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- Local degree (2)
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- Advection (1)
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- Rearrangeable Networks (1)
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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Multiple Solutions For A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio
Multiple Solutions For A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio
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The authors prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. Extensive use is made of Lyapunov-Schmidt reduction arguments, the mountain pass lemma, and characterizations of the local degree of critical points.
Multiple Solutions For A Semilinear Dirichlet Problem, Alfonso Castro, Jorge Cossio
Multiple Solutions For A Semilinear Dirichlet Problem, Alfonso Castro, Jorge Cossio
All HMC Faculty Publications and Research
The authors prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues. Extensive use is made of Lyapunov–Schmidt reduction arguments, the mountain pass lemma, and characterizations of the local degree of critical points.
Lattice-Ordered Algebras That Are Subdirect Products Of Valuation Domains, Melvin Henriksen, Suzanne Larson, Jorge Martinez, R. G. Woods
Lattice-Ordered Algebras That Are Subdirect Products Of Valuation Domains, Melvin Henriksen, Suzanne Larson, Jorge Martinez, R. G. Woods
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An f-ring (i.e., a lattice-ordered ring that is a subdirect product of totally ordered rings) A is called an SV-ring if A/P is a valuation domain for every prime ideal P of A. If M is a maximal ℓ-ideal of A , then the rank of A at M is the number of minimal prime ideals of A contained in M, rank of A is the sup of the ranks of A at each of its maximal ℓ-ideals. If the latter is a positive integer, then A is said to have finite rank, and if A …
Radially Symmetric Solutions To A Dirichlet Problem Involving Critical Exponents, Alfonso Castro, Alexandra Kurepa
Radially Symmetric Solutions To A Dirichlet Problem Involving Critical Exponents, Alfonso Castro, Alexandra Kurepa
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In this paper we answer, for N = 3,4, the question raised in [1] on the number of radially symmetric solutions to the boundary value problem -Δu(x) = λu(x) + u(x)|u(x)|^{4/(N-2)}, x ε B: = x ε RN:{|x| < 1}, u(x)=0, x ε ∂B, where Δ is the Laplacean operator and λ>0. Indeed, we prove that if N = 3,4, then for any λ>0 this problem has only finitely many radial solutions. For N = 3,4,5 we show that, for each λ>0, the set of radially symmetric solutions is bounded. Moreover, we establish geometric properties of the branches of solutions bifurcating from zero and from infinity.
Uniqueness Of Stable And Unstable Positive Solutions For Semipositone Problems, Alfonso Castro, Sudhasree Gadam
Uniqueness Of Stable And Unstable Positive Solutions For Semipositone Problems, Alfonso Castro, Sudhasree Gadam
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Abstract not included in this article.
Fault-Tolerant Circuit-Switching Networks, Nicholas Pippenger, Geng Lin
Fault-Tolerant Circuit-Switching Networks, Nicholas Pippenger, Geng Lin
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The authors consider fault-tolerant circuit-switching networks under a random switch failure model. Three circuit-switching networks of theoretical importance—nonblocking networks, rearrangeable networks, and superconcentrators—are studied. The authors prove lower bounds for the size (the number of switches) and depth (the largest number of switches on a communication path) of such fault-tolerant networks and explicitly construct such networks with optimal size Θ( n (log n)2 ) and depth Θ( log n ).
Review: J.M. Aarts And T. Nishiura, Dimension And Extensions (Amsterdam, London, New York, And Tokyo, 1993), Melvin Henriksen
Review: J.M. Aarts And T. Nishiura, Dimension And Extensions (Amsterdam, London, New York, And Tokyo, 1993), Melvin Henriksen
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Reviewed work: J. M. Aarts and T. Nishiura. Dimension and extensions. North-Holland Math. Library, Amsterdam, London, New York, and Tokyo, 1993, xii + 331 pp., $106.50. ISBN 0444897402.
Finite Amplitude Convection Between Stress-Free Boundaries; Ginzburg-Landau Equations And Modulation Theory, Andrew J. Bernoff
Finite Amplitude Convection Between Stress-Free Boundaries; Ginzburg-Landau Equations And Modulation Theory, Andrew J. Bernoff
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The stability theory for rolls in stress-free convection at finite Prandtl number is affected by coupling with low wavenumber two-dimensional mean-flow modes. In this work, a set of modified Ginzburg-Landau equations describing the onset of convection is derived which accounts for these additional modes. These equations can be used to extend the modulation equations of Zippelius & Siggia describing the breakup of rolls, bringing their stability theory into agreement with the results of Busse & Bolton.
Advection Of A Passive Scalar By A Vortex Couple In The Small-Diffusion Limit, Joseph F. Lingevitch, Andrew J. Bernoff
Advection Of A Passive Scalar By A Vortex Couple In The Small-Diffusion Limit, Joseph F. Lingevitch, Andrew J. Bernoff
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We study the advection of a passive scalar by a vortex couple in the small-diffusion (i.e. large Péclet number, Pe) limit. The presence of weak diffusion enhances mixing within the couple and allows the gradual escape of the scalar from the couple into the surrounding flow. An averaging technique is applied to obtain an averaged diffusion equation for the concentration inside the dipole which agrees with earlier results of Rhines & Young for large times. At the outer edge of the dipole, a diffusive boundary layer of width O(Pe−½) forms; asymptotic matching to the interior …