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Liwen Gao

Publications and source records attributed to Liwen Gao.

8 recordsLinked to original sources
arXiv2026

Joint Beamforming Design and Port Selection in Fluid Antenna-Assisted Multi-Cell Networks: A Personalized Federated Learning Approach

This paper investigates joint beamforming and port selection in multi-cell fluid antenna-assisted (FAS) networks. In such networks, active beamforming and discrete FA port selection are coupled through intra-cell and inter-cell interference and are jointly optimized to maximize the weighted sum-rate (WSR). We develop a federated representation learning (FedRep) framework with a position-aware dual-branch deep neural network (PA-DNN). The PA-DNN uses channel state information and port positional encoding as inputs, and jointly outputs beamforming vectors and port selections through two task-specific branches. To support decentralized training across heterogeneous cells, the FedRep framework shares global beamforming-related parameters among base stations while keeping port-selection parameters local for cell-specific adaptation. Simulation results show that the proposed scheme achieves a higher weighted sum-rate than conventional FL and port-selection benchmark schemes.

cs.IT↗
arXiv2026

Inequalities for $ζ(s)-ψ(1-s)$ related to a conjecture of Henry

In this paper we investigate analytic inequalities related to a conjecture of Henry involving the difference between the Riemann zeta function and the digamma function. By treating $ζ(s)-ψ(1-s)$ as a unified analytic object, we establish its strict convexity and monotonicity on suitable intervals. Moreover, we obtain explicit boundary limits of the derivative, expressed in terms of $π$, $\log (2π)$ and Stieltjes constants. These results lead to new inequalities for $ζ(s)-ψ(1-s)$ and shed further light on the conjecture.

math.NT↗
arXiv2025

Integrality of a trigonometric determinant arising from a conjecture of Sun

In this paper we resolve a conjecture of Zhi-Wei Sun concerning the integrality and arithmetic structure of certain trigonometric determinants. Our approach builds on techniques developed in our previous work, where trigonometric determinants were studied via special values of Dirichlet $L$-functions. The method is refined by establishing a connection between odd characters modulo $4n$ and even characters modulo $n$. The results highlight a close connection between trigonometric determinant matrices, Fourier-analytic structures, and arithmetic invariants.

math.NT↗
arXiv2025

Trigonometric Determinants via special values of Dirichlet $L$-Functions

In this paper, we investigate the determinants involving some trigonometric functions. We establish a connection between these determinants and the special values of Dirichlet L-functions, thereby extending Guo's results to arbitrary positive integers n. In addition, we also prove a conjecture raised by Zhi-Wei Sun. Our main tool is the spectral decomposition of some linear operators. By the same method we obtain an explicit formula for the determinants of sine matrices. This formula is expressed as a product of Gauss sums attached to Dirichlet characters.

math.NT↗
arXiv2025

Generation of optomicrowave and optomagnonic entanglements in cascaded optomagnomechanical systems

The optomagnomechanical system, which involves flexible nonlinearities, is one of the promising physical platforms for studying the preparation and manipulation of quantum entanglements, as well as the construction of hybrid quantum networks. A scheme for entanglement enhancement and quadripartite entanglement generation is proposed, based on a cascaded optomagnomechanical system. On the one hand, optomicrowave and optomagnonic entanglements within the two subsystems are investigated, and their parameter dependence, such as detuning, decay, coupling strength, and transmission efficiency, is discussed. On the other hand, the parameter conditions for achieving optimal optomicrowave and optomagnonic quadripartite entanglements are also obtained. The results show that significant enhancement of optomicrowave and optomagnonic entanglements in the second cavity can be obtained in a certain range of parameters. Under optimized parameter conditions, optomicrowave and optomagnonic quadripartite entanglements can be generated throughout the entire cascaded system. This research provides a theoretical basis for the manipulation of quantum entanglement, the transmission of the magnon's state, and the construction of hybrid quantum networks involving different physical systems.

quant-ph↗
arXiv2023

A new approach for constructing graph being determined by their generalized $Q$-spectrum

Given a graph $G$, we have the adjacency matrix $A(G)$ and degree diagonal matrix $D(G)$. The $Q$-spectrum is the all eigenvalues of $Q$-matrix $Q(G)=A(G)+D(G)$. A class of graphs is determined by their generalized $Q$-spectrum (DGQS for short) if any two graphs among the class have the same $Q$-spectrum and so do their complement imply that they are isomorphic. In [11], the authors provides a new way to construct $DGQS$ graphs by considering the rooted product graphs $G\circ P_{k}$ and they prove when $k=2,3$, $G\circ P_{k}$ is $DGQS$ for a special graph $G$. In this paper, we will prove that under the same conditions for $G$, the conclusion is true for any positive integer $k$.

math.SP↗
arXiv2023

Lower bound estimates for the rank of universal quadratic forms in some families of real cubic fields with density one

In this paper, we establish the explicit lower bound estimates for the rank of universal quadratic forms in some certain families of real cubic fields under the condition of density one. The more general results that represent all multiples of a given rational integer are obtained for totally positive definite quadratic lattices. Our main tools are some properties of indecomposable integers with trace in these fields and short vectors in quadratic lattices.

math.NT↗