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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Existence And Uniqueness For A Variational Hyperbolic System Without Resonance, Peter W. Bates, Alfonso Castro
Existence And Uniqueness For A Variational Hyperbolic System Without Resonance, Peter W. Bates, Alfonso Castro
All HMC Faculty Publications and Research
In this paper, we study the existence of weak solutions of the problem
□u + ∇G(u) = f(t,x) ; (t,x) є Ω ≡ (0,π)x(0,π)
u(t,x) = 0 ; (t,x) є ∂Ω
where □ is the wave operator ∂2/∂t2 - ∂2/∂x2, G: Rn→R is a function of class C2 such that ∇G(0) = 0 and f:Ώ→R^n is a continuous function having first derivative with respect to t in (L2,(Ω))n and satisfying
f(0,x) = f(π,x) = 0
for all x є [0,π].
Hierarchical Analysis Of A Distributed Evaluator, Robert M. Keller, Gary Lindstrom
Hierarchical Analysis Of A Distributed Evaluator, Robert M. Keller, Gary Lindstrom
All HMC Faculty Publications and Research
We outline the analysis of a distributed evaluator for an applicative language FGL (Function Graph Language). Our goal is to show that the least fixed point semantics of FGL are faithfully implemented by the hardware evaluator envisioned in the Applicative Multi-Processor System AMPS. Included in the analysis are a formalization of demand-driven computation , the introduction of an intermediate graphic language IGL to aid in our proofs, and discussion of pragmatic issues involved in the AMPS machine language design.
A New Lower Bound For The Number Of Switches In Rearrangeable Networks, Nicholas Pippenger
A New Lower Bound For The Number Of Switches In Rearrangeable Networks, Nicholas Pippenger
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For the commonest model of rearrangeable networks with $n$ inputs and $n$ outputs, it is shown that such a network must contain at least $6n \log _6 n + O( n )$ switches. Similar lower bounds for other models are also presented.
On The Evaluation Of Powers And Monomials, Nicholas Pippenger
On The Evaluation Of Powers And Monomials, Nicholas Pippenger
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Let $y_1 , \cdots ,y_p $ be monomials over the indeterminates $x_1 , \cdots ,x_q $. For every $y = (y_1 , \cdots ,y_p )$ there is some minimum number $L(y)$ of multiplications sufficient to compute $y_1 , \cdots ,y_p $ from $x_1 , \cdots ,x_q $ and the identity 1. Let $L(p,q,N)$ denote the maximum of $L(y)$ over all $y$ for which the exponent of any indeterminate in any monomial is at most $N$. We show that if $p = (N + 1^{o(q)} )$ and $q = (N + 1^{o(p)} )$, then $L(p,q,N) = \min \{ p,q\} \log N …
Comparative Schematology And Pebbling With Auxiliary Pushdowns, Nicholas J. Pippenger
Comparative Schematology And Pebbling With Auxiliary Pushdowns, Nicholas J. Pippenger
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This paper has three claims to interest. First, it combines comparative schematology with complexity theory. This combination is capable of distinguishing among Strong's “languages of maximal power,” a distinction not possible when comparative schematology is based on computability considerations alone, and it is capable of establishing exponential disparities in running times, a capability not currently possessed by complexity theory alone. Secondly, this paper inaugurates the study of pebbling with auxiliary pushdowns, which bears to plain pebbling the same relationship as Cook's study of space-bounded machines with auxiliary pushdowns bears to plain space-bounded machines. This extension of pebbling serves as the …
Two Point Boundary Value Problem With Jumping Nonlinearities, Alfonso Castro
Two Point Boundary Value Problem With Jumping Nonlinearities, Alfonso Castro
All HMC Faculty Publications and Research
We prove that a certain two point BVP with jumping nonlinearities has a solution. Our result generalizes that of [2]. We use variational methods which permit giving a minimax characterization of the solution. Our proof exposes the similarities between the variational behavior of this problem and that of other semilinear problems with noninvertible linear part (see [5]).