Lipschitz Estimates for Commutators of N-dimensional Fractional Hardy Operators

In this paper, it is proved that the commutator Hβ,b which is generated by the n-dimensional fractional Hardy operator Hβ and b ∈λα （R^n） is bounded from L^p（R^n） to L^q（R^n）, where 0 〈 α 〈 1, 1 〈 p, q 〈 ∞ and 1/P - 1/q = （α＋β）/n. Furthermore, the boundedness of Hβ,b on the homogenous Herz space Kq^α,p（R^n） is obtained.

General calculation formulas and recurrence relations of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0

In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.

On Multiplicative Generators of n-Dimensional Overlap Functions

In this paper, inspired by the multiplicative generators of overlap functions, we mainly propose the concepts of multiplicative generator pairs of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n. We present the condition under which the pair (g, h) can multiplicatively generate an n-dimensional overlap function Og,h. we focus on the homogeneity and idempotency property on multiplicatively generated n-dimensional overlap functions.

Solutions of Laplace Equation in n-Dimensional Spaces

The solutions of the Laplace equation in n-dimensional space are studied. The angular eigenfunctions have the form of associated Jacob/polynomials. The radial solution of the Helmholtz equation is derived.

Recent Advances in In-Memory Computing:Exploring Memristor and Memtransistor Arrays with 2D Materials

The conventional computing architecture faces substantial chal-lenges,including high latency and energy consumption between memory and processing units.In response,in-memory computing has emerged as a promising alternative architecture,enabling computing operations within memory arrays to overcome these limitations.Memristive devices have gained significant attention as key components for in-memory computing due to their high-density arrays,rapid response times,and ability to emulate biological synapses.Among these devices,two-dimensional(2D)material-based memristor and memtransistor arrays have emerged as particularly promising candidates for next-generation in-memory computing,thanks to their exceptional performance driven by the unique properties of 2D materials,such as layered structures,mechanical flexibility,and the capability to form heterojunctions.This review delves into the state-of-the-art research on 2D material-based memristive arrays,encompassing critical aspects such as material selection,device perfor-mance metrics,array structures,and potential applications.Furthermore,it provides a comprehensive overview of the current challenges and limitations associated with these arrays,along with potential solutions.The primary objective of this review is to serve as a significant milestone in realizing next-generation in-memory computing utilizing 2D materials and bridge the gap from single-device characterization to array-level and system-level implementations of neuromorphic computing,leveraging the potential of 2D material-based memristive devices.

Relation Between Dimension and Angular Momentum for Radially Symmetric Potential in N-Dimensional Space

It is proved that when solving SchrSdinger equations for radially symmetric potentials the effect of higher dimensions on the radial wave function is equivalent to the effect of higher angular momenta in lower-dimensional cases. This result is applied to giving solutions for several radially symmetric potentials in N dimensions.

Low profile cavity-embedded ultra-wideband UHF array antenna with end-fire beams

A low-profile,vertically polarized,ultra-wideband array antenna with end-fire beams operating in an ultra-high frequency(UHF)band is developed in this paper.The array antenna consists of 1×16 log-periodic top-hat loaded monopole antenna arrays and is feasible to embed into a shallow cavity to further reduce the array height.Capacitance is introduced in the proposed antenna element to reduce profile height and the rectangular top hats are carefully designed to minimize the transverse dimension.Simulated results show that when the antenna array operates in a frequency range of 300 MHz-900 MHz,the end-fire radiation pattern achieves±45°scanning range in the horizontal plane.Then prototypes of the proposed end-fire antenna element and a uniformly spaced linear array(1×2)are fabricated and validated.The end-fire antenna array should be suitable for airborne applications where low-profile and conformal scanning phased antenna arrays with end-fire radiations are required.This design is attractive for airborne platform applications that are used to search,discover,identify,and scout the aerial target with vertically polarized beams.

L_p(1≤p≤∞) APPROXIMATION BY AN n-DIMENSIONAL SUBSPACE ON A SET OF n+1 POINTS

Some new characterizations and immediate explicit expressions of best L(1≤p≤∞) approximation and their deviations by an n-dimensional subspace on a set of n+1 points are given.

Customization of FeNi alloy nanosheet arrays inserted with biomass-derived carbon templates for boosted electromagnetic wave absorption

Electromagnetic wave(EMW)-absorbing materials have considerable capacity in the military field and the prevention of EMW radiation from harming human health.However,obtaining lightweight,high-performance,and broadband EMW-absorbing material remains an overwhelming challenge.Creating dielectric/magnetic composites with customized structures is a strategy with great promise for the development of high-performance EMW-absorbing materials.Using layered double hydroxides as the precursors of bimetallic alloys and combining them with porous biomass-derived carbon materials is a potential way for constructing multi-interface heterostructures as efficient EMW-absorbing materials because they have synergistic losses,low costs,abundant resources,and light weights.Here,FeNi alloy nanosheet array/Lycopodium spore-derived carbon(FeNi/LSC)was prepared through a simple hydrothermal and carbonization method.FeNi/LSC presents ideal EMW-absorbing performance by benefiting from the FeNi alloy nanosheet array,sponge-like structure,capability for impedance matching,and improved dielectric/magnetic losses.As expected,FeNi/LSC exhibited the minimum reflection loss of-58.3 dB at 1.5 mm with 20wt%filler content and a widely effective absorption bandwidth of 4.92 GHz.FeNi/LSC composites with effective EMW-absorbing performance provide new insights into the customization of biomass-derived composites as high-performance and lightweight broadband EMW-absorbing materials.

CANONICAL REPRESENTATIONS AND DEGREE OF FREEDOM FORMULAE OF ORTHOGONAL TENSORS IN N-DIMENSIONAL EUCLIDEAN SPACE

In this paper, with the help of the eigenvalue properties of orthogonal tensors in n-dimensional Euclidean space and the representations of the orthogonal tensors in 2-dimensional space, the canonical representations of orthogonal tensors in n-dimensional Euclidean space are easily gotten. The paper also gives all the constraint relationships among the principal invariants of arbitrarily given orthogonal tensor by use of Cayley-Hamilton theorem; these results make it possible to solve all the eigenvalues of any orthogonal tensor based on a quite reduced equation of m-th order, where m is the integer part ofn \2. Finally, the formulae of the degree of freedom of orthogonal tensors are given.

Application and prospect of the fluid cooling system of solar arrays for probing the Sun

The Solar Close Observations and Proximity Experiments(SCOPE)mission,which has been proposed by the Yunnan Observatories,Chinese Academy of Sciences,aiming to operate at a distance of 5 to 10 solar radii from the Sun,plans to complete the in situ detection of the solar eruption process and observation of the magnetic field structure response.The solar flux received by the satellite ranges from 10^(3) to 10^(6) Wm^(-2),which poses challenges for thermal management of the solar arrays.In this work,the solar array cooling system of the Parker Solar Probe is discussed,the developments of the fluid loop technique are reviewed,and a research plan for a next-generation solar array cooling system is proposed.This paper provides a valuable reference for novel thermal control systems in spacecraft for solar observation.

Sparse antenna array design methodologies:A review

Designing a sparse array with reduced transmit/receive modules(TRMs)is vital for some applications where the antenna system’s size,weight,allowed operating space,and cost are limited.Sparse arrays exhibit distinct architectures,roughly classified into three categories:Thinned arrays,nonuniformly spaced arrays,and clustered arrays.While numerous advanced synthesis methods have been presented for the three types of sparse arrays in recent years,a comprehensive review of the latest development in sparse array synthesis is lacking.This work aims to fill this gap by thoroughly summarizing these techniques.The study includes synthesis examples to facilitate a comparative analysis of different techniques in terms of both accuracy and efficiency.Thus,this review is intended to assist researchers and engineers in related fields,offering a clear understanding of the development and distinctions among sparse array synthesis techniques.

Low-Complexity Reconstruction of Covariance Matrix in Hybrid Uniform Circular Array

Spatial covariance matrix(SCM) is essential in many multi-antenna systems such as massive multiple-input multiple-output(MIMO). For multi-antenna systems operating at millimeter-wave bands, hybrid analog-digital structure has been widely adopted to reduce the cost of radio frequency chains.In this situation, signals received at the antennas are unavailable to the digital receiver, and as a consequence, traditional sample average approach cannot be used for SCM reconstruction in hybrid multi-antenna systems. To address this issue, beam sweeping algorithm(BSA) which can reconstruct the SCM effectively for a hybrid uniform linear array, has been proposed in our previous works. However, direct extension of BSA to a hybrid uniform circular array(UCA)will result in a huge computational burden. To this end, a low-complexity approach is proposed in this paper. By exploiting the symmetry features of SCM for the UCA, the number of unknowns can be reduced significantly and thus the complexity of reconstruction can be saved accordingly. Furthermore, an insightful analysis is also presented in this paper, showing that the reduction of the number of unknowns can also improve the accuracy of the reconstructed SCM. Simulation results are also shown to demonstrate the proposed approach.

Simulation and fabrication of in vitro microfluidic microelectrode array chip for patterned culture and electrophysiological detection of neurons

To enable the detection and modulation of modularized neural networks in vitro,this study proposes a microfluidic microelectrode array chip for the cultivation,compartmentalization,and control of neural cells.The chip was designed based on the specific structure of neurons and the requirements for detection and modulation.Finite-element analysis of the chip’s flow field was conducted using the COMSOL Multiphysics software,and the simulation results show that the liquid within the chip can flow smoothly,ensuring stable flow fields that facilitate the uniform growth of neurons within the microfluidic channels.By employing MEMS technology in combination with nanomaterial modification techniques,the microfluidic microelectrode array chip was fabricated successfully.Primary hippocampal neurons were cultured on the chip,forming a well-defined neural network.Spontaneous electrical activity of the detected neurons was recorded,exhibiting a 23.7%increase in amplitude compared to neuronal discharges detected on an open-field microelectrode array.This study provides a platform for the precise detection and modulation of patterned neuronal growth in vitro,potentially serving as a novel tool in neuroscience research.

Chiral bound states in a staggered array of coupled resonators

We study the chiral bound states in a coupled-resonator array with staggered hopping strengths,which interacts with a two-level small atom through a single coupling point or two adjacent ones.In addition to the two typical bound states found above and below the energy bands,this system presents an extraordinary chiral bound state located within the energy gap.We use the chirality to quantify the breaking of the mirror symmetry.We find that the chirality value undergoes continuous changes by tuning the coupling strengths.The preferred direction of the chirality is controlled not only by the competition between the intracell and the intercell hoppings in the coupled-resonator array,but also by the coherence between the two coupling points.In the case with one coupling point,the chirality values varies monotonously with difference between the intracell hopping and the intercell hoppings.While in the case with two coupling points,due to the coherence between the two coupling points the perfect chiral states can be obtained.

A Retrodirective Array Enabled by CMOS Chips for Two-Way Wireless Communication with Automatic Beam Tracking

This article proposes and demonstrates a retrodirective array(RDA)for two-way wireless communication with automatic beam tracking.The proposed RDA is enabled by specifically designed chips made using a domestic complementary metal-oxide semiconductor(CMOS)process.The highly integrated CMOS chip includes a receiving(Rx)chain,a transmitting(Tx)chain,and a unique tracking phaselocked loop(PLL)for the crucial conjugated phase recovery in the RDA.This article also proposes a method to reduce the beam pointing error(BPE)in a conventional RDA.To validate the above ideas simply yet without loss of generality,a 2.4 GHz RDA is demonstrated through two-way communication links between the Rx and Tx chains,and an on-chip quadrature coupler is designed to achieve a nonretrodirective signal suppression of 23 dBc.The experimental results demonstrate that the proposed RDA,which incorporates domestically manufactured low-cost 0.18 lm CMOS chips,is capable of automatically tracking beams covering±40with a reduced BPE.Each CMOS chip in the RDA has a compact size of 4.62 mm^(2) and a low power consumption of 0.15 W.To the best of the authors’knowledge,this is the first research to demonstrate an RDA with a fully customized CMOS chip for wireless communication with automatic beam tracking。

A Generalized Array Factor for Time-Modulated Hexagonal Based Antenna Array Geometry With Novel Trapezoidal Switching

The concept of the time-modulated array has been emerging as an alternative to the complex phase shifters,which lowers the cost of the array feeding network due to the utilization of radio frequency(RF)switches.The various forms of hexagonal antenna array geometries can be used for applications like surveillance tracking in phased array radar and wireless communication systems.This work proposes the generalized array factor(AF)for the hexagonal antenna array geometry based on time modulation.The time modulation in generalized hexagonal geometry can maintain the fixed static amplitude excitation,giving more flexibility over time.Furthermore,a novel trapezoidal switching function is also proposed and applied to the generalized array factor to enable future researchers to use this array factor in the field of advancement to observe how switching schemes like trapezoidal and rectangular affect the array pattern's side lobe level(SLL).The generalized equation can be utilized for the analysis and synthesis of radiation characteristics of the time-modulated hexagonal array(TMHA),time-modulated concentric hexagonal array(TMCHA),time-modulated hexagonal cylindrical array(TMHCA),and time-modulated hexagonal concentric cylindrical array(TMHCCA).The numerical result illustrates the generation of AF of time-modulated hexagonal structures and also shows that the trapezoidal switching sequence outperforms the rectangular switch using the cat swarm optimization(CSO)approach.

Design and construction of charged-particle telescope array for study of exotic nuclear clustering structure

The exploration of exotic shapes and properties of atomic nuclei,e.g.,αcluster and toroidal shape,is a fascinating field in nuclear physics.To study the decay of these nuclei,a novel detector aimed at detecting multipleα-particle events was designed and constructed.The detector comprises two layers of double-sided silicon strip detectors(DSSD)and a cesium iodide scintillator array coupled with silicon photomultipliers array as light sensors,which has the advantages of their small size,fast response,and large dynamic range.DSSDs coupled with cesium iodide crystal arrays are used to distinguish multipleαhits.The detector array has a compact and integrated design that can be adapted to different experimental conditions.The detector array was simulated using Geant4,and the excitation energy spectra of someα-clustering nuclei were reconstructed to demonstrate the performance.The simulation results show that the detector array has excellent angular and energy resolutions,enabling effective reconstruction of the nuclear excited state by multipleαparticle events.This detector offers a new and powerful tool for nuclear physics experiments and has the potential to discover interesting physical phenomena related to exotic nuclear structures and their decay mechanisms.

Theoretical optimization of micropillar arrays for structurally stable bioinspired dry adhesives

Inspired by the excellent adhesion performances of setae structure from organisms,micro/nano-pillar array has become one of the paradigms for adhesive surfaces.The micropillar arrays are composed of the resin pillars for adhesion and the substrate with different elastic modulus for supporting.The stress singularity at the bi-material corner between the pillars and the substrate can induce the failure of the micropillar-substrate corner and further hinder the fabrication and application of micropillar arrays,yet the design for the stability of the micropillar array lacks systematical and quantitative guides.In this work,we develop a semi-analytical method to provide the full expressions for the stress distribution within the bi-material corner combining analytical derivations and numerical calculations.The predictions for the stress within the singularity field can be obtained based on the full expressions of the stress.The good agreement between the predictions and the FEM results demonstrates the high reliability of our method.By adopting the strain energy density factor approach,the stability of the pillar-substrate corner is assessed by predicting the failure at the corner.For the elastic mismatch between the pillar and substrate given in this paper,the stability can be improved by increasing the ratio of the shear modulus of the substrate to that of the micropillar.Our study provides accurate predictions for the stress distribution at the bi-material corner and can guide the optimization of material combinations of the pillars and the substrate for more stable bioinspired dry adhesives.

The FAST Core Array

The Five-hundred-meter Aperture Spherical Radio Telescope(FAST)Core Array is a proposed extension of FAST,integrating 24 secondary 40-m antennas implanted within 5 km of the FAST site.This original array design will combine the unprecedented sensitivity of FAST with a high angular resolution(4.3"at a frequency of 1.4 GHz),thereby exceeding the capabilities at similar frequencies of next-generation arrays such as the Square Kilometre Array Phase 1 or the next-generation Very Large Array.This article presents the technical specifications of the FAST Core Array,evaluates its potential relatively to existing radio telescope arrays,and describes its expected scientific prospects.The proposed array will be equipped with technologically advanced backend devices,such as real-time signal processing systems.A phased array feed receiver will be mounted on FAST to improve the survey efficiency of the FAST Core Array,whose broad frequency coverage and large field of view(FOV)will be essential to study transient cosmic phenomena such as fast radio bursts and gravitational wave events,to conduct surveys and resolve structures in neutral hydrogen galaxies,to monitor or detect pulsars,and to investigate exoplanetary systems.Finally,the FAST Core Array can strengthen China's major role in the global radio astronomy community,owing to a wide range of potential scientific applications from cosmology to exoplanet science.