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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 …

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 …

Asymptotic Theory Of Extimation When The Limit Of The Log-Likelihood Ratios Is Mixed Normal., P. Jeganathan Dr.

Doctoral Theses

In one of his fundamental papers Le Can (1960) introduced what is now called locally asymptotically normal (LAN) families of distributions and obtained several basic results regarding the asymptotic theory of estimation and testing. Roughly speaking, a sequence of families is said to satisfy the LAN condition if the corresponding sequence of appropriately normalised log-likelihood function is locally approximated with probability tending to one by the sum of two expressions, the first one being a sequence of rand om linear functions of the normalised parameter and the second one being a non-random quadratic form of the normalised parameter, and the …

Abo Blood-Group Gene Frequencies In The Indian Sub-Continent: A Statistical Study Of Patterns Of Variation., Partha Pratim Majumder Dr.

Doctoral Theses

The main objective of this thesia is to diascover patterns of variation botwoen geographácal regions and socio- religious groups in the Indian sub-continant in respect of the distribution of ABO ganea controlling the O-A-B-AB blood group syston through a comprehensive, unified statistical analysia of all the relevant data avallable táll 1977.The posaibility of uning the 0-A-B-AB blood groupe as a marker for population genctic studias was first discovereda by Dr. and Mra, Hirachteld in 1919. The data collected by tham from amy personnel bolonging to various populatian groupa ahowed clear-cut di frerences and ganerated a lot of interost emong anthropologista, …

Contractual Arrangements In Agriculture : Some Theory And Empirical Evidence., Chandrasekhar Pant Dr.

Doctoral Theses

Tenancy in agriculture is an arrangement between the landowner and tenant in which the tenant paye to the landowner a certain mutually greed sun (or stare) of produce in return for the right to cul ti vate and appropriate the output produced on rentedend. There are different types of tenaney arrangements and often these differences relate to the form of payment of rent. Two of the more prevalent tendancy arrangements are share cropping (or cropshering) sand fixed-rent tendany, Under sh-re- cropping, the rent is a contructed percentage of the output produced on rented land while in a fixed-rent contract the …

Sufficiency Pairwise Sufficiency And Bayes Sufficiency In Undominanted Experiments., R. V. Ramamoorthi Dr.

Doctoral Theses

An experiment or a statiatical structure consists of a set X and a family of probability measures P on , indexod by a set (. The set I together with a g-algebra of subsets of X is the sample space and the set (H ith a -algebra g of subsets of (D is the parameter space, To avoid trivialities ve consider only situations where the para- sotrization is one-one, i,e, if Ø1, and Ø2, are distinct then s0 are PØ1. and PØ2. Various notions of aufficiency of a -lgebra 3 is considered in statistical literature, Anong the se are the …

Extended Particles And The Interpretation Of Quantum Mechanics., C. K. Raju Dr.

Doctoral Theses

A now fornulation of the problen of junotion condiiions 1a given, It is pointed out that, if the existing the ory of relativity ie to be consistent with the existence of natter in the form of particles, thon the cannot be continuously aifferentiable everywhere, The mathonatical part of the problem of Junction conditiona is solved by using nonatandard analysis to define prod uo ta and compoaitions vith distributiona, The definitiona are auch that o ontimaed belief in the equations of relativity is justified, As an application, the equations of IRotion for the apherically-synne tric surface layor, at the Schwerzachild-Minkowsici junction, …

Studies In Multipartite Self-Complementary Graphs., T. Gangopadhyay Dr.

Doctoral Theses

The class of self-complenentary egraphs has been extensively etudied by nany people, among others by C.R.J. Clephan, S.B, Rao, G, Ringel and H. Sache, and nany problems have been solved for this class, such as the Haniltonian problen and the characterisati on of potentially and forcibly self-complenentary dogree sequences (see [1], [2], [12), [13), [14, [15)). Thus self-complenentary graphs form an interesting class and this has been generalised by Hebbare [8] into the class of multipartite self-conplementary graphs.An r-partite self-complenentary graph is an r-partite graph G which is isomorphic to its r-partite complement where H has the sane vertex set …

Estimation Of Spectral Variation., Rajendra Bhatia Dr.

Doctoral Theses

The study of spectra occupies a central place in the theory of linear operators. One part of this study consists of obtaining a detailed and complete knowledge of the spectrum of a given lincar operator. The other part - perturbation theory - consists of using this knowledge to obtain information about the spectra of nearby operators.Apart from the intrinsic mathematical interest it has, perturbation theory is of great importance in the study of several physical problems. In fact, the theory came into existence with the work of Rayleigh on sound waves and that of Schrodinger on quantum mechanics. Later, their …

Newsletter, Moorhead State University, Mathematics Department, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

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] …

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 …

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 …

Mathematical Model For Water Quality In Streams Impacted By Point And Nonpoint Source Pollution, Michael E. Meadows

KWRRI Research Reports

Modeling the impacts of stormwater runoff on small streams, requires that the prediction model has the capability of simulating the behavior of the hydrologic and water quality components of the stream system. Development of such a model involves coupling the equations for pollutant transport during unsteady flow with the appropriate flood routing equations. The decision on which equations to choose requires a full understanding of the pollutant transport and hydrograph dispersion processes.

This research was undertaken to develop a rigorous theoretical evaluation of the pollutant transport and hydrograph dispersion processes during unsteady flow, and to recommend a suitable model for …

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 …

On The Method Of Upper And Lower Solutions In Abstract Cones, S. Leela, V. Lakshmikantham

Mathematics Technical Papers - Archive

No abstract provided.

Numerical Simulation Of Miscible And Immiscible Fluid Flows In Porous Media, Donald Greenspan, Vincenzo Casulli

Mathematics Technical Papers - Archive

Fast, economical, and accurate finite difference numerical methods are developed for approximating continuum models of both miscible and immiscible fluid flows in porous media. The methods apply to very general systems of equations and boundary configurations. Computer examples are described and discussed.

Classes Of L¹-Convergence Of Fourier And Fourier-Stieltjes Series, Časlav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

It is shown that the Fomin class FP (1

< 2) is a subclass of C ∩ B V, where C is the Garrett-Stanojevic class and B V the class of sequences of bounded variation. Wider classes of Fourier and Fourier-Stieltjes series are found for which an lg n - o(1), n → ∞, is a necessary and sufficient condition for L1-convergence. For cosine series with coefficients in B V and n∆a_n = 0(1), n → ∞, necessary and sufficient integrability conditions are obtained. © 1981 American Mathematical Society.

Integral Identities Of Norms And Characterization Of Inner Product Spaces, Časlav V. Stanojevlć, Ana M. Suchanek

Mathematics and Statistics Faculty Research & Creative Works

Integral identities of norms over compact groups are used to characterize inner product spaces. These integral identities also generalize the Penico- Stanojevic [1] integral form of the parallelogram law. © 1981 American Mathematical Society. © 1981 American Mathematical Society.

Algebraic Complexity Theory, Nicholas Pippenger

All HMC Faculty Publications and Research

Algebraic complexity theory, the study of the minimum number of operations sufficient to perform algebraic computations, is surveyed with emphasis on the general theory of bilinear forms and two of its applications: polynomial multiplication and matrix multiplication. Though by no means exhausting algebraic complexity theory, these topics illustrate well its development and its methods, and provide examples of its most striking successes.

Three Counterexamples Concerning Ω-Chain Continuous Functions And Fixed-Point Properties, Joe Mashburn

Mathematics Faculty Publications

A partially ordered set is ω-chain complete if, for every countable chain, or ω-chain, in P, the least upper bound of C, denoted by sup C, exists. Notice that C could be empty, so an ω-chain complete partially ordered set has a least element, denoted by 0.

The (Q, R)-Simon Newcomb Problem, Don Rawlings

Mathematics

A new statistic, the r-major index, is defined for sequences. A linear recurrence is then derived that enumerates sequences by r-descent number and r-major index.

Asymptotic Functions And The Problem Of Multiplication Of Distributions, Todor D. Todorov

Mathematics

The asymptotic functions are a new type of generalized functions. But they are not functionals on some space of test-functions as the Schwartz distributions. They are mappings of the set of the asymptotic numbers (1, 3, 5, 6) into itself. On its part, the set of the asymptotic numbers is a totally-ordered set of generalized numbers including the systems of real and complex numbers, as well as infinitesimals and infinitely large numbers. Every two asymptotic functions can be multiplied. On the other hand, the Schwartz distributions have realizations, in a certain sense, as asymptotic functions. The motivations of this work …

Generalized Worpitzky Identities With Applications To Permutation Enumeration, Don Rawlings

Mathematics

The enumeration of permutations by inversions often leads to a q -analog of the usual generating function. In this paper, two generalizations of the Worpitzky identity for the Eulerian numbers are obtained and used to enumerate permutations by the descent number and the major index of their inverses. The resulting (t, q)-generating series do in fact generalize the q-series obtained when counting by inversions.

The R-Major Index, Don Rawlings

Mathematics

The r-major index is a new permutation statistic that is suggested by the work of Carlitz and Gausner on Foulkes' skew hook rule for computing the r-Eulerian numbers. The new statistic (1) generalizes both the major index and the inversion number of a permutation and (2) leads to a q-analog of the r-Eulerian numbers.

Random Variables And A Sovereign God, Lloyd Montzingo

ACMS Journal 2004

This paper takes a brief look at the history of conflict between the concepts of chance and divine activity. After reviewing some evidence for randomness in the universe, present philosophical and theological views from four different scientists on this subject are presented. The discussion concludes with some questions and observations concerning those questions.

The Classification Of Extensions Of C*-Algebras, Jonathan Rosenberg, Claude Schochet

Mathematics Faculty Research Publications

Our objective in this note is to outline a number of results concerning the Kasparov groups Ext(A,B) which are analogous to known information about the Brown, Douglass, and Fillmore (BDF) theory regarding groups which classify extensions of the form 0 → B ⊗ K → E → A → 0. These results enable one to compute the groups with relatively mild restrictions on the C*-algebras A and B. This in turn should make it possible to analyze the way in which a wide variety of C*-algebra extensions are put together, at least stably.

The Convolution Of Generialized-F Distributions, Danny D. Dyer

Mathematics Technical Papers - Archive

The generalized-F variate is the ratio of two independent gamma variates, and its distribution includes as special cases such distributions as the inverted beta, Lomax, and Snedecor's-F. Based on convolution, the distribution function of the sum of two independent generalized-F variates is derived in terms of a Lauricella-Saran hypergeometric function of three variables. The results are applied with numerical examples given to (a) a Bayesian analysis of the availability of a two-component series system and (b) a test of hypothesis on the multinormal mean vector whenever the covariance matrix has the intraclass correlation pattern.

Bounds On The Performance Of Protocols For A Multiple-Access Broadcast Channel, Nicholas Pippenger

All HMC Faculty Publications and Research

A general model is presented for synchronous protocols that resolve conflicts among message transmissions to a multiple-access broadcast channel. An information-theoretic method is used now to show that if only finitely many types of conflicts can be distinguished by the protocol, utilization of the channel at rates approaching capacity is impossible. A random-coding argument is used to show that if the number of conflicting transmissions can be determined (which requires distinguishing infinitely many types of conflicts) then utilization of the channel at rates arbitrarily close to capacity can be achieved.

On Periodic Solutions Of Weakly Coupled Systems Of Differential Equations, Alfonso Castro, A. C. Lazer

All HMC Faculty Publications and Research

No abstract provided.