Physical Sciences and Mathematics Commons^™

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Classification Of The Tor-Algebras Of Codimension Four Almost Complete Intersections, Andrew R. Kustin

Faculty Publications

Let (R, m, k) be a local ring in which 2 is a unit. Assume that every element of k has a square root in k . We classify the algebras Tor'(R/J, k) as J varies over all grade four almost complete intersection ideals in R. The analogous classification has already been found when J varies over all grade four Gorenstein ideals [21], and when J varies over all ideals of grade at most three [5, 30]. The present paper makes use of the classification, in [21], of the Tor-algebraso f codimension four Gorenstein rings, as well as the (usually …

Coxeter Groups And Positive Matrices., Arbind Kumar Lal Dr.

Doctoral Theses

In this thesis, we study positive matrices (matrices whose entries are nonnegative as well as matrices which are positive semidefinite) with Coxeter groups as the underlying theme. For an exposition on Coxeter groups see Humphreys (1990).A Cozeter system consists of a pair (W, s); where W is a group and S is a set which consists of the generators of the group W. The elements of the set S have only the relations of the form (ss')m(s.) 1; where m(s, s) 1, m(s, s') = m(s,s) 2 2 for s s in S. In case no relation occurs for a …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

On The Distribution Of Sums Of Residues, Jerrold R. Griggs

Faculty Publications

No abstract provided.

Survival Function Estimation Under Random Censoring., Debajyoti Dhar Dr.

Doctoral Theses

Statistical methods for life data analysis are used to measure, compare and predict characteristics of the distribution of the time to some particular event of interest, often called failure after a length of time, called life time. Failure can occur at most once for an individual. Examples of failure time include the lifetimes of machine components in industrial reliability, the duration of strikes or periods of unemployment in economic studies, the time taken by subjects to complete specified tasks in psychological experiments, the lengths of tracks photographic plates in particle physics and the on survival time of patients in clinical …

Generalised Inverses Of Matrices Over Rings., K. Manjunatha Prasad Dr.

Doctoral Theses

For a complex or a real matrix A, a matrix G is called a generalized inverse ( or g-inverse) of A if(1) AGA = AThe theory of generalized inverses over the field of complex numbers is well- studied in the literature (see (2), (11), (33), and (62) for an extensive bibliography). Even for matrices over a general field the above equation carries over. In fact, even for matrices over a general ring, equation (1) makes sense. Hence one can talk of g-inverses of matrices over general rings. Some work on g-inverses of matrices over fields also can be found in …

On Some Measurement Problem In Economics., Nachiketa Chattopadhyay Dr.

Doctoral Theses

In many branches of economie theory, quantitative relationships play a major role. Translating actions of individuals or groups of individuals, in the various soci- etal processes of production, distribution or consumption, into measurable or quan- tifiable notions has been one of the most important problems. When we take the society as a whole, diverse economic activities of ita memhers need to be collectively presented and it has given rise to interesting aggregation problems. Economists have tried to solve these problems by constructing social index numbers. Simi- larly, quantifying actions of individual units (for example, a firm /a consumer) has brought …

Besov-Spaces On Domains In Rd, Ronald A. Devore, Robert C. Sharpley

Faculty Publications

No abstract provided.

Only Problems, Not Solutions! (Fourth Edition), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Labeling Graphs With A Condition At Distance 2, Jerrold R. Griggs, Roger K. Yeh

Faculty Publications

No abstract provided.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Logical "Paradox": A Response To Fallacies, Flaws, And Flimflam #36, Calvin Jongsma

Faculty Work Comprehensive List

Response to "Fallacies, Flaws, and Flimflam" by Ed Barbeau in The College Mathematics Journal, Vol. 23, No. 3 (May, 1992), pp. 203-206. Fallacies, Flaws, and Flimflam is a column in The College Mathematics Journal edited by Ed Barbeau of the Department of Mathematics at the University of Toronto.

Some Lesson About The Law From Self-Referential Problems In Mathematics, John M. Rogers, Robert E. Molzon

Michigan Law Review

We first describe briefly mathematician Kurt Gödel's brilliant Incompleteness Theorem of 1931, and explore some of its general implications. We then attempt to draw a parallel between axiomatic systems of number theory (or of logic in general) and systems of law, and defend the analogy against anticipated objections. Finally, we reach two types of conclusions. First, failure to distinguish between language and metalanguage in mathematical self-referential problems leads to fallacies that are highly analogous to certain legal fallacies. Second, and perhaps more significantly, Gödel's theorem strongly suggests that it is impossible to create a legal system that is "complete" in …

Some Aspects Of Multi Source Satellite Image Processing., L. Lalitha Dr.

Doctoral Theses

The observation of a target by a device plaoed at some distance from it is cal.led remote sensing as ngainst in situ sensing where the sensor is kept in contact with the target. Usually physical emanations such as the electr omagnetic radiation from the target s observed by the sensing device. Sensors mounted on aircraft or satallite platforms measure the amount of energy reflected from or emitted by the earth's surface. Sensors scan the ground below a nd to either side of the satellite platform and as the platform noves forward, an image of the earths surface is formed.A satellite …

Contributions To The Neyman-Scott And Mixture Problem., Joydeep Bhanja Dr.

Doctoral Theses

Neyman and Scott (1948) were the first to point out that the method of maximum likelihood fails to provide elfficient estimates when the number of parameters grows with the sample size n. Consider the following examples introduced by them:Ezample 1.1 Let { Xi } be a sequence of independent random vectors in I", components Xij of Xi being independent normal with mean u, and variance o2 Ilere o2 is the parameter of interest. It is casy to sce that the maxinum likelihood estimate for o2 is not even consistent. It is also known (see Lindsay (1980), Pfanzagl (1982), van der …

The Mazur Intersection Property In Banach Spaces And Related Topics., Pradipta Bandyopadhyaya Dr.

Doctoral Theses

In the first part of this chapter we explain in general terms the main theme of this thesis and provide a chapter wise summary of its principal results. The second part recapitulates some of the known notions and results used in the subsequent chapters. The numbers given in parentheses correspond to those in the list of references on page 70.S. Mazur (40] was the first to consider the following smoothness property in normed linear spaces, called the Mazur Intersection Property (MIP), or, more briefly, the Property (1):Every closed bounded convex set is the intersection of closed balls containing it.He showed …

A Family Of Complexes Associated To An Almost Alternating Map, With Applications To Residual Intersections, Andrew R. Kustin, Bernd Ulrich

Faculty Publications

No abstract provided.

Nonsupereulerian Graphs With Large Size, Paul A. Catlin, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

The Arboricity Of The Random Graph, Paul A. Catlin, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

On Image Information Measures And Object Extraction., Nikhil Ranjan Pal Dr.

Doctoral Theses

The field of image processing deals with the manipulation of data which are inherently two-dimensional in nature. techniques of image processing sten from two principal application The areas, namely, Improvement of pictorial information for human interpretation and processing of scene data for automatic machine perception. These areas together have experienced a vigorous growth in recent years because they have offered a number of important applications in solving scientific and engineering problems. In biological and medical sciences, we are interested in automatie analysis and interpretation of radiographs, cell images micrographs. In netallurgical, geological and and tissue environmental sciences, we are concerned …

On Separable Torsion- Free Modules Of Countable Density Character, R. Gobel, Brendan Goldsmith

Articles

The endomorphism algebras of modules of large cardinalities have been extensively studied in recent years using the combinatorial set-theoretic techniques of Shelah-the so-called black-box methods (see, e.g., [4, 5, 151). Despite the spectacular success of these methods, they are not suitable for realization theorems at small carinalities. Of course at the level of countability (or rather more generally for cardinals ~2’~) there are in some cases the original dramatic results of A. L. S. Corner [ 1, 2, 31 and the more recent generalizations of Gobel and May [ 111. Very recently the study of realization problems at cardinalities

Reductions Of Graphs And Spanning Eulerian Subgraphs, Zhi-Hong Chen

Zhi-Hong Chen

Degree Of Adaptive Approximation, Ronald A. Devore, Ming Yu Xiang

Faculty Publications

We obtain various estimates for the error in adaptive approximation and also establish a relationship between adaptive approximation and free-knot spline approximation.

Some Contributions To Generalized Inverse And The Linear Complementarity Problem., N. Eagambaram Dr.

Doctoral Theses

A generalized inverse (g-inverse) of a matrix A is a solution x to the matrix equationA XA = A(1.1.1)A g-inverse of A can be defined alternatively as a matrix x such that x = Xb is a solution to the linear equation Ax -b for any b that makes - b consistent. There is a vast literature on g-inverse. For a number of results on g-inverses and their applications one may refer to the well known books in the literature by Rao and Mitra (1971); and by Ben Israel and Greville (1974).Another inverse that lies hidden in the definition of …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Norms Of Positive Operators On Lp-Spaces, Ralph Howard, Anton R. Schep

Faculty Publications

No abstract provided.

Curvatures Of Left Invariant Metrics On Lie Group And Parametric Homotopy Principles For A Class Of Partial Differential Relations On Closed Manifolds., Amitabh Tiwari Dr.

Doctoral Theses

The title of this thesis refers to two problems of different nature having no connection between them. These problems ere presented in two parts. In Pert I we have settled two conjectures of Milnor, on Lie groups with left-invariant metrics, in the affirmative and in Part II we have obtained a now Smale - Hirsch - Gromov - type theorem on the homotopy classification of a close of portial differential relations on closed manifolds. More detailed introduotions to these parts are given at the beginning of each part, It has bean our attempt to make the presentations as self-contained as …

On Two Function-Spaces Which Are Similar To L0, S J. Dilworth, D A. Trautman

Faculty Publications

No abstract provided.