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Scs 38: Treillis Continus Et Treillis Complètement Distributifs, Morike Kamara Jul 1977

Scs 38: Treillis Continus Et Treillis Complètement Distributifs, Morike Kamara

Seminar on Continuity in Semilattices

No abstract provided.

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The Method Of Nonlinear Variation Of Constants For Difference Equations, M. E. Lord Jun 1977

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.

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Sobolev Type Differential Equations, M. E. Lord, V. Lakshmikantham Jun 1977

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 …

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Fragments Of 1st-Order Logic, I: Universal Horn Logic, George F. Mcnulty Jun 1977

Fragments Of 1st-Order Logic, I: Universal Horn Logic, George F. Mcnulty

Faculty Publications

No abstract provided.

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Scs 37: Comments On The Spectral Theory Of Continuous Lattices, Oswald Wyler May 1977

Scs 37: Comments On The Spectral Theory Of Continuous Lattices, Oswald Wyler

Seminar on Continuity in Semilattices

No abstract provided.

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Scs 36: Quotients Of Distributive Continuous Lattices: A Result Of S. A. Jalali, Dana S. Scott May 1977

Scs 36: Quotients Of Distributive Continuous Lattices: A Result Of S. A. Jalali, Dana S. Scott

Seminar on Continuity in Semilattices

No abstract provided.

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Efficiency In Estimation Of Mean Time To Failure In A Two-Parameter Exponential Failure Model, Danny D. Dyer May 1977

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.

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Efficiency Contours For Estimators Of Reliability In A 2-Parameter Exponential Failure Model, I-Le Lu, Danny D. Dyer May 1977

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 …

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Differential Inequalities And Flow-Invariance Via Linear Functionals, V. Lakshmikantham, Jerome Eisenfeld May 1977

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.

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Infinitely Many Perfect And Unitary Perfect Polynomials Over Some Gf(Q), Mickie Sue Harbin, A.T. Bullock, Jacob T. B. Beard Jr. May 1977

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 …

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System Identification Problems And The Method Of Moments, Jerome Eisenfeld, S. W. Cheng, Stephen R. Bernfeld May 1977

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 …

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Linear Algebraic Computational Procedures For System Identification Problems, Jerome Eisenfeld, B. Soni May 1977

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.

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Existence And Comparison Results For Nonlinear Volterra Integral Equations In A Banach Space, Randy Vaughn May 1977

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] = …

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Existence And Uniqueness Of Solutions Of Delay Differential Equations On A Closed Subset Of A Banach Space, V. Moauro, S. Leela, V. Lakshmikantham May 1977

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, …

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Existence In Mathematics, Willis Alberda Apr 1977

Existence In Mathematics, Willis Alberda

ACMS Conference Proceedings 1977

Contemplation of the existence of mathematical entities for very apparent reasons generates a mental cycling of arguments dealing with the nature of mathematical truth, meaning in mathematics, and the obviously related question of which of these two problems should be solved first. The problem of the existence of mathematical entities dates from the first thoughts and ideas of a mathematical nature. The problem of existence in mathematics is fundamental to the domain of speculation and research on the foundations of mathematics. When we try to put ourselves in the place of those philosophers who first explored this problem we must …

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Infinity & Reality, John W. Warner Apr 1977

Infinity & Reality, John W. Warner

ACMS Conference Proceedings 1977

This paper examines the topics of infinity and reality as relevant to the conference, proposing a possible relationship between the two in order to stimulate further discussions.

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Epistomology To Ontology, Charles R. Hampton Apr 1977

Epistomology To Ontology, Charles R. Hampton

ACMS Conference Proceedings 1977

This paper offers commentary on the various philosophical approaches to the foundations of mathematics and then indicates how these ideas have implications in consideration of the existence question.

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Recent Problems In The Foundationsof Mathematics, Terence H. Perciante Apr 1977

Recent Problems In The Foundationsof Mathematics, Terence H. Perciante

ACMS Conference Proceedings 1977

This paper examines the foundational crises that have haunted twentieth-century mathematics, beginning with a brief review of the effects generated by Gauss, Lobachevsky, and Bolyai who each developed non-Euclidean parallel axiom. Though of mathematical interest in their own right, the significance of the new geometries was greatly magnified when it was discerned that they could be used to adequately model physical space, even to the extent that Einstein’s theory of relativity later employed as its model a non-Euclidean geometry developed by Riemann. The question that obviously presented itself was how could any given geometry be called true when it and …

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The Foundations Of Mathematics And The Mathematics Curriculum, Bayard Baylis Apr 1977

The Foundations Of Mathematics And The Mathematics Curriculum, Bayard Baylis

ACMS Conference Proceedings 1977

In teaching the foundations of mathematics within the framework of a Christian college, and particularly that of a Christian liberal arts college, there are two groups of students which must be served. The first consisted of the non-mathematics majors—those non-scientifically oriented “general anything” students who, as a catalog might put it, are to receive “an introduction to and an appreciation of the history, foundations, culture and applications of mathematics.” The second group consists of the mathematics majors, and the few science majors who have not been frightened away by the calculus. The gulf between these two groups is sufficiently large, …

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A Brief Introduction To Gödel’S Theorems, Michael Detlefsen Apr 1977

A Brief Introduction To Gödel’S Theorems, Michael Detlefsen

ACMS Conference Proceedings 1977

Gödel’s two famous incompleteness theorems are results that have come up a number of times in the discussions at the 1977 ACMS conference. This paper provides a brief and relatively non-technical statement on these results and of their significance for the foundations of mathematics.

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Current Work On Mathematical Truth, Michael Detlefsen Apr 1977

Current Work On Mathematical Truth, Michael Detlefsen

ACMS Conference Proceedings 1977

The overall aim of this paper is to serve as an introduction to the work currently being done on the topic of mathematical truth. It provides an overview of the major developments concerning mathematical truth and also evaluates those developments as potential contributions to mathematician’s understanding of the subject.

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Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley Apr 1977

Recent Parallels Between The Philosophy Of Science And Mathematics, Joseph Spradley

ACMS Conference Proceedings 1977

Following World War I European philosophy of science formed an alliance with mathematics culminating in an attitude of certainty and autonomy that rejected all non empirical claims to truth and purported to make all science presupposition less. The rise and fall of logical positivism has been one of the major themes of of twentieth century thought and illustrates the danger of placing too much emphasis on science and mathematics as an ideal for all knowledge. The restriction of rational inquiry to the modes of scientific verification and the processes of mathematical logic was far too confining for the containment of …

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Formalizing The Liar Paradox, Frank Meyer Apr 1977

Formalizing The Liar Paradox, Frank Meyer

ACMS Conference Proceedings 1977

No abstract provided.

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God: All Sufficient Or Infinite, Thomas E. Iverson Apr 1977

God: All Sufficient Or Infinite, Thomas E. Iverson

ACMS Conference Proceedings 1977

No abstract provided.

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Getting Their Interest - Initiating Students Into The Study Of Foundational Issues In Mathematics, Harold Heie Apr 1977

Getting Their Interest - Initiating Students Into The Study Of Foundational Issues In Mathematics, Harold Heie

ACMS Conference Proceedings 1977

No abstract provided.

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Wanted: Christian Perspectives In The Philosophy Of Mathematics, Arthur F. Holmes Apr 1977

Wanted: Christian Perspectives In The Philosophy Of Mathematics, Arthur F. Holmes

ACMS Conference Proceedings 1977

This paper describes the three types of theory about universals, beginning in each case with a classical historical formulation and moving to its restatement in recent analytic philosophy. It will then suggest ways in which Christian perspectives bear on theories of universals and so on mathematics.

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A Christian Point Of View, A. Wayne Roberts Apr 1977

A Christian Point Of View, A. Wayne Roberts

ACMS Conference Proceedings 1977

Does the fact that you are a Christian affect the way that you teach mathematics? This paper seeks to answer the question, what contributions can a mathematics teacher in a Christian school make to the distinctive purpose of such a school?

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Of Men, Models, And Mathematics, Charles Hatfield Apr 1977

Of Men, Models, And Mathematics, Charles Hatfield

ACMS Conference Proceedings 1977

No abstract provided.

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Skolem’S Paradox And The Predestination/Free-Will Discussion, Gene B. Chase Apr 1977

Skolem’S Paradox And The Predestination/Free-Will Discussion, Gene B. Chase

ACMS Conference Proceedings 1977

The purpose of this paper is to show that both sides of the predestination/free-will discussion are admissible in a way that is more profound than simply the wave-particle duality of light. In wave-particle duality there are two competing physical models of reality which are contradictory. This paper will show that not a contradiction but a difference in viewpoint is the fundamental issue in the discussion of predestination and free will. A discussion of Skolem’s paradox is helpful in this demonstration.

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Introduction (1977), Robert Brabenec Apr 1977

Introduction (1977), Robert Brabenec

ACMS Conference Proceedings 1977

No abstract provided.

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