CHEBYSHEV APPROXIMATION BY FUNCTIONS HAVING RESTRICTED RANGES WITH EQUALITIES

In this paper, we establish a new type of alternation theory for more general restricted ranges Chebyshev approximation with equalities. The uniqueness and strong uniqueness theorems are given. Applying the results, we obtain the alternation theorem and uniqueness theorem for best coposilive approximation.

PROBLEM OF EQUALITIES IN EIGENVALUE INEQUALITIES FOR PRODUCTS OF POSITIVE SEMIDEFINITE HERMITIAN MATRICES

Let A∈Cm×n,set eigenvalues of matrix A with |λ1 （A）|≥|λ2（A）|≥…≥|λn（A）|,write A≥0 if A is a positive semidefinite Hermitian matrix, and denote∧k （A）=diag （λ1（A）,…,λk（A））,∧(（n-k）.（A）=diag (λk+1（A）,…,λn（A）)for any k=1, 2,...,n if A≥0. Denote all n order unitary matrices by Un×n.Problem of equalities to hold in eigenvalue inequalities for products of matrices

Relating Optimization Problems to Systems of Inequalities and Equalities

In quantitative decision analysis, an analyst applies mathematical models to make decisions. Frequently these models involve an optimization problem to determine the values of the decision variables, a system S of possibly non- linear inequalities and equalities to restrict these variables, or both. In this note, we relate a general nonlinear programming problem to such a system S in such a way as to provide a solution of either by solving the other—with certain limitations. We first start with S and generalize phase 1 of the two-phase simplex method to either solve S or establish that a solution does not exist. A conclusion is reached by trying to solve S by minimizing a sum of artificial variables subject to the system S as constraints. Using examples, we illustrate how this approach can give the core of a cooperative game and an equilibrium for a noncooperative game, as well as solve both linear and nonlinear goal programming problems. Similarly, we start with a general nonlinear programming problem and present an algorithm to solve it as a series of systems S by generalizing the “sliding objective function method” for two-dimensional linear programming. An example is presented to illustrate the geometrical nature of this approach.

Nonequilibrium work equalities in isolated quantum systems

We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities .in isolated quantum Hamiltonian sys- tems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some resultsare given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.

Rank Equalities for Anti-involutory Matrices

Some rank equalities are established for anti-involutory matrices. In particular, we get the formulas for the rank of the difference, the sum and the commutator of anti-involutory matrices.

Numerical Radius Inequalities for Sums and Products of Operators

A numerical radius inequality due to Shebrawi and Albadawi says that: If Ai, Bi, Xi are bounded operators in Hilbert space, i = 1,2,..., n , and f,g be nonnegative continuous functions on [0, ∞) satisfying the relation f(t)g(t) = t (t∈[0, ∞)), then for all r≥1. We give sharper numerical radius inequality which states that: If Ai, Bi, Xi are bounded operators in Hilbert space, i = 1,2,..., n , and f,g be nonnegative continuous functions on [0, ∞) satisfying the relation f(t)g(t) = t (t∈[0, ∞)), then ?where . Moreover, we give many numerical radius inequalities which are sharper than related inequalities proved recently, and several applications are given.

Weighted variation inequalities for differential operators and singular integrals in higher dimensions

We prove weighted q-variation inequalities with 2<q<∞for sharp truncations of singular integral operators in higher dimensions.The vector-valued extensions of these inequalities are also given.Parallel results are proven for differential operators.

A 28/56 Gb/s NRZ/PAM-4 dual-mode transceiver with 1/4 rate reconfigurable 4-tap FFE and half-rate slicer in a 28-nm CMOS

A 28/56 Gb/s NRZ/PAM-4 dual-mode transceiver(TRx)designed in a 28-nm complementary metal-oxide-semiconduc-tor(CMOS)process is presented in this article.A voltage-mode(VM)driver featuring a 4-tap reconfigurable feed-forward equal-izer(FFE)is employed in the quarter-rate transmitter(TX).The half-rate receiver(RX)incorporates a continuous-time linear equal-izer(CTLE),a 3-stage high-speed slicer with multi-clock-phase sampling,and a clock and data recovery(CDR).The experimen-tal results show that the TRx operates at a maximum speed of 56 Gb/s with chip-on board(COB)assembly.The 28 Gb/s NRZ eye diagram shows a far-end vertical eye opening of 210 mV with an output amplitude of 351 mV single-ended and the 56 Gb/s PAM-4 eye diagram exhibits far-end eye opening of 33 mV(upper-eye),31 mV(mid-eye),and 28 mV(lower-eye)with an output amplitude of 353 mV single-ended.The recovered 14 GHz clock from the RX exhibits random jitter(RJ)of 469 fs and deterministic jitter(DJ)of 8.76 ps.The 875 Mb/s de-multiplexed data features 593 ps horizontal eye opening with 32.02 ps RJ,at bit-error rate(BER)of 10-5(0.53 UI).The power dissipation of TX and RX are 125 and 181.4 mW,respectively,from a 0.9-V sup-ply.

Equalization Reconstruction Algorithm Based on Reference Signal Frequency Domain Block Joint for DTMB-Based Passive Radar

Channel equalization plays a pivotal role within the reconstruction phase of passive radar reference signals.In the context of reconstructing digital terrestrial multimedia broadcasting(DTMB)signals for low-slow-small(LSS)target detection,a novel frequency domain block joint equalization algorithm is presented in this article.From the DTMB signal frame structure and channel multipath transmission characteristics,this article adopts a unconventional approach where the delay and frame structure of each DTMB signal frame are reconfigured to create a circular convolution block,facilitating concurrent fast Fourier transform(FFT)calculations.Following equalization,an inverse fast Fourier transform(IFFT)-based joint output and subsequent data reordering are executed to finalize the equalization process for the DTMB signal.Simulation and measured data confirm that this algorithm outperforms conventional techniques by reducing signal errors rate and enhancing real-time processing.In passive radar LSS detection,it effectively suppresses multipath and noise through frequency domain equalization,reducing false alarms and improving the capabilities of weak target detection.

A New Equalization Method for Lithium-Ion Battery Packs Based on CUK

Aiming at the traditional CUK equalizer can only perform energy equalization between adjacent batteries,if the two single batteries that need to be equalized are far away from each other,there will be the problem of longer energy transmission path and lower equalization efficiency,this paper optimizes the CUK equalizer and optimizes its peripheral selection circuit,which can support the equalization of single batteries at any two positions.The control strategy adopts the open-circuit voltage(OVC)of the battery and the state of charge(SOC)of the battery as the equalization variables,and selects the corresponding equalization variables according to the energy conditions of the two batteries that need to be equalized,and generates the adaptive equalization current with an adaptive PID controller in order to improve the equalization efficiency.Simulation modeling is performed in Matlab/Simulink 2021b,and the experimental results show that the optimized CUK equalizer in this paper improves the equalization time by 25.58%compared with the traditional CUK equalizer.In addition,compared with the mean value difference(MVD)method,the adaptive PID method reduces the equalization time by about 30%in the static and charging and discharging experimental environments,which verifies the superiority of this equalization scheme.

Automatic SOC Equalization Strategy of Energy Storage Units with DC Microgrid Bus Voltage Support

In this paper,an improved sag control strategy based on automatic SOC equalization is proposed to solve the problems of slow SOC equalization and excessive bus voltage fluctuation amplitude and offset caused by load and PV power variations in a stand-alone DC microgrid.The strategy includes primary and secondary control.Among them,the primary control suppresses the DC microgrid voltage fluctuation through the I and II section control,and the secondary control aims to correct the P-U curve of the energy storage system and the PV system,thus reducing the steady-state bus voltage excursion.The simulation results demonstrate that the proposed control strategy effectively achieves SOC balancing and enhances the immunity of bus voltage.The proposed strategy improves the voltage fluctuation suppression ability by approximately 39.4%and 43.1%under the PV power and load power fluctuation conditions,respectively.Furthermore,the steady-state deviation of the bus voltage,△U_(dc) is only 0.01–0.1 V,ensuring stable operation of the DC microgrid in fluctuating power environments.

Assessing the Spatial Equality of COVID Testing Sites Maintaining Zero COVID Policy

Rapid and timely testing is essential to minimize the COVID-19 spread. Decision makers and policy planners need to determine the equal distribution and accessibility of testing sites. This study mainly examines the spatial equality of COVID-19 testing sites that maintain a zero COVID policy in Guangzhou City. The study has identified the spatial disparities of COVID testing sites, characteristics of testing locations, and accessibility. The study has obtained information on COVID testing sites in Guangzhou City and population data. Point pattern analyses, Euclidian distance and allocation, and network analyses are the main methods used to achieve the research objectives, and 1183 total COVID testing sites can be recognized in Guangzhou City. Results revealed that spatial disparities could be noticed over the study area. Testing locations of Guangzhou City are highly clustered. The most significant testing sites are located in Haizhu District, which has the third largest population. The highest population density can be identified in Yuexiu District. However, only 94 testing sites are located there. According to all the results, higher disparities can be identified, and a lack of testing sites is located in the north part of the study area. Some people in the northern part have to travel more than 10 km to reach a testing site. Finally, this paper suggests increasing the number of testing sites in the north and south parts of the study area and keeping the same distribution, considering the area, total population, and population density. This kind of research will be helpful to decision-makers in making proper decisions to maintain a zero COVID policy.

Pursuing Common Good for All under Heaven

Fairness,justice,and equality are long existing pursuits of Chinese philosophers from ancient times to today.AS a political ideal,the ancient Chinese saying“Tian Xia Wei Gong”,or“pursuing common good for all under heaven”has been influencing Chinese politics and collective mind of the Chinese people since the time Confucius proposed it.

GENDER EQUALITY IN THE CHINESE WORKPLACE

Gender equality is a significant issue in the economic and social sectors.A McKinsey study found that promoting gender equality in the workplace could contribute US$13 trillion to global GDP growth.And if China reaches the forefront of gender equality in the workplace in the Asia-Pacific region,it would generate about US$3 trillion in GDP.

News-Clips(2024. 02-2024. 03)

February 2024 State councilor urges high-quality work for women,children Chinese State Councilor Shen Yiqin has urged efforts to advance the high-quality development of work for women and children during her inspection tour in east China’s Fujian Province.From Feb.2 to Feb.3,Shen inspected local service centers for women and children in the provincial capital city of Fuzhou and visited rural areas and urban communities to learn about relevant work.Shen,also president of the All-China Women’s Federation,called for efforts to ensure the Party’s leadership over the work of women’s federations,focus on the most practical and tangible matters for women and their families,and promote gender equality and all-around development of women and children.

Advancement Towards Spatial Justice:The Barrier-Free Environment Construction from a Gender Perspective

Space is both a product and a producer of social relations.In the spatial domain,gender blindness has long existed,limiting women’s rights of access to and use of space,leading to structural oppression of women’s rights,and giving rise to new gender inequalities.The barrier-free environment construction has the functions of eliminating physical barriers and generating societal norms,and when combined with social changes,can facilitate justice correction across multiple dimensions.However,barrier-free environment construction itself,as a means of justice correction,also suffers from gender blindness.There remains room for improvement in the areas of facility construction,information exchange,and social services within the realm of barrier-free environments.In response to this phenomenon,gender equality offers a new critical perspective.Therefore,integrating a gender perspective into the barrier-free environment construction,focusing on the spatial rights of women,especially groups with multiple vulnerabilities,such as disabled women and elderly women,can contribute to the advancement towards spatial justice.

THE EQUALITIES OF THE CHERN CLASSES

In this paper we generalize the results of [1]and prove that,for any given 4≤k≤n,theChern classes of hypersurface V_n corresponding to the partitions of k also satisfy some equalities.Furthermore,we obtain the equalities of Chern classes concretely for k=4,5,6.

Near-Field Beam Training for Holographic MIMO Communications: Typical Methods, Challenges and Future Directions

Holographic multiple-input multiple-output(HMIMO)has become an emerging technology for achieving ultra-high frequency spectral efficiency and spatial resolution in future wireless systems.The increasing antenna aperture leads to a more significant characterization of the spherical wavefront in near-field communications in HMIMO scenarios.Beam training as a key technique for wireless communication is worth exploring in this near-field scenario.Compared with the widely researched far-field beam training,the increased dimensionality of the search space for near-field beam training poses a challenge to the complexity and accuracy of the proposed algorithm.In this paper,we introduce several typical near-field beam training methods:exhaustive beam training,hierarchical beam training,and multi-beam training that includes equal interval multi-beam training and hash multi-beam training.The performances of these methods are compared through simulation analysis,and their effectiveness is verified on the hardware testbed as well.Additionally,we provide application scenarios,research challenges,and potential future research directions for near-field beam training.

Bound State Description of Particles from a Quantum Field Theory of Fermions and Bosons, Compatible with Relativity

Both, the dilemma to find a quantum field theory consistent with Einstein’s law of relativity and the problem to describe existing particles as bound states of matter has been solved by calculating bound state matrix elements from a dual fermion-boson Lagrangian. In this formalism, the fermion binding energies are compensated by boson energies, indicating that particles can be generated out of the vacuum. This yields quantitative solutions for various mesons ω (0.78 GeV) - Υ (9.46 GeV) and all leptons e, μ and τ, with uncertainties in the extracted properties of less than 1‰. For transparency, a Web-page with the address htpps://h2909473.stratoserver.net has been constructed, where all calculations can be run on line and also the underlying fortran source code can be inspected.

On the Case of Equalities in Comparison Results for Elliptic Equations Related to Gauss Measure

In this paper, we deal with a Dirichlet problem for linear elliptic equations related to Gauss measure. For this problem, we study the converse of some inequalities proved by other authors, in the sense that we study the case of equalities and show that equalities are achieved only in the ＂symmetrized＂ situations. In addition, under other assumptions, we give a different form of comparison results and discuss the corresponding case of equalities.