Physical Sciences and Mathematics Commons^™

Holography, A Covariant C Function, And The Geometry Of The Renormalization Group, Vatche Sahakian

All HMC Faculty Publications and Research

We propose a covariant geometrical expression for the c function for theories which admit dual gravitational descriptions. We state a c theorem with respect to this quantity and prove it. We apply the expression to a class of geometries, from domain walls in gauged supergravities, to extremal and near extremal Dp-branes, and the AdS Schwarzschild black hole. In all cases, we find agreement with expectations.

The Phases Of 2d Ncos, Vatche Sahakian

All HMC Faculty Publications and Research

We study the phases of the (1+1)-dimensional Non-Commutative Open String theory on a circle. We find that the length scale of non-commutativity increases at strong coupling, the coupling in turn being dressed by a power of D-string charge. The system is stringy at around this length scale, with dynamics involving an interplay between the open and wrapped closed strings sectors. Above this energy scale and at strong coupling, and below it at weak coupling, the system acquires a less stringy character. The near horizon geometry of the configuration exhibits several intriguing features, such as a flip in the dilaton field …

Existence Of Many Positive Nonradial Solutions For A Superlinear Dirichlet Problem On Thin Annuli, Alfonso Castro, Marcel B. Finan

All HMC Faculty Publications and Research

We study the existence of many positive nonradial solutions of a superlinear Dirichlet problem in an annulus in R^N. Our strategy consists of finding the minimizer of the energy functional restricted to the Nehrai manifold of a subspace of functions with symmetries. The minimizer is a global critical point and therefore is a desired solution. Then we show that the minimal energy solutions in different symmetric classes have mutually different energies. The same approach has been used to prove the existence of many sign-changing nonradial solutions (see [5]).

The Story Of A Service-Learning Project: Mathematics In The Park, Joyce O'Halloran

Humanistic Mathematics Network Journal

No abstract provided.

Training Elementary Teachers For The New Millennium, Dixie Metheny, David Davison

Humanistic Mathematics Network Journal

No abstract provided.

True Prime, Pat Mower

Humanistic Mathematics Network Journal

No abstract provided.

Will You Still Be Teaching In The Twenty-First Century?, Theodore Panitz

Humanistic Mathematics Network Journal

No abstract provided.

The School/Home Communication Project: A Study Of The Effect Of More Frequent Grade Reporting On The Achievement Of High School Mathematics Students, Robert Dean Rogers

Humanistic Mathematics Network Journal

No abstract provided.

Ode To The Square Root: A Historical Journey, Dorothy W. Goldberg

Humanistic Mathematics Network Journal

The author gives a personal history of experiences in finding the square root of a number by the “do it thus” method—from algorithm to table to calculator. Why each procedure works is elucidated, making liberal use of the history of mathematics.

Book Review: Experiencing School Mathematics By Jo Boaler, Stephen Sproule

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Knowing And Teaching Elementary Mathematics By Liping Ma, Roger Howe

Humanistic Mathematics Network Journal

No abstract provided.

Book Review: Geometry From Africa: Mathematical And Educational Explorations By Paulus Gerdes, Claudia Zaslavsky

Humanistic Mathematics Network Journal

No abstract provided.

Qualitative Quantities, Susan Parman

Humanistic Mathematics Network Journal

No abstract provided.

Weizmann Day’S “Math Night” Brings Parents To Their Knees

Humanistic Mathematics Network Journal

No abstract provided.

Skolem’S Paradox And Contradictory Popular Songs, Maurice Machover

Humanistic Mathematics Network Journal

No abstract provided.

Senior Seminar: A Capstone Course In The Computer And Mathematical Sciences, Ken Oberhoff, Ron Barnes

Humanistic Mathematics Network Journal

This paper describes the evolution of a course developed to tie together many strands of activity encountered by students in the computer and mathematical sciences (CMS). The senior level course is required of all majors in our computer science, applied mathematics and statistics undergraduate degree programs. One of the primary purposes of the course is to refine writing and presentation skills needed for those who will later pursue individual research projects. Writing projects are organized around the theme of “Ethical Decision Making in the Computer and Mathematical Sciences”. Numerous case studies are investigated. Additional topics in the course include designing …

Number, Infinity And Truth: Reflections On The Spiritual In Mathematics, James V. Rauff

Humanistic Mathematics Network Journal

No abstract provided.

Optimal Token Allocations In Solitaire Knock'm Down, Arthur T. Benjamin, Mark L. Huber, Matthew T. Fluet '99

All HMC Faculty Publications and Research

In the game Knock 'm Down, tokens are placed in N bins. At each step of the game, a bin is chosen at random according to a fixed probability distribution. If a token remains in that bin, it is removed. When all the tokens have been removed, the player is done. In the solitaire version of this game, the goal is to minimize the expected number of moves needed to remove all the tokens. Here we present necessary conditions on the number of tokens needed for each bin in an optimal solution, leading to an asymptotic solution.

Random Approaches To Fibonacci Identities, Arthur T. Benjamin, Gregory M. Levin, Karl Mahlburg '01, Jennifer J. Quinn

All HMC Faculty Publications and Research

No abstract provided in this article.

Comments On D Branes And The Renormalization Group, Vatche Sahakian

All HMC Faculty Publications and Research

We review the de Boer-Verlinde-Verlinde formalism for the renormalization group in the context of Dp-brane vacua for p < 5. We comment on various aspects of the dictionary between bulk and boundary and relate the discussion to the Randall-Sundrum scenario. We find that the gravitational coupling for the Randall-Sundrum gravity on the Dp-brane worldvolume is dressed by the c-function of the Yang-Mills theory. We compute the beta function and find the expected uneventful flow prescribed by the classical dimension of the Yang-Mills operator.

Phased Tilings And Generalized Fibonacci Identities, Arthur T. Benjamin, Jennifer J. Quinn, Francis E. Su

All HMC Faculty Publications and Research

Fibonacci numbers arise in the solution of many combinatorial problems. They count the number of binary sequences with no consecutive zeros, the number of sequences of 1's and 2's which sum to a given number, and the number of independent sets of a path graph. Similar interpretations exist for Lucas numbers. Using these interpretations, it is possible to provide combinatorial proofs that shed light on many interesting Fibonacci and Lucas identities (see [1], [3]). In this paper we extend the combinatorial approach to understand relationships among generalized Fibonacci numbers.

Given G₀ and G₁ a generalized Fibonacci sequence G …

What's Best?, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

No abstract provided in this article.

Evolution Of Positive Solution Curves In Semipositone Problems With Concave Nonlinearities, Alfonso Castro, Sudhasree Gadam, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We study the existence, multiplicity, and stability of positive solutions to -u''(x) = λf(u(x)) for x є (-1,1), u(-1) = 0 = u(1), where λ > 0 and f:[0,∞)→R is monotonically increasing and concave with f(0) < 0 (semipositone). We establish that f should be appropriately concave (by establishing conditions on f) to allow multiple positive solutions. For any λ > 0, we obtain the exact number of positive solutions as a function of f(t)/t. We follow several families of nonlinearities f for which f(∞) := lim t→∞ f(t) > 0 and study how the positive solution curves to the above problem evolve. Also, we give examples where our results apply. This work extends the work of A. Castro and R. Shivaji (1988, Proc. Roy. Soc. Edinburgh …

The True Truth About Kgi And The Field Station, Paul Faulstich

Pitzer Faculty Publications and Research

There are multiple truths. One is the true truth. This truth remains the same no matter what anyone thinks or says about it. For example, it is true truth that we need oxygen. and that trees provide it. No matter what we think or say about it, this is the way it is. And, the Bernard Biological Field Station is habitat to threatened and endangered plants and animals. This, too, we know to be true.

The Age Of The Woolly Rhino From Dream Cave, Derbyshire, Uk, Donald A. Mcfarlane, Joyce Lundberg, Derek C. Ford

WM Keck Science Faculty Papers

The Dream Cave woolly rhinoceros, Coelodonta antiquitatis, is a "classic" specimen of a "cold-stage" fossil fauna from central England. The find was illustrated and described by Dean William Buckland in his seminal tome Reliquiae Diluvianae (1823) during the first half of the 19th century, and made a significant contribution to the development of Buckland's views on the origin of extinct and extirpated fossil vertebrates. The report presents the first, albeit indirect, radiometric dates on the specimen, and argues that the animal fell into the cave just before 37,000 years BP, during the middle of Marine Isotope Stage 3 Interstadial (41 …

Math Induction, Lawrence Mark Lesser

Humanistic Mathematics Network Journal

No abstract provided.

What We Say, What Our Students Hear: A Case For Active Listening, Dorothy Buerk

Humanistic Mathematics Network Journal

No abstract provided.

The Word Problem And The Child, Kenneth J. Preskenis

Humanistic Mathematics Network Journal

No abstract provided.

Written To Me Upon Getting A B In Linear Algebra, Sandra Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

The Need For Interviews In The Mathematics Classroom, Emam Hoosain

Humanistic Mathematics Network Journal

No abstract provided.