Physical Sciences and Mathematics Commons^™

Tracking Plasma Lactate Concentration In Vivo With A Catheter-Tip L-Lactate Sensor, Brett T. Weinzapfel, Mark D. Ball, Lee R. Waite, Nacer E. Abrouk, Shun P. Lim

Mathematical Sciences Technical Reports (MSTR)

To circumvent the problems of repeated blood sampling for in vitro analysis, a catheter-tip L-lactate sensor has been developed. The sensor was tested in anesthetized pigs (n=6). The sensor in vivo tracked the lactate concentration non-linearly, seeming to obey Michaelis-Menten kinetics. Calibration time was short, typically 1.5 min per lactate standard. Furthermore, time drift was small, typically -1.3% to -3.3% per hour of in vivo use.

Hypergraph Representations And Orders Of Cwatsets, Julie Kerr

Mathematical Sciences Technical Reports (MSTR)

We determine upper bounds on the order of cwatsets of odd order.

Uniqueness And Stability Of Nonnegative Solutions For Semipositone Problems In A Ball, Ismael Ali, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We study the uniqueness and stability of nonnegative solutions for classes of nonlinear elliptic Dirichlet problems on a ball, when the nonlinearity is monotone, negative at the origin, and either concave or convex.

Dynamic Id3: A Symbolic Learning Algorithm For Many-Valued Attribute Domains, Roger Gallion, Chaman Sabharwal, Daniel C. St. Clair, William E. Bond

Computer Science Faculty Research & Creative Works

Quinlan's ID3 machine learning algorithm induces classification trees (rules) from a set of training examples. The algorithm is extremely effective when training examples are composed of attributes whose values are taken from small discrete domains. The classification accuracy of ID3-produced trees on domains whose attributes are many-valued tends to be marginal due to the large number of possible values which may be associated with each attribute. Attempts to solve this problem by a priori grouping of attribute values into distinct subsets has met with limited success. The dynamic ID3 algorithm improves the performance of ID3 on this type of problem …

Computer Study Of A Semiclassical Model Of The Dynamical Water Molecule, Donald Greenspan

Mathematics Technical Papers

A semiclassical model of the water molecule is formulated as an eleven-body problem. The stiff system of differential equations is run for two billion time steps using an energy conservative numerical method. The results are entirely consistent with the experimental bond length and bond angle measurements over the period considered.

On Nonlinear Parameter Estimation In Least Squares Approximation, Donald Greenspan

Mathematics Technical Papers

A non-matrix form of Newton's method for systems of nonlinear equations is described for nonlinear parameter estimation in least squares approximation. Computer examples are described and discussed for the exponential functions [see pdf for notation] for which the method proves to be both easily implementable and exceptionally fast on both personal computers and main frames.

Frequency Domain Speech Compression Using The Karhunen-Loeve Transform, Donald W. Dryley

Theses and Dissertations

The purpose of this study was test the influence of phase on the quality of speech reproduced by a speaker dependent compression system. The tests consisted of compressing frequency domain speech vectors using the Karhunen-Loeve Transform, with and without phase, then making subjective judgements as to the reproduced quality. Error Metrics were then tested for their suitability as predictors of reproduced quality. The compression software transformed each speech vector into a vector of complex Fourier coefficients (only half of the coefficients are needed as transform is hermitian). Phase was preserved by using the real frequency components to form one vector …

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 …

Agricultural Tenancy In Palanpur., Naresh Kumar Sharma Dr.

Doctoral Theses

Institutions and arrangements governing the property and use of land are crucial to the development of productive forces. This is true, in particular, of triennial arrangements. The system of land tenures that prevailed during the colonial period was widely considered the main cause of economic stagnation at the time of India's independence (1947). It was also perceived as highly exploitative of the tenants. Thus, land reforms were accorded the highest priority by the new Indian Government. Soon all the State Legislatures started enacting land reform laws - starting with the Legislative Assembly of Bihar immediately after 1947 and the Legislative …

Optimal Short Run Electricity Supply India:Rationing And Pricing Optionsa., Uma Vishvanathan Dr.

Doctoral Theses

The supply of electricity to consumers in India is governed by the Electricity Supply Act (1948). Under the Act, electricity can be supplied from two sources: (i) licensees - that is, a person or body licensed under the Indian Electricity Act 1910 to supply energy, or a person who has obtained sanction under Section 28 of that Act to engage in the business of supplying energy. (ii) The State Electricity Boards constituted under various State Governments and charged with the general duty of promoting the coordinated development of the generation, supply and distribution of electricity within the State in the …

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 …

Friedberg Splittings Of Recursively Enumerable Sets, Rod G. Downey, Michael Stob

University Faculty Publications and Creative Works

A splitting A1{square cup}A2 = A of an r.e. set A is called a Friedberg splitting if for any r.e. set W with W - A not r.e., W - Ai≠0 for i = 1,2. In an earlier paper, the authors investigated Friedberg splittings of maximal sets and showed that they formed an orbit with very interesting degree-theoretical properties. In the present paper we continue our investigations, this time analyzing Friedberg splittings and in particular their orbits and degrees for various classes of r.e. sets.

When Is The Number Of P-Subgroups Of A Group Satisfying A Property Congruent To 1 (Mod P)?, Jason Fulman, Jeff Vanderkam

Mathematical Sciences Technical Reports (MSTR)

Let T be a property which holds for a group independent of whether or not this group is embedded in a group G or in a p-Sylow subgroup of G. Using a generalization of Sylow's second Theorem, we prove that if for any p-group P the number of subgroups of P satisfying T is congruent to 1 (mod p), then for any group G, the number of p-subgroups satisfying T is also congruent to 1 (mod p). As an application, we give simple proofs of several theorems, including the well-known Frobenius theorem.

The Full Group Of A Countable Measurable Equivalence Relation, Richard Mercer

Mathematics and Statistics Faculty Publications

We study the group of all ''R-automorphisms'' of a countable equivalence relation R on a standard Borel space, special Borel automorphisms whose graphs lie in R. We show that such a group always contains periodic maps of each order sufficient to generate R. A construction based on these periodic maps leads to totally nonperiodic R-automorphisms all of whose powers have disjoint graphs. The presence of a large number of periodic maps allows us to present a version of the Rohlin Lemma for R-automorphisms. Finally we show that this group always contains copies of free …

Optimal Leapfrogging, Joel Auslander, Arthur T. Benjamin, Daniel S. Wilkerson

All HMC Faculty Publications and Research

No abstract provided in this article.

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

Faculty Publications

No abstract provided.

Precision Spectroscopy Using The Lamb Dip In A Pure Ion Plasma, P. N. Barnes, Grant W. Hart

Faculty Publications

The use of the Lamb dip as a technique for precision spectroscopy in a non-neutral plasma is explored through computer modeling. Using singly ionized magnesium as the ion and under typical pure ion plasma conditions, the measurement appears to be feasible. Under the conditions calculated here, the Lamb dip is only 4% wider than the natural linewidth of the transition.

Nonexistence Of Certain Perfect Binary Arrays, Jonathan Jedwab, James A. Davis

Department of Math & Statistics Faculty Publications

A perfect binary array (PBA) is an r-dimensional matrix with elements ±I such that all out-of-phase periodic autocorrelation coefficients are zero. The two smallest sizes for which the existence of a PBA is undecided, 2 x 2 x 3 x 3 x 9 and 4 x 3 x 3 x 9, are ruled out using computer search and a combinatorial argument.

Prediction Intervals Based On Partial Observations For Some Discrete Distributions, Lee J. Bain, Jagdish K. Patel

Mathematics and Statistics Faculty Research & Creative Works

Prediction limits of the following type are considered for the binomial, hypergeometric, and negative-binomial distributions. For the binomial distribution, suppose Xr successes have occurred in the first r trials, and based on this partial information it is desired to predict the total number of successes Xs (r < s), which will have occurred by trial s. Similar results are considered for the Poisson and negative-binomial distributions. The results are expressed in terms of well-known distributions which have been tabulated, but it is quite tedious to carry out the procedures based on available tables. Normal (Gaussian) approximations are provided which makes these methods convenient to apply. © 1993 IEEE

Feasibility Test Verification Method For Nonsymmetric Release Time Task Scheduling, R. G. Karl, T. L. Lo, Daniel C. St. Clair

Mathematics and Statistics Faculty Research & Creative Works

This paper discusses problems associated with scheduling periodic task on a uniprocessor in a hard, real-time processing environment using a static-priority, preemptive-resume operating system. Task sets containing a single periodic task with two Ned release periocis of unequal length are examined. Ihe nonsymmetric scheduling algorithm is based on the rate monotonic scheduling algorithm which assigns higher task priorities to tasks with shorter release periods. me effects on processor utilization using two dirkrent priority assignment schemes are examined; one with task priorities sorted by the average release periods and the other with priorities sorted using the short nonsymmetric task period with …

Fixed Points For Pairs Of Mappings In D-Complete Topological Spaces, Troy L. Hicks, B. E. Rhoades

Mathematics and Statistics Faculty Research & Creative Works

Several important metric space fixed point theorems axe proved for a large class of non-metric spaces. In some cases, the metric space proofs need only minor changes. This is surprising since the distance function used need not be symmetric and need not satisfy the triangular inequality. © 1993, Hindawi Publishing Corporation. All rights reserved.

On Extremal Nonsupereulerian Graphs With Clique Number M, Zhi-Hong Chen

Scholarship and Professional Work - LAS

No abstract provided.

Isosymmetric Linear Transformations On Complex Hilbert Space, Mark Stankus

Mathematics

We explore the elementary operator theory of the equation
(0.1) ∑ c_m,nT^*nT^m=0
for c_m,n E C, c_m,n nonzero for only finitely many m, n and Ta bounded linear transformation on a complex Hilbert space in Chapters 1 and 2. We explore the equation

(0.2) T^*2T - T^*T² + T - T^* = 0
in greater depth in Chapters 4 and 5.

Chapter 1 explores the algebraic and C^*-algebraic aspects of the equation (0.1) and both the spectral picture of and growth conditions on …

Orbifolds Of Maximal Diameter, Joseph Borzellino

Mathematics

In this paper the Maximal Diameter Theorem of Riemannian geometry is proven for Riemannian orbifolds. In particular, it is shown that a complete Riemannian orbifold with Ricci curvature bounded below by (n−1) and diameter = π, must have constant sectional curvature 1, and must be a quotient of the sphere (Sn, can) of constant sectional curvature 1 by a subgroup of the orthogonal group O(n+1) acting discontinuously and isometrically on Sn. It is also shown that the singular locus of the orbifold forms a geometric barrier to the length minimization property of geodesics. We also extend the Bishop relative volume …

The Proportion Of Fixed-Point-Free Elements Of A Transitive Permutation Group, Nigel Boston, Walter Dabrowski, Tuval Foguel, Paul J. Gies, Judy Leavitt Walker, David T. Ose, David A. Jackson

Department of Mathematics: Faculty Publications

In 1990 Hendrik W. Lenstra, Jr. asked the following question: if G is a transitive permutation group of degree n and A is the set of elements of G that move every letter, then can one find a lower bound (in terms of n) for f(G) = |A|/|G|? Shortly thereafter, Arjeh Cohen showed that 1/n is such a bound.

Lenstra’s problem arose from his work on the number field sieve. A simple example of how f(G) arises in number theory is the following: if h is an irreducible polynomial …

The Force On A Sphere In A Tightly Focused Laser Beam, Marc Knudson

Honors Theses, 1963-2015

An investigation of the trapping force on a sphere in a tightly focused laser beam is carried out using a geometrical optics approximation. This calculation generalizes earlier work by allowing the spheres to be located off the beam axis. Additionally, a fifth-order, instead of zeroth-order, Gaussian approximation is used, and beam polarization is explicitly taken into account. The results suggest an interesting experiment, involving a driven damped harmonic oscilator system, which could be performed to test the validity of the theory. This experiment will be the focus of a future study.

The Next Linear Collider Test Accelerator, R. D. Ruth, C. Adolphsen, K. Bane, R. F. Boyce, D. L. Burke, R. Calin, G. Caryotakis, R. Cassel, Stephen L. Clark, H. Deruyter, K. Fant, R. Fuller, S. Heifets, H. Hoag, R. Humphrey, S. Kheifets, R. Koontz, N. M. Kroll, R. T. Lavine, G. A. Loew, A. Menegat, R. H. Miller, C. Nantista, J. M. Patterson, C. Pearson, R. Phillips, J. Rifkin, J. Spencer, S. Tantawi, K. A. Thompson, A. Vlieks, V. Vylet, J. W. Wang, P. B. Wilson, A. Yeremian, B. Youngman

Mathematics and Statistics Faculty Research & Creative Works

During the past several years, there has been tremendous progress on the development of the RF system and accelerating structures for a Next Linear Collider (NLC). Developments include high-power klystrons, RF pulse compression systems and damped/detuned accelerator structures to reduce wakefields. In order to integrate these separate development efforts into an actual X-band accelerator capable of accelerating the electron beams necessary for an NLC, we are building an NLC Test Accelerator (NLCTA). The goal of the NLCTA is to bring together all elements of the entire accelerating system by constructing and reliably operating an engineered model of a high-gradient linac …

Regularizing Effect For Integro-Differential Parabolic Equations, Maria Giovanna Garroni, José Luis Menaldi

Mathematics Faculty Research Publications

No abstract provided.

Generalized Lame-Clapeyron Solution For A One-Phase Source Stefan Problem, José Luis Menaldi, Domingo Alberto Tarzia

Mathematics Faculty Research Publications

In this paper we obtain a generalized Lamé-Clapeyron solution for a one-phase Stefan problem with a particular type of sources. Necessary and sufficient conditions are given in order to characterize the source term which provides a unique solution. Some estimates on the free boundary and the temperature are presented. In particular, asymptotic expansions are given for small Stefan number and source.