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Jinjiang Li

Publications and source records attributed to Jinjiang Li.

At least 19 recordsLinked to original sources

A quaternary Diophantine inequality with prime numbers of a special form (II)

Let $N$ be a sufficiently large real number. In this paper, it is proved that, for $1 0$, the Diophantine inequality \begin{equation*} \big|p_1^c+p_2^c+p_3^c+p_4^c-N\big|<(\log N)^{-E} \end{equation*} is solvable in prime variables $p_1,p_2,p_3,p_4$ such that each of the numbers $p_i+2\,(i=1,2,3,4)$ has, counted according to multiplicity, at most $[\frac{31250}{5179-3909c}]$ prime factors, which constitutes a large improvement upon the previous results of Dimitrov [13] and Li-Xue-Zhang [22], respectively.

math.NT↗

On a variant of the Piatetski-Shapiro prime number theorem

Denote by $Π_γ(x)$ the number of primes $p \leqslant x$ such that $[p^{1/γ}]$ is also a prime. In this paper, it is proved that the expected asymptotic formula \begin{equation*} Π_γ(x)=\frac{γx}{(\log x)^2} (1+o(1)) \end{equation*} holds for $γ> 15/13$, which constitutes an improvement upon the previous result of Balog [2] who showed that the above asymptotic formula holds for $γ> 6/5$.

math.NT↗

On Piatetski-Shapiro primes from almost primes

Denote by $\mathcal{P}_r$ an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this manuscript, it is established that, for any fixed $0.98353<γ<1$, there exist infinitely many primes of the form $p=[n^{1/γ}]$, where $n$ is an almost-prime $\mathcal{P}_7$. This result constitutes an improvement upon the previous result of Baker, Banks, Guo and Yeager [1], who showed that there exist infinitely many primes $p$ such that $p=[n^{1/γ}]$ with $n\in\mathcal{P}_8$ for $γ$ near to one.

math.NT↗

On the distribution of $αp^2$ modulo one in the intersection of two Piatetski--Shapiro sets

Let $\lfloor t\rfloor$ denote the integer part of $t\in\mathbb{R}$ and $\|x\|$ the distance from $x$ to the nearest integer. Suppose that $1/2<γ_2<γ_1<1$ are two fixed constants. In this paper, it is proved that, whenever $α$ is an irrational number and $β$ is any real number, there exist infinitely many prime numbers $p$ in the intersection of two Piatetski--Shapiro sets, i.e., $p=\lfloor n_1^{1/γ_1}\rfloor=\lfloor n_2^{1/γ_2}\rfloor$, such that \begin{equation*} \|αp^2+β\|<p^{-\frac{14(γ_1+γ_2)-27}{43}+\varepsilon}, \end{equation*} provided that $27/14<γ_1+γ_2<2$. This result constitutes an generalization upon the previous result of Dimitrov [4].

math.NT↗

On a system of two Diophantine inequalities with six prime variables

Suppose that $c,d,α,β$ are real numbers satisfying the inequalities $1<d<c<79/71$ and $1<α<β<6^{1-d/c}$. In this paper, it is proved that, for sufficiently large real numbers $N_1$ and $N_2$ subject to $α\leqslant N_2/N_1^{d/c}\leqslantβ$, the following Diophantine inequalities system \begin{align*} \begin{cases} |p_1^c+p_2^c+p_3^c+p_4^c+p_5^c+p_6^c-N_1|<\varepsilon_1 (N_1) \\ |p_1^d+p_2^d+p_3^d+p_4^d+p_5^d+p_6^d-N_2|<\varepsilon_2 (N_2) \end{cases} \end{align*} is solvable in prime variables $p_1, p_2, p_3, p_4, p_5, p_6$, where \begin{align*} \begin{cases} \varepsilon_1 (N_1)=N_1^{-(1/c)(79/71-c)} (\log N_1)^{201}, \\ \varepsilon_2 (N_2)=N_2^{-(1/d)(79/71-d)} (\log N_2)^{201} . \end{cases} \end{align*} This result constitutes an improvement upon the previous result of Han-Liu-Zhang [5].

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Empowering Semantic-Sensitive Underwater Image Enhancement with VLM

In recent years, learning-based underwater image enhancement (UIE) techniques have rapidly evolved. However, distribution shifts between high-quality enhanced outputs and natural images can hinder semantic cue extraction for downstream vision tasks, thereby limiting the adaptability of existing enhancement models. To address this challenge, this work proposes a new learning mechanism that leverages Vision-Language Models (VLMs) to empower UIE models with semantic-sensitive capabilities. To be concrete, our strategy first generates textual descriptions of key objects from a degraded image via VLMs. Subsequently, a text-image alignment model remaps these relevant descriptions back onto the image to produce a spatial semantic guidance map. This map then steers the UIE network through a dual-guidance mechanism, which combines cross-attention and an explicit alignment loss. This forces the network to focus its restorative power on semantic-sensitive regions during image reconstruction, rather than pursuing a globally uniform improvement, thereby ensuring the faithful restoration of key object features. Experiments confirm that when our strategy is applied to different UIE baselines, significantly boosts their performance on perceptual quality metrics as well as enhances their performance on detection and segmentation tasks, validating its effectiveness and adaptability.

cs.CV↗

DFPF-Net: Dynamically Focused Progressive Fusion Network for Remote Sensing Change Detection

Change detection (CD) has extensive applications and is a crucial method for identifying and localizing target changes. In recent years, various CD methods represented by convolutional neural network (CNN) and transformer have achieved significant success in effectively detecting difference areas in bi-temporal remote sensing images. However, CNN still exhibit limitations in local feature extraction when confronted with pseudo changes caused by different object types across global scales. Although transformers can effectively detect true change regions due to their long-range dependencies, the shadows cast by buildings under varying lighting conditions can introduce localized noise in these areas. To address these challenges, we propose the dynamically focused progressive fusion network (DFPF-Net) to simultaneously tackle global and local noise influences. On one hand, we utilize a pyramid vision transformer (PVT) as a weight-shared siamese network to implement change detection, efficiently fusing multi-level features extracted from the pyramid structure through a residual based progressive enhanced fusion module (PEFM). On the other hand, we propose the dynamic change focus module (DCFM), which employs attention mechanisms and edge detection algorithms to mitigate noise interference across varying ranges. Extensive experiments on four datasets demonstrate that DFPF-Net outperforms mainstream CD methods.

eess.IV↗

On the quadratic Waring-Goldbach problem with primes in Piatetski-Shapiro sets

In this paper, it is proved that, for any $γ_1,γ_2,γ_3,γ_4,γ_5\in(\frac{28}{29},1)$, every sufficiently large integer $n$ subject to $n\equiv5\pmod{24}$ can be represented as the sum of five squares of primes, i.e., \begin{equation*} n=p_1^2+p_2^2+p_3^2+p_4^2+p_5^2, \end{equation*} such that $p_i=\lfloor m_i^{1/γ_i}\rfloor$ for some $m_i\in\mathbb{N}^+$ for each $1\leqslant i\leqslant 5$. This result constitutes an improvement upon the previous result of Zhang and Zhai [29].

math.NT↗

On the mean square of the error term for the asymmetric two-dimensional divisor problem with congruence conditions

Suppose that $a$ and $b$ are positive integers subject to $(a,b)=1$. For $n\in\mathbb{Z}^+$, denote by $τ_{a,b}(n;\ell_1,M_1,l_2,M_2)$ the asymmetric two--dimensional divisor function with congruence conditions, i.e., \begin{equation*} τ_{a,b}(n;\ell_1,M_1,l_2,M_2)=\sum_{\substack{n=n_1^an_2^b\\ n_1\equiv\ell_1\!\!\!\!\!\pmod{M_1}\\ n_2\equiv\ell_2\!\!\!\!\!\pmod{M_2}}}1. \end{equation*} In this paper, we shall establish an asymptotic formula of the mean square of the error term of the sum $\sum_{n\leqslant M_1^aM_2^bx}τ_{a,b}(n;\ell_1,M_1,l_2,M_2)$. This result constitutes an enhancement upon the previous result of Zhai and Cao [16].

math.NT↗

On Higher-Power Moments of $ Δ_a(x) $ for $-1/2<a<0$

Let $-1/2<a<0$ be a fixed real number and \begin{equation*} Δ_{a}(x)=\sideset{}{'}\sum_{n\leq x} σ_a(n)-ζ(1-a)x-\frac{ζ(1+a)}{1+a}x^{1+a}+\frac{1}{2}ζ(-a). \end{equation*} In this paper, we investigate the higher--power moments of $Δ_a(x)$ and give the corresponding asymptotic formula for the integral $\int_{1}^{T}Δ_a^k(x)\mathrm{d}x$, which constitutes an improvement upon the previous result of Zhai [9] for $k=3,4,5$ and an enlargement of the upper bound of $k$ to $7$.

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Vinogradov's three primes theorem in the intersection of multiple Piatetski-Shapiro sets

Vinogradov's three primes theorem indicates that, for every sufficiently large odd integer $N$, the equation $N=p_1+p_2+p_3$ is solvable in prime variables $p_1,p_2,p_3$. In this paper, it is proved that Vinogradov's three primes theorem still holds with three prime variables constrained in the intersection of multiple Piatetski-Shapiro sequences.

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Cubic Waring-Goldbach problem with Piatetski-Shapiro primes

In this paper, it is proved that, for $γ\in(\frac{317}{320},1)$, every sufficiently large odd integer can be written as the sum of nine cubes of primes, each of which is of the form $[n^{1/γ}]$. This result constitutes an improvement upon the previous result of Akbal and Güloğlu [1].

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Wavelet-Guided Dual-Frequency Encoding for Remote Sensing Change Detection

Change detection in remote sensing imagery plays a vital role in various engineering applications, such as natural disaster monitoring, urban expansion tracking, and infrastructure management. Despite the remarkable progress of deep learning in recent years, most existing methods still rely on spatial-domain modeling, where the limited diversity of feature representations hinders the detection of subtle change regions. We observe that frequency-domain feature modeling particularly in the wavelet domain an amplify fine-grained differences in frequency components, enhancing the perception of edge changes that are challenging to capture in the spatial domain. Thus, we propose a method called Wavelet-Guided Dual-Frequency Encoding (WGDF). Specifically, we first apply Discrete Wavelet Transform (DWT) to decompose the input images into high-frequency and low-frequency components, which are used to model local details and global structures, respectively. In the high-frequency branch, we design a Dual-Frequency Feature Enhancement (DFFE) module to strengthen edge detail representation and introduce a Frequency-Domain Interactive Difference (FDID) module to enhance the modeling of fine-grained changes. In the low-frequency branch, we exploit Transformers to capture global semantic relationships and employ a Progressive Contextual Difference Module (PCDM) to progressively refine change regions, enabling precise structural semantic characterization. Finally, the high- and low-frequency features are synergistically fused to unify local sensitivity with global discriminability. Extensive experiments on multiple remote sensing datasets demonstrate that WGDF significantly alleviates edge ambiguity and achieves superior detection accuracy and robustness compared to state-of-the-art methods. The code will be available at https://github.com/boshizhang123/WGDF.

cs.CV↗

Prototype-Driven Structure Synergy Network for Remote Sensing Images Segmentation

In the semantic segmentation of remote sensing images, acquiring complete ground objects is critical for achieving precise analysis. However, this task is severely hindered by two major challenges: high intra-class variance and high inter-class similarity. Traditional methods often yield incomplete segmentation results due to their inability to effectively unify class representations and distinguish between similar features. Even emerging class-guided approaches are limited by coarse class prototype representations and a neglect of target structural information. Therefore, this paper proposes a Prototype-Driven Structure Synergy Network (PDSSNet). The design of this network is based on a core concept, a complete ground object is jointly defined by its invariant class semantics and its variant spatial structure. To implement this, we have designed three key modules. First, the Adaptive Prototype Extraction Module (APEM) ensures semantic accuracy from the source by encoding the ground truth to extract unbiased class prototypes. Subsequently, the designed Semantic-Structure Coordination Module (SSCM) follows a hierarchical semantics-first, structure-second principle. This involves first establishing a global semantic cognition, then leveraging structural information to constrain and refine the semantic representation, thereby ensuring the integrity of class information. Finally, the Channel Similarity Adjustment Module (CSAM) employs a dynamic step-size adjustment mechanism to focus on discriminative features between classes. Extensive experiments demonstrate that PDSSNet outperforms state-of-the-art methods. The source code is available at https://github.com/wangjunyi-1/PDSSNet.

cs.CV↗

MGCR-Net:Multimodal Graph-Conditioned Vision-Language Reconstruction Network for Remote Sensing Change Detection

With the advancement of remote sensing satellite technology and the rapid progress of deep learning, remote sensing change detection (RSCD) has become a key technique for regional monitoring. Traditional change detection (CD) methods and deep learning-based approaches have made significant contributions to change analysis and detection, however, many outstanding methods still face limitations in the exploration and application of multimodal data. To address this, we propose the multimodal graph-conditioned vision-language reconstruction network (MGCR-Net) to further explore the semantic interaction capabilities of multimodal data. Multimodal large language models (MLLM) have attracted widespread attention for their outstanding performance in computer vision, particularly due to their powerful visual-language understanding and dialogic interaction capabilities. Specifically, we design a MLLM-based optimization strategy to generate multimodal textual data from the original CD images, which serve as textual input to MGCR. Visual and textual features are extracted through a dual encoder framework. For the first time in the RSCD task, we introduce a multimodal graph-conditioned vision-language reconstruction mechanism, which is integrated with graph attention to construct a semantic graph-conditioned reconstruction module (SGCM), this module generates vision-language (VL) tokens through graph-based conditions and enables cross-dimensional interaction between visual and textual features via multihead attention. The reconstructed VL features are then deeply fused using the language vision transformer (LViT), achieving fine-grained feature alignment and high-level semantic interaction. Experimental results on four public datasets demonstrate that MGCR achieves superior performance compared to mainstream CD methods. Our code is available on https://github.com/cn-xvkong/MGCR

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Underwater Variable Zoom: Depth-Guided Perception Network for Underwater Image Enhancement

Underwater scenes intrinsically involve degradation problems owing to heterogeneous ocean elements. Prevailing underwater image enhancement (UIE) methods stick to straightforward feature modeling to learn the mapping function, which leads to limited vision gain as it lacks more explicit physical cues (e.g., depth). In this work, we investigate injecting the depth prior into the deep UIE model for more precise scene enhancement capability. To this end, we present a novel depth-guided perception UIE framework, dubbed underwater variable zoom (UVZ). Specifically, UVZ resorts to a two-stage pipeline. First, a depth estimation network is designed to generate critical depth maps, combined with an auxiliary supervision network introduced to suppress estimation differences during training. Second, UVZ parses near-far scenarios by harnessing the predicted depth maps, enabling local and non-local perceiving in different regions. Extensive experiments on five benchmark datasets demonstrate that UVZ achieves superior visual gain and delivers promising quantitative metrics. Besides, UVZ is confirmed to exhibit good generalization in some visual tasks, especially in unusual lighting conditions. The code, models and results are available at: https://github.com/WindySprint/UVZ.

cs.CV↗

Almost primes of the form $[p^{1/γ}]$

Let $\mathcal{P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, it is proved that, for $0.989<γ<1$, there exist infinitely many primes $p$ such that $[p^{1/γ}]=\mathcal{P}_7$, which constitutes an improvement upon the previous result of Banks-Guo-Shparlinski [4] who showed that there exist infinitely many primes $p$ such that $[p^{1/γ}]=\mathcal{P}_8$ for $γ$ near to one.

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