Digital Commons Network^™

A New Conjecture About Minimal Imperfect Graphs, H. Meyniel, Stephan Olariu

Computer Science Faculty Publications

H. Meyniel proved that in every minimal imperfect graph, every pair of vertices is joined by a chordless path containing an odd number of edges. We conjectured that in every minimal imperfect graph, every pair of vertices is joined by a path containing an even number of edges. We give an equivalent version of this new conjecture.

Applied Chaotic Dynamics: An Introduction, James Frankenfield

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

These lecture notes served as the basis for a two credit graduate level seminar offered through the USU physics department during the fall quarter of 1989. It was oriented towards graduate students in physics and engineering and assumed no mathematical background beyond introductory differential equations. All problems were attempted by the students and discussed as a group. The seminar appears to have been successful in that the students enjoyed it and learned a lot.

Dilatations Des Commutants D'Opérateurs Pour Des Espaces De Krein De Fonctions Analytiques, Daniel Alpay

Mathematics, Physics, and Computer Science Faculty Articles and Research

Let K1 and K2 be two Krein spaces of functions analytic in the unit disk and invariant for the left shift operator R0(R0f(z)=(f(z)−f(0))/z), and let A be a linear continuous operator from K1 into K2 whose adjoint commutes with R0. We study dilations of A which preserve this commuting property and such that the Hermitian forms defined by I−AA∗ and I−BB∗ have the same number of negative squares. We thus obtain a version of the commutant lifting theorem in the framework of Krein spaces of analytic functions. To prove this result we suppose that the graph of the operator A∗, …

Organizational Inducements And Social Motives: A Game Theoretic Analysis, Richard G. Davis

Dissertations and Theses

Game theory was used to analyze compensation systems based on individual and group incentives. Payoff formulas were developed for these incentives assuming different preferences for individual and social outcomes. Two levels of contributions were considered: (1) Defection. The minimum acceptable level of contributions, and (2) Cooperation. A level of discretionary contributions above the minimum. The discretionary contributions associated with cooperation were represented as a cost to the individual.

A classification scheme for uniform n-person games was developed using the approach of Rappaport and Guyer (1966) for 2 x 2 games. This classification scheme defines the natural outcome (cooperation or defection) …

A Humanistic Academic Environment For Learning Undergraduate Mathematics, Clarence F. Stephens

Humanistic Mathematics Network Journal

No abstract provided.

Letter From A Harvey Mudd College Student, Chris Jewell

Humanistic Mathematics Network Journal

No abstract provided.

Increasing Learning By Decreasing Math Anxiety, Gregg Turner

Humanistic Mathematics Network Journal

No abstract provided.

Letter From The Editor, Issue 3, 1988, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical Metaphors From Advanced Placement Students, Dorothy Buerk

Humanistic Mathematics Network Journal

No abstract provided.

Transparadigm Mathematics Research Initiative, EleméR E. Rosinger

Humanistic Mathematics Network Journal

No abstract provided.

An Innovative Curriculum Idea For The First Two Years Of College Mathematics, Larry Copes

Humanistic Mathematics Network Journal

No abstract provided.

For Whom Nobel Tolls, William Dunham

Humanistic Mathematics Network Journal

No abstract provided.

Report On Work At Brunel University, Anthony Briginshaw

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics And Its Application, Jack V. Wales Jr.

Humanistic Mathematics Network Journal

No abstract provided.

The Compensatory Bargaining Set Of A Cooperative N-Person Game With Side Payments, Irinel C. Dragan

Mathematics Technical Papers - Archive

The bargaining sets have been introduced as solution concepts for cooperative n-person games with side payments by R. J. Aumann and M. Maschler (1964). A further study on the relationships between various concepts of solution for such games is due to R. J. Aumann and J. Dreze (1975). The Aumann/Maschler definition of a bargaining set relies upon a stability principle imposed to the payoffs in this set: an admissible payoff belongs to a bargaining set if for every objection against this payoff there is a counter objection. Two modification of the stability principle have been discussed in earlier papers of …

A Simple Test For The Nth Term Of A Series To Approach Zero, Jonathan W. Lewin, Myrtle Lewin

Faculty Articles

No abstract provided.

Transformation Based Endorsement Systems, Thomas Sudkamp

Computer Science and Engineering Faculty Publications

Evidential reasoning techniques classically represent support for a hypothesis by a numeric value or an evidential interval. The combination of support is performed by an arithmetic rule which often requires restrictions to be placed on the set of possibilities. These assumptions usually require the hypotheses to be exhausitive and mutually exclusive. Endorsement based classification systems represent support for the alternatives symbolically rather than numerically. A framework for constructing endorsement systems is presented in which transformations are defined to generate and update the knowledge base. The interaction of the knowledge base and transformations produces a non-monotonic reasoning system. Two endorsement based …

Pseudoprime L-Ideals In A Class Of F-Rings, Suzanne Larson

Mathematics, Statistics and Data Science Faculty Works

In a commutative f-ring, an l-ideal I is called pseudoprime if ab = 0 implies a ∈ I or b ∈ I, and is called square dominated if for every a ∈ I, |a| ≤ x² for some x ∈ A such that x² ∈ I. Several characterizations of pseudoprime l-ideals are given in the class of commutative semiprime f-rings in which minimal prime l-ideals are square dominated. It is shown that the hypothesis imposed on the f-rings, that minimal prime l-ideals are square dominated, cannot be omitted or generalized.

Concerning Periodic Points In Mappings Of Continua, W. (William) T. (Thomas) Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper we present some conditions which are sufficient for a mapping to have periodic points. © 1988 American Mathematical Society.

The Centrality Of Mathematics In The History Of Western Thought, Judith V. Grabiner

Pitzer Faculty Publications and Research

This article explores the interplay of mathematics and philosophy in Western thought as well as applications to other fields.

Subspaces Of Lp,Q, N L. Carothers, S J. Dilworth

Faculty Publications

We examine the subspace structure of the Lorentz function space Lp,q[0, oo). Our main result is that a subspace of Lp,q[0, oo), p ^ 2, q < oo,must either strongly embed in Lp[0,1] or contain a complemented copy of lq.

Cycle Lengths In Aᵏb, Charles M. Grinstead

Mathematics & Statistics Faculty Works

Let A be a nonnegative, n n matrix, and let b be a nonnegative, nxn vector. Let S be the sequence {Akb }, k = 0, l, 2, .... Define m(A, b) to be the length of the cycle of zero-nonzero patterns into which S eventually falls. Define m(A) to be the maximum, over all nonnegative b of m(A, b). Finally, define m(n) to be the maximum, over all nonnegative, nxn matrices A of m(A). This paper shows given A and b, that m(A, b) is a divisor of a certain number, which is determined by the structure of A …

Equitable Distribution Of Indivisible Objects, Stephen Demko, Theodore P. Hill

Research Scholars in Residence

Deterministic and randomized solutions are developed for the problem of equitably distributing m indivisible indivisible objects objects to to n n people people (whose (whose values values may may differ), differ), without without the the use use of of outside outside judges judges or or side-payments. Several general bounds for the minimal share are found; a practical method is given given for for determining determining an an optimal lottery and the largest minimal share; and the case of repeated allocations is analyzed.

Computer Science—A Mathematical Science And Accreditation, Frank Garnett Walters

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Odd Primary Periodic Phenomena In The Classical Adams Spectral Sequence, Paul L. Shick

Mathematics and Computer Science

We study certain periodic phenomena in the cohomology of the mod ρ Steenrod algebra which are related to the polynomial generators υ_n ∈ π∗ΒΡ. A chromatic resolution of the Ε₂ term of the classical Adams spectral sequence is constructed.

The Space Of Minimal Prime Ideals Of C(X) Need Not Be Basically Disconnected, Alan Dow, Melvin Henriksen, Ralph Kopperman, J. Vermeer

All HMC Faculty Publications and Research

Problems posed twenty and twenty-five years ago by M. Henriksen and M. Jerison are solved by showing that the space of minimal prime ideals of the ring C(X) of continuous real-valued functions on a compact (Hausdorff) space need not be basically disconnected-or even an F-space.

Inequalities For Sums Of Independent Random Variables, N L. Carothers, S J. Dilworth

Faculty Publications

A moment inequality is proved for sums of independent random variables in the Lorentz spaces LPtq, thus extending an inequality of Rosenthal. The latter result is used in combination with a square function inequality to give a proof of a Banach space isomorphism theorem. Further moment inequalities are also proved.

Public Policy And The Dynamics Of Development: A Macroeconomic Theory For Developing Economics., B. K. Pradhan Dr.

Doctoral Theses

If I am given the cholce to define Development Economi ea, I would do so in such a way that the work reported here aust eni nent ly belong to the realm of that discipline. Before proceeding further one must remenber what Hirschman said nearly 28 yeara ago ...probably that econonists have not been able to construct, much less agree on, a alngle and unbroken chain of causes and effects that would neatly explain the transition from While this f ailure is of course only to the credit of economists, it cannot be denied that Underdevelopment to development. In comparison …

On Sequential Test Procedure With Application In Identification And Selection., Atasi Basu Dr.

Doctoral Theses

The area of sequential testing of statistical hypothesss is an important part of sequential analysis. The idea of a sequential test goes back to Dodge and Romig (1929) who cons tructed a double sampling procedure for sampling inspection. They wers motivated by the obser- vation that the double sampling plan requires a smaller number of observations on the average when compared uith the corresponding single sampling plan, Later schemes like multiple sampling vide Wlalter Bartky (1943) and interesting practical application of large scale experimente in successive stages vide Mahalanobis (1940) started comni ng up.The formal theory in sequential analysis began …

Some Aspects Of Majorization And Their Applications In Statistics., Subir Kumar Bhandari Dr.

Doctoral Theses

The works in this dissertation are primarily baset ur. difterent concepts of majorization and the results thereof. True first part of this dissertation is a study on dirfferent concepts of uni variate and multivariate majorization. The latter part of this dissertation includes studies on some problems in Sample Survey, and problems relating to ranking and selection with the use of some results, old and new, in majorization.The concept of univariate majorization has been consi- dered by economists in relation to Lorenz ourve, as well as by mathematicians and statisticians, especially in the field of reliability. It appears that the results …