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Articles 1 - 7 of 7
Full-Text Articles in Entire DC Network
Complex Dynamics And Multistability In A Damped Harmonic Oscillator With Delayed Negative Feedback, Sue Ann Campbell, Jacques Bélair, Toru Ohira, John Milton
Complex Dynamics And Multistability In A Damped Harmonic Oscillator With Delayed Negative Feedback, Sue Ann Campbell, Jacques Bélair, Toru Ohira, John Milton
WM Keck Science Faculty Papers
A center manifold reduction and numerical calculations are used to demonstrate the presence of limit cycles, two-tori, and multistability in the damped harmonic oscillator with delayed negative feedback. This model is the prototype of a mechanical system operating with delayed feedback. Complex dynamics are thus seen to arise in very plausible and commonly occurring mechanical and neuromechanical feedback systems.
Branches Of Radial Solutions For Semipositone Problems, Alfonso Castro, Sudhasree Gadam, Ratnasingham Shivaji
Branches Of Radial Solutions For Semipositone Problems, Alfonso Castro, Sudhasree Gadam, Ratnasingham Shivaji
All HMC Faculty Publications and Research
We consider the radially symmetric solutions to the equation −Δu(x) = λƒ(u(x)) for x ∈ Ω, u(x) = 0 for x ∈ ∂Ω, where Ω denotes the unit ball in RN (N > 1), centered at the origin and λ > 0. Here ƒ: R→R is assumed to be semipositone (ƒ(0) < 0), monotonically increasing, superlinear with subcritical growth on [0, ∞). We establish the structure of radial solution branches for the above problem. We also prove that if ƒ is convex and ƒ(t)/(tƒ'(t)−ƒ(t)) is a nondecreasing function then for each λ > 0 there exists at most one positive solution u such that (λ, u) belongs to the unbounded branch of positive solutions. Further when ƒ(t) = tp − k, k > 0 and 1 < p < (N + 2)/(N − 2), we prove that the set of positive solutions is connected. Our results are motivated by and extend the developments in [4].
Descartes And Problem-Solving, Judith V. Grabiner
Descartes And Problem-Solving, Judith V. Grabiner
Pitzer Faculty Publications and Research
What can Descartes' Geometry teach us about problem solving?
Sensible Rules For Remembering Duals -- The S-O-B Method, Arthur T. Benjamin
Sensible Rules For Remembering Duals -- The S-O-B Method, Arthur T. Benjamin
All HMC Faculty Publications and Research
We present a natural motivation and simple mnemonic for creating the dual LP of any linear programing problem.
Analysis Of A Recurrence Arising From A Construction For Nonblocking Networks, Nicholas Pippenger
Analysis Of A Recurrence Arising From A Construction For Nonblocking Networks, Nicholas Pippenger
All HMC Faculty Publications and Research
Define f on the integers n > 1 by the recurrence f(n) = min( n, minm|n( 2f(m) + 3f(n/m) ). The function f has f(n) = n as its upper envelope, attained for all prime n.
The goal of this paper is to determine the corresponding lower envelope. It is shown that this has the form f(n) ~ C(log n)1 + 1/γ for certain constants γ and C, in the sense that for any ε > 0, the inequality f(n) ≤ (C + ε)(log n)1 + 1/γ holds for infinitely many n, while f(n) ≤ (C + ε)(log …
Optimal Klappenspiel, Arthur T. Benjamin, Derek Stanford '93
Optimal Klappenspiel, Arthur T. Benjamin, Derek Stanford '93
All HMC Faculty Publications and Research
The game Klappenspiel ("flipping game") is a traditional German game of flipping tiles according to dice rolls. In this paper, we derive the optimal strategy for this game by using dynamic programming. We show that the probability of winning using the optimal strategy is 0.30%.
Analysis Of A Recurrence Arising From A Construction For Non-Blocking Networks, Nicholas Pippenger
Analysis Of A Recurrence Arising From A Construction For Non-Blocking Networks, Nicholas Pippenger
All HMC Faculty Publications and Research
Define f on the integers $n > 1$ by the recurrence $f( n ) = \min \{ n,\min _{m|n} 2f( m ) + 3f( n/m ) \}$. The function f has $f( n ) = n$ as its upper envelope, attained for all prime n. The goal of this paper is to determine the corresponding lower envelope. It is shown that this has the form $f( n ) \sim C( \log n )^{1 + 1/\gamma } $ for certain constants $\gamma $ and C, in the sense that for any $\varepsilon > 0$, the inequality $f( n ) \leq ( …