The Global Existence for the Derivative Nonlinear Schr\"odinger Equation with solitons

The global existence of the solution for the second-type derivative nonlinear Schr\"odinger (DNLSII) equation with solitons is presented for the first time on the line with weighted Sobolev initial data in $H^2( \mathbb{R}) \cap H^{1,1}(\mathbb{R} )$. The modified Darboux transformation is applied as a main research tool to analyze the global existence for the Cauchy problem by adding or subtracting a finite number of zeros of the scattering data. For this purpose, it is necessary to study the invertibility and uniqueness of the Darboux transformation first acting on the weighted Sobolev space. The analysis of time evolution comprehensively demonstrates the existence of a unique global solution to the DNLSII equation with Cauchy problem in $H^2( \mathbb{R}) \cap H^{1,1}(\mathbb{R} )$

The ∂ˉ\bar{{\partial}}-dressing Method for Two (2+1)-dimensional Equations and Combinatorics

The soliton solutions of two different (2+1)-dimensional equations with the third order and second order spatial spectral problems are studied by the $\bar{{\partial}}$-dressing method. The 3-reduced and 5-reduced equations of CKP equation are obtained for the first time by the binary Bell polynomial approach. The $\bar{{\partial}}$-dressing method is a very important method to explore the solution of a nonlinear soliton equation without analytical regions. Two different types of equations, the (2+1)-dimensional Kaup-Kuperschmidt equation named CKP equation and a generalized (2+1)-dimensional nonlinear wave equation, are studied by analyzing the eigenfunctions and Green's functions of their Lax representations as well as the inverse spectral transformations, then the new $\bar{{\partial}}$ problems are deduced to construct soliton solutions by choosing proper spectral transformations. Furthermore, once the time evolutions of the spectral data are determined, we will be able to completely obtain the solutions formally of the CKP equation and the generalized (2+1)-dimensional nonlinear wave equation. The reduced problem of the (2+1)-dimensional Kaup-Kuperschmidt is discussed. The main method is binary Bell polynomials related about the $\mathcal{Y}$-constraints and $P$-conditions which turns out to be an effective tool to represent the bilinear form. On the basis of this method, the bilinear form is determined under the scaling transformation. Starting from the bilinear representation, the CKP equation is reduced to Kaup-Kuperschmidt~equation and bidirectional Kaup-Kuperschmidt equation under the reduction of $t_3$ and $t_5$, respectively

An active control scheme for rotor vibration based on predictive variable learning gain

To our knowledge, iterative learning control (ILC) is an effective method for active vibration control of mechanical systems with periodically varying parameters, merits of ILC mainly include simplicity and completely compensating for nonlinear. However, during application of ILC, transient growth or instability for system is sometimes dramatic large which is in fact detrimental to system, we attribute such phenomena to non-periodic factors, so, an improvement to iterative learning control (ILC), predictive gain iterative learning control (PILC) is put forward to suppress the rotor displacement and the amplifier current mainly resulted from the unbalance forces. Discretization is applied to get the system model including the parameters analysis, and then, the obtained model is transformed into a new style where the learning gain is input, next, based on the new model, a feedback predictive control algorithm is carried out to obtain the learning gain at present time, then, at the next time, the gain is updated by the same mean. The improved method achieves arbitrary damping and gets a high speed and accuracy output tracking for mechanical system. The simulation results show that the control technique can reduce transient growth and can significantly increase the stability of the rotor system

Serum cystatin C and chemerin levels in diabetic retinopathy

Peer reviewedPublisher PD

Significantly enhanced critical current densities in MgB2 tapes made by a scaleable, nano-carbon addition route

Nanocarbon-doped Fe-sheathed MgB2 tapes with different doping levels were prepared by the in situ powder-in-tube method. Compared to the undoped tapes, Jc for all the C-doped samples was enhanced by more than an order of magnitude in magnetic fields above 9 T. At 4.2 K, the transport Jc for the 5 at% doped tapes reached 1.85x104 A/cm2 at 10 T and 2.8x103 A/cm2 at 14 T, respectively. Moreover, the critical temperature for the doped tapes decreased slightly. Transmission electron microscopy showed a number of intra-granular dislocations and the dispersed nanoparticles embedded within MgB2 grains induced by the C doping. The mechanism for the enhancement of flux pinning is also discussed. These results indicate that powder-in-tube-processed MgB2 tape is very promising for high-field applications.Comment: 13 pages, 5 figures. to be published soo

Inferring Gene Regulatory Network from Bayesian Network Model Based on Re-Sampling

Nowadays, gene chip technology has rapidly produced a wealth of information about gene expression activities. But the time-series expression data present a phenomenon that the number of genes is in thousands and the number of experimental data is only a few dozen. For such cases, it is difficult to learn network structure from such data. And the result is not ideal. So it needs to take measures to expand the capacity of the sample. In this paper, the Block bootstrap re-sampling method is utilized to enlarge the small expression data. At the same time, we apply “K2+T” algorithm to Yeast cell cycle gene expression data. Seeing from the experimental results and comparing with the semi-fixed structure EM learning algorithm, our proposed method is successful in constructing gene networks that capture much more known relationships as well as several unknown relationships which are likely to be novel

A Method for Filling up the Missed Data in Information Table

Almost algorithms based on the rough sets, such as mean value method, maximum frequency method, mode method are week in supporting the hidden rules in the information tablel. By the breaking point sets in the information system, a new method for packing the missed attribute value is provided in the paper,. The method is more efficient for indicating the decision rules