WEIGHTED ESTIMATES FOR COMMUTATORS OF MULTILINEAR CALDERóN-ZYGMUND OPERATORS WITH NON-DOUBLING MEASURES

Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multilinear CalderSn-Zygmund op- erators and RBMO（μ） functions.

BOUNDEDNESS OF FRACTIONAL INTEGRALS IN HARDY SPACES WITH NON-DOUBLING MEASURE—In Memory of Professor Sun Yongsheng

Let μ be a Borel measure on R^d which may be non doubling. The only condition that μ must satisfy is μ（Q） ≤ col（Q）^n for any cube Q belong to R^d with sides parallel to the coordinate axes and for some fixed n with 0 〈 n ≤ d. The purpose of this paper is to obtain a boundedness property of fractional integrals in Hardy spaces H^1（μ）.

Boundedness of Multilinear Singular Integrals and Their Commutators on Morrey-Herz Spaces with Non-doubling Measures

Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz spaces are obtained if T is bounded from L^1（μ）χ…χ L^1（μ） to L1/m,∞（μ）.

BOUNDEDNESS OF VECTOR-VALUED CALDERN-ZYGMUND OPERATORS ON HERZ SPACES WITH NON-DOUBLING MEASURES

In the paper we obtain vector-valued inequalities for Calderon-Zygmund operator, simply CZO on Herz space and weak Herz space. In particular, we obtain vector-valued inequalities for CZO on L^q（R^d,｜x｜^α d μ）space, with 1〈q〈∞,-n〈α〈n（q-1）,and on L^1,∞ （R^d,｜x｜^α d μ）space,with -n〈α〈0.

Iterated Commutators for Multilinear Singular Integral Operators on Morrey Space with Non-Doubling Measures

Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on Morrey spaces?.Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.

Morrey Spaces for Non-doubling Measures

The authors give a natural definition of Morrey spaces for Radon measures which may be non-doubling but satisfy certain growth condition, and investigate the boundedness in these spaces of some classical operators in harmonic analysis and their vector-valued extension.

Boundedness in Lebesgue spaces for commutators of multilinear singular integrals and RBMO functions with non-doubling measures

The boundedness in Lebesgue spaces for commutators generated by multilinear singular integrals and RMBO(μ) functions of Tolsa with non-doubling measures is obtained, provided that ∥μ∥ = ∞ and multilinear singular integrals are bounded from L 1(μ) × L 1(μ) to L 1/2,∞(μ).

Boundedness of Some Maximal Commutators in Hardy-type Spaces with Non-doubling Measures

Let μ be a non-negative Radon measure on R^d which satisfies only some growth conditions. Under this assumption, the boundedness in some Hardy-type spaces is established for a class of maximal Calderón-Zygmund operators and maximal commutators which are variants of the usual maximal commutators generated by Calder6ón- Zygmund operators and RBMO（μ） functions, where the Hardytype spaces are some appropriate subspaces, associated with the considered RBMO（μ） functions, of the Hardv soace H^I（μ） of Tolsa.

Θ-type Calderón-Zygmund Operators with Non-doubling Measures

Let μ be a Radon measure on Rd which may be non-doubling. The only condition that μ must satisfy is μ（B（x,r）） ≤ Urn for all x∈Rd, r 〉 0 and for some fixed 0 〈 n 〈 d. In this paper, under this assumption, we prove that 0-type Calder6n-Zygmund operator which is bounded on L2 （μ） is also bounded from L^∞（μ） into RBMO （μ） and from Hb （μ） into L1（μ）. According to the interpolation theorem introduced by Tolsa, the LP（μ）-boundedness （1 〈 p 〈 ∞） is established for θ-type Calder6n-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of θ-type CMderθn-Zygmundoperator with RBMO （μ） function are bounded on LP（μ） （1 〈 p 〈 ∞）.

Atomic Hardy-type Spaces between H1 and L1 on Metric Spaces with Non-doubling Measures

Let （y, d, dλ） be （Rn, ｜·｜,μ）, where ｜·｜ is the Euclidean distance, μ is a nonnegative Radon measure on Rn satisfying the polynomial growth condition, or the Gauss measure metric space （Rn, ｜·｜,dγ）, or the space （S, d, p）, where S - Rn×R＋ is the （ax ＋ b）-group, d is the left-invariant Riemannian metric and p is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces {Xs（Y））0〈s≤∞ and the BM0-type spaces {BM0（y, s）}0〈s≤∞. Let Hi（Y） be the known atomic Hardy space and L01（y） the subspace of f ∈ L1（Y） with integral 0. The authors prove that the dual space of Xs（Y） is SM0（Y,s） when s∈ （0, ∞）, Xs（Y） = H1（Y） when s ∈ （0, 1], and X∞（y） = L01（Y） （or L1（Y））. As applications, the authors show that if T is a linear operator bounded from H1 （Y） to L1 （Y） and from L1（y） to L1,∞（Y）, then for all r ∈ （1, ∞） and s ∈ （r, ∞], T is bounded from Xr（y） to the Lorentz space L1,8（y）, which applies to the Calderon-Zygmund operator on （Rn, ｜·｜,μ）, the imaginary powers of the 0rnstein-Uhlenbeck operator on （Rn, ｜·｜,dγ） and the spectral operator associated with the spectral multiplier on （S, d, p）. All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces.

Endpoint Estimates for Multilinear Fractional Integrals with Non-doubling Measures

Under the assumption that μ is a non-doubling measure on R^d which only satisfies the polynomial growth condition, the authors obtain the boundedness of the multilinear fractional integrals on Morrey spaces, weak-Morrey spaces and Lipschitz spaces associated with it, which, in the case when μ is the d-dimensional Lebesgue measure, also improve the known results.

HealthMeasures患者报告结局报告清单的解读

美国匹兹堡大学和HealthMeasures指导委员会及PROMIS健康组织标准委员会共同发表了HealthMeasures患者报告结局报告清单,旨在促进不同患者报告结局测量工具的标准化报告,帮助研究人员提高工具报告质量及结果解释的准确性,进一步改善跨研究间的比较分析。本文对HealthMeasures患者报告结局报告清单的主要内容进行介绍和解读,以期为中国患者报告结局研究者提供参考和借鉴。

Applying the Shearlet-Based Complexity Measure for Analyzing Mass Transfer in Continuous-Flow Microchannels

Continuous-flow microchannels are widely employed for synthesizing various materials,including nanoparticles,polymers,and metal-organic frameworks(MOFs),to name a few.Microsystem technology allows precise control over reaction parameters,resulting in purer,more uniform,and structurally stable products due to more effective mass transfer manipulation.However,continuous-flow synthesis processes may be accompanied by the emergence of spatial convective structures initiating convective flows.On the one hand,convection can accelerate reactions by intensifying mass transfer.On the other hand,it may lead to non-uniformity in the final product or defects,especially in MOF microcrystal synthesis.The ability to distinguish regions of convective and diffusive mass transfer may be the key to performing higher-quality reactions and obtaining purer products.In this study,we investigate,for the first time,the possibility of using the information complexity measure as a criterion for assessing the intensity of mass transfer in microchannels,considering both spatial and temporal non-uniformities of liquid’s distributions resulting from convection formation.We calculate the complexity using shearlet transform based on a local approach.In contrast to existing methods for calculating complexity,the shearlet transform based approach provides a more detailed representation of local heterogeneities.Our analysis involves experimental images illustrating the mixing process of two non-reactive liquids in a Y-type continuous-flow microchannel under conditions of double-diffusive convection formation.The obtained complexity fields characterize the mixing process and structure formation,revealing variations in mass transfer intensity along the microchannel.We compare the results with cases of liquid mixing via a pure diffusive mechanism.Upon analysis,it was revealed that the complexity measure exhibits sensitivity to variations in the type of mass transfer,establishing its feasibility as an indirect criterion for assessing mass transfer intensity.The method presented can extend beyond flow analysis,finding application in the controlling of microstructures of various materials(porosity,for instance)or surface defects in metals,optical systems and other materials that hold significant relevance in materials science and engineering.

Bunch-length measurement at a bunch-by-bunch rate based on time–frequency-domain joint analysis techniques and its application

This paper presents a new technique for measuring the bunch length of a high-energy electron beam at a bunch-by-bunch rate in storage rings.This technique uses the time–frequency-domain joint analysis of the bunch signal to obtain bunch-by-bunch and turn-by-turn longitudinal parameters,such as bunch length and synchronous phase.The bunch signal is obtained using a button electrode with a bandwidth of several gigahertz.The data acquisition device was a high-speed digital oscilloscope with a sampling rate of more than 10 GS/s,and the single-shot sampling data buffer covered thousands of turns.The bunch-length and synchronous phase information were extracted via offline calculations using Python scripts.The calibration coefficient of the system was determined using a commercial streak camera.Moreover,this technique was tested on two different storage rings and successfully captured various longitudinal transient processes during the harmonic cavity debugging process at the Shanghai Synchrotron Radiation Facility(SSRF),and longitudinal instabilities were observed during the single-bunch accumulation process at Hefei Light Source(HLS).For Gaussian-distribution bunches,the uncertainty of the bunch phase obtained using this technique was better than 0.2 ps,and the bunch-length uncertainty was better than 1 ps.The dynamic range exceeded 10 ms.This technology is a powerful and versatile beam diagnostic tool that can be conveniently deployed in high-energy electron storage rings.

A New Device for Gas-Liquid Flow Measurements Relying on Forced Annular Flow

A new measurement device,consisting of swirling blades and capsule-shaped throttling elements,is proposed in this study to eliminate typical measurement errors caused by complex flow patterns in gas-liquid flow.The swirling blades are used to transform the complex flow pattern into a forced annular flow.Drawing on the research of existing blockage flow meters and also exploiting the single-phase flow measurement theory,a formula is introduced to measure the phase-separated flow of gas and liquid.The formula requires the pressure ratio,Lockhart-Martinelli number(L-M number),and the gas phase Froude number.The unknown parameters appearing in the formula are fitted through numerical simulation using computational fluid dynamics(CFD),which involves a comprehensive analysis of the flow field inside the device from multiple perspectives,and takes into account the influence of pressure fluctuations.Finally,the measurement model is validated through an experimental error analysis.The results demonstrate that the measurement error can be maintained within±8%for various flow patterns,including stratified flow,bubble flow,and wave flow.

Enhancing Energy Efficiency with a Dynamic Trust Measurement Scheme in Power Distribution Network

The application of Intelligent Internet of Things(IIoT)in constructing distribution station areas strongly supports platform transformation,upgrade,and intelligent integration.The sensing layer of IIoT comprises the edge convergence layer and the end sensing layer,with the former using intelligent fusion terminals for real-time data collection and processing.However,the influx of multiple low-voltage in the smart grid raises higher demands for the performance,energy efficiency,and response speed of the substation fusion terminals.Simultaneously,it brings significant security risks to the entire distribution substation,posing a major challenge to the smart grid.In response to these challenges,a proposed dynamic and energy-efficient trust measurement scheme for smart grids aims to address these issues.The scheme begins by establishing a hierarchical trust measurement model,elucidating the trust relationships among smart IoT terminals.It then incorporates multidimensional measurement factors,encompassing static environmental factors,dynamic behaviors,and energy states.This comprehensive approach reduces the impact of subjective factors on trust measurements.Additionally,the scheme incorporates a detection process designed for identifying malicious low-voltage end sensing units,ensuring the prompt identification and elimination of any malicious terminals.This,in turn,enhances the security and reliability of the smart grid environment.The effectiveness of the proposed scheme in pinpointing malicious nodes has been demonstrated through simulation experiments.Notably,the scheme outperforms established trust metric models in terms of energy efficiency,showcasing its significant contribution to the field.

Measuring small longitudinal phase shifts via weak measurement amplification

Weak measurement amplification,which is considered as a very promising scheme in precision measurement,has been applied to various small physical quantities estimations.Since many physical quantities can be converted into phase signals,it is interesting and important to consider measuring small longitudinal phase shifts by using weak measurement.Here,we propose and experimentally demonstrate a novel weak measurement amplification-based small longitudinal phase estimation,which is suitable for polarization interferometry.We realize one order of magnitude amplification measurement of a small phase signal directly introduced by a liquid crystal variable retarder and show that it is robust to the imperfection of interference.Besides,we analyze the effect of magnification error which is never considered in the previous works,and find the constraint on the magnification.Our results may find important applications in high-precision measurements,e.g.,gravitational wave detection.

Unknown Environment Measurement Mapping by Unmanned Aerial Vehicle Using Kalman Filter-Based Low-Cost Estimated Parallel 8-Beam LIDAR

The measurement and mapping of objects in the outer environment have traditionally been conducted using ground-based monitoring systems,as well as satellites.More recently,unmanned aerial vehicles have also been employed for this purpose.The accurate detection and mapping of a target such as buildings,trees,and terrains are of utmost importance in various applications of unmanned aerial vehicles(UAVs),including search and rescue operations,object transportation,object detection,inspection tasks,and mapping activities.However,the rapid measurement and mapping of the object are not currently achievable due to factors such as the object’s size,the intricate nature of the sites,and the complexity of mapping algorithms.The present system introduces a costeffective solution for measurement and mapping by utilizing a small unmanned aerial vehicle(UAV)equipped with an 8-beam Light Detection and Ranging(LiDAR)system.This approach offers advantages over traditional methods that rely on expensive cameras and complex algorithm-based approaches.The reflective properties of laser beams have also been investigated.The system provides prompt results in comparison to traditional camerabased surveillance,with minimal latency and the need for complex algorithms.The Kalman estimation method demonstrates improved performance in the presence of noise.The measurement and mapping of external objects have been successfully conducted at varying distances,utilizing different resolutions.

Improved spatio-temporal alignment measurement method for hull deformation

In this paper,an improved spatio-temporal alignment measurement method is presented to address the inertial matching measurement of hull deformation under the coexistence of time delay and large misalignment angle.Large misalignment angle and time delay often occur simultaneously and bring great challenges to the accurate measurement of hull deformation in space and time.The proposed method utilizes coarse alignment with large misalignment angle and time delay estimation of inertial measurement unit modeling to establish a brand-new spatiotemporal aligned hull deformation measurement model.In addition,two-step loop control is designed to ensure the accurate description of dynamic deformation angle and static deformation angle by the time-space alignment method of hull deformation.The experiments illustrate that the proposed method can effectively measure the hull deformation angle when time delay and large misalignment angle coexist.

A new centrality measure based on neighbor loop structure for network dismantling

Nearly all real-world networks are complex networks and usually are in danger of collapse.Therefore,it is crucial to exploit and understand the mechanisms of network attacks and provide better protection for network functionalities.Network dismantling aims to find the smallest set of nodes such that after their removal the network is broken into connected components of sub-extensive size.To overcome the limitations and drawbacks of existing network dismantling methods,this paper focuses on network dismantling problem and proposes a neighbor-loop structure based centrality metric,NL,which achieves a balance between computational efficiency and evaluation accuracy.In addition,we design a novel method combining NL-based nodes-removing,greedy tree-breaking and reinsertion.Moreover,we compare five baseline methods with our algorithm on ten widely used real-world networks and three types of model networks including Erd€os-Renyi random networks,Watts-Strogatz smallworld networks and Barabasi-Albert scale-free networks with different network generation parameters.Experimental results demonstrate that our proposed method outperforms most peer methods by obtaining a minimal set of targeted attack nodes.Furthermore,the insights gained from this study may be of assistance to future practical research into real-world networks.