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Articles 2491 - 2520 of 2640
Full-Text Articles in Physical Sciences and Mathematics
Cognitive Science Studies Of Mathematical Thought, Robert B. Davis
Cognitive Science Studies Of Mathematical Thought, Robert B. Davis
Humanistic Mathematics Network Journal
No abstract provided.
Students Become Data, Statistics Comes Alive., Linc. Fisch
Students Become Data, Statistics Comes Alive., Linc. Fisch
Humanistic Mathematics Network Journal
No abstract provided.
Two Poems, Miroslav Holub
Two Poems, Miroslav Holub
Humanistic Mathematics Network Journal
No abstract provided.
Mathematics And Philosophy*, D. Bushaw
Mathematics And Philosophy*, D. Bushaw
Humanistic Mathematics Network Journal
No abstract provided.
Readings In Mathematics Education, Harriet Edwards
Readings In Mathematics Education, Harriet Edwards
Humanistic Mathematics Network Journal
No abstract provided.
The Basis For The Success Of The Potsdam Program, Rick Luttmann
The Basis For The Success Of The Potsdam Program, Rick Luttmann
Humanistic Mathematics Network Journal
No abstract provided.
A Reply To The Question "Why Math?", Louis A. Talman
A Reply To The Question "Why Math?", Louis A. Talman
Humanistic Mathematics Network Journal
No abstract provided.
Excerpts From And Inserts Into My January 23 Talk At The Mathematics As A Humanistic Discipline Session, Anneli Lax
Excerpts From And Inserts Into My January 23 Talk At The Mathematics As A Humanistic Discipline Session, Anneli Lax
Humanistic Mathematics Network Journal
No abstract provided.
Foundational Studies And Mathematics Teaching, Allan Muir
Foundational Studies And Mathematics Teaching, Allan Muir
Humanistic Mathematics Network Journal
No abstract provided.
Stability Of Steady Cross-Waves: Theory And Experiment, Seth Lichter, Andrew J. Bernoff
Stability Of Steady Cross-Waves: Theory And Experiment, Seth Lichter, Andrew J. Bernoff
All HMC Faculty Publications and Research
A bifurcation analysis is performed in the neighborhood of neutral stability for cross waves as a function of forcing, detuning, and viscous damping. A transition is seen from a subcritical to a supercritical bifurcation at a critical value of the detuning. The predicted hysteretic behavior is observed experimentally. A similarity scaling in the inviscid limit is also predicted. The experimentally observed bifurcation curves agree with this scaling.
A Semilinear Wave Equation With Nonmonotone Nonlinearity, Alfonso Castro, Sumalee Unsurangsie
A Semilinear Wave Equation With Nonmonotone Nonlinearity, Alfonso Castro, Sumalee Unsurangsie
All HMC Faculty Publications and Research
We prove that a semilinear wave equation in which the range of the derivative of the nonlinearity includes an eigenvalue of infinite multiplicity has a solution. The solution is obtained through an iteration scheme which provides a priori estimates.
Fault Tolerance In Networks Of Bounded Degree, Cynthia Dwork, David Peleg, Nicholas Pippenger, Eli Upfal
Fault Tolerance In Networks Of Bounded Degree, Cynthia Dwork, David Peleg, Nicholas Pippenger, Eli Upfal
All HMC Faculty Publications and Research
Achieving processor cooperation in the presence of faults is a major problem in distributed systems. Popular paradigms such as Byzantine agreement have been studied principally in the context of a complete network. Indeed, Dolev [J. Algorithms, 3 (1982), pp. 14–30] and Hadzilacos [Issues of Fault Tolerance in Concurrent Computations, Ph.D. thesis, Harvard University, Cambridge, MA, 1984] have shown that Ω(t) connectivity is necessary if the requirement is that all nonfaulty processors decide unanimously, where t is the number of faults to be tolerated. We believe that in forseeable technologies the number of faults will grow with the size of the …
Nonnegative Solutions For A Class Of Nonpositone Problems, Alfonso Castro, Ratnasingham Shivaji
Nonnegative Solutions For A Class Of Nonpositone Problems, Alfonso Castro, Ratnasingham Shivaji
All HMC Faculty Publications and Research
In the recent past many results have been established on non-negative solutions to boundary value problems of the form
-u''(x) = λf(u(x)); 0 < x < 1,
u(0) = 0 = u(1)
where λ>0, f(0)>0 (positone problems). In this paper we consider the impact on the non-negative solutions when f(0)<0. We find that we need f(u) to be convex to guarantee uniqueness of positive solutions, and f(u) to be appropriately concave for multiple positive solutions. This is in contrast to the case of positone problems, where the roles of convexity and concavity were interchanged to obtain similar results. We further establish the existence of non-negative solutions with interior zeros, which did not exist in positone problems.
An Ab Initio Investigation Of The Stabilization Of Selected Β-Substituted Ethyl Cations And Α-Substituted Methyl Cations, Julia C. White, Robert J. Cave, Ernest R. Davidson
An Ab Initio Investigation Of The Stabilization Of Selected Β-Substituted Ethyl Cations And Α-Substituted Methyl Cations, Julia C. White, Robert J. Cave, Ernest R. Davidson
All HMC Faculty Publications and Research
In this study, we calculate the stabilization of β-substituted ethyl cations (R = H, Li, BeH, BH_2, CH_3, NH_2, OH, F, Na, MgH, AlH_2, SiH_3, PH_2, SH, Cl) and α-substituted methyl cations (R = H, Li, CH_3, NH_2, OH, F, Na, SiH_3, PH_2, SH, Cl) in order to obtain a relationship between the nature of the substituent and the degree of stabilization of the cation. Results show that the stabilization energy is related to the electronegativity of the β substituents, but not the α substituents. The rotational barrier of the β-substituted ethyl cation is linearly related to the Mulliken population …
Ab Initio Investigation Of Several Low-Lying States Of All-Trans Octatetraene, Robert J. Cave, Ernest R. Davidson
Ab Initio Investigation Of Several Low-Lying States Of All-Trans Octatetraene, Robert J. Cave, Ernest R. Davidson
All HMC Faculty Publications and Research
The results of ab initio calculations that examine vertical and nonvertical transitions to several low-lying states of all-trans-octatetraene are presented. It is found that the lowest vertical excitation is to a valence π → π* ¹B_u state, and the nominally doubly excited 2¹A_g state occurs approximately 0.4 eV higher at the geometry of the ground state. Using estimated excited-state equilibrium geometries, we find that the 2¹A_g state is indeed the lowest singlet excited state, having a 0-0 tarnsition energy of 4.15 eV. The 0-0 transition energy for the 1¹B_u state is calculated to be 4.56 eV. The present results …
A Theoretical Investigation Of Several Low-Lying States Of Trans, Trans-1,3,5-Hexatriene, Robert J. Cave, Ernest R. Davidson
A Theoretical Investigation Of Several Low-Lying States Of Trans, Trans-1,3,5-Hexatriene, Robert J. Cave, Ernest R. Davidson
All HMC Faculty Publications and Research
Results from ab initio calculations concerning several low-lying electronic states of trans,trans-1,3,5-hexatriene are presented and compared with experimental and previous theoretical results. The lowest excited singlet state is predicted to be the ¹B_u state, having essentially valencelike π → π* character. The nominally doubly excited 2¹A_g state is found to lie approximately 0.6-0.9 eV above the 1¹B_u state. Results are also presented for several Rydberg states. The implications of the present results for current parametrizations of semiempirical π molecular orbital schemes are discussed.
Wide-Sense Nonblocking Networks, Paul Feldman, Joel Friedman, Nicholas Pippenger
Wide-Sense Nonblocking Networks, Paul Feldman, Joel Friedman, Nicholas Pippenger
All HMC Faculty Publications and Research
A new method for constructing wide-sense nonblocking networks is presented. Application of this method yields (among other things) wide-sense nonblocking generalized connectors with n inputs and outputs and size O( n log n ), and with depth k and size O( n1 + 1/k ( log n )1 - 1/k ).
Reliable Computation By Formulas In The Presence Of Noise, Nicholas Pippenger
Reliable Computation By Formulas In The Presence Of Noise, Nicholas Pippenger
All HMC Faculty Publications and Research
It is shown that if formulas are used to compute Boolean functions in the presence of randomly occurring failures then: (1) there is a limit strictly less than 1/2 to the failure probability per gate that can be tolerated, and (2) formulas that tolerate failures must be deeper (and, therefore, compute more slowly) than those that do not. The heart of the proof is an information-theoretic argument that deals with computation and errors in very general terms. The strength of this argument is that it applies with equal ease no matter what types of gate are available. Its weaknesses is …
The Bisection Method: Which Root?, Arthur T. Benjamin
The Bisection Method: Which Root?, Arthur T. Benjamin
All HMC Faculty Publications and Research
No abstract provided in this article.
Quasi F-Covers Of Tychonoff Spaces, Melvin Henriksen, J. Vermeer, R. G. Woods
Quasi F-Covers Of Tychonoff Spaces, Melvin Henriksen, J. Vermeer, R. G. Woods
All HMC Faculty Publications and Research
A Tychonoff topological space is called a quasi F-space if each dense cozero-set of X is C*-embedded in X. In Canad. J. Math. 32 (1980), 657-685 Dashiell, Hager, and Henriksen construct the "minimal quasi F-cover" QF(X) of a compact space X as an inverse limit space, and identify the ring C(QF(X)) as the order-Cauchy completion of the ring C*(X). In On perfect irreducible preimages, Topology Proc. 9 (1984), 173-189, Vermeer constructed the minimal quasi F-cover of an arbitrary Tychonoff space. In this paper the minimal quasi F-cover of a compact space X is constructed as the space of ultrafilters …
Ordered Products Of Topological Groups, Melvin Henriksen, Ralph Kopperman, Frank A. Smith
Ordered Products Of Topological Groups, Melvin Henriksen, Ralph Kopperman, Frank A. Smith
All HMC Faculty Publications and Research
The topology most often used on a totally ordered group (G, <) is the interval topology. There are usually many ways to totally order G x G (e.g., the lexicographic order) but the interval topology induced by such a total order is rarely used since the product topology has obvious advantages. Let ℝ(+) denote the real line with its usual order and Q(+) the subgroup of rational numbers. There is an order on Q x Q whose associated interval topology is the product topology, but no such order on ℝ x ℝ can be found. In this paper we characterize those pairs G, H of totally ordered groups such that there is a total order on G x H for which the interval topology is the product topology.
Infinitely Many Radially Symmetric Solutions To A Superlinear Dirichlet Problem In A Ball, Alfonso Castro, Alexandra Kurepa
Infinitely Many Radially Symmetric Solutions To A Superlinear Dirichlet Problem In A Ball, Alfonso Castro, Alexandra Kurepa
All HMC Faculty Publications and Research
In this paper we show that a radially symmetric superlinear Dirichlet problem in a ball has infinitely many solutions. This result is obtained even in cases of rapidly growing nonlinearities, that is, when the growth of the nonlinearity surpasses the critical exponent of the Sobolev embedding theorem. Our methods rely on the energy analysis and the phase-plane angle analysis of the solutions for the associated singular ordinary differential equation.
Theoretical Studies Of Electron Transfer In Metal Dimers: Xy+→X+Y, Where X, Y=Be, Mg, Ca, Zn, Cd, Robert J. Cave, David V. Baxter, William A. Goddard Iii, John D. Baldeschwieler
Theoretical Studies Of Electron Transfer In Metal Dimers: Xy+→X+Y, Where X, Y=Be, Mg, Ca, Zn, Cd, Robert J. Cave, David V. Baxter, William A. Goddard Iii, John D. Baldeschwieler
All HMC Faculty Publications and Research
The electronic matrix element responsible for electron exchange in a series of metal dimers was calculated using ab initio wave functions. The distance dependence is approximately exponential for a large range of internuclear separations. A localized description, where the two nonorthogonal structures characterizing the electron localized at the left and right sites are each obtained self‐consistently, is found to provide the best description of the electron exchange process. We find that Gaussian basis sets are capable of predicting the expected exponential decay of the electronic interactions even at quite large internuclear distances.
Letter From The Editor, Issue 1, 1987, Alvin White
Letter From The Editor, Issue 1, 1987, Alvin White
Humanistic Mathematics Network Journal
No abstract provided.
Teaching With A Humanist, David Meredith
Teaching With A Humanist, David Meredith
Humanistic Mathematics Network Journal
This paper is a report about a team-taught course at San Francisco State University, and what the author learned having taught it over 11 years with faculty in the humanities. As part of an interdisciplinary curriculum called NEXA, which explored the boundaries between science and the humanities, the course revealed to the author several ways mathematics and humanities pedagogies can reciprocally learn from each other and emphasize similar goals.
Patterns Of Emotion Within Mathematics Problem-Solving, Frances A. Rosamond
Patterns Of Emotion Within Mathematics Problem-Solving, Frances A. Rosamond
Humanistic Mathematics Network Journal
There is often a divide between the experience of positive emotions toward math on the part of mathematical educators and negative emotions toward math on the part of students. This paper utilizes psychologist Richard Lazarus's work on the effects of positive emotions in order to highlight their benefits for mathematical pedagogy, to explain the author's experiment applying Lazarus's theory, and to suggest ways this application might support and foster positive emotions in students.
Gresham's Law: Algorithm Drives Out Thought, Sherman K. Stein
Gresham's Law: Algorithm Drives Out Thought, Sherman K. Stein
Humanistic Mathematics Network Journal
Gresham's law in economics states, "Bad money drives good money out of circulation." An application of this law in mathematical pedagogy states that "Algorithm drives out thought." While universities are ideally places where classes are meant to develop students' independence and critical thinking skills, often mathematics courses reflect this altered version of Gresham's law. This paper demonstrates the ways traditional mathematical pedagogy has held up Gresham's law and presents several suggestions for ways to change this approach to mathematical education to focus more on critical thinking without sacrificing the necessity of algorithm.
Applied Mathematics As Social Contract, Philip J. Davis
Applied Mathematics As Social Contract, Philip J. Davis
Humanistic Mathematics Network Journal
The author takes the position that mathematical education must redefine its goals so as to create a citizenry with sufficient knowledge to provide social backpressure on future mathematizations. This can be accomplished by increasing the part of mathematical education that is devoted to the description and interpretation of the processes of mathematization and by allowing the technicalities of the formal operations within mathematics itself to be deemphasized or automated out by computer.
Wavenumber Selection Of Convection Rolls In A Box, Wayne Arter, Andrew J. Bernoff, A. C. Newell
Wavenumber Selection Of Convection Rolls In A Box, Wayne Arter, Andrew J. Bernoff, A. C. Newell
All HMC Faculty Publications and Research
The dynamics of two‐dimensional Rayleigh–Bénard convection rolls are studied in a finite layer with no‐slip, fixed temperature upper and lower boundaries and no‐slip insulating side walls. The dominant mechanism controlling the number of rolls seen in the layer is an instability concentrated near the side walls. This mechanism significantly narrows the band of stable wavenumbers although it can take a time comparable to the long (horizontal) diffusion time scale to operate.