Solution of the spin-one DKP oscillator under an external magnetic field in noncommutative space with minimal length

The spin-one Duffin-Kemmer-Petiau （DKP） oscillator under a magnetic field in the presence of Ihe minimal length in the noncommutative coordinate space is studied by using the momentum space representation. The explicit form of energy eigenvalues is found, and the eigenfunctions are obtained in terms of the Jacobi polynomials. It shows that for the same azimuthal quantum number, the energy E increases monotonically with respect to the noncomnmtative parameter and the minimal length parameter. Additionally, we also report some special cases aiming to discuss the effect of the noncommutative coordinate space and the minimal length in the energy spectrum.

THE INFLUENCE OF INHOMOGENEOUS WIND DISTRIBUTION ON DATA QUALITY FOR WIND PROFILING RADAR

Horizontal wind measured by wind profiling radar(WPR) is based on uniform wind assumption in volume of lateral beam. However, this assumption cannot completely meet in the real atmosphere. The subject of this work is to analyze the influence of atmospheric inhomogeneities for wind measurement. Five-beam WPR can measure two groups of horizontal wind components U and V independently, using the difference of horizontal wind components U and V can evaluate the influence of the inhomogeneity of the atmospheric motion on wind measurement. The influences can be divided into both inhomogeneous distribution of horizontal motion and vertical motion. Based on wind measurements and meteorological background information, a new means of coordinate rotation the two kinds of inhomogeneous factor was separated, and the impact in different weather background was discussed. From analysis of the wind measured by type of PB-II WPR(445MHz) during 2012 at Yanqing of Beijing, it is shown that the inhomogeneity of horizontal motion is nearly the same in U and V direction. Both the inhomogeneities of horizontal motion and vertical motion have influence on wind measurement, and the degrees of both influences are associated with changes of wind speed. In clear air, inhomogeneity of horizontal motion is the main influence on wind measurement because of small vertical velocity.In precipitation, the two influences are larger than that in clear air.

REPRESENTATION OF MARTINGALE ADDITIVE FUNCTIONALS 0N BANACH SPACES

Assume that B is a separable real Banach space and X(t) is a diffusion process on B. In thispaper, we will establish the representation theorem of martingale additive functionals of X(t).

DECOMPOSITION OF A CLASS OF FUNCTIONALS AND THE PREDICTABLE REPRESENTATION THEOREM ON BANACH SPACES

Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a regular 0-quadratic variation process. On this basis, weestablish the predictable representation theorem of X(t).

Representations of Knot Groups and Twisted Alexander Polynomials

We present a twisted version of the Alexander polynomial associated with a matrix rep- resentation of the knot group.Examples of two knots with the same Alexander module but different twisted Alexander polynomials are given.

Models and performance of SBAS and PPP of BDS

Satellite Based Augmentation System(SBAS)is one of the services provided by the BeiDou Navigation Satellite System(BDS).It broadcasts four types of diferential corrections to improve user application performance.These corrections include the State Space Representation(SSR)based satellite orbit/clock corrections and ionospheric grid corrections,and the Observation Space Representation(OSR)based partition comprehensive corrections.The algorithms generating these SBAS corrections are not introduced in previous researches,and the user SBAS positioning performance with the contribution of BDS-3 has not been evaluated.In this paper,we present the BDS SBAS algorithms for these diferential corrections in detail.Four types of Precise Point Positioning(PPP)function models for BDS Dual-Frequency(DF)and Single-Frequency(SF)users using the OSR and SSR parameters are also proposed.One week of data in 2020 is collected at 20 reference stations including the observations of both BeiDou-2 Navigation Satellite System(BDS-2)and BeiDou-3 Navigation Satellite System(BDS-3)satellites,and the PPP under various scenarios are performed using all the datasets and the BDS SBAS broadcast corrections.The results show that the performance of BDS-2/BDS-3 combination is superior to that of BDS-2 only constellation.The positioning errors in Root Mean Square(RMS)for the static DF PPP are better than 8 cm/15 cm in horizontal/vertical directions,while for the static SF PPP are 11 cm/24 cm.In the scenarios of simulated kinematic PPP,three Dimension(3D)positioning errors can reach 0.5 m in less than 10 min for the DF PPP and 30 min for the SF PPP,and the RMSs of the DF and SF PPP are better than 17 cm/21 cm and 20 cm/32 cm in horizontal/vertical directions.In a real-time single-and dual-frequency kinematic positioning test,the positioning errors of all three components can reach 0.5 m within 30 min,and the positioning accuracy after solution convergence in the N,E and U directions is better than 0.3 m.

Comprehensive assessment of real-time precise products from IGS analysis centers

Real-Time Precise Point Positioning(RT-PPP)has been one of the research hotspots in GNSS(Global Navigation Satellite System)community for decades.Real-time precise products of satellite orbits and clocks are the prerequisite for RT-PPP.Thus,it is of great importance to investigate the current multi-GNSS real-time precise products in State Space Representation(SSR)from diferent analysis centers.In this article,SSR products from 10 analysis centers are comprehensively evaluated by comparing them with the fnal products and performing the kinematic PPP.The results show that analysis centers CNES(Centre National D’Etudes Spatiales)and WHU(GNSS Research Center of Wuhan University)provide the most complete products with the best quality.Concerning the accuracy of real-time products for the GNSSs,the accuracies of orbit and clock products are better than 5 cm and 0.15 ns,respectively,for Global Positioning System(GPS),followed by Galileo navigation satellite system(Galileo),BeiDou-3 Navigation Satellite System(BDS-3),GLObal NAvigation Satellite System(GLONASS),and BeiDou-2 Navigation Satellite System(BDS-2).Meanwhile,the results of the RT-PPP with quad-system show that the positioning accuracies are 1.76,1.12 and 2.68 cm in east,north,and up directions,respectively,and the convergence time to 0.1,0.1,0.2 m for corresponding directions is 15.35 min.

A general approach to attribute reduction in rough set theory

The concept of a consistent approximation representation space is introduced. Many types of information systems can be treated and unified as consistent approximation representation spaces. At the same time, under the framework of this space, the judgment theorem for determining consistent attribute set is established, from which we can obtain the approach to attribute reductions in information systems. Also, the characterizations of three important types of attribute sets （the core attribute set, the relative necessary attribute set and the unnecessary attribute set） are examined.

Layer-Wise Pre-Training Low-Rank NMF Model for Mammogram-Based Breast Tumor Classification

Image-based breast tumor classification is an active and challenging problem.In this paper,a robust breast tumor classification framework is presented based on deep feature representation learning and exploiting available information in existing samples.Feature representation learning of mammograms is fulfilled by a modified nonnegative matrix factorization model called LPML-LRNMF,which is motivated by hierarchical learning and layer-wise pre-training(LP)strategy in deep learning.Low-rank(LR)constraint is integrated into the feature representation learning model by considering the intrinsic characteristics of mammograms.Moreover,the proposed LPML-LRNMF model is optimized via alternating direction method of multipliers and the corresponding convergence is analyzed.For completing classification,an inverse projection sparse representation model is introduced to exploit information embedded in existing samples,especially in test ones.Experiments on the public dataset and actual clinical dataset show that the classification accuracy,specificity and sensitivity achieve the clinical acceptance level.