arXiv subjects
Publications and source records attributed to Zhi Jiang.
Let $A$ be a complex abelian surface. We prove that $A$ admits a dominant rational map of degree three to $\PP^2$ if and only if it admits a polarization of type $(1,1)$, $(1,2)$, $(1,3)$, or $(1,6)$. Consequently, the degree of irrationality of $A$ is $3$ precisely in these four cases and is $4$ otherwise.
We report an ambient pressure liquid metal assisted CVD strategy that enables shape programmable growth of micro scale diamond by coupling liquid metl Ga In with ferrocene (Fe(C5H5)2) as an carbon precursor, nanodiamond seeds, and nanosilicon. Building on liquid metal diamond synthesis, this approach pushes liquid metal growth toward a low temperature (900 °C, 1 atm) while enabling single crystal diamonds to be scaled from ~10 μm to several tens of micrometers with well developed faceting. Ferrocene decomposition supplies a sustained interfacial carbon flux that is captured and redistributed by the Ga In melt toward seed rich liquid solid interfaces. Defect rich nanodiamond provides the crystallographic template required for reliable sp3 nucleation despite the intrinsically low carbon solubility of Ga In. Nanosilicon plays a distinct, complementary role by tuning interfacial kinetics and facet competition, enabling deliberate control of crystal habit: cubic (~10 μm), truncated tetrahedral, and fully faceted octahedral diamonds are reproducibly obtained by adjusting the nanosilicon:nanodiamond ratio, with octahedral crystals reaching ~50 μm. Importantly, crystal size is further scaled by regulating hydrogen flow: lowering the H2 rate increases net carbon retention at the liquid metal interface, raises effective supersaturation, and accelerates diamond deposition. Together, habit control (via nanosilicon: nanodiamond) and size scaling (via H2 flow) establish a practical route silicon driven facet regulation and size under ambient pressure, offering a pathway to tunable micro sized single crystal diamonds under mild conditions.
Diamond and diamond color centers have become prime hardware candidates for solid state-based technologies in quantum information and computing, optics, photonics and (bio)sensing. The synthesis of diamond materials with specific characteristics and the precise control of the hosted color centers is thus essential to meet the demands of advanced applications. Yet, challenges remain in improving the concentration, uniform distribution and quality of these centers. Here, we perform a review and meta-analysis of some of the main diamond synthesis methods and their parameters for the synthesis of N-, Si-, Ge- and Sn-vacancy color-centers. We extract quantitative data from over 60 experimental papers and organize it in a large database (170 data sets and 1692 entries). We then use the database to train two machine learning algorithms to make robust predictions about the fabrication of diamond materials with specific properties from careful combinations of synthesis parameters. We use traditional statistical indicators to benchmark the performance of the algorithms and show that they are powerful and resource-efficient tools for researchers and material scientists working with diamond color centers and their applications.
For all nonsingular projective $n$-folds $V$ of general type, we prove the existence of Noether type inequalities in the following form: $$\text{vol}(V)\geq a_{n,k}h^0(Ω_V^k)-b_{n,k}$$ where $0< k\leq n$, $a_{n,k}$ and $b_{n,k}$ are positive constants only depending on $n$ and $k$. As applications, we prove the minimal volume conjecture for $3$-folds of general type with $χ({\mathcal O})\neq 2,3$ and disclose a new type of lifting principles for the sequence of canonical stability indices for varieties of general type. Finally we prove a theorem about ``strong lifting principle'' on varieties $V$ of general type with $q>\dim(V)$.
High-efficiency second-harmonic generation (SHG) in compact integrated photonic systems is crucial for advancing nonlinear optical technologies. However, achieving exceptional conversion efficiencies while maintaining stable performance remains a significant challenge. Here, we report a high-Q single-resonant photonic crystal nanobeam cavity (PCNBC) on a polymer-loaded lithium niobate on insulator (LNOI) platform, which enables bright second-harmonic (SH) emission. Through synergistic optimization of modal confinement and spatial overlap in a y-cut LN architecture, our device achieves a normalized SHG conversion efficiency of 163%/W, outperforming previous LN-based photonic crystal cavities LN-based photonic crystal cavities by over three orders of magnitude. The visible SH emission at 768.77 nm exhibits a single-lobe radiation pattern with precise spectral alignment between fundamental (FH) and second-harmonic (SH) modes, a critical feature for integrated photonic circuits. Remarkably, the conversion efficiency remains stable under thermal variations up to 20°C, addressing a key limitation of multi-resonant systems. High-order cavity modes are directly visualized via CCD imaging, confirming strong spatial overlap. This work establishes a record SHG conversion efficiency for LN microcavities and provides a scalable, temperature-insensitive architecture for nonlinear light sources, with immediate applications in quantum optics and chip-scale interconnects.
On chip acousto-optic (AO) modulation represents a significant advancement in the development of highly integrated information processing systems. However, conventional photonic devices face substantial challenges in achieving efficient conversion due to the limited overlap between acoustic waves and optical waves. In this study, we address this limitation by demonstrating an enhanced conversion effect of photonic crystal nanobeam cavities (PCNBCs) in AO modulation on a polymer-loaded lithium niobate integrated platform. Attributed to the high ratio of quality factor (Q) to mode volume (V) and optimal light-sound overlap within the nanocavity, PCNBCs-based AO modulator exhibits a significantly enhanced extinction ratio of 38 dB with a threshold RF power below -50 dBm, which is two orders of magnitude lower than that based on micro-ring resonator (MRRs). In addition, robust digital amplitude shift keying modulations using selected RF and optical channels of the PCNBCs-enhanced AO modulators. These findings validate the compelling properties of the PCNBCs photonic platform, establishing it as a promising candidate for on-chip integrated microwave photonics, optical transceivers, and computing applications.
For the first time, the fatigue behavior involving external oxygen in highly Sc-doped AlN ferroelectric film was observed using transmission electron microscope techniques. Despite increasing the Sc composition in AlScN film contributes to reducing the device operation voltage, the inherent affinity of Sc for oxygen introduces instability in device performance. In this study, oxygen incorporation at top electrode edges and grain boundaries accompanied with an increase in current leakage and the disappearance of ferroelectric properties, was observed in nanoscale after long-term field cycling. This observation indicates the emergence of non-ferroelectric and even amorphous states. This presented work revealed solid experimental evidence of an oxygen-involved fatigue mechanism, providing valuable insights into the physical nature of the ferroelectric properties of AlScN films.
We classify minimal surfaces $S$ with $p_g=q=2$ and $K_S^2=5$ or $6$.
In this paper, we study syzygies of rational homogeneous varieties. We extend Manivel's result that a $p$-th power of an ample line bundle on a flag variety satisfies Propery $(N_p)$ to many rational homogeneous varieties of type $B$, $C$, $D$, and $G_2$.
Pareschi showed that an ample divisor of degree $d$ on a simple abelian variety of dimension $g$ has mild singularities when $d<g$. We extend his result to general polarized abelian varieties. We also show that ample divisors of degree $3$ or $4$ on an abelian variety have mild singularities.
Ellenberg and Gijswijt gave the best known asymptotic upper bound for the cardinality of subsets of $\mathbb F_q^n$ without 3-term arithmetic progressions. We improve this bound by a factor $\sqrt{n}$. In the case $q=3$, we also obtain more explicit upper bounds for the Cap Set Problem.
We apply Angehrn-Siu-Helmke's method to estimate basepoint freeness thresholds of higher dimensional polarized abelian varieties. We showed that a conjecture of Caucci holds for very general polarized abelian varieties in the moduli spaces $\mathcal A_{g, l}$ with only finitely many possible exceptions of polarization types $l$ in each dimension $g$. We improved the bound of basepoint freeness thresholds of any polarized ableian $4$-folds and simple abelian $5$-folds.
In this paper, we prove that the group $\mathrm{Aut}_\mathbb{Q}(X)$ of numerically trivial automorphisms are uniformly bounded for smooth projective threefolds $X$ of general type which either satisfy $q(X)\geq 3$ or have a Gorenstein minimal model. If $X$ is furthermore of maximal Albanese dimension, then $|\mathrm{Aut}_\mathbb{Q}(X)|\leq 4$, and equality can be achieved by an unbounded family of threefolds previously constructed by the third author. Along the way we prove a Noether type inequality for log canonical pairs of general type with the coefficients of the boundary divisor from a given subset $\mathcal{C}\subset (0,1]$ such that $\mathcal{C}\cup\{1\}$ attains the minimum.
Shitov recently gave a counterexample to Comon's conjecture that the symmetric tensor rank and tensor rank of a symmetric tensor are the same. In this paper we show that an analog of Comon's conjecture for the G-stable rank introduced by Derksen is true: the symmetric G-stable rank and G-stable rank of a symmetric tensor are the same. We also show that the log-canonical threshold of a singularity is bounded by the G-stable rank of the defining ideal.
For an irregular variety $X$ of general type, we show that if a general fiber $F$ of the Albanese morphism of $X$ satisfies certain Hodge theoretic condition, the $0$-th cohomological support loci of $K_X$ generates the Picard variety of $X$ . We then show that the condition that the $0$-th cohomological support loci of $K_X$ generates the Picard variety of $X$ can often be applied to prove the birationality of certain pluricanonical maps of $X$.
Most current recommender systems used the historical behaviour data of user to predict user' preference. However, it is difficult to recommend items to new users accurately. To alleviate this problem, existing user cold start methods either apply deep learning to build a cross-domain recommender system or map user attributes into the space of user behaviour. These methods are more challenging when applied to online travel platform (e.g., Fliggy), because it is hard to find a cross-domain that user has similar behaviour with travel scenarios and the Location Based Services (LBS) information of users have not been paid sufficient attention. In this work, we propose a LBS-based Heterogeneous Relations Model (LHRM) for user cold start recommendation, which utilizes user's LBS information and behaviour information in related domains and user's behaviour information in travel platforms (e.g., Fliggy) to construct the heterogeneous relations between users and items. Moreover, an attention-based multi-layer perceptron is applied to extract latent factors of users and items. Through this way, LHRM has better generalization performance than existing methods. Experimental results on real data from Fliggy's offline log illustrate the effectiveness of LHRM.
We extend the so called Chen-Jiang decomposition for pushforward of pluricanocanical bundles to abelian varieties to the setting of klt pairs. We also provide a geometric application of this decomposition.
We study syzygies of abelian varieties via the methods of Caucci and Ito based on computations of cohomological rank functions. We provide some strong evidences to a conjecture of Ito and Lozovanu.