INVERSE PROBLEMS FOR A GENERAL MULTI-CONNECTED BOUNDED DRUM WITH APPLICATIONS IN PHYSICS

This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =exp, where are the eigenvalues of the negative Laplacian -in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum ft which is surrounded by simply connected bounded domains Ωi with smooth boundaries Ωi(i = 1,… ,m) where the Dirichlet, Neumann and Robin boundary conditions on Ωi(i = 1,…,m) are considered. Some geometrical properties of Ω are determined. The thermodynamic quantities for an ideal gas enclosed in Ω are examined by using the asymptotic expansions of (t) for short-time t. It is shown that the ideal gas can not feel the shape of its container Ω, although it can feel some geometrical properties of it.

Toeplitz Operators on the Bergman Space of Multi-connected Domains

In this paper, we investigate the Toeplitz operators with positive measure symbols on the Bergman spaces of bounded multi-connected domains and show that a Toeplitz operator is bounded or compact if and only if the symbol measure is a Carleson or vanishing Carleson measure respectively.

Learning-based user association and dynamic resource allocation in multi-connectivity enabled unmanned aerial vehicle networks

Unmanned Aerial Vehicles(UAvs)as aerial base stations to provide communication services for ground users is a flexible and cost-effective paradigm in B5G.Besides,dynamic resource allocation and multi-connectivity can be adopted to further harness the potentials of UAVs in improving communication capacity,in such situations such that the interference among users becomes a pivotal disincentive requiring effective solutions.To this end,we investigate the Joint UAV-User Association,Channel Allocation,and transmission Power Control(J-UACAPC)problem in a multi-connectivity-enabled UAV network with constrained backhaul links,where each UAV can determine the reusable channels and transmission power to serve the selected ground users.The goal was to mitigate co-channel interference while maximizing long-term system utility.The problem was modeled as a cooperative stochastic game with hybrid discrete-continuous action space.A Multi-Agent Hybrid Deep Reinforcement Learning(MAHDRL)algorithm was proposed to address this problem.Extensive simulation results demonstrated the effectiveness of the proposed algorithm and showed that it has a higher system utility than the baseline methods.

The 3D Inverse Problem of the Wave Equation for a General Multi-connected Vibrating Membrane with a Finite Number of Piecewise Smooth Boundary Conditions

The trace of the wave kernel μ（t） =∑ω=1^∞ exp（-itEω^1/2）, where {Eω}ω^∞=1 are the eigenvalues of the negative Laplacian -△↓2 = -∑k^3=1 （δ/δxk）^2 in the （x^1, x^2, x^3）-space, is studied for a variety of bounded domains, where -∞ 〈 t 〈 ∞ and i= √-1. The dependence of μ （t） on the connectivity of bounded domains and the Dirichlet, Neumann and Robin boundary conditions are analyzed. Particular attention is given for a multi-connected vibrating membrane Ω in Ra surrounded by simply connected bounded domains Ω j with smooth bounding surfaces S j （j = 1,……, n）, where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components Si^＊ （i = 1 ＋ kj-1,……, kj） of the bounding surfaces S j are considered, such that S j = Ui-1＋kj-1^kj Si^＊, where k0=0. The basic problem is to extract information on the geometry Ω by using the wave equation approach from a complete knowledge of its eigenvalues. Some geometrical quantities of Ω （e.g. the volume, the surface area, the mean curvuture and the Gaussian curvature） are determined from the asymptotic expansion ofexpansion of μ（t） for small │t│.

Ultra Reliable Load-Aware Connection Management(LACM)Algorithm in WIA-FA Systems

The increasing demand for industrial automation and intelligence has put forward higher requirements for the reliability of industrial wireless communication technology.As an international standard based on 802.11,Wireless networks for Industrial Automation-Factory Automation(WIA-FA)greatly improves the reliability in factory automation scenarios by Time Division Multiple Access(TDMA).However,in ultra-dense WIA-FA networks with mobile users,the basic connection management mechanism is inefficient.Most of the handover and resource management algorithms are all based on frequency division multiplexing,not suitable for the TDMA in the WIA-FA network.Therefore,we propose Load-aware Connection Management(LACM)algorithm to adjust the linkage and balance the load of access devices to avoid blocking and improve the reliability of the system.And then we simulate the algorithm to find the optimal settings of the parameters.After comparing with other existing algorithms,the result of the simulation proves that LACM is more efficient in reliability and maintains high reliability of more than 99.8%even in the ultra-dense moving scenario with 1500 field devices.Besides,this algorithm ensures that only a few signaling exchanges are required to ensure load bal-ancing,which is no more than 5 times,and less than half of the best state-of-the-art algorithm.

一类二层多目标规划的若干性质

本文对于下层为线性多目标规划的二层规划问题,在约束域非空有界的条件下证明了可行集的弱拟凸性、连通性,为算法设计提供了理论依据．

Global attractor of 2D autonomous g-Navier-Stokes equations

In this paper, the existence of global attractors for the 2D autonomous g- Navier-Stokes equations on multi-connected bounded domains is investigated under the general assumptions of boundaries. The estimation of the Hausdorff dimensions for global attractors is given.

THE EXISTENCE OF BUCKLED STATES ON A PERFORATED THIN PLATE

On the bafis of the generalized von K(?)rm(?)n theory for perforated thin plates established in [1,2], the existence of buckled states for perforated plates subjected to self-equilibrating inplane forces along each edge systematically is investigated. This work completely generalizes the results in [3, 4].

几乎C-类凸集值映射向量优化问题超有效点集的连通性

利用集值最优化问题所引入的超有效解的概念,在Hausdorff拓扑空间中利用标量化的方法讨论了当目标函数为几乎C-类凸的集值映射时,其目标空间里的超有效点集是连通的.

A robust beam tracking scheme for millimeter wave HetNets

Millimeter Wave(mmWave)communication has been widely acknowledged as an attractive solution to address high-speed transmission of massive data in 5G and beyond 5G systems due to the promising spectrum availability.However,mmWave signals are highly susceptible to blockage and may suffer from rapidly changing channels.Thus,directional/beam tracking becomes imperative yet essential for robust mmWave communications.To address this challenge,we propose a robust beam tracking scheme for mmWave Heterogeneous Networks(HetNets)with multi-connectivity.Different from most existing schemes,the proposed beam tracking scheme is effective for outage events.We first discuss theμWave-assisted beam tracking procedure with and without candidate beams,and then analyze the inherent correlation between mmWave link quality and the operating beamwidth and occlusion range to derive the optimal beamwidth.Theoretical and numerical results show that the proposed beam tracking scheme can improve the robustness of mmWave communications while guaranteeing the rate performance.

关于多因子方差模型的互补约束和互补连通性

对于多因子不完全实验和模型,笔者提出了效应互补约束和模型互补连通问题;证明了具有互补约束和两个方差模型,其最小无偏设计的网子点子集也具有互补性.这一互补连通原理将文[1]关于谱系效应模型连通性和定理扩展为关于谱系余效应模型的相应结果.

FRACTIONAL ANGULAR MOMENTUM AND THE MAGNETIC FLUX QUANTIZATION

Recently Wilczek pointed out that fractional angular momentum would exist in two-dimensional multi-connected spaces. This is a new concept different from that in usual quantum mechanics, A theoretical model of the fractional angular momentum is the flux-tube-charged boson composite called anyon. Wilczek also predicted that an-

Joint User Association and Resource Allocation for mmWave Communication:A Neural Network Approach

With the rapid growth of wireless data demand and the shortage of global bandwidth,the use of millimeter-wave(mmWave)frequency band for wireless cellular networks has become the core content of the fifth generation cellular network.Because mmWave communication has different characteristics from microwave communication,using traditional optimization techniques to manage the resource of mmWave communication networks is inappropriate.In this paper,we propose a neural network-based algorithm to solve the joint user association and resource allocation for mmWave communication system with multi-connectivity(MC)and integrated access backhaul(IAB).The resource allocation problem is formulated as a mixed-integer quadratically constrained quadratic programming(MIQCQP),which is very difficult to solve.First,we decompose the MIQCQP into two sub-problems,i.e.,binary associated matrix sub-problem and continuous IAB ratio sub-problem.Then we propose a neural network to solve the binary associated matrix inference problem and a resource allocation algorithm to find the sub-optimal IAB ratio.Simulation results show that the proposed algorithm can achieve good performance with a fast inference speed.