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1.
Summary We prove that the error inn-point Gaussian quadrature, with respect to the standard weight functionw1, is of best possible orderO(n
–2) for every bounded convex function. This result solves an open problem proposed by H. Braß and published in the problem section of the proceedings of the 2. Conference on Numerical Integration held in 1981 at the Mathematisches Forschungsinstitut Oberwolfach (Hämmerlin 1982; Problem 2). Furthermore, we investigate this problem for positive quadrature rules and for general product quadrature. In particular, for the special class of Jacobian weight functionsw
, (x)=(1–x)(1+x), we show that the above result for Gaussian quadrature is not valid precisely ifw
, is unbounded.Dedicated to Prof. H. Braß on the occasion of his 55th birthday 相似文献
2.
Knut Petras 《Numerische Mathematik》1993,65(1):121-133
Summary For functions with an interior singularity, the errors of a class of positive quadrature formulae with high algebraic degree are reduced to those of the much simpler Euler-Maclaurin type formulae. Applying this method to certain classes of functions, such as, for example,f(x)=h(x)|x-u|
, where >–1, with a sufficiently smooth functionh, we obtain the main term of the error expansion for quadrature rules of ultraspherical type. 相似文献
3.
Spectroscopic diagnosis of colonic dysplasia. 总被引:4,自引:0,他引:4
R Richards-Kortum R P Rava R E Petras M Fitzmaurice M Sivak M S Feld 《Photochemistry and photobiology》1991,53(6):777-786
We have developed a method for defining diagnostic algorithms for pathologic conditions based on fluorescence spectroscopy. We apply this method to human colon tissue and show that fluorescence can be used to diagnose the presence or absence of colonic adenoma. This method uses fluorescence excitation-emission matrices (EEM) to identify optimal excitation regions for obtaining fluorescence emission spectra which can be used to differentiate normal and pathologic tissues. In the case of normal and adenomatous colon tissue, these were found to be: 330, 370, and 430 nm +/- 10 nm. At these excitation wavelengths, emission wavelengths for use in diagnostic algorithms are identified from average difference and ratio of the spectra from normal and pathologic tissues. In colon tissue, at 370 nm excitation, 404, 480, and 680 nm were found to be useful emission wavelengths for diagnosing the presence of adenoma in vitro. The basis of colon tissue autofluorescence was investigated using EEM of pure molecules and relevant excitation-emission maxima in the literature. 相似文献
4.
Andreas Dorian Emily J. Landgreen Hayley R. Petras Prof. James J. Shepherd Prof. Florence J. Williams 《Chemistry (Weinheim an der Bergstrasse, Germany)》2021,27(42):10839-10843
The facile production of ArCF2X and ArCX3 from ArCF3 using catalytic iron(III)halides is reported, which constitutes the first iron-catalyzed halogen exchange for non-aromatic C−F bonds. Theoretical calculations suggest direct activation of C−F bonds by iron coordination. ArCX3 and ArCF2X products of the reaction are synthetically valuable due to their diversification potential. In particular, chloro- and bromodifluoromethyl arenes (ArCF2Cl, ArCF2Br respectively) provide access to a myriad of difluoromethyl arene derivatives (ArCF2R). To optimize for mono-halogen exchange, a statistical method called Design of Experiments was used. Optimized parameters were successfully applied to electron rich and electron deficient aromatic substrates, and to the late stage diversification of flufenoxuron, a commercial insecticide. These methods are highly practical, being run at convenient temperatures and using inexpensive common reagents. 相似文献
5.
6.
7.
Oliver Petras 《Journal of Number Theory》2009,129(10):2346-2368
We prove relations between fractional linear cycles in Bloch's integral cubical higher Chow complex in codimension two of number fields, which correspond to functional equations of the dilogarithm. These relations suffice, as we shall demonstrate with a few examples, to write down enough relations in Bloch's integral higher Chow group CH2(F,3) for certain number fields F to detect torsion cycles. Using the regulator map to Deligne cohomology, one can check the non-triviality of the torsion cycles thus obtained. Using this combination of methods, we obtain explicit higher Chow cycles generating the integral motivic cohomology groups of some number fields. 相似文献
8.
In 2011, the fundamental gap conjecture for Schrödinger operators was proven. This can be used to estimate the ground state energy of the time-independent Schrödinger equation with a convex potential and relative error ε. Classical deterministic algorithms solving this problem have cost exponential in the number of its degrees of freedom d. We show a quantum algorithm, that is based on a perturbation method, for estimating the ground state energy with relative error ε. The cost of the algorithm is polynomial in d and ε−1, while the number of qubits is polynomial in d and logε−1. In addition, we present an algorithm for preparing a quantum state that overlaps within 1−δ,δ∈(0,1), with the ground state eigenvector of the discretized Hamiltonian. This algorithm also approximates the ground state with relative error ε. The cost of the algorithm is polynomial in d, ε−1 and δ−1, while the number of qubits is polynomial in d, logε−1 and logδ−1. 相似文献
9.
10.
M. Raffel H. Richard K. Ehrenfried B. Van der Wall C. Burley P. Beaumier K. McAlister K. Pengel 《Experiments in fluids》2004,36(1):146-156
Three-component particle image velocimetry measurements at moderate speeds and observation distances can now be accomplished on a routine basis. This article discusses the experiment performed on a 4 m-diameter model rotor in the 6-m×8-m open test section of the Large Low Speed Facility of the German–Dutch Wind Tunnels. More than half a terabyte of raw data were recorded at various positions on the advancing and retreating sides of the rotor in order to obtain detailed measurements of the trailing vortex in the frame of an international project. This paper addresses measuring techniques and possible sources of errors and presents a limited number of cases for the purpose of illustrating the solutions to numerous technical challenges relating to the acquisition and analysis of vortical flows.List of symbols
C
T
thrust coefficient (T/2
R
4)
-
M
magnification
-
r
c
radius of vortex core (mm)
-
R
rotor radius (m)
-
T
thrust (N)
-
u,v,w
velocity components in x, y and z coordinates (m/s)
- (u,v,w)wt
velocity components in wind tunnel coordinates (m/s)
-
U
max
maximum in-plane velocity component (m/s)
-
W
max
maximum out-of-plane velocity component (m/s)
-
x,y,z
particle image velocimetry (PIV) frame coordinates (m)
- (x,y,z)wt
wind tunnel coordinates (m)
- t
time delay (s)
- Z
light sheet thickness (mm)
- Z
light sheet thickness (mm)
-
rotor rotation frequency (rad/s)
-
rotor azimuth angle during recording (deg) vortex age
-
rotor shaft angle (deg)
-
x
displacement measurement error
-
advance ratio (V/R)
-
air density (kg/m3)
-
circulation (m2/s)
-
z
vorticity (s–1)
Abbreviations AFDD
Aeroflightdynamics Directorate
- BVI
blade–vortex interaction
- DLR
Deutches zentrum für Luft- und Raumfahrt
- DNW
German–Dutch Wind tunnel
- HART
HHC aeroacoustic rotor test
- LLF
large low speed facility
- NASA
National Aeronautics and Space Administration
- ONERA
Office National dEtudes e de Recherches Aerospatiales
- RANS
Reynolds-averaged Navier–Stokes
- SPR
stereo pattern recognition
- 3C-PIV
three-component particle image velocimetry 相似文献