Creek Site, A Multicomponent Campsite In Titus County, Texas, Wayne C. Young

Documents from the Texas State Department of Highways-Archive

Test excavations of the Tankersley Creek Site, 41TT108, in Titus County, Texas, uncovered a multi-component campsite ranging in time from the Early La Harpe Aspect to Caddo IV times. Component I was the earliest recognized occupation and was characterized by slightly expanding stem dart points. Component II followed Component I and was recognized by a dominance of Large Gary dart points. Component III appeared to represent an early Caddo I occupation and contained Small Gary points and decorated pottery that is usually affiliated with the Caddo I Period. Interestingly, this component lacked the Alba arrowpoints normally found in sites of …

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An Estimate For The Roots Of Random Algebraic Polynomial With Application, M. Sambandham, G. S. Ladde Jun 1981

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.

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Existence Theorems For A Class Of Functional Differential Systems, B. G. Pachpatte, G. S. Ladde Jun 1981

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. …

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Monotone Method For Equations Describing Transport Phenomena In A Banach Space, A. S. Vatsala, B. G. Pachpatte Jun 1981

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 …

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A New County Courthouse And Square For Dallas, Texas, Richard Wintersole May 1981

A New County Courthouse And Square For Dallas, Texas, Richard Wintersole

School of Architecture Theses - Archive

Dallas County recently purchased a site in downtown which the City's Master Plan has earmarked for a new County Courthouse to be constructed in 1995. The site is located at the northern edge of an open urban space which contains John F Kennedy Memorial Plaza and John Neely Bryan County Park. Existing on the site and providing an integral edge to the open urban square is the Purse Building, a warehouse constructed in the Chicago Style in 1898. Representatives of the County and the County Historic Commission have expressed an interest in incorporating the Purse Building into the design for …

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Aspects Of Korean Narration, Shin Ja Joo Hwang May 1981

Aspects Of Korean Narration, Shin Ja Joo Hwang

Linguistics & TESOL Dissertations - Archive

A dominant trend in linguistics has been sentence grammar, which deals with structures leading up to the sentence level. With more studies on semantics and pragmatics, however, there has been a growing concern for discourse grammar. Discourse, I believe, is the most natural unit of language that forms a meaningful whole. The reasons for discourse study derive from four sources: (1) from phonology come suprasegmental considerations like intonation and pitch which typically stretch over the sentence boundary; (2) from semantics comes the sense that the meaning or message is conveyed through the overall discourse, not through aggregates of sentences; (3) …

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Method Of Quasi-Upper And Lower Solutions In Abstract Cones, V. Lakshmikantham, A. S. Vatsala, S. Leela May 1981

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 ≤ …

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Linear Monotone Method For Nonlinear Boundary Value Problems In Banach Spaces, V. Lakshmikantham, Stephen R. Bernfeld May 1981

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 …

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Periodic Solution For Nonlinear Delay Equation In Higher Order, Sen-Wo Du May 1981

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.

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Theme In Greek Hortatory Discourse: Van Dijk And Beekman-Callow Approaches Applied To 1 John, Helen Louise Miehle May 1981

Theme In Greek Hortatory Discourse: Van Dijk And Beekman-Callow Approaches Applied To 1 John, Helen Louise Miehle

Linguistics & TESOL Dissertations - Archive

Two independently motivated linguistic models of text analysis (the cognitively-based model of Van Dijk and the literary-semantic approach of Beekman and Callow) are used to show that the First Epistle of John is actually hierarchical in its organization, and not merely associative as many Biblical scholars have assumed. The Van Dijk and Beekman-Callow models are also compared, contrasted and combined into a composite approach, which is then applied to the text of I John chapter one to take advantage of the pragmatic emphasis of Van Dijk and the practicality of the Beekman-Callow procedures. The two models are shown to complement …

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Bounded Solutions For Some Gradient Type Systems, A. R. Aftabizadeh Apr 1981

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, …

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On Washout In Nonlinear Compartmental Systems, Jerome Eisenfeld Apr 1981

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.

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On None Approach To Equilibrium In Compartmental Systems, Jerome Eisenfeld Apr 1981

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.

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Monotone Method For Nonlinear Boundary Value Problems Arising In Transport Process, B. G. Pachpatte, V. Lakshmikantham Apr 1981

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 …

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The Threshold Problem For Fitzhugh-Nagumo Equations, C. Corduneanu Mar 1981

The Threshold Problem For Fitzhugh-Nagumo Equations, C. Corduneanu

Mathematics Technical Papers - Archive

No abstract provided.

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Quasi-Invariant Manifolds, Stability, And Generalized Hopf Bifurcation, L. Salvadori, Stephen R. Bernfeld Mar 1981

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 …

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Fixed Point Theorems For Expanding Maps, B. B. Williams, A. A. Gillespie Mar 1981

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 …

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Generalized Transversality, Exchange Of Stability And Hopf Bifurcation, Stephen R. Bernfeld Feb 1981

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] …

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On Approach To Equilibrium In Nonlinear Compartmental Systems, Jerome Eisenfeld Feb 1981

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 …

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Monotone Iterative Technique For Differential Equations In A Banach Space, V. Lakshmikantham, Sen-Wo Du Feb 1981

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 …

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On The Theory Of Terminal Value Problems For Ordinary Differential Equations, V. Lakshmikantham, A. R. Aftabizadeh Feb 1981

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 …

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