The Hyers-Ulam Stability of a Functional Equation Deriving from Quadratic and Cubic Functions in Quasi-β-normed Spaces

In this paper, we investigate the Hyers-Ulam stability of the following function equation 2f（2x ＋ y） ＋ 2f（2x - y） = 4f（x ＋ y） ＋ 4f（x - y） ＋ 4f（2x） ＋ f（2y） - Sf（x） - 8f（y） in quasi-β-normed spaces.

Freezing imaginarity of quantum states based onℓ_(1)-norm

We discuss freezing of quantum imaginarity based onℓ_(1)-norm.Several properties about a quantity of imaginarity based onℓ_(1)-norm are revealed.For a qubit(2-dimensional)system,we characterize the structure of real quantum operations that allow for freezing the quantity of imaginarity of any state.Furthermore,we characterize the structure of local real operations which can freeze the quantity of imaginarity of a class of N-qubit quantum states.

DOA estimation of high-dimensional signals based on Krylov subspace and weighted l_(1)-norm

With the extensive application of large-scale array antennas,the increasing number of array elements leads to the increasing dimension of received signals,making it difficult to meet the real-time requirement of direction of arrival(DOA)estimation due to the computational complexity of algorithms.Traditional subspace algorithms require estimation of the covariance matrix,which has high computational complexity and is prone to producing spurious peaks.In order to reduce the computational complexity of DOA estimation algorithms and improve their estimation accuracy under large array elements,this paper proposes a DOA estimation method based on Krylov subspace and weighted l_(1)-norm.The method uses the multistage Wiener filter(MSWF)iteration to solve the basis of the Krylov subspace as an estimate of the signal subspace,further uses the measurement matrix to reduce the dimensionality of the signal subspace observation,constructs a weighted matrix,and combines the sparse reconstruction to establish a convex optimization function based on the residual sum of squares and weighted l_(1)-norm to solve the target DOA.Simulation results show that the proposed method has high resolution under large array conditions,effectively suppresses spurious peaks,reduces computational complexity,and has good robustness for low signal to noise ratio(SNR)environment.

General Solution and Stability of Quattuordecic Functional Equation in Quasi β-Normed Spaces

In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.

1-TYPE LIPSCHITZ SELECTIONS IN GENERALIZED 2-NORMED SPACES

We shall introduce 1-type Lipschitz multifunctions from R into generalized 2-normed spaces, and give some results about their 1-type Lipschitz selections.

Statistically Convergent Double Sequence Spaces in 2-Normed Spaces Defined by Orlicz Function

The concept of statistical convergence was introduced by Stinhauss [1] in 1951. In this paper, we study con- vergence of double sequence spaces in 2-normed spaces and obtained a criteria for double sequences in 2-normed spaces to be statistically Cauchy sequence in 2-normed spaces.

A Note on Linear Extension of Isometries Between the Unit Spheres in β-normed Spaces

In this paper, we give four general results on linear extension of isometries between the unit spheres in β-normed spaces. These results improve the corresponding theorems in β-normed spaces.

The Aleksandrov Problem in Non-Archimedean 2-Fuzzy 2-Normed Spaces

We introduce the definition of non-Archimedean 2-fuzzy 2-normed spaces and the concept of isometry which is appropriate to represent the notion of area preserving mapping in the spaces above. And then we can get isometry when a mapping satisfies AOPP and (*) (in article) by applying the Benz’s theorem about the Aleksandrov problem in non-Archimedean 2-fuzzy 2-normed spaces.

1-Norm/2-Norm约束及小波多尺度2D体波走时成像

在对浅地表复杂地下介质层析成像时,由于观测系统局限性及方法本身对特定岩石地球物理属性的不敏感性等因素,造成地球物理反演存在多解性。在地震走时成像中,地震射线数量在低速区域分布较少形成阴影区,造成其对低速区域成像分辨率较低。同时因为观测数据包含干扰信息以及不同反演方法的局限性等因素造成反演结果包含次生假异常。这里主要研究了空间域的L1-norm、L2-norm约束反演及小波域小波系数稀疏约束反演,对比不同反演方式及约束条件对地质模型的分辨能力。通过测试孤立异常模型、层状地层模型、倾斜地层模型,得出三种不同反演方式分别具有对不同特定模型的分辨特性。在实际资料成像中,可以通过使用多种反演方式,对比反演结果合理性以期达到更准确的地质构造解释。

分次Quasi-内射模和分次Quasi-投射模

设G是一个群 ,R是一个G 分次环 研究分次quasi 内射模 ,分次quasi 投射模分别与quasi 内射模和quasi 投射模的关系 特别地 。

Adaptive multiple subtraction using a constrained L1-norm method with lateral continuity

The Lt-norm method is one of the widely used matching filters for adaptive multiple subtraction. When the primaries and multiples are mixed together, the L1-norm method might damage the primaries, leading to poor lateral continuity. In this paper, we propose a constrained L1-norm method for adaptive multiple subtraction by introducing the lateral continuity constraint for the estimated primaries. We measure the lateral continuity using prediction-error filters （PEF）. We illustrate our method with the synthetic Pluto dataset. The results show that the constrained L1-norm method can simultaneously attenuate the multiples and preserve the primaries.

A NEURAL-BASED NONLINEAR L_1-NORM OPTIMIZATION ALGORITHM FOR DIAGNOSIS OF NETWORKS*

Based on exact penalty function, a new neural network for solving the L1-norm optimization problem is proposed. In comparison with Kennedy and Chua’s network(1988), it has better properties.Based on Bandler’s fault location method(1982), a new nonlinearly constrained L1-norm problem is developed. It can be solved with less computing time through only one optimization processing. The proposed neural network can be used to solve the analog diagnosis L1 problem. The validity of the proposed neural networks and the fault location L1 method are illustrated by extensive computer simulations.

Quasi-90-day oscillation observed in the MLT region at low latitudes from the Kunming meteor radar and SABER

Observations of a quasi-90-day oscillation in the mesosphere and lower thermosphere(MLT) region from April 2011 to December 2014 are presented in this study. There is clear evidence of a quasi-90-day oscillation in temperatures obtained from the Kunming meteor radar(25.6°N, 103.8°E) and Sounding of the Atmosphere using Broadband Emission Radiometry(SABER), as well as in wind observed by the Kunming meteor radar. The quasi-90-day oscillation appears to be a prominent feature in the temperatures and meridional wind tides and presents quite regular cycles that occur approximately twice per year. The amplitudes and phases of the quasi-90-day oscillation in the SABER temperature show a feature similar to that of upward-propagated diurnal tides, which have a vertical wavelength of ～20 km above 70 km. In the lower atmosphere, a similar 90-day variability is presented in the surface latent heat flux and correlates with the temperature in the MLT region. Similar to the quasi-90-day oscillation in temperature, a 90-day variability of ozone(O3) is also present in the MLT region and is considered to be driven by a similar variability in the upwardly-propagated diurnal tides generated in the lower atmosphere. Moreover, the 90-day variability in the absorption of ultraviolet(UV) radiation by daytime O3 in the MLT region is an in situ source of the quasi-90-day oscillation in the MLT temperature.

Image reconstruction from few views by l_0-norm optimization

In the medical computer tomography （CT） field, total variation （TV）, which is the l1-norm of the discrete gradient transform （DGT）, is widely used as regularization based on the compressive sensing （CS） theory. To overcome the TV model＇s disadvantageous tendency of uniformly penalizing the image gradient and over smoothing the low-contrast structures, an iterative algorithm based on the l0-norm optimization of the DGT is proposed. In order to rise to the challenges introduced by the l0-norm DGT, the algorithm uses a pseudo-inverse transform of DGT and adapts an iterative hard thresholding （IHT） algorithm, whose convergence and effective efficiency have been theoretically proven. The simulation demonstrates our conclusions and indicates that the algorithm proposed in this paper can obviously improve the reconstruction quality.

Characteristics of the quasi-16-day wave in the mesosphere and lower thermosphere region as revealed by meteor radar,Aura satellite,and MERRA2 reanalysis data from 2008 to 2017

This study presents an analysis of the quasi-16-day wave(Q16DW)at three stations in the middle latitudes by using a meteor radar chain in conjunction with Aura Microwave Limb Sounder temperature data and MERRA2(Modern-Era Retrospective Analysis for Research and Applications,Version 2)reanalysis data from 2008 to 2017.The radar chain consists of three meteor radar stations located at Mohe(MH,53.5°N,122.3°E),Beijing(BJ,40.3°N,116.2°E),and Wuhan(WH,30.5°N,114.6°E).The Q16DW wave exhibits similar seasonal variation in the neutral wind and temperature,and the Q16DW amplitude is generally strong during winter and weak around summer.The Q16DW at BJ was found to have secondary enhancement around September in the zonal wind,which is rarely reported at similar latitudes.The latitudinal variations of the Q16DW in the neutral wind and temperature are quite different.The Q16DW at BJ is the most prominent in both neutral wind components among the three stations and the Q16DW amplitudes at MH and WH are comparable,whereas the wave amplitude in temperature decreases with decreasing latitude.The quasi-geostrophic refractive index squared at the three stations in the period from 2008 to 2017 was revealed.The results indicate that the Q16DW in the mesosphere and lower thermosphere(MLT)at MH has a limited contribution from the lower atmosphere.Around March and October,the Q16DW in the troposphere at BJ can propagate upward into the MLT region,whereas at WH,the contribution to the Q16DW in the MLT region is largely from the mesosphere.

Quasi-6-day waves in the mesosphere and lower thermosphere region and their possible coupling with the QBO and solar 27-day rotation

By using atmospheric wind data in the mesopause and lower thermosphere(MLT)region,features of seasonal variations in the quasi-6-day wave(6DW)at different latitudes are analyzed,and modulation of the 6DW by the diurnal tide and solar 27-day period is discussed.The data used in the analysis are extracted from a wind dataset collected by a meteor radar chain from December 2008 to November 2017.The meteor radar chain includes four stations,in Mohe,Beijing,Wuhan,and Sanya.Features of seasonal variations in the 6DW indicate that in summer the 6DW is usually strongest during July and August,followed by stronger variations in January and April.At certain altitudes over Wuhan and Sanya,the 6DW is slightly different in different years and altitudes.In our analysis of seasonal variations in the 6DW,we find that it is generally affected by annual oscillations and semiannual oscillations.The annual oscillations of the 6DW in the mid-low latitudes are modulated by the quasibiennial oscillation in the diurnal tide,resulting in seasonal features that are different from those at other latitudes.In addition,the 6DW amplitude at mid-high latitudes has a significant 27-day solar rotation variation,which was prominent in 2016.

Polarization sensitive photodetector based on quasi-1D ZrSe_(3)

The in-plane anisotropy of transition metal trichalcogenides(MX_(3))has a significant impact on the molding of materi-als and MX_(3) is a perfect choice for polarized photodetectors.In this study,the crystal structure,optical and optoelectronic aniso-tropy of one kind of quasi-one-dimensional(1D)semiconductors,ZrSe_(3),are systematically investigated through experiments and theoretical studies.The ZrSe_(3)-based photodetector shows impressive wide spectral response from ultraviolet(UV)to near in-frared(NIR)and exhibits great optoelectrical properties with photoresponsivity of 11.9 mA·W^(-1) and detectivity of~106 at 532 nm.Moreover,the dichroic ratio of ZrSe_(3)-based polarized photodetector is around 1.1 at 808 nm.This study suggests that ZrSe_(3) has potential in optoelectronic applications and polarization detectors.

A Block Parallel l_0-Norm Penalized Shrinkage and Widely Linear Affine Projection Algorithm for Adaptive Filter

To improve the identification capability of AP algorithm in time-varying sparse system, we propose a block parallel l_0-SWL-DCD-AP algorithm in this paper. In the proposed algorithm, we first introduce the l_0-norm constraint to promote its application for sparse system. Second, we use the shrinkage denoising method to improve its track ability. Third, we adopt the widely linear processing to take advantage of the non-circular properties of communication signals. Last, to reduce the high computational complexity and make it easy to implemented, we utilize the dichotomous coordinate descent(DCD) iterations and the parallel processing to deal with the tapweight update in the proposed algorithm. To verify the convergence condition of the proposed algorithm, we also analyze its steadystate behavior. Several simulation are done and results show that the proposed algorithm can achieve a faster convergence speed and a lower steady-state misalignment than similar APA-type algorithm. When apply the proposed algorithm in the decision feedback equalizer(DFE), the bite error rate(BER) decreases obviously.

Fixed Point of a Countable Family of Uniformly Totally Quasi- <i>&Oslash</i>-Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications

The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).

Strong Convergence for a Countable Family of Total Quasi-φ-asymptotically Nonexpansive Nonself Mappings in Banach Space

The purpose of this article is to introduce a class of total quasi-Ф- asymptotically nonexpansive nonself mappings. Strong convergence theorems for common fixed points of a countable family of total quasi-Ф-asymptotically nonexpan- sive mappings are established in the framework of Banach spaces based on modified Halpern and Mann-type iteration algorithm. The main results presented in this article extend and improve the corresponding results of many authors.