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Jinjiang Li

Publications and source records attributed to Jinjiang Li.

At least 37 records · Page 2Linked to original sources
arXiv2024

MFDS-Net: Multi-Scale Feature Depth-Supervised Network for Remote Sensing Change Detection with Global Semantic and Detail Information

Change detection as an interdisciplinary discipline in the field of computer vision and remote sensing at present has been receiving extensive attention and research. Due to the rapid development of society, the geographic information captured by remote sensing satellites is changing faster and more complex, which undoubtedly poses a higher challenge and highlights the value of change detection tasks. We propose MFDS-Net: Multi-Scale Feature Depth-Supervised Network for Remote Sensing Change Detection with Global Semantic and Detail Information (MFDS-Net) with the aim of achieving a more refined description of changing buildings as well as geographic information, enhancing the localisation of changing targets and the acquisition of weak features. To achieve the research objectives, we use a modified ResNet_34 as backbone network to perform feature extraction and DO-Conv as an alternative to traditional convolution to better focus on the association between feature information and to obtain better training results. We propose the Global Semantic Enhancement Module (GSEM) to enhance the processing of high-level semantic information from a global perspective. The Differential Feature Integration Module (DFIM) is proposed to strengthen the fusion of different depth feature information, achieving learning and extraction of differential features. The entire network is trained and optimized using a deep supervision mechanism. The experimental outcomes of MFDS-Net surpass those of current mainstream change detection networks. On the LEVIR dataset, it achieved an F1 score of 91.589 and IoU of 84.483, on the WHU dataset, the scores were F1: 92.384 and IoU: 86.807, and on the GZ-CD dataset, the scores were F1: 86.377 and IoU: 76.021. The code is available at https://github.com/AOZAKIiii/MFDS-Net

cs.CV↗
arXiv2024

DmADs-Net: Dense multiscale attention and depth-supervised network for medical image segmentation

Deep learning has made important contributions to the development of medical image segmentation. Convolutional neural networks, as a crucial branch, have attracted strong attention from researchers. Through the tireless efforts of numerous researchers, convolutional neural networks have yielded numerous outstanding algorithms for processing medical images. The ideas and architectures of these algorithms have also provided important inspiration for the development of later technologies.Through extensive experimentation, we have found that currently mainstream deep learning algorithms are not always able to achieve ideal results when processing complex datasets and different types of datasets. These networks still have room for improvement in lesion localization and feature extraction. Therefore, we have created the Dense Multiscale Attention and Depth-Supervised Network (DmADs-Net).We use ResNet for feature extraction at different depths and create a Multi-scale Convolutional Feature Attention Block to improve the network's attention to weak feature information. The Local Feature Attention Block is created to enable enhanced local feature attention for high-level semantic information. In addition, in the feature fusion phase, a Feature Refinement and Fusion Block is created to enhance the fusion of different semantic information.We validated the performance of the network using five datasets of varying sizes and types. Results from comparative experiments show that DmADs-Net outperformed mainstream networks. Ablation experiments further demonstrated the effectiveness of the created modules and the rationality of the network architecture.

eess.IV↗
arXiv2023

Primes in the intersection of two Piatetski-Shapiro sets

Let $π(x;γ_1,γ_2)$ denote the number of primes $p$ with $p\leqslant x$ and $p=\lfloor n^{1/γ_1}_1\rfloor=\lfloor n^{1/γ_2}_2\rfloor$, where $\lfloor t\rfloor$ denotes the integer part of $t\in\mathbb{R}$ and $1/2<γ_2<γ_1<1$ are fixed constants. In this paper, we show that $π(x;γ_1,γ_2)$ holds an asymptotic formula for $21/11<γ_1+γ_2<2$, which constitutes an improvement upon the previous result of Baker [1].

math.NT↗
arXiv2023

On Chen's theorem over Piatetski-Shapiro type primes and almost-primes

In this paper, we establish a new mean value theorem of Bombieri-Vinogradov type over Piatetski-Shapiro sequence. Namely, it is proved that for any given constant $A>0$ and any sufficiently small $\varepsilon>0$, there holds \begin{equation*} \sum_{\substack{d\leqslant x^ξ\\ (d,l)=1}}\Bigg|\sum_{\substack{A_1(x)\leqslant a<A_2(x)\\ (a,d)=1}}g(a) \Bigg(\sum_{\substack{ap\leqslant x\\ ap\equiv l\!\pmod d \\ ap=[k^{1/γ}]}}1 -\frac{1}{φ(d)}\sum_{\substack{ap\leqslant x\\ ap=[k^{1/γ}] }} 1\Bigg)\Bigg|\ll\frac{x^γ}{(\log x)^A}, \end{equation*} provided that $1\leqslant A_1(x)<A_2(x)\leqslant x^{1-\varepsilon}$ and $g(a)\ll τ_r^s(a)$, where $l\not=0$ is a fixed integer and \begin{equation*} ξ:=ξ(γ)=\frac{2^{38}+17}{38}γ-\frac{2^{38}-1}{38}-\varepsilon \end{equation*} with \begin{equation*} 1-\frac{18}{2^{38}+17}<γ<1. \end{equation*} Moreover, for $γ$ satisfying \begin{equation*} 1-\frac{0.03208}{2^{38}+17}<γ<1, \end{equation*} we prove that there exist infinitely many primes $p$ such that $p+2=\mathcal{P}_2$ with $\mathcal{P}_2$ being Piatetski-Shapiro almost-primes of type $γ$, and there exist infinitely many Piatetski-Shapiro primes $p$ of type $γ$ such that $p+2=\mathcal{P}_2$. These results generalize the result of Pan and Ding [37] and constitutes an improvement upon a series of previous results of [29,31,39,47].

math.NT↗
arXiv2022

A generalization of Piatetski-Shapiro sequences (II)

Suppose that $α,β\in\mathbb{R}$. Let $α\geqslant1$ and $c$ be a real number in the range $1<c< 12/11$. In this paper, it is proved that there exist infinitely many primes in the generalized Piatetski--Shapiro sequence, which is defined by $(\lfloorαn^c+β\rfloor)_{n=1}^\infty$. Moreover, we also prove that there exist infinitely many Carmichael numbers composed entirely of primes from the generalized Piatetski--Shapiro sequences with $c\in(1,\frac{19137}{18746})$. The two theorems constitute improvements upon previous results by Guo and Qi.

math.NT↗
arXiv2021

Piatetski-Shapiro primes in the intersection of multiple Beatty sequences

Suppose that $α_1, α_2,β_1, β_2 \in\mathbb{R}$. Let $α_1, α_2 > 1$ be irrational and of finite type such that $1, α_1^{-1}, α_2^{-1}$ are linearly independent over $\mathbb{Q}$. Let $c$ be a real number in the range $1 < c < 12/11$. In this paper, it is proved that there exist infinitely many primes in the intersection of Beatty sequences $\mathcal{B}_{α_1,β_1} = \lfloorα_1 n + β_1\rfloor, \mathcal{B}_{α_2, β_2} = \lfloorα_2 n + β_2\rfloor$ and the Piatetski-Shapiro sequence $\mathscr{N}^{(c)} = \lfloor n^c\rfloor$. Moreover, we also give a sketch proof of Piatetski-Shapiro primes in the intersection of multiple Beatty sequences.

math.NT↗
arXiv2021

Beatty primes from fractional powers of almost-primes

Let $α>1$ be irrational and of finite type, $β\in\mathbb{R}$. In this paper, it is proved that for $R\geqslant13$ and any fixed $c\in(1,c_R)$, there exist infinitely many primes in the intersection of Beatty sequence $\mathcal{B}_{α,β}$ and $\lfloor n^c\rfloor$, where $c_R$ is an explicit constant depending on $R$ herein, $n$ is a natural number with at most $R$ prime factors, counted with multiplicity.

math.NT↗
arXiv2021

On the least almost-prime in arithmetic progression

Let $\mathcal{P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. Suppose that $a$ and $q$ are positive integers satisfying $(a,q)=1$. Denote by $\mathcal{P}_2(a,q)$ the least almost-prime $\mathcal{P}_2$ which satisfies $\mathcal{P}_2\equiv a\pmod q$. In this paper, it is proved that for sufficiently large $q$, there holds \begin{equation*} \mathcal{P}_2(a,q)\ll q^{1.8345}. \end{equation*} This result constitutes an improvement upon that of Iwaniec, who obtained the same conclusion, but for the range $1.845$ in place of $1.8345$.

math.NT↗
arXiv2021

On the distribution of $αp^2$ modulo one with prime $p$ of a special form

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 $α\in\mathbb{R}\backslash\mathbb{Q},\,β\in\mathbb{R}$ and $0<θ<10/1561$, there exist infinitely many primes $p$, such that $\|αp^2+β\|<p^{-θ}$ and $p+2=\mathcal{P}_4$, which constitutes an improvement upon the previous result.

math.NT↗
arXiv2020

On two Diophantine inequalities over primes (II)

Let $1<c<\frac{26088036}{12301745},c\not=2$ and $N$ be a sufficiently large real number. In this paper, it is proved that, for almost all $R\in (N,2N]$, the Diophantine inequality \begin{equation*} \big|p_1^c+p_2^c+p_3^c-R\big|<\log^{-1}N \end{equation*} is solvable in primes $p_1,p_2,p_3$. Moreover, we also prove that the following Diophantine inequality \begin{equation*} \big|p_1^c+p_2^c+p_3^c+p_4^c+p_5^c+p_6^c-N\big|<\log^{-1}N \end{equation*} is solvable in prime variables $p_1,p_2,p_3,p_4,p_5,p_6$, which improves the previous result $1<c<\frac{37}{18},c\neq2$.

math.NT↗
arXiv2020

On Waring-Goldbach Problem for Squares, Cubes and Higher Powers

Let $\mathcal{P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, we generalize the result of Vaughan for ternary admissible exponent. Moreover, we use the refined admissible exponent to prove that, for $3\leqslant k\leqslant 14$ and for every sufficiently large even integer $n$, the following equation \begin{equation*} n=x^2+p_1^2+p_2^3+p_3^3+p_4^3+p_5^k \end{equation*} is solvable with $x$ being an almost-prime $\mathcal{P}_{r(k)}$ and the other variables primes, where $r(k)$ is defined in Theorem. This result constitutes a deepening upon that of previous results.

math.NT↗
arXiv2020

An Additive Problem over Piatetski-Shapiro Primes and Almost-primes

Let $\mathcal{P}_r$ denote an almost-prime with at most $r$ prime factors, counted according to multiplicity. In this paper, we establish a theorem of Bombieri-Vinogradov type for the Piatetski-Shapiro primes $p=[n^{1/γ}]$ with $\frac{85}{86}<γ<1$. Moreover, we use this result to prove that, for $0.9989445<γ<1$, there exist infinitely many Piatetski-Shapiro primes such that $p+2=\mathcal{P}_3$, which improves the previous results of Lu, Wang and Cai, and Peneva.

math.NT↗
arXiv2019

On a Diophantine equation with five prime variables

Let $[x]$ denote the integral part of the real number $x$, and $N$ be a sufficiently large integer. In this paper, it is proved that, for $1<c<\frac{4109054}{1999527}, c\not=2$, the Diophantine equation $N=[p_1^c]+[p_2^c]+[p_3^c]+[p_4^c]+[p_5^c]$ is solvable in prime variables $p_1,p_2,p_3,p_4,p_5$.

math.NT↗
arXiv2018

A Diophantine inequality with four prime variables

Let $N$ be a sufficiently large real number. In this paper, it is proved that, for $1<c<\frac{1193}{889}$, the following Diophantine inequality \begin{equation*} \big|p_1^c+p_2^c+p_3^c+p_4^c-N\big|<\log^{-1}N \end{equation*} is solvable in prime variables $p_1,p_2,p_3,p_4$, which improves the result of Mu.

math.NT↗
arXiv2017

On the Waring-Goldbach Problem for One Square and Five Cubes

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 every sufficiently large even integer $N$, the equation \begin{equation*} N=x^2+p_1^3+p_2^3+p_3^3+p_4^3+p_5^3 \end{equation*} is solvable with $x$ being an almost-prime $\mathcal{P}_6$ and the other variables primes. This result constitutes an improvement upon that of Cai, who obtained the same conclusion, but with $\mathcal{P}_{36}$ in place of $\mathcal{P}_6$.

math.NT↗
arXiv2017

On the Fourth Power Moment of the Error Term for the Divisor Problem with Congruence Conditions

Let $d(n;\ell_1,M_1,\ell_2,M_2)$ denote the number of factorizations $n=n_1n_2$, where each of the factors $n_i\in\mathbb{N}$ belongs to a prescribed congruence class $\ell_i\bmod M_i\,(i=1,2)$. Let $Δ(x;\ell_1,M_1,\ell_2,M_2)$ be the error term of the asymptotic formula of $\sum\limits_{n\leqslant x}d(n;\ell_1,M_1,\ell_2,M_2)$. In this paper, we establish an asymptotic formula of the fourth power moment of $Δ(M_1M_2x;\ell_1,M_1,\ell_2,M_2)$ and prove that \begin{equation*} \int_1^TΔ^4(M_1M_2x;\ell_1,M_1,\ell_2,M_2)\mathrm{d}x=\frac{1}{32π^4}C_4\Big(\frac{\ell_1}{M_1},\frac{\ell_2}{M_2}\Big) T^2+O(T^{2-\vartheta_4+\varepsilon}), \end{equation*} with $\vartheta_4=1/8$, which improves the previous value $θ_4=3/28$ of K. Liu.

math.NT↗
arXiv2017

On the Fourth Power Moment of Fourier Coefficients of Cusp Form

Let $a(n)$ be the Fourier coefficients of a holomorphic cusp form of weight $κ=2n\geqslant12$ for the full modular group and $A(x)=\sum\limits_{n\leqslant x}a(n)$. In this paper, we establish an asymptotic formula of the fourth power moment of $A(x)$ and prove that \begin{equation*} \int_1^TA^4(x)\mathrm{d}x=\frac{3}{64κπ^4}s_{4;2}(\tilde{a}) T^{2κ}+O\big(T^{2κ-δ_4+\varepsilon}\big) \end{equation*} with $δ_4=1/8$, which improves the previous result.

math.NT↗