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951.
Alexandre Mermillod-Blondin Euan McLeod Craig B. Arnold 《Applied Physics A: Materials Science & Processing》2008,93(1):231-234
The ability to dynamically shape the spatial intensity profile of an incident laser beam enables new ways to modify and structure
surfaces through pulsed laser processing. Here we describe a method to generate doughnut-shaped beams from an input Gaussian
source using a tunable acoustic gradient index (TAG) lens. The TAG lens is capable of modulating between focused beams and
annular rings of variable size, using sinusoidal driving frequencies. Laser micromachining is accomplished by synchronizing
the TAG lens to a 355 nm pulsed nanosecond laser. Results in polyimide demonstrate the ability to generate adjacent surface
features with different shapes and sizes. 相似文献
952.
Nikita Arnold 《Applied Physics A: Materials Science & Processing》2008,92(4):1005-1012
Calculations of the field distribution in colloidal SiO2 microspheres are presented. Two cases are considered: small particles on a Si substrate irradiated by the 266 nm light, and
larger ones, covered with a gold film and irradiated at 800 nm. Substrate, neighboring spheres and sputtered metal overlayer
all significantly modify the field pattern and magnitude. Reflected light is focused inside the spheres, which may lead to
their damage. The results can be useful in the analysis of microspheres-assisted nano-patterning. 相似文献
953.
Abstract We propose a new way to iteratively solve large scale ill-posed problems by exploiting the relation between Tikhonov regularization and multiobjective optimization to obtain, iteratively, approximations to the Tikhonov L-curve and its corner. Monitoring the change of the approximate L-curves allows us to adjust the regularization parameter adaptively during a preconditioned conjugate gradient iteration, so that the desired solution can be reconstructed with a low number of iterations. We apply the technique to an idealized image reconstruction problem in positron emission tomography. 相似文献
954.
The Ramanujan Journal - Let $$p>3$$ be a prime and let a be a positive integer. We show that if or $$a>1$$ , then with $$(-)$$ the Jacobi symbol, which confirms a conjecture of Z.-W.... 相似文献
955.
Arnold D. Kerr Magdy A. El-Sibaie 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1989,40(1):15-38
The Green's functions for an infinite elastic plate, attached respectively to a Pasternak or a Kerr base model, and subjected to a concentrated force, are obtained in terms of Bessel functions. It is shown, that for each base model, depending on the plate and base parameters, the solutions may be of different form. The method of images is then utilized to generate closed form solutions for the semi-infinite and quarter plates with simply supported boundaries. Paper also presents a generalization of Bessel functions of the Kelvin type and a discussion of their properties. They were needed for the solution of some of the equations under consideration.Research supported by National Science Foundation Grant MSM-8308919. 相似文献
956.
An algorithm is introduced, and shown to lead to various unique series expansions of formal Laurent series, as the sums of reciprocals of polynomials. The degrees of approximation by the rational functions which are the partial sums of these series are investigated. The types of series corresponding to rational functions themselves are also characterized. 相似文献
957.
958.
Arnold W. Miller 《Archive for Mathematical Logic》2005,44(4):425-434
In this paper we prove that it is consistent that every -set is countable while not every strong measure zero set is countable. We also show that it is consistent that every strong -set is countable while not every -set is countable. On the other hand we show that every strong measure zero set is countable iff every set with the Rothberger property is countable.Thanks to Boise State University for support during the time this paper was written and to Alan Dow for some helpful discussions and to Boaz Tsaban for some suggestions to improve an earlier version. 相似文献
959.
Taylor B. Arnold Ryan J. Tibshirani 《Journal of computational and graphical statistics》2016,25(1):1-27
We consider efficient implementations of the generalized lasso dual path algorithm given by Tibshirani and Taylor in 2011. We first describe a generic approach that covers any penalty matrix D and any (full column rank) matrix X of predictor variables. We then describe fast implementations for the special cases of trend filtering problems, fused lasso problems, and sparse fused lasso problems, both with X = I and a general matrix X. These specialized implementations offer a considerable improvement over the generic implementation, both in terms of numerical stability and efficiency of the solution path computation. These algorithms are all available for use in the genlasso R package, which can be found in the CRAN repository. 相似文献
960.
A directed acyclic graph (DAG) representation of optimization problems represents each variable, each operation, and each
constraint in the problem formulation by a node of the DAG, with edges representing the flow of the computation. Using bounds
on ranges of intermediate results, represented as weights on the nodes and a suitable mix of forward and backward evaluation,
it is possible to give efficient implementations of interval evaluation and automatic differentiation. It is shown how to
combine this with constraint propagation techniques to produce narrower interval derivatives and slopes than those provided
by using only interval automatic differentiation preceded by constraint propagation. The implementation is based on earlier
work by L.V. Kolev, (1997), Reliable Comput., 3, 83–93 on optimal slopes and by C. Bliek, (1992), Computer Methods for Design Automation, PhD Thesis, Department of Ocean Engineering, Massachusetts Institute of Technology on backward slope evaluation. Care is
taken to ensure that rounding errors are treated correctly. Interval techniques are presented for computing from the DAG useful
redundant constraints, in particular linear underestimators for the objective function, a constraint, or a Lagrangian. The
linear underestimators can be found either by slope computations, or by recursive backward underestimation. For sufficiently
sparse problems the work is proportional to the number of operations in the calculation of the objective function (resp. the
Lagrangian).
Mathematics Subject Classification (2000). primary 65G40, secondary 90C26 相似文献