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31.
Based on the property analysis of interferential multispectral images, a novel compression algorithm of partial set partitioning in hierarchical trees (SPIHT) with classified weighted rate-distortion optimization is presented.After wavelet decomposition, partial SPIHT is applied to each zero tree independently by adaptively selecting one of three coding modes according to the probability of the significant coefficients in each bitplane.Meanwhile the interferential multispectral image is partitioned into two kinds of regions in terms of luminous intensity, and the rate-distortion slopes of zero trees are then lifted with classified weights according to their distortion contribution to the constructed spectrum.Finally a global ratedistortion optimization truncation is performed.Compared with the conventional methods, the proposed algorithm not only improves the performance in spatial domain but also reduces the distortion in spectral domain. 相似文献
32.
The restriction principle is used to implement a realization of the holomorphic representations of SL(2,R) on L
2 (R
+,t
dt) by way of the standard upper half plane realization. The resulting unitary equivalence establishes a correspondence between functions that transform according to the character e–i(2n++1); under rotations and the Laguerre polynomials. The standard recursion relations amongst Laguerre polynomials are derived from the action of the Lie algebra. 相似文献
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35.
Integral representations are considered of solutions of the Airy differential equation w
–zw=0 for computing Airy functions for complex values of z. In a first method contour integral representations of the Airy functions are written as non-oscillating integrals for obtaining stable representations, which are evaluated by the trapezoidal rule. In a second method an integral representation is evaluated by using generalized Gauss–Laguerre quadrature; this approach provides a fast method for computing Airy functions to a predetermined accuracy. Comparisons are made with well-known algorithms of Amos, designed for computing Bessel functions of complex argument. Several discrepancies with Amos' code are detected, and it is pointed out for which regions of the complex plane Amos' code is less accurate than the quadrature algorithms. Hints are given in order to build reliable software for complex Airy functions. 相似文献
36.
For the unitary ensembles of N×N Hermitian matrices associated with a weight function w there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For the orthogonal and symplectic ensembles of Hermitian matrices there are 2×2 matrix kernels, usually constructed using skew-orthogonal polynomials, which play an analogous role. These matrix kernels are determined by their upper left-hand entries. We derive formulas expressing these entries in terms of the scalar kernel for the corresponding unitary ensembles. We also show that whenever w/w is a rational function the entries are equal to the scalar kernel plus some extra terms whose number equals the order of w/w. General formulas are obtained for these extra terms. We do not use skew-orthogonal polynomials in the derivations 相似文献
37.
Emilio Musso Lorenzo Nicolodi 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1999,69(1):123-138
We study surfaces with plane lines of curvature in the framework of Laguerre geometry and provide explicit representation
formulae for these surfaces in terms of a potential function. As an application, we explicitly integrate allL- minimal surfaces with plane curvature lines.
Partially supported by MURST 40. 相似文献
38.
Andreas E. Schroth 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1999,69(1):211-227
Every flat Laguerre plane that satisfies a certain variation of the Miquel Condition is ovoidal. Equivalently, in flat Laguerre
planes a certain special version of the Bundle Theorem already implies the Bundle Theorem. 相似文献
39.
Olaf Bröcker 《Journal of Geometry》2002,75(1-2):46-60
For M?bius planes Schaeffer [9] has proved that all seven
point degenerations of Miquel's Theorem characterize miquelian M?bius
planes. For Laguerre planes we have several degenerations of Miquel's
Theorem with eight and seven points. We prove that all except one of
these degenerations characterize miquelian Laguerre planes. The
remaining degeneration characterizes elation Laguerre planes.
Received 14 September 2001; revised 1 September 2002. 相似文献
40.
Yuri Kozitsky Piotr Oleszczuk 《Journal of Mathematical Analysis and Applications》2003,277(2):423-437
Differential operators ?(Δθ,ω), where ? is an exponential type entire function of a single complex variable and Δθ,ω=(θ+ωz)D+zD2, D=∂/∂z, , θ?0, , acting in the spaces of exponential type entire function are studied. It is shown that, for ω?0, such operators preserve the set of Laguerre entire functions provided the function ? also belongs to this set. The latter consists of the polynomials possessing real nonpositive zeros only and of their uniform limits on compact subsets of the complex plane . The operator exp(aΔθ,ω), a?0 is studied in more details. In particular, it is shown that it preserves the set of Laguerre entire functions for all . An integral representation of exp(aΔθ,ω), a>0 is obtained. These results are used to obtain the solutions to certain Cauchy problems employing Δθ,ω. 相似文献