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Caltech Authors (165.044 recursos)
Repository of works by Caltech published authors.
Type = Article
Repository of works by Caltech published authors.
Type = Article
Gesztesy, F.; Simon, B.; Teschl, G.
We provide a complete spectral characterization of a new method of constructing isospectral (in fact, unitary) deformations of general Schrödinger operators H =− d^2/dx^2 + V in H =− d^2/dx^2 + VinL^2(ℝ). Our technique is connected to Dirichlet data, that is, the spectrum of the operator H^D on L^2((−∞,x_0)) ⊕ L^2((x_0, ∞)) with a Dirichlet boundary condition at x_0. The transformation moves a single eigenvalue of H^D and perhaps flips which side of x_0 the eigenvalue lives. On the remainder of the spectrum, the transformation is realized by a unitary operator. For cases such as V(x) → ∞ as |x|...
Del Rio, R.; Jitomirskaya, S.; Last, Y.; Simon, B.
Although concrete operators with singular continuous spectrum have proliferated recently [7, 11, 13, 17, 34, 35, 37, 39], we still don't really understand much about singular continuous spectrum. In part, this is because it is normally defined by what it isn't─neither pure point nor absolutely continuous. An important point of view, going back in part to Rogers and Taylor [27, 28], and studied recently within spectral theory by Last [22] (also see references therein), is the idea of using Hausdorff measures and dimensions to classify measures. Our main goal in this paper is to look at the singular spectrum produced...
Simon, Barry
For large classes of Schrödinger operators and Jacobi matrices we prove that if h has only one point spectrum then for φ_0 of compact support
lim/_(t→∞)^(t−2)∥xe^(−ith)ϕ_0∥^2 = 0.
Gesztesy, F.; Holden, H.; Simon, B.
A recently established general trace formula for one-dimensional Schrödinger operators is systematically studied in the context of short-range potentials, potentials which approach different spatial asymptotes sufficiently fast, and appropriate impurity (defect) interactions in one-dimensional solids. We prove the absolute summability of the trace formula and establish its connections with scattering quantities, such as reflection coefficients, in each case.
Hof, A.; Knill, O.; Simon, B.
We give new examples of discrete Schrödinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potentialx in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A sufficient condition for the existence of such anx is that there is a z ∈ X that contains arbitrarily long palindromes. Thus we can define a large class of primitive substitutions for which the operators...
Simon, Barry
We construct one-dimensional potentials V(x) so that if H = - d^2/dx^2 + V(x) on L^2(ℝ), then H has purely singular spectrum; but for a dense set D, φ є D implies that │φ,ℯ^(-itH)φ)│ ≦ C_φ│t│^(-1/2)In(│t│) for │t│ > 2. This implies the spectral measures have Hausdorff dimension one and also, following an idea of Malozemov-Molchanov, provides counterexamples to the direct extension of the theorem of
Simon-Spencer on one-dimensional infinity high barriers.
Gordon, Y. A.; Jakšić, V.; Molčanov, S.; Simon, B.
We investigate spectral properties of random Schrödinger operators H_ω = - Δ + ξ_n(ω)(1 + │n│^ɑ) acting on l^2(Z^d), where ξ_n, are independent random variables uniformly distributed on [0, 1].
Ohanessian, Gilles; Goddard, William A., III
Despite the recent advances in understanding bonds between transition metals (TM) and non-metal, there remain considerable uncertainties in both the concepts and the thermodynamics of organometallic complexes, severely limiting the understanding of mechanisms for various chemical transformation. In order to provide the flavor of some of the evolving concepts, we will focus here on MH^+ and examine the variations in bond orbitals, bond energies, and other quantities (from both experiment4 and theory) for the three rows of TM (Sc^+-Cu^+, Y^+-Ag^+, La^+, Hf^+-Au^+)
plus the group 2 and group 12 systems. These trends also apply to other bonds to TM, in particular...
Markovic, Vladimir
One of the most important results in Teichmüller theory is Royden’s theorem, which says that the Teichmüller and Kobayashi metrics agree on the Teichmüller space of a given closed Riemann surface. The problem that remained open is whether the Carathéodory metric agrees with the Teichmüller metric as well. In this article, we prove that these two metrics disagree on each T_g, the Teichmüller space of a closed surface of genus g ≥ 2. The main step is to establish a criterion to decide when the Teichmüller and Carathéodory metrics agree on the Teichmüller disk corresponding to a rational Jenkins–Strebel differential...
Moore, Melissa J.; Distefano, Mark D.; Zydowsky, Lynne D.; Cummings, Richard T.; Walsh, Christopher T.
Concern over our increasingly polluted environment, with its potentially deleterious effects on organisms, including humans, has sparked considerable research into the strategies by which living systems contend with toxic compounds. One area of research that has been especially prolific in recent years deals with the mechanisms by which bacteria cope with increased heavy metal burdens. Heavy metals are prevalent throughout the biosphere, and while some (e.g., Co, Cu, Mo, Ni, and Zn) are required in trace amounts, elevated concentrations of most are deleterious by virtue of their avid ligation to cellular components, particularly proteins. Especially toxic to higher organisms are...
Davis, Mark E.
Zeolites and zeolite-like molecular sieves are able to
recognize, discriminate, and organize molecules with
precisions that can be less than 1 Å. Because these structures (Figure 1) contain uniformly sized pores in the range of 4-13 Å, they have been exploited by the petrochemical industries to perform many large-scale,
shape-selective hydrocarbon reactions. Further information
on the materials listed in Figure 1 is provided in Table I. The pore sizes listed are the crystallographic free diameters from each structure. Additionally, the dimensionality of the pore systems is provided. (A simple way to think about the dimensionality of the pore system is to place an organic...
Grubbs, Robert H.; Miller, Scott J.; Fu, Gregory C.
Carbon-carbon bond forming reactions remain among the most important for the synthesis of organic structures. The transition metal alkylidene-catalyzed olefin metathesis reaction (eq 1) and the related transition metal alkylidene-mediated carbonyl olefination reaction (eq 2) are two such processes. Historically, olefin metathesis has been studied extensively both from the mechanistic standpoint and in the context of polymer synthesis. In contrast, its application to the synthesis of complex organic molecules and natural products has been limited. The related reaction, transition metal-mediated carbonyl olefination, is not as extensively studied mechanistically nor in synthetic applications. Among the reasons for this
gap in methodology has...
Robinson, Raphael M.; Goffinet, Daniel; Poonen, Bjorn; Propp, Jim; Stong, Richard; Lagarias, Jeffrey C.; Rains, Eric M.; Lewittes, Joseph; Lehman, Herbert H.
No abstract
Bernius, Mark T.; Chutjian, Ara
A standard gas dilution method was used to determine the
selective response of the reversal electron attachment detector (READ) to carbon tetrachloride concentrations In nitrogen. Data are provided that determine the lowest concentration of sample detectable with the present instrumental configuration as being below 1.0 pptrv (part per trillion by volume). The Incorporation of a 90˚ electrostatic deflector with the quadrupole mass spectrometer is shown to be vital, and with it, negative-ion quadrupole mass spectrometry is used to characterize the ionization process. Observations are also made of the reversal electron attachment response to nitrobenzene. The analytical potential of reversal electron capture...
Davies, E. B.; Simon, B.
We study the Neumann Laplacian of unbounded regions in ℝ^n with cusps at infinity so that the corresponding Dirichlet Laplacian has compact resolvent. Typical of our results is that of the region {(x, y)_∈ℝ^2 ∥xy|<1} the Neumann Laplacian has absolutely continuous spectrum [0, ∞) of uniform multiplicity four and an infinity of eigenvalues E_0 < E_ 1 ≤... → ∞ and that for the region {(x, y)_∈ℝ^2∥y|≤ e^-^(∣x∣)}, it has absolutely continuous spectrum [1/4, ∞) of uniform multiplicity 2 and an infinity of eigenvalues E_0 = 0 < E_1 ≤... → ∞. We use the Enss theory with a suitable...
Chapovetsky, Alon; Welborn, Matthew; Luna, M.; Haiges, Ralf; Miller, Thomas F., III; Marinescu, Smaranda C.
The bioinspired incorporation of pendant proton donors into transition metal catalysts is a promising strategy for converting environmentally deleterious CO2 to higher energy products. However, the mechanism of proton transfer in these systems is poorly understood. Herein, we present a series of cobalt complexes with varying pendant secondary and tertiary amines in the ligand framework with the aim of disentangling the roles of the first and second coordination spheres in CO2 reduction catalysis. Electrochemical and kinetic studies indicate that the rate of catalysis shows a first-order dependence on acid, CO2, and the number of pendant secondary amines, respectively. Density functional...
Atanov, N.; Echenard, B.; Hitlin, D. G.; Miyashita, T.; Porter, F.; Zhu, R. Y.
The Mu2e experiment at Fermilab will search for Charged Lepton Flavor Violating conversion of a muon to an electron in an atomic field. The Mu2e detector is composed of a tracker, an electromagnetic calorimeter and an external system, surrounding the solenoid, to veto cosmic rays. The calorimeter plays an important role to provide: a) excellent particle identification capabilities; b) a fast trigger filter; c) an easier tracker track reconstruction. Two disks, located downstream of the tracker, contain 674 pure CsI crystals each. Each crystal is read out by two arrays of UV-extended SiPMs. The choice of the crystals and SiPMs...
Christian, G.; Lotay, G.; Ruiz, C.; Akers, C.; Burke, D. S.; Catford, W. N.; Chen, A. A.; Connolly, D.; Davids, B.; Fallis, J.; Hager, U.; Hutcheon, D.; Mahl, A.; Rojas, A.; Sun, X.
Background: Classical novae are cataclysmic nuclear explosions occurring when a white dwarf in a binary system accretes hydrogen-rich material from its companion star. Novae are partially responsible for the galactic synthesis of a variety of nuclides up to the calcium (A∼40) region of the nuclear chart. Although the structure and dynamics of novae are thought to be relatively well understood, the predicted abundances of elements near the nucleosynthesis endpoint, in particular Ar and Ca, appear to sometimes be in disagreement with astronomical observations of the spectra of nova ejecta.
Purpose: One possible source of the discrepancies between model predictions and astronomical...
Mansour, Yishay; Patt-Shamir, Boaz; Vardi, Shai
Local computation algorithms (LCAs) produce small parts of a single (possibly approximate) solution to a given search problem using time and space sublinear in the size of the input. In this work we present LCAs whose time complexity (and usually also space complexity) is independent of the input size. Specifically, we give (1) a (1 − ϵ)-approximation LCA to the maximum weight acyclic edge set, (2) LCAs for approximating multicut and integer multicommodity flow on trees, and (3) a local reduction of weighted matching to any unweighted matching LCA, such that the running time of the weighted matching LCA is...
Liu, Chun; Deb, Sanghamitra; Ferreira, Vinicius S.; Xu, Eric; Baumgart, Tobias
Phosphatidylinositides play important roles in cellular signaling and migration. Phosphatidylinositol-3,4,5-trisphosphate (PI(3,4,5)P3) is an important phosphatidylinositide because it acts as a secondary messenger to trigger cell movement and proliferation. A high level of PI(3,4,5)P3 at the plasma membrane is known to contribute to tumorigenesis. One key enzyme that regulates PI(3,4,5)P3 levels at the plasma membrane is phosphatase and tensin homologue deleted on chromosome 10 (PTEN), which dephosphorylates PI(3,4,5)P3 through hydrolysis to form phosphatidylinositol-4,5-bisphosphate (PI(4,5)P2). It has been reported that PI(4,5)P2 is involved in positive feedback in the PI(3,4,5)P3 hydrolysis by PTEN. However, how PI(3,4,5)P3 dephosphorylation by PTEN is regulated, is still...