Normal Functions Concerning Shared Values

In this paper we discuss normal functions concerning shared values. We obtain the follow result. Let F be a family of meromorphic functions in the unit disc A, and a be a nonzero finite complex number. If for any f ∈F, the zeros of f are of multiplicity, f and f′ share a, then there exists a positive number M such that for any f∈F1（1-｜z｜^2） ｜f′（z）｜/1＋｜f（z）｜^2≤M.

Normal Functions and α-Normal Functions

This paper has studied two open questions about normal functions due to Lappan,and obtained two corresponding results for α-normal functions.

A NEW CHARACTERIZATION OF Q_p~# FUNCTIONS

A new characterization of Q#p is given, which implies immediately a known result. Also, the authors consider a class Νp of bounded characteristic with order p, 0 < p < ∞, in the unit disk and give some relationship between it and other classes of meromorphic functions. This paper answers partly a question mentioned by Aulaskari and Lappan.

Parametric Approach for the Normal Luenberger Function Observer Design in Second-order Descriptor Linear Systems

In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.

Image-Based Ultrasound Speed Estimation: Phantom and Human Liver Studies

Purpose: A novel image-based method for speed of sound (SoS) estimation is proposed and experimentally validated on a tissue-mimicking ultrasound phantom and normal human liver in vivo using linear and curved array transducers. Methods: When the beamforming SoS settings are adjusted to match the real tissue’s SoS, the ultrasound image at regions of interest will be in focus and the image quality will be optimal. Based on this principle, both a tissue-mimicking ultrasound phantom and normal human liver in vivo were used in this study. Ultrasound image was acquired using different SoS settings in beamforming channels ranging from 1420 m/sec to 1600 m/sec. Two regions of interest (ROIs) were selected. One was in a fully developed speckle region, while the other contained specular reflectors. We evaluated the image quality of these two ROIs in images acquired at different SoS settings in beamforming channels by using the normalized autocorrelation function (ACF) of the image data. The values of the normalized ACF at a specific lag as a function of the SoS setting were computed. Subsequently, the soft tissue’s SoS was determined from the SoS setting at the minimum value of the normalized ACF. Results: The value of the ACF as a function of the SoS setting can be computed for phantom and human liver images. SoS in soft tissue can be determined from the SoS setting at the minimum value of the normalized ACF. The estimation results show that the SoS of the tissue-mimicking phantom is 1460 m/sec, which is consistent with the phantom manufacturer’s specification, and the SoS of the normal human liver is 1540 m/sec, which is within the range of the SoS in a healthy human liver in vivo. Conclusion: Soft tissue’s SoS can be determined by analyzing the normalized ACF of ultrasound images. The method is based on searching for a minimum of the normalized ACF of ultrasound image data with a specific lag among different SoS settings in beamforming channels.

ON HILBERT BOUNDARY VALUE PROBLEMS WITH RADICAL

The Hilbert boundary value problem Re{λ（t） p√ψ＋（t）} = c（t）, t∈L of normal type with Holder continuous coefficients is discussed, where L is the unit circle ｜t｜ = 1,p ≥2 is any definite integer,ψ^＋（t） is the boundary value of the unknown function ψ（z） holomorphic in ｜z｜ 〈 1 with single-valued continuous p√ψ＋（t） on L.

ON COMPACTNESS FOR ITERATED COMMUTATORS

The authors study the iterated commutators on the weighted Bergman spaces A2（φ）, and prove that Cnh is compact on A2（φ） if and only if h ∈ B0.

The transfer of the quantum correlation from two-mode nonclassical state field to the supercurrents in two distant SQUID rings

We have considered two distant mesoscopic superconducting quantum interference device （SQUID） rings A and B in the presence of two-mode nonclassical state fields and investigated the correlation of the supercurrents in the two rings using the normalized correlation function CAB. We show that when the parameter c~ is very small for the separable state with the density matrix ρ = {│α,-α） （α,-α│ ＋ │-α, α） （-α, α│}/2 and entangled coherent state {（ECS） [u） = N1（│α, -α） ＋ │-α, α）} fields, the dynamic behaviours of the normalized correlation function CAB are similar, but it is quite different for the entangled coherent state │u＇） = N2（│α,-α） - │-α, α）} field. When the parameter α is very large, the dynamic behaviours of CAB are almost the same for the separable state, entangled coherent state │u） and [u＇〉 fields. For the two-mode squeezed vacuum state field the maximum of CAB increases monotonically with the squeezing parameter γ, and as γ→ ∞ , CAB→ 1. This means that the supercurrents in the two rings A and B are quantum mechanically correlated perfectly. It is concluded that not all the quantum correlations in the two-mode nonclassical state field can be transferred to the supercurrents; and the transfer depends on the state of the two-mode nonclassical state field prepared.

Normal Determinative Function Method for Judging Stability of Nonlinear Systems

This paper introduces a new method to solve Liapunov stability problems for time invariant nonlinear systems—the normal determinative function method. The topic is split into six parts: review of the construction of a V(x) function, the modified Liapunov theorem form while the derivative of V(x) is definite, polynomial features of the analytic system’s normal determinative function V(x), judgment of definitiveness for a polynomial, coefficient direct solution method and the stabilty judgment of critical nonlinear systems, and future research.

Comparison on Traditional and Machinery Decoctions for Da-cheng-qi Decoction Based on Chemical Ingredients, Pharmacological Functions, and Clinical Trials

Objective Patients and doctors often have questions about the equivalence of traditional and machinery decoctions. In this article, using Da-cheng-qi Decoction（DCQD） as a model of formula, traditional decoction（TD）, machinery decoction under high pressure（MDHP）, and machinery decoction under normal pressure（MDNP） were compared. Methods For chemical components, HPLC fingerprints were established and evaluated using AHP combined with CRITIC weighing method; For animals＇ effects, the experiments of small intestinal propulsion were conducted; For clinical effects, a randomized clinical trial（RCT） was designed and performed. Results Although there were some differences between TD and MDNP in chemical ingredients, there was no significant difference in animal experiments and clinical trials（P 〉 0.05）. Conclusion The traditional and machinery decoctions of DCQD could be used bioequivalently.

BERGMAN TYPE OPERATOR ON MIXED NORM SPACES WITH APPLICATIONS

The authors investigate the conditions for the boundedness of Bergman type operators Ps,t in mixed norm space L_(p),q(φ)on the unit ball of C^(n)(n≥1),and obtain a sufficient condition and a necessary condition for general normal functionφ,and a sufficient and necessary condition forφ(r)=(1-r 2)αlogβ(2(1-r)-1)(α>0,β≥0).This generalizes the result of Forelli Rudin on Bergman operator in Bergman space.As applications,a more natural method is given to compute the duality of the mixed norm space,solve the Gleason's problem for mixed norm space and obtain the characterization of mixed norm space in terms of partial derivatives.Moreover,it is proved thatf∈L(0)∞,q(φ)iff all the functions(1-|z|2)|α||α|fzα(z)∈L(0)∞,q(φ)for holomorphic functionf,1≤q≤∞.

Wavelet-Based Elman Neural Network with the Modified Differential Evolution Algorithm for Forecasting Foreign Exchange Rates

It is challenging to forecast foreign exchange rates due to the non-linear characters of the data. This paper applied a wavelet-based Elman neural network with the modified differential evolution algorithm to forecast foreign exchange rates. Elman neural network has dynamic characters because of the context layer in the structure. It makes Elman neural network suit for time series problems. The main factors, which affect the accuracy of the Elman neural network, included the transfer functions of the hidden layer and the parameters of the neural network. We applied the wavelet function to replace the sigmoid function in the hidden layer of the Elman neural network, and we found there was a "disruption problem" caused by the non-linear performance of the wavelet function. It didn’t improve the performance of the Elman neural network, but made it get worse in reverse. Then, the modified differential evolution algorithm was applied to train the parameters of the Elman neural network. To improve the optimizing performance of the differential evolution algorithm, the crossover probability and crossover factor were modified with adaptive strategies, and the local enhanced operator was added to the algorithm. According to the experiment, the modified algorithm improved the performance of the Elman neural network, and it solved the "disruption problem" of applying the wavelet function.These results show that the performance of the Elman neural network would be improved if both of the wavelet function and the modified differential evolution algorithm were applied integratedly.

Extended Cesàro Operators between Different Bergman Spaces in the Ball

In this paper,we obtain the characterizations on μ for（p,q）-φCarleson measure,and discuss the boundedness（and compactness） of the extended Cesaro operators T g between different weighted Bergman spaces as some application.