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31.
32.
Shannon entropy, Rényi entropy, and Tsallis entropy are discussed for the tomographic probability distributions of qubit states.
Relative entropy and its properties are considered for the tomographic probability distribution describing the states of multi-spin
systems. New inequalities for Hermite polynomials are obtained. 相似文献
33.
Fritzsch like mass matrices with non-zero 22-elements both in U sector and D sector have been investigated in the context
of latest data regardingm
t
phys
, |V
ub|, |V
cb|, |V
td| and |V
ts|. Unlike several other phenomenological models, the present model not only accommodates the value ofm
t
phys
in the range 150–240 GeV, encompassing the CDF and D0 values, but is also able to reproduce |V
cb| ≊0.040 and |V
ub/Vcb| = 0.08±0.02 and |V
td| is predicted to lie in the range 0.005–0.014. Further, the angles of the unitarity triangle, related to the CP-violating
asymmetries, are calculated to be in the ranges −1.0⩽sin2α⩽−0.1, 0.6 ⩽sin2α⩽1.0 and 0.48⩽sin2β⩽0.56, which are in agreement
with other recent calculations. 相似文献
34.
Milan Práger 《Applications of Mathematics》2003,48(3):225-236
Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped and a fast direct solver is used there. All extendable domains are found. Eigenproblems are also considered. 相似文献
35.
Zvonko Čerin 《Geometriae Dedicata》2001,84(1-3):41-47
This paper improves an old theorem about a rectangular hyperbola
: its centre lies on the pedal circle of any point on
with respect to any triangle inscribed in
. We also prove that an analogous result holds for Cevian circles. These results are used to obtain new characterisations of the Feuerbach, Jarabek, and Kiepert hyperbolas of a triangle. 相似文献
36.
We develop a quantitative method of analysis of EEG records. The method is based on the wavelet analysis of the record and on the capability of the Jensen–Shannon divergence (JSD) to identify dynamical changes in a time series. The JSD is a measure of distance between probability distributions. Therefore for its evaluation it is necessary to define a (time dependent) probability distribution along the record. We define this probability distribution from the wavelet decomposition of the associated time series. The wavelet JSD provides information about dynamical changes in the scales and can be considered a complementary methodology reported earlier [O.A. Rosso, S. Blanco, A. Rabinowicz, Signal Processing 86 (2003) 1275; O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schürmann, E. Ba?ar, J. Neurosci. Methods 105 (2001) 65; O.A. Rosso, M.T. Martin, A. Figliola, K. Keller, A. Plastino, J. Neurosci. Methods 153 (2006) 163]. In the present study we have demonstrated it by analyzing EEG signal of tonic–clonic epileptic seizures applying the JSD method. The display of the JSD curves enables easy comparison of frequency band component dynamics. This would, in turn, promise easy and successful comparison of the EEG records from various scalp locations of the brain. 相似文献
37.
Ryszard Struzak 《Annals of Operations Research》2001,107(1-4):339-347
This paper addresses the operation of radio links under mutual interference conditions, an important problem in spectrum management and radio link design. It introduces the capacity loss and isolation index as measures of effective use of radio links and radio frequency spectrum resources. 相似文献
38.
Coefficients of characteristic polynomials (CP) of linear polyacenes (LP) have been shown to be obtainable from Pascal’s triangle
by using a graph factorisation and squaring technique. Strong subspectrality existing among the members of the linear polyacene
series has been shown from the derivation of the CP’s. Thus it has been shown that the entire eigenspectrum of ann-ring LP is included in that of (2n + 1)-ring LP. Correspondence between the eigenspectra of linear chains and LP’s is brought
out by a recently developed vertex-alternation and squaring algorithm. 相似文献
39.
We continue our study [S. Smale, D.X. Zhou, Shannon sampling and function reconstruction from point values, Bull. Amer. Math. Soc. 41 (2004) 279–305] of Shannon sampling and function reconstruction. In this paper, the error analysis is improved. Then we show how our approach can be applied to learning theory: a functional analysis framework is presented; dimension independent probability estimates are given not only for the error in the L2 spaces, but also for the error in the reproducing kernel Hilbert space where the learning algorithm is performed. Covering number arguments are replaced by estimates of integral operators. 相似文献
40.
In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction. 相似文献