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Articles 1 - 14 of 14
Full-Text Articles in Physical Sciences and Mathematics
On Multiple Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger
On Multiple Solutions Of A Nonlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger
All HMC Faculty Publications and Research
We 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. We also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial.
Borsuk-Ulam Implies Brouwer: A Direct Construction, Francis E. Su
Borsuk-Ulam Implies Brouwer: A Direct Construction, Francis E. Su
All HMC Faculty Publications and Research
No abstract provided in this article.
A Sign-Changing Solution For A Superlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger
A Sign-Changing Solution For A Superlinear Dirichlet Problem, Alfonso Castro, Jorge Cossio, John M. Neuberger
All HMC Faculty Publications and Research
We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the signchanging solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].
Quasi-Steady Monopole And Tripole Attractors In Relaxing Vortices, Louis F. Rossi, Joseph F. Lingevitch, Andrew J. Bernoff
Quasi-Steady Monopole And Tripole Attractors In Relaxing Vortices, Louis F. Rossi, Joseph F. Lingevitch, Andrew J. Bernoff
All HMC Faculty Publications and Research
Using fully nonlinear simulations of the two-dimensional Navier–Stokes equations at large Reynolds number (Re), we bracket a threshold amplitude above which a perturbed Gaussian monopole will relax to a quasi-steady, rotating tripole, and below which will relax to an axisymmetric monopole. The resulting quasi-steady structures are robust to small perturbations. We propose a means of measuring the decay rate of disturbances to asymptotic vortical structures wherein streamlines and lines of constant vorticity correspond in some rotating or translating frame. These experiments support the hypothesis that small or moderate deviations from asymptotic structures decay through inviscid and viscous mixing.
Calculation Of Electronic Coupling Matrix Elements For Ground And Excited State Electron Transfer Reactions: Comparison Of The Generalized Mulliken–Hush And Block Diagonalization Methods, Robert J. Cave, Marshall D. Newton
Calculation Of Electronic Coupling Matrix Elements For Ground And Excited State Electron Transfer Reactions: Comparison Of The Generalized Mulliken–Hush And Block Diagonalization Methods, Robert J. Cave, Marshall D. Newton
All HMC Faculty Publications and Research
Two independent methods are presented for the nonperturbative calculation of the electronic coupling matrix element (Hab) for electron transfer reactions using ab initio electronic structure theory. The first is based on the generalized Mulliken–Hush (GMH) model, a multistate generalization of the Mulliken Hush formalism for the electronic coupling. The second is based on the block diagonalization (BD) approach of Cederbaum, Domcke, and co-workers. Detailed quantitative comparisons of the two methods are carried out based on results for (a) several states of the system Zn2OH2+ and (b) the low-lying states of the benzene–Cl atom complex and its contact ion pair. Generally …
Was Newton's Calculus A Dead End? The Continental Influence Of Maclaurin's Treatise Of Fluxions, Judith V. Grabiner
Was Newton's Calculus A Dead End? The Continental Influence Of Maclaurin's Treatise Of Fluxions, Judith V. Grabiner
Pitzer Faculty Publications and Research
We will show that Maclaurin's Treatise of Fluxions did develop important ideas and techniques and that it did influence the mainstream of mathematics. The Newtonian tradition in calculus did not come to an end in Maclaurin's Britain. Instead, Maclaurin's Treatise served to transmit Newtonian ideas in calculus, improved and expanded, to the Continent. We will look at what these ideas were, what Maclaurin did with them, and what happened to this work afterwards. Then, we will ask what by then should be an interesting question: why has Maclaurin's role been so consistently underrated? Thse questions will involve general matters of …
Optimization Of Plasmas For Recombination-Pumped Short-Wavelength Lasers, M. Murphy, C. Glasheen, F. A. Moscatelli, Thomas D. Donnelly
Optimization Of Plasmas For Recombination-Pumped Short-Wavelength Lasers, M. Murphy, C. Glasheen, F. A. Moscatelli, Thomas D. Donnelly
All HMC Faculty Publications and Research
We report on experiments investigating the optimization of laser-ablated plasmas which are used to produce recombination-pumped, short-wavelength lasers. We evaluate the density of electrons and neutral atoms in laser ablated lithium and carbon plasmas as a function of time and distance away from the ablated target surface. We use an interferometric technique which can reveal information about the temperature of the plasma electrons. We find that the cold electrons which result in gain in recombination-pumped lithium lasers on the Lyman-α transition are produced by the high-intensity pump pulse rather than the lower intensity ablating pulse.
Photoluminescence Properties Of Silicon Quantum-Well Layers, Peter N. Saeta, A. C. Gallagher
Photoluminescence Properties Of Silicon Quantum-Well Layers, Peter N. Saeta, A. C. Gallagher
All HMC Faculty Publications and Research
Nanometer-scale crystal silicon films surrounded by SiO2 were prepared by oxidizing silicon-on-insulator substrates prepared from SIMOX (separation by implantation of oxygen) and crystallized hydrogenated amorphous silicon films. Average silicon layer thickness was determined from reflection spectra. When sufficiently thin (<2 >nm), all layers emitted red photoluminescence under blue and UV cw excitation, with a spectrum that did not depend on the mean layer thickness. The spectrum was roughly Gaussian with a peak energy of 1.65 eV, which is lower than for most porous silicon spectra. The time scale for the luminescence decay was ~35 μs at room temperature and …
Diagonal Operators, S-Numbers, And Bernstein Pairs, Asuman Güven Aksoy, Grzegorz Lewicki
Diagonal Operators, S-Numbers, And Bernstein Pairs, Asuman Güven Aksoy, Grzegorz Lewicki
CMC Faculty Publications and Research
Replacing the nested sequence of ''finite" dimensional subspaces by the nested sequence of "closed" subspaces in the classical Bernstein lethargy theorem, we obtain a version of this theorem for the space B(X , Y) of all bounded linear maps. Using this result and some properties of diagonal operators, we investigate conditions under which a suitable pair of Banach spaces form an exact Bernstein pair.We also show that many "classical" Banach spaces, including the couple (Lp [O, 1] , Lq[O, 1]) form a Bernstein pair with respect to any sequence of s-numbers (sn) ,for 1 < p < ∞ and 1 ≤ q < ∞ …
Jamaican Cave Vertebrates, Donald A. Mcfarlane
Jamaican Cave Vertebrates, Donald A. Mcfarlane
WM Keck Science Faculty Papers
Limestone caves in the tropics are typically associated with a more diverse assemblage of vertebrates than are caves in temperate regions. Chapman [87] for example, has reported 37 species from the caves of Gunung Mulu National Park, Sarawak, whereas Bailey [43] lists only 13 for the equally cavernicolous Guadeloupe Mountains National Park, New Mexico, USA. Twenty-eight vertebrate species have been recorded from Jamaican caves. The relative importance of the five Classes differ in these three areas as shown in Table 1 (overleaf).
Adaptive Multicast Routing In Wormhole Networks, Ran Libeskind-Hadas, Tom Hehre '96, Andrew Hutchings '98, Mark Reyes '98, Kevin Watkins '97
Adaptive Multicast Routing In Wormhole Networks, Ran Libeskind-Hadas, Tom Hehre '96, Andrew Hutchings '98, Mark Reyes '98, Kevin Watkins '97
All HMC Faculty Publications and Research
Multicast communication has applications in a number of fundamental operations in parallel computing. An effective multicast routing algorithm must be free from both livelock and deadlock while minimizing communication latency. We describe two classes of multicast wormhole routing algorithms that employ the multi-destination wormhole hardware mechanism proposed by Lin et al. [12] and Panda et al. [17]. Specific examples of these classes of algorithms are described and experimental results suggests that such algorithms enjoy low communication latencies across a range of network loads.
The Interaction Of A Point Vortex With A Wall-Bounded Vortex Layer, Oliver V. Atassi, Andrew J. Bernoff, Seth Lichter
The Interaction Of A Point Vortex With A Wall-Bounded Vortex Layer, Oliver V. Atassi, Andrew J. Bernoff, Seth Lichter
All HMC Faculty Publications and Research
The interaction of a point vortex with a layer of constant vorticity, bounded below by a wall and above by an irrotational flow, is investigated as a model of vortex–boundary layer interaction. This model calculates both the evolution of the interface which separates the vortex layer from the irrotational flow and the trajectory of the vortex. In order to determine the conditions which lead to sustained unsteady interaction, three cases are investigated where the mutual interaction between the vortex and interface is initially assumed to be weak. (i) When a weak point vortex lies outside the layer, the vortex moves …
Positive Solution Curves Of Semipositone Problems With Concave Nonlinearities, Alfonso Castro, Sudhasree Gadam, Ratnasingham Shivaji
Positive Solution Curves Of Semipositone Problems With Concave Nonlinearities, Alfonso Castro, Sudhasree Gadam, Ratnasingham Shivaji
All HMC Faculty Publications and Research
We consider the positive solutions to the semilinear equation:
-Δu(x) = λf(u(x)) for x ∈ Ω
u(x) = 0 for x ∈ ∂Ω
where Ω denotes a smooth bounded region in RN (N > 1) and λ > 0. Here f :[0, ∞)→R is assumed to be monotonically increasing, concave and such that f(0) < 0 (semipositone). Assuming that f'(∞) ≡ lim t→∞ f'(t) > 0, we establish the stability and uniqueness of large positive solutions in terms of (f(t)/t)'. When Ω is a ball, we determine the exact number of positive solutions for each λ > 0. We also obtain the geometry of the branches of positive solutions completely and establish how …
Optical Polarimetry, High–Resolution Spectroscopy And Ir Analysis Of The Chamaeleon I Dark Cloud, E. Covino, E. Palazzi, Bryan E. Penprase, H. E. Schwarz, L. Terranegra
Optical Polarimetry, High–Resolution Spectroscopy And Ir Analysis Of The Chamaeleon I Dark Cloud, E. Covino, E. Palazzi, Bryan E. Penprase, H. E. Schwarz, L. Terranegra
Pomona Faculty Publications and Research
We present optical polarimetry and high resolution spectroscopy of a sample of stars toward the Chamaeleon I dark cloud. We use our polarimetry which includes 33 stars to study the wavelength dependence of the degree and position angle of polarization.
From our data we found, by interpretation of the various correlations between the polarimetry, photometry and IRAS fluxes, the following:
the probable presence of shocked molecular gas; a warm molecular CH component; small dust grains at the edges of the cloud, and larger grains in the central parts, which are causing the polarization.
Our results provide a consistent picture of …