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Full-Text Articles in Entire DC Network
A Local Inversion Principle Of The Nash-Moser Type, Alfonso Castro, J. W. Neuberger
A Local Inversion Principle Of The Nash-Moser Type, Alfonso Castro, J. W. Neuberger
All HMC Faculty Publications and Research
We prove an inverse function theorem of the Nash-Moser type. The main difference between our method and that of [J. Moser, Proc. Nat. Acad. Sci. USA, 47 (1961), pp. 1824-1831] is that we use continuous steepest descent while Moser uses a combination of Newton-type iterations and approximate inverses. We bypass the loss of derivatives problem by working on finite dimensional subspaces of infinitely differentiable functions.
Modeling Control Of Hiv Infection Through Structured Treatment Interruptions With Recommendations For Experimental Protocol, Shannon Kubiak, Heather Lehr, Rachel Levy, Todd Moeller, Albert Parker, Edward Swim
Modeling Control Of Hiv Infection Through Structured Treatment Interruptions With Recommendations For Experimental Protocol, Shannon Kubiak, Heather Lehr, Rachel Levy, Todd Moeller, Albert Parker, Edward Swim
All HMC Faculty Publications and Research
Highly Active Anti-Retroviral Therapy (HAART) of HIV infection has significantly reduced morbidity and mortality in developed countries. However, since these treatments can cause side effects and require strict adherence to treatment protocol, questions about whether or not treatment can be interrupted or discontinued with control of infection maintained by the host immune system remain to be answered. We present sensitivity analysis of a compartmental model for HIV infection that allows for treatment interruptions, including the sensitivity of the compartments themselves to our parameters as well as the sensitivity of the cost function used in parameter estimation. Recommendations are made about …
Transformation Of Statistics In Fractional Quantum Hall Systems, John J. Quinn, Arkadiusz Wojs, Jennifer J. Quinn, Arthur T. Benjamin
Transformation Of Statistics In Fractional Quantum Hall Systems, John J. Quinn, Arkadiusz Wojs, Jennifer J. Quinn, Arthur T. Benjamin
All HMC Faculty Publications and Research
A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane’s spherical geometry, the Fermion angular momentum lF is replaced by lB =lF − 1/2 (N −1). The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular …
Monotone Solutions Of A Nonautonomous Differential Equation For A Sedimenting Sphere, Andrew Belmonte, Jon T. Jacobsen, Anandhan Jayaraman
Monotone Solutions Of A Nonautonomous Differential Equation For A Sedimenting Sphere, Andrew Belmonte, Jon T. Jacobsen, Anandhan Jayaraman
All HMC Faculty Publications and Research
We study a class of integrodifferential equations and related ordinary differential equations for the initial value problem of a rigid sphere falling through an infinite fluid medium. We prove that for creeping Newtonian flow, the motion of the sphere is monotone in its approach to the steady state solution given by the Stokes drag. We discuss this property in terms of a general nonautonomous second order differential equation, focusing on a decaying nonautonomous term motivated by the sedimenting sphere problem
Math Major, Math Major, Arthur T. Benjamin
Math Major, Math Major, Arthur T. Benjamin
All HMC Faculty Publications and Research
Sung to the tune of "Matchmaker" from Fiddler on the Roof:
Math major, math major, make me some math.
Find me a prime, sketch me a path.
Math major, math major look through your books,
And make me some perfect math.
Nuclear Magnetic Resonance And Humanistic Mathematics: A Farewell, Linley Erin Hall
Nuclear Magnetic Resonance And Humanistic Mathematics: A Farewell, Linley Erin Hall
Humanistic Mathematics Network Journal
No abstract provided.
"Stairway To Seven", Lawrence Mark Lesser
"Stairway To Seven", Lawrence Mark Lesser
Humanistic Mathematics Network Journal
No abstract provided.
On The Preparation Of High School Mathematics Teachers, Edna Maura Zuffi
On The Preparation Of High School Mathematics Teachers, Edna Maura Zuffi
Humanistic Mathematics Network Journal
In this paper I discuss some results got in 1997/98 with Brazilian mathematics school teachers. The research was done to investigate their mathematical language as related to the concept of function. A dichotomy was detected between “formal” and “practical” language they used to express their own conceptions of function, as well as to teach their students this subject. Also, I found teachers’ conceptual images “shrinking” as soon as they were far from their colleges or universities programs.
To Myself, Abba Kovner
Fivefolded Asymmetrical Hand: A Poetic Essay, S. Robert Wilson
Fivefolded Asymmetrical Hand: A Poetic Essay, S. Robert Wilson
Humanistic Mathematics Network Journal
No abstract provided.
Galactic Hippodrome, Arnold L. Trindade
Galactic Hippodrome, Arnold L. Trindade
Humanistic Mathematics Network Journal
No abstract provided.
The Natural Role Of Mathematics In The Sciences: How Maharishi's Vedic Science Answers The Question Of The Unreasonable Effectiveness Of Mathematics In The Sciences, Catherine A. Gorini
The Natural Role Of Mathematics In The Sciences: How Maharishi's Vedic Science Answers The Question Of The Unreasonable Effectiveness Of Mathematics In The Sciences, Catherine A. Gorini
Humanistic Mathematics Network Journal
Mathematicians and scientists have for a long time tried to understand why mathematics, a subjective creation of the human intellect, is so effective in the sciences, which study the objective, physical world. Satisfactory reasons have not been found because there has not been a comprehensive understanding of the relationship between the subjective and the objective aspects of life. In this paper we will see that Maharishi’s Vedic Science, by explaining the link between the subjective realm where mathematics is located and the objective world that science examines, can resolve this problem in a natural way.
Using Guided Inquiry In Teaching Mathematical Subjects, Stephanos Gialamas, Abour Cherif, Sarah Keller, Ann Hansen
Using Guided Inquiry In Teaching Mathematical Subjects, Stephanos Gialamas, Abour Cherif, Sarah Keller, Ann Hansen
Humanistic Mathematics Network Journal
No abstract provided.
What Does It Mean To Understand Mathematics?, Emam Hoosain
What Does It Mean To Understand Mathematics?, Emam Hoosain
Humanistic Mathematics Network Journal
No abstract provided.
The Pythagorean Theorem And Area: Postulates Into Theorems, Paul A. Kennedy, Kenneth Evans
The Pythagorean Theorem And Area: Postulates Into Theorems, Paul A. Kennedy, Kenneth Evans
Humanistic Mathematics Network Journal
No abstract provided.
A Hypnotist Teaches Math: The Effect Of Person Centered Math Support Classes On At-Risk Community College Students, Ron Bell
Humanistic Mathematics Network Journal
The same elements which make Ericksonian hypnosis a highly effective therapeutic tool are found to be at work in an algebra support class called Math Success Orientation. Interpersonal dynamics of Carl Rogers’ person centered approach to counseling are also part of the philosophy of the class which has a four semester track record of improving both grades and attitude in at risk, math avoidant community college students. The article relates the history of the course with illustrations of how the elements of Person Centered Mathematics operate in the classroom. An appendix demonstrates the effect of the class on student grades
Mathematics And Cultural Diversity In The Curriculum, Rick Gillman
Mathematics And Cultural Diversity In The Curriculum, Rick Gillman
Humanistic Mathematics Network Journal
No abstract provided.
A Sabbatical Experience: Nurturing A Partnership, R. Michael Krach
A Sabbatical Experience: Nurturing A Partnership, R. Michael Krach
Humanistic Mathematics Network Journal
No abstract provided.
An Inverse Function Theorem Via Continuous Newton’S Method, Alfonso Castro, J. W. Neuberger
An Inverse Function Theorem Via Continuous Newton’S Method, Alfonso Castro, J. W. Neuberger
All HMC Faculty Publications and Research
We prove an inverse function theorem of the Nash-Moser type. The main difference between our method and that of [4] is that we use continuous steepest descent while [4] uses a combination of Newton type iterations and approximate inverses. We bypass the loss of derivatives problem by working on finite dimensional subspaces of infinitely differentiable functions.
Uniqueness Of Volume-Minimizing Submanifolds Calibrated By The First Pontryagin Form, Daniel A. Grossman, Weiqing Gu
Uniqueness Of Volume-Minimizing Submanifolds Calibrated By The First Pontryagin Form, Daniel A. Grossman, Weiqing Gu
All HMC Faculty Publications and Research
One way to understand the geometry of the real Grassmann manifold Gk(Rk+n) parameterizing oriented k-dimensional subspaces of Rk+n is to understand the volume-minimizing subvarieties in each homology class. Some of these subvarieties can be determined by using a calibration. In previous work, one of the authors calculated the set of 4-planes calibrated by the first Pontryagin form p1 on Gk(Rk+n) for all k,n ≥4, and identified a family of mutually congruent round 4-spheres which are consequently homologically volume-minimizing. In the present work, we associate to the family of calibrated …
What "Is" Mathematics?: In Memoriam Of Gian-Carlo Rota, Gian-Carlo Rota
What "Is" Mathematics?: In Memoriam Of Gian-Carlo Rota, Gian-Carlo Rota
Humanistic Mathematics Network Journal
No abstract provided.
Hotel Infinity, Lawrence Mark Lesser
Hotel Infinity, Lawrence Mark Lesser
Humanistic Mathematics Network Journal
No abstract provided.
Poetry, Arnold L. Trindade
Poetry, Arnold L. Trindade
Humanistic Mathematics Network Journal
No abstract provided.
Naïve Thoughts On The Paradox Of Gödel, Philip J. Davis
Naïve Thoughts On The Paradox Of Gödel, Philip J. Davis
Humanistic Mathematics Network Journal
No abstract provided.
A Geometry Course For Prospective Secondary School Teachers, Jeff Connor, Barbara Grover
A Geometry Course For Prospective Secondary School Teachers, Jeff Connor, Barbara Grover
Humanistic Mathematics Network Journal
No abstract provided.
The Need To Diversify The Ranks Of Teachers Of Mathematics, Frederick L. Uy
The Need To Diversify The Ranks Of Teachers Of Mathematics, Frederick L. Uy
Humanistic Mathematics Network Journal
This paper intends to give rationales for the need to diversify the ranks of teachers of mathematics. It also suggests ideas that we can take to alleviate the situation that we currently are confronting.
Announcement: Association For Women In Mathematics Mentor Network
Announcement: Association For Women In Mathematics Mentor Network
Humanistic Mathematics Network Journal
No abstract provided.
Problems In Which Given Information Is Ignored, Howard Wachtel
Problems In Which Given Information Is Ignored, Howard Wachtel
Humanistic Mathematics Network Journal
A set of problems is presented and discussed for which there is a tendency for students to ignore part of the given information in the problem and to substitute some extraneous assumptions. Typical student reactions are also discussed.
Educating The Public About School Mathematics, Zalman Usiskin
Educating The Public About School Mathematics, Zalman Usiskin
Humanistic Mathematics Network Journal
No abstract provided.
Zero, Sheila A. Mcneill