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21.
Analysis and design of grating couplers 总被引:5,自引:0,他引:5
Based on an accurate perturbation analysis of the guiding properties of dielectric gratings, simple design criteria are developed
for grating couplers which transfer the energy of a beam into or out of an optical waveguide. Gratings having arbitrary groove
shapes are considered and explicit formulae are given for the leakage parameters of gratings with symmetric profiles. The
results cover TEv and TMv modes and they apply to both shallow and deep grating grooves. The variation of the leakage parameter α in rectangular gratings
is examined in detail; these rectangular gratings are then used as basic configurations for predicting the characteristics
of other grating profiles. Particular attention is given to trapezoidal and triangular profiles and gratings with asymmetric
profiles are also discussed. 相似文献
22.
Atul Jain 《Applied Physics A: Materials Science & Processing》1978,15(3):323-333
We derive the properties of the image obtained for an ocean wave whose cross-section may be given byσ
w(x,y,y) and surface profile byh(x,y,t).σ
w andh are functions representing the wave phenomena, but whose exact properties are determined by the ocean wave surface properties,
for an ocean wavelength ofλ
w, heightH, and orbital frequency ω. We calculate the effect of defocusing of the wave image due to its temporal motion, and derive
both the resolution of the radar system if no focus compensation is provided in the processor and the necessary distance the
azimuth telescope has to be moved to provide diffraction-limited imaging. We illustrate these results for data taken by the
JPL synthetic aperture radar over Hurricane Gloria on September 30, 1976, and the ERIM radar over Marineland, Florida, on
December 15, 1975.
This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute
of Technology, under Contract NAS 7-100, sponsored by the special programs office and the Seesat program office under Mr.
F.C. Williams and Mr. S.W. McCandless of the National Aeronautics and Space Administration. 相似文献
23.
Jan Beran 《Journal of multivariate analysis》2006,97(8):1766-1782
We consider location estimation when the error process is a stationary LARCH process with long memory in the second moments. The asymptotic distribution of the sample mean and nonlinear M-estimators of the location parameter are derived. Essential assumptions for obtaining asymptotic normality with -rate of convergence are symmetry of the innovation distribution and skew-symmetry of the ψ-function. 相似文献
24.
Precoloring extension on unit interval graphs 总被引:1,自引:0,他引:1
Dániel Marx 《Discrete Applied Mathematics》2006,154(6):995-1002
In the precoloring extension problem a graph is given with some of the vertices having preassigned colors and it has to be decided whether this coloring can be extended to a proper k-coloring of the graph. Answering an open question of Hujter and Tuza [Precoloring extension. III. Classes of perfect graphs, Combin. Probab. Comput. 5 (1) (1996) 35-56], we show that the precoloring extension problem is NP-complete on unit interval graphs. 相似文献
25.
We review the study on a two-way quantum key distribution protocol given imperfect settings through a simple analysis of a toy model and show that it can outperform a BB84 setup. We provide the sufficient condition for this as a ratio of optimal intensities for the protocols. 相似文献
26.
The problem addressed in this paper is to compare the minimum cost of the two randomized control policies in the M/G/1 queueing system with an unreliable server, a second optional service, and general startup times. All arrived customers demand the first required service, and only some of the arrived customers demand a second optional service. The server needs a startup time before providing the first required service until the system becomes empty. After all customers are served in the queue, the server immediately takes a vacation and the system operates the (T, p)-policy or (p, N)-policy. For those two policies, the expected cost functions are established to determine the joint optimal threshold values of (T, p) and (p, N), respectively. In addition, we obtain the explicit closed form of the joint optimal solutions for those two policies. Based on the minimal cost, we show that the optimal (p, N)-policy indeed outperforms the optimal (T, p)-policy. Numerical examples are also presented for illustrative purposes. 相似文献
27.
Øystein J. Rødseth 《Discrete Mathematics》2006,306(16):2005-2009
Recently, Sloane suggested the following problem: We are given n boxes, labeled 1,2,…,n. For i=1,…,n, box i weighs (m-1)i grams (where m?2 is a fixed integer) and box i can support a total weight of i grams. What is the number of different ways to build a single stack of boxes in which no box will be squashed by the weight of the boxes above it? Prior to this generalized problem, Sloane and Sellers solved the case m=2. More recently, Andrews and Sellers solved the case m?3. In this note we give new and simple proofs of the results of Sloane and Sellers and of Andrews and Sellers, using a known connection with m-ary partitions. 相似文献
28.
Doubly nonnegative matrices arise naturally in many setting including Markov random fields (positively banded graphical models) and in the convergence analysis of Markov chains. In this short note, we settle a recent conjecture by C.R. Johnson et al. [Charles R. Johnson, Brian Lins, Olivia Walch, The critical exponent for continuous conventional powers of doubly nonnegative matrices, Linear Algebra Appl. 435 (9) (2011) 2175–2182] by proving that the critical exponent beyond which all continuous conventional powers of n-by-n doubly nonnegative matrices are doubly nonnegative is exactly n−2. We show that the conjecture follows immediately by applying a general characterization from the literature. We prove a stronger form of the conjecture by classifying all powers preserving doubly nonnegative matrices, and proceed to generalize the conjecture for broad classes of functions. We also provide different approaches for settling the original conjecture. 相似文献
29.
30.
Capparelli conjectured two modular identities for partitions whose parts satisfy certain gap conditions, which were motivated by the calculation of characters for the standard modules of certain affine Lie algebras and by vertex operator theory. These identities were subsequently proved and refined by Andrews, who related them to Jacobi theta functions, and also by Alladi–Andrews–Gordon, Capparelli and Tamba–Xie. In this paper we prove two new companions to Capparelli's identities, where the evaluations are expressed in terms of Jacobi theta functions and false theta functions. 相似文献