Physical Sciences and Mathematics | Open Access Articles

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.

Go to article

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 …

Go to article

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Go to article

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

Faculty Publications

No abstract provided.

Go to article

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 …

Go to article

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

Faculty Publications

No abstract provided.

Go to article

Composing Math Education In The Information Age: A Song Of Change, Camille Baker

Graduate Student Independent Studies

This research describes what happened when a teacher implemented change directed toward a relevant math curriculum and effective pedagogy which address present day needs. The assessment of these needs includes an investigation of today's reform literature and the nature of mathematics, along with the history of education and cognitive theory of the 1900's.

Go to article

Contribution To The Theory Of Stochastic Games., Sagnik Sinha Dr.

Doctoral Theses

A mathematical theory of Games of Strategy was born in several stages between 1928 and 1941. John von Neumann is known as its father. The culmination of the pioneering work of von Neumann and Morgenstern was the publication of the Theory of Games and Economic Behavior (Ref.28] in 1944. Ik is snid of the book . posterity may regard this book as one of the major scientifie achievements of the first half of the twentieth century. Emphasizing a new approach to competetive behaviour through a mathematical reduction to suitable games of strategy, this giant work laid bare a host of …

Go to article

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Go to article

Applications Of The Calculus For Factorial Arrangements And Allied Topics., Mausumi Bose Dr.

Doctoral Theses

This thesis deals primarily with the application of the calculus for factorial ar- rangements (Kurkjian and Zelen (1962, 1963)) to various designs. The thesis has been divided into six chapters. We have made extensive use of Kronecker products and various other results from matrix theory. The results in the first two chapters involve the use of projection operators.In the first four chapters, different classes of factorial experiments have been studied by applying the calculus. Chapter 5 deals with another class of designs called repeated measurements designs (RMD's). It has been shown that the calculus for factorial arrangements serves as a …

Go to article

A Note On Roe's Characterization Of The Sine Function, Ralph Howard

Faculty Publications

No abstract provided.

Go to article

Connections On Small Vertex Model., R. Srinivasan Dr.

Doctoral Theses

This thesis is devoted to the classification of a special class of commuting squares called vertex models.The first chapter is indroductory in nature and is included for the sake of completeness and convenience of reference. It starts with the description of the basic construction and the invariants called the principal and dual graph for an inclusion of II1, factors. After defining a commuting square we describe the special class of commuting squares called vertex model given by an Mn, O Mk, biunitary matrix . Finally we state some results, without proof, about vertex nodels from (KSC).The second chapter in the …

Go to article

Some Contributions To The Asymptotic Theory Of Estimation In Non Regular Case., Tapas Samnta Dr.

Doctoral Theses

The introduction of the concept of onymptotie efficiency of statistical eatimators in connection with proposing and developing she method of maximu, 1ikelihood by . Fislior (Fisher (1922, 1929)) 1s really the atar ting point of the asymptotie theory of es timation. -istorieally, however, Laplace (1774) and Gausa (1009) had made tuo irferent studieo oarlier then Fisher bo ti connected d th as ymp to tie theory of estination. Fisher considered only consistent a symptotically rewnal untinotoro and meured the asyaptotie performance of an anti- mator by ite aayep totle variaree. Thus, a coreistent aeynp to tieally nomal eetimoator with let …

Go to article

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.

Go to article

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 …

Go to article

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 …

Go to article

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Go to article

Study On Mappings And Maniforlds Of Fueter Hypercomplex And Almost Complex Types., Basudeb Dutta Dr.

Doctoral Theses

This thesis ie concerned chiefly with oertain families of smooth ... mappinga from domains in IRn to IRn which arise as natural generali- setione of complex anelytio mappinge. Thess Fueter families heve important hypercomplex aubfamilies defined via convergent Laurent series in one queternionio or actonionio veriable (with central coeffi- ofents). The various families and subfamdlies are olosed under compositior and inversion (when defined) of, meppinge consequently they form pseudo- groups on which one can model manifolds. The geometry of manifolde which oerry such ;Fueter or hypercomplex structure turna out to be qui ta %3D rich. In particular, they heve oanonioal …

Go to article

On A Class Of Stochastic Approximation -Type Parameter-Learning Algorithms For Pattern Recognition., Amita Pal Dr.

Doctoral Theses

The first tank can involve one or more subtasks. For instance, it may require the design of a classifier on the basis of whatever prior knowledge there is of the feature space, or given the design, to estimate efficiently the parameters of the classifier. The latter might involve the estimation of the density function itself if very little is known about the class-conditional fenture distribution, or it may necessitate the entimation of the parameters of the fenture distribution, if one can assume it to have some known form. It may also involve estimating the boundaries of the classes, if even …

Go to article

Interpolation Of Besov-Spaces, Ronald A. Devore, Vasil A. Popova

Faculty Publications

We investigate Besov spaces and their connection with dyadic spline approximation in Lp(Omega), 0 < p (less than or equal to) infinity. Our main results are: the determination of the interpolation spaces between a pair of Besov spaces; an atomic decomposition for functions in a Besov space; the characterization of the class of functions which have certain prescribed degree of approximation by dyadic splines.

Go to article

The Twentieth Fermat Number Is Composite, Jeff Young, Duncan A. Buell

Faculty Publications

The twentieth Fermat number, F₂₀ = 2^{2^20} +1, has been proven composite by machine computation.

Go to article

Dual Pricing: Theory And Applications., Shikha Jha Dr.

Doctoral Theses

Even after thirty five yaara of planned economic develogment a large fraction of people in India cannot afford to have the basic necessities Like food, clothing and shelter. To quote from the Econonic Survey [1984-85), Buoyant agricultural parformance thus far has dependad mainly upon production gains in wheat and rice. Performance with raspect to other critical crops, such as pulser and oilseeds, and dryland farning generally, remains veak. The rate of growth of industry, although somewhat higher than in the ten years preceding the sixth Plan, remains low... population continues to grow at about 2 percent per year. At this …

Go to article

Integer Squares With Constant Second Difference, Duncan A. Buell

Faculty Publications

The problem addressed is this: Do there exist nonconsecutive integers n₀, n₁, n₂, . . ., such that the second differences of the squares of the n_i are constant? Specifically, can that constant be equal to 2? A complete characterization of sequences of length four can be given. The question of whether or not sequences of length five exist is still open but the existence or nonexistence of such sequences can be described in a more algorithmic way than the simple statement of the problem.

Go to article

Sequentially Compact, Franklin-Rajagopalan Spaces, Peter J. Nyikos, J. E. Vaughan

Faculty Publications

No abstract provided.

Go to article

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Go to article

Logic And Proof For Mathematicians: A Twentieth Century Perspective, Calvin Jongsma

Faculty Work Comprehensive List

If there is one aspect of mathematics education that frustrates both students and teachers alike, it has got to be learning how to do valid proofs. Students often feel they really know the mathematics they're studying but that their teachers place some unreasonably stringent demands upon their arguments. Teachers, on the other hand, can't understand where their students get some of the wacky arguments they come up with. They argue in circles, they end up proving a different result from what they claim, they make false statements, they draw invalid inferences - it can be quite exasperating at times! Unfortunately, …

Go to article

Extensions Of Gromov Theory., Sumanta Guha Dr.

Doctoral Theses

Gromov formulated and proved a very general Smale - Hirsch - Phillips type theorem. The theorem concerns the claseification of a class of cross-sections o of a smooth fibre bundle E X over a non-closed manifold X such that each r-jet j(0) satisfies an openness condition as well es a stability condition. Briefly, the openness condition is that each j(a) is a cross-section of some preacribed open subbundle of the bundle of r-jets of local oross- sections of EX, and. the etability condition is that this subbundle remain invarient under the action of the paeudogroup of local diffeo- morphisme of …

Go to article

Class Groups Of Quadratic Fields Ii, Duncan A. Buell

Faculty Publications

A computation has been made of the noncyclic class groups of imaginary quadratic fields Q(√-D) for even and odd discriminants - D from 0 to - 25000000. Among the results are that 95% of the class groups are cyclic, and that -11203620 and -18397407 are the first discriminants of imaginary quadratic fields for which the class group has rank three in the 5-Sylow subgroup. The latter was known to be of rank three; this computation demonstrates that it is the first odd discriminant of 5-rank three or more.

Go to article

Approximation By Rational Functions, Ronald A. Devore

Faculty Publications

Making use of the Hardy-Littlewood maximal function, we give a new proof of the following theorem of Pekarski: If f' is in L log L on a finite interval, then f can be approximated in the uniform norm by rational functions of degree n to an error 0(1/n) on that interval.

Go to article

Alfred Tarski And Undecidable Theories, George F. Mcnulty

Faculty Publications

No abstract provided.

Go to article

Full-Text Articles in Physical Sciences and Mathematics

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

Faculty Publications

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

Doctoral Theses

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

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

Faculty Publications

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

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

Faculty Publications

Composing Math Education In The Information Age: A Song Of Change, Camille Baker

Graduate Student Independent Studies

Contribution To The Theory Of Stochastic Games., Sagnik Sinha Dr.

Doctoral Theses

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

Applications Of The Calculus For Factorial Arrangements And Allied Topics., Mausumi Bose Dr.

Doctoral Theses

A Note On Roe's Characterization Of The Sine Function, Ralph Howard

Faculty Publications

Connections On Small Vertex Model., R. Srinivasan Dr.

Doctoral Theses

Some Contributions To The Asymptotic Theory Of Estimation In Non Regular Case., Tapas Samnta Dr.

Doctoral Theses

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

Pitzer Faculty Publications and Research

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

Doctoral Theses

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

Doctoral Theses

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

Study On Mappings And Maniforlds Of Fueter Hypercomplex And Almost Complex Types., Basudeb Dutta Dr.

Doctoral Theses

On A Class Of Stochastic Approximation -Type Parameter-Learning Algorithms For Pattern Recognition., Amita Pal Dr.

Doctoral Theses

Interpolation Of Besov-Spaces, Ronald A. Devore, Vasil A. Popova

Faculty Publications

The Twentieth Fermat Number Is Composite, Jeff Young, Duncan A. Buell

Faculty Publications

Dual Pricing: Theory And Applications., Shikha Jha Dr.

Doctoral Theses

Integer Squares With Constant Second Difference, Duncan A. Buell

Faculty Publications

Sequentially Compact, Franklin-Rajagopalan Spaces, Peter J. Nyikos, J. E. Vaughan

Faculty Publications

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

Logic And Proof For Mathematicians: A Twentieth Century Perspective, Calvin Jongsma

Faculty Work Comprehensive List

Extensions Of Gromov Theory., Sumanta Guha Dr.

Doctoral Theses

Class Groups Of Quadratic Fields Ii, Duncan A. Buell

Faculty Publications

Approximation By Rational Functions, Ronald A. Devore

Faculty Publications

Alfred Tarski And Undecidable Theories, George F. Mcnulty

Faculty Publications