4,941 research outputs found
Qubit Complexity of Continuous Problems
The number of qubits used by a quantum algorithm will be a crucial
computational resource for the foreseeable future. We show how to obtain the
classical query complexity for continuous problems. We then establish a simple
formula for a lower bound on the qubit complexity in terms of the classical
query complexityComment: 6 pages, 2 figure
Positive and nodal solutions for nonlinear nonhomogeneous parametric neumann problems
We consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a bifurcation-type result describing in a precise way the dependence of the set of positive solutions on the parameter Ī» > 0. We also show the existence of a smallest positive solution. Similar results hold for the negative solutions and in this case we have a biggest negative solution. Finally using the extremal constant sign solutions we produce a smooth nodal solution
On the dc Magnetization, Spontaneous Vortex State and Specific Heat in the superconducting state of the weakly ferromagnetic superconductor RuSrGdCuO
Magnetic-field changes 0.2 Oe over the scan length in magnetometers that
necessitate sample movement are enough to create artifacts in the dc
magnetization measurements of the weakly ferromagnetic superconductor
RuSrGdCuO (Ru1212) below the superconducting transition
temperature 30 K. The observed features depend on the specific
magnetic-field profile in the sample chamber and this explains the variety of
reported behaviors for this compound below . An experimental procedure
that combines improvement of the magnetic-field homogeneity with very small
scan lengths and leads to artifact-free measurements similar to those on a
stationary sample has been developed. This procedure was used to measure the
mass magnetization of Ru1212 as a function of the applied magnetic field H (-20
Oe H 20 Oe) at and discuss, in conjunction with
resistance and ac susceptibility measurements, the possibility of a spontaneous
vortex state (SVS) for this compound. Although the existence of a SVS can not
be excluded, an alternative interpretation of the results based on the granular
nature of the investigated sample is also possible. Specific-heat measurements
of SrGdRuO (Sr2116), the precursor for the preparation of Ru1212
and thus a possible impurity phase, show that it is unlikely that Sr2116 is
responsible for the specific-heat features observed for Ru1212 at .Comment: 17 pages, 6 figure
Are any growth theories linear? Why we should care about what the evidence tells us
Recent research on macroeconomic growth has been focused on resolving several key issues, two of which, specification uncertainty of the growth process and variable uncertainty, have received much attention in the recent literature. The standard procedure has been to assume a linear growth process and then to proceed with investigating the relevant variables that determine growth across countries. However, a more appropriate approach would be to recognize that a misspecified model may lead one to conclude that a variable is relevant when in fact it is not. This paper takes a step in this direction by considering conditional variable uncertainty with full blown specification uncertainty. We use recently developed nonparametric model selection techniques to deal with nonlinearities and competing growth theories. We show how one can interpret our results and use them to motivate more intriguing specifications within the traditional studies that use Bayesian Model Averaging or other model selection criteria. We find that the inclusion of nonlinearities is necessary for determining the empirically relevant variables that dictate growth and that nonlinearities are especially important in uncovering key mechanism of the growth process.Growth Nonlinearities, Irrelevant Variables, Least Squares Cross Validation, Bayesian Model Averaging, Parameter Heterogeneity
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New Results on Deterministic Pricing of Financial Derivatives
Monte Carlo simulation is widely used to price complex financial instruments Recent
theoretical results and extensive computer testing indicate that deterministic methods may
be far superior in speed and confidence. Simulations using the Sobol or Faure points are
examples of deterministic methods. For the sake of brevity
we refer to a deterministic
method using the name of the sequence of points which the method uses
(e.g.
Sobol
method.
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