arXiv subjects

Jialin Zhu

Publications and source records attributed to Jialin Zhu.

28 records · Page 2Linked to original sources

arXiv2023

Spectrum Sharing between UAV-based Wireless Mesh Networks and Ground Networks

The unmanned aerial vehicle (UAV)-based wireless mesh networks can economically provide wireless services for the areas with disasters. However, the capacity of air-to-air communications is limited due to the multi-hop transmissions. In this paper, the spectrum sharing between UAV-based wireless mesh networks and ground networks is studied to improve the capacity of the UAV networks. Considering the distribution of UAVs as a three-dimensional (3D) homogeneous Poisson point process (PPP) within a vertical range, the stochastic geometry is applied to analyze the impact of the height of UAVs, the transmit power of UAVs, the density of UAVs and the vertical range, etc., on the coverage probability of ground network user and UAV network user, respectively. The optimal height of UAVs is numerically achieved in maximizing the capacity of UAV networks with the constraint of the coverage probability of ground network user. This paper provides a basic guideline for the deployment of UAV-based wireless mesh networks.

cs.RO↗

arXiv2023

Adiabatic limit, Witten deformation and analytic torsion forms

We consider a smooth fibration equipped with a flat complex vector bundle and a hypersurface cutting the fibration into two pieces. Our main result is a gluing formula relating the Bismut-Lott analytic torsion form of the whole fibration to that of each piece. This result confirms a conjecture proposed in a conference in Goettingen in 2003. Our approach combines an adiabatic limit along the normal direction of the hypersurface and a Witten type deformation on the flat vector bundle. Due to disagreement among authors, author Zhang unilaterally decides to never publish this paper. If you saw this paper published somewhere, it must be without Zhang's approvement.

math.DG↗

arXiv2023

Atiyah-Patodi-Singer index and domain-wall eta invariants

In this paper we establish a formula, expressing the generalized Atiyah-Patodi-Singer index in terms of eta invariants of domain-wall massive Dirac operators, without assuming that the Dirac operator on the boundary is invertible. Compared with the original Atiyah-Patodi-Singer index theorem, this formula has the advantage that no global spectral projection boundary conditions appear. Our main tool is an asymptotic gluing formula for eta invariants proved by using a splitting principle developed by Douglas and Wojciechowski in adiabatic limit. The eta invariant splits into a contribution from the interior, one from the boundary, and an error term vanishing in the adiabatic limit process.

math.DG↗

arXiv2022

A comparison of the absolute and relative real analytic torsion forms

In this paper we establish a comparison formula of the absolute and relative real analytic torsion forms over fibrations with boundaries. The key tool is a gluing formula of analytic torsion forms proved by M. Puchol, Y. Zhang and the author. As a consequence of the comparison formula, we prove another version of the gluing formula of the analytic torsion forms conjectured originally by the author.

math.DG↗

arXiv2021

Seamless Satellite-image Synthesis

We introduce Seamless Satellite-image Synthesis (SSS), a novel neural architecture to create scale-and-space continuous satellite textures from cartographic data. While 2D map data is cheap and easily synthesized, accurate satellite imagery is expensive and often unavailable or out of date. Our approach generates seamless textures over arbitrarily large spatial extents which are consistent through scale-space. To overcome tile size limitations in image-to-image translation approaches, SSS learns to remove seams between tiled images in a semantically meaningful manner. Scale-space continuity is achieved by a hierarchy of networks conditioned on style and cartographic data. Our qualitative and quantitative evaluations show that our system improves over the state-of-the-art in several key areas. We show applications to texturing procedurally generation maps and interactive satellite image manipulation.

cs.CV↗

arXiv2021

A comparison between the Bismut-Lott torsion and the Igusa-Klein torsion

We consider a fibration with compact fiber together with a unitarily flat complex vector bundle over the total space. Under the assumption that the fiberwise cohomology admits a filtration with unitary factors, we construct Bismut-Lott analytic torsion classes. The analytic torsion classes obtained satisfy Igusa's and Ohrt's axiomatization of higher torsion invariants. As a consequence, we obtain a higher version of the Cheeger-Müller/Bismut-Zhang theorem: for trivial flat line bundles, the Bismut-Lott analytic torsion classes coincide with the Igusa-Klein higher topological torsions up to a normalization.

math.DG↗

arXiv2019

Scattering Matrix and Analytic Torsion

For a compact manifold, which has a part isometric to a cylinder of finite length, we consider an adiabatic limit procedure, in which the length of the cylinder tends to infinity. We study the asymptotic of the spectrum of Hodge-Laplacian and the asymptotic of the $L^2$-metric on de Rham cohomology. As an application, we give a pure analytic proof of the gluing formula for analytic torsion.

math.DG↗

arXiv2017

The first terms in the expansion of the Bergman kernel in higher degrees

We establish the cancellation of the first $2j$ terms in the diagonal asymptotic expansion of the restriction to the $(0,2j)$-forms of the Bergman kernel associated to the spin${}^c$ Dirac operator on high tensor powers of a positive line bundle twisted by a (non necessarily holomorphic) complex vector bundle, over a compact Kähler manifold. Moreover, we give a local formula for the first and the second (non-zero) leading coefficients.

math.DG↗

arXiv2014

Gluing formula of real analytic torsion forms and adiabatic limit

In this article we use the adiabatic method to prove the gluing formula of real analytic torsion forms for a flat vector bundle on a smooth fibration under the assumption that the fiberwise twisted cohomology groups associated to the fibration of the cutting hypersurface are vanished. In this paper we assume that the metrics have product structures near the cutting hypersurface.

math.GT↗

arXiv2014

On the gluing formula of real analytic torsion forms

In this paper we extend first the Bismut-Lott's analytic torsion form for flat vector bundles to the boundary case, then we establish its gluing formula on a smooth fibration under the assumption that a fiberwise Morse function exists. We assume that the metrics have product structures near the cutting hypersurface.

math.GT↗