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Some Generalizations of Monotonicity Condition and Applications 被引量:2
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作者 虞旦盛 周颂平 《数学进展》 CSCD 北大核心 2006年第6期755-757,共3页
0 Introduction It is well known that there axe a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the cond... 0 Introduction It is well known that there axe a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the condition to quasi-monotonicity, O-regularly varying quasi-monotonicity, etc.. 展开更多
关键词 LIM Some generalizations of Monotonicity Condition and Applications
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Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws
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作者 Xian-Guo Geng Fei-Ying Guo Yun-Yun Zhai 《Chinese Physics B》 SCIE EI CAS CSCD 2020年第5期70-73,共4页
With the aid of Lenard recursion equations, an integrable hierarchy of nonlinear evolution equations associated with a 2 × 2 matrix spectral problem is proposed, in which the first nontrivial member in the positi... With the aid of Lenard recursion equations, an integrable hierarchy of nonlinear evolution equations associated with a 2 × 2 matrix spectral problem is proposed, in which the first nontrivial member in the positive flows can be reduced to a new generalization of the Wadati–Konno–Ichikawa(WKI) equation. Further, a new generalization of the Fokas–Lenells(FL) equation is derived from the negative flows. Resorting to these two Lax pairs and Riccati-type equations, the infinite conservation laws of these two corresponding equations are obtained. 展开更多
关键词 integrable generalizations positive flow and negative flow infinite conservation laws
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SOME GENERALIZATIONS ON THE BOUNDEDNESS OF BILINEAR OPERATORS
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作者 Li Xiaochun Lu Shanzhen Yang Dachun(Beijing Normal University, China) 《Analysis in Theory and Applications》 1997年第3期8-28,共21页
For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or ... For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the standard fractional integral with the Calderon-Zygmund operator. The authors prove that such mapping properties hold if and only if these operators satisfy certain cancellation conditions. 展开更多
关键词 MATH SOME generalizations ON THE BOUNDEDNESS OF BILINEAR OPERATORS
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INTERPOLATION WITH LAGRANGE POLYNOMIALS A SIMPLE PROOF OF MARKOV INEQUALITY AND SOME OF ITS GENERALIZATIONS
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作者 A.Shadrin 《Analysis in Theory and Applications》 1992年第3期51-61,共11页
The following theorem is proved Theorem 1.Let q be a polynomial of degree n(qP_n)with n distinct zeroes lying in the interval[-1,1] and △'_q={-1}∪{τ_i:q'(τ_i)=0,i=1,n-1}∪{1}. If polynomial pP_n satisfies ... The following theorem is proved Theorem 1.Let q be a polynomial of degree n(qP_n)with n distinct zeroes lying in the interval[-1,1] and △'_q={-1}∪{τ_i:q'(τ_i)=0,i=1,n-1}∪{1}. If polynomial pP_n satisfies the inequality then for each k=1,n and any x[-1,1]its k-th derivative satisfies the inequality 丨p^(k)(x)丨≤max{丨q^((k))(x)丨,丨1/k(x^2-1)q^(k+1)(x)+xq^((k))(x)丨}. This estimate leads to the Markov inequality for the higher order derivatives of polynomials if we set q=T_n,where Tn is Chebyshev polynomial least deviated from zero. Some other results are established which gives evidence to the conjecture that under the conditions of Theorem 1 the inequality ‖p^((k))‖≤‖q^(k)‖holds. 展开更多
关键词 INTERPOLATION WITH LAGRANGE POLYNOMIALS A SIMPLE PROOF OF MARKOV INEQUALITY AND SOME OF ITS generalizations
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Generalizations of Euler Numbers and Euler Numbers of Higher Order 被引量:5
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作者 LUOQiu-ming QIFeng 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2005年第1期54-58,共5页
The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler... The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended. 展开更多
关键词 Euler numbers higher order Euler numbers generalized Euler numbers generalized higher order Euler numbers recursion formula
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GENERALIZATIONS OF THE SUZUKI AND KANNAN FIXED POINT THEOREMS IN G-CONE METRIC SPACES 被引量:1
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作者 Mohammad Sadegh Asgari Zohreh Abbasbigi 《Analysis in Theory and Applications》 2012年第3期248-262,共15页
In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in gener... In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces. 展开更多
关键词 fixed point D-metric space 2-metric space generalized cone metric space Kannan mapping generalized Kannan mapping contractive mapping
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SOME FURTHER GENERALIZATIONS OF KY FAN’S MINIMAX INEQUALITY AND ITS APPLICATIONS TO VARIATIONAL INEQUALITIES 被引量:1
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作者 张石生 杨干山 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第11期1027-1034,共8页
The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general version of the famous KKM theorem and Ky Fan's minimax inequality. As applications, we utilize the result... The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general version of the famous KKM theorem and Ky Fan's minimax inequality. As applications, we utilize the results presented in this paper to study the saddle . point problem and the existence problem of solutions for a class of quasi-variational inequalities. The results obtained in this paper extend and improve some recent results of[1-6] 展开更多
关键词 generalized KKM mapping upper-semicontinuous γ-diagonally quasi-convex saddle point
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Generalizations of Some Formulas of the Reciprocal Sum and Alternating Sum for Generalized Lucas Numbers
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作者 YE Xiao-li LIU Mai-xue 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第1期99-103,共5页
The purpose of this article is to provide the inversion relationships between the reciprocal sum S(1, 2,…, m) and the alternating sum T(1, 2,…, m) for generalized Lucas numbers which generalizes the Melham's re... The purpose of this article is to provide the inversion relationships between the reciprocal sum S(1, 2,…, m) and the alternating sum T(1, 2,…, m) for generalized Lucas numbers which generalizes the Melham's results. 展开更多
关键词 generalized Lucas numbers reciprocal sum alternating sum
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Properties of Elliptic Integrals and Their Generalizations
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作者 ZHANGXiao-hui QIUSong-fiang 《杭州电子工业学院学报》 2004年第6期55-58,共4页
In this paper, a conjecture put forward by G. D. Anderson, S.-L. Qiu and M. K. Vamanamurthy in 1995 and concerning elliptic integrals is proved to be true, and some monotoneity and onvexity properties of certain combi... In this paper, a conjecture put forward by G. D. Anderson, S.-L. Qiu and M. K. Vamanamurthy in 1995 and concerning elliptic integrals is proved to be true, and some monotoneity and onvexity properties of certain combinations of generalized elliptic integrals are obtained. 展开更多
关键词 generalized ELLIPTIC INTEGRALS monotoneity CONVEXITY CONJECTURE proof
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基于空洞因果卷积的学生成绩预测及分析方法
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作者 赖英旭 张亚薇 +1 位作者 庄俊玺 刘静 《北京工业大学学报》 北大核心 2026年第3期252-267,共16页
针对使用循环神经网络对学生长序列行为数据进行特征提取存在梯度消失或爆炸、长期依赖关系提取能力不足、深度学习模型缺乏可解释性等问题,提出一种面向长序列数据的空洞因果卷积(dilated causal convolution,DCC)成绩预测及分析方法... 针对使用循环神经网络对学生长序列行为数据进行特征提取存在梯度消失或爆炸、长期依赖关系提取能力不足、深度学习模型缺乏可解释性等问题,提出一种面向长序列数据的空洞因果卷积(dilated causal convolution,DCC)成绩预测及分析方法。首先,采用生成对抗网络(generative adversarial network,GAN)生成符合少数类学生原始行为数据分布规律的新样本,并将新样本加入学生数据集中以达到均衡数据集的目的;然后,提出一种基于DCC的成绩预测模型,DCC和门控循环单元(gated recurrent unit,GRU)相结合的结构提高了模型对长序列数据依赖关系的提取能力;最后,使用沙普利加性解释(Shapley additive explanations,SHAP)方法并结合三因素理论对影响学生成绩的因素进行重要性分析和解释。在公开数据集上的实验结果表明,在成绩预测任务中提出的方法与基线方法相比,加权F1分数提高了约6个百分点,并进一步验证了所提方法中关键模块的有效性和模型的泛化能力。此外,通过对比优秀学生和风险学生的学习特点发现,良好的学习习惯、课堂学习的主动性以及不同行为环境等因素会对学生成绩产生重要影响。 展开更多
关键词 学生成绩预测 空洞因果卷积(dilated causal convolution DCC) 不均衡数据 生成对抗网络(generative adversarial network GAN) 沙普利加性解释(Shapley additive explanations SHAP)方法 成绩影响因素分析
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Discrete Generalizations of Some N-Independent-Variable Integral Inequalities of Langenhop-Gollwitzer Type 被引量:5
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作者 杨恩浩 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1990年第3期230-242,共13页
We establish some new n-independent-variable discrete inequalities which are analo- gous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author in J. Math.Anal.Appl.,109(1985),171-181.A... We establish some new n-independent-variable discrete inequalities which are analo- gous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author in J. Math.Anal.Appl.,109(1985),171-181.An application to hyperbolic summary-difference equations in n variables is also sketched. 展开更多
关键词 Discrete generalizations of Some N-Independent-Variable Integral Inequalities of Langenhop-Gollwitzer Type
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Computational Modelling of Control of Laminar Separation Bubble over an Airfoil Using an Integrated Tubercle and Vortex Generator 被引量:1
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作者 MustafaÖzden Sinem Keskin +3 位作者 ErenAnılSezer Muhammed Hatem Mustafa Serdar Genç Halil Hakan Açıkel 《Computer Modeling in Engineering & Sciences》 2026年第2期402-430,共29页
This paper examines a model that combines vortex generators and leading-edge tubercles for controlling the laminar separation bubble(LSB)over an airfoil at low Reynolds numbers(Re).This new concept of passive flow con... This paper examines a model that combines vortex generators and leading-edge tubercles for controlling the laminar separation bubble(LSB)over an airfoil at low Reynolds numbers(Re).This new concept of passive flow control technique utilizing a tubercle and vortex generator(VG)close to the leading edge was analyzed numerically for a NACA0015 airfoil.In this study,the Shear Stress Transport(SST)turbulence model was employed in the numerical modelling.Numerical modelling was completed using the ANSYS-Fluent 18.2 solver.Analyses were conducted to investigate the flow pattern and understand the underlying LSB control phenomena that enabled the new passive flow control method to provide this significant performance benefit.The findings indicated that the new concept of passive flow control technique suppressed the formation of an LSB at the suction surface of the NACA0015 airfoil,resulting in a higher lift coefficient and improved aerodynamic performance.Improvements in LSB dynamics and aerodynamic performance through the passive flow control method lead to increased energy output and enhanced stability. 展开更多
关键词 Laminar separation bubble AIRFOIL tubercle vortex generator flow control
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Dynamics of Nonlinear Rossby Waves With the Derivative-Expansion Method
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作者 TIAN Hongxiao ZHANG Ruigang LIU Quansheng 《应用数学和力学》 北大核心 2026年第3期313-328,共16页
Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,... Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,was mainly used to investigate Rossby waves under the combined effects of the generalizedβ-effect and the basic flow effect.The derivative expansion method has the advantage of capturing the multi-scalecharacteristics of wave processes simultaneously.In the case where the perturbation expansion is independentof secular terms,the nonlinear equations describing the amplitude evolution of nonlinear waves were derived,such as the Korteweg-de Vries equation,the Boussinesq equation and Zakharov-Kuznetsov equation.Both quali-tative and quantitative analyses indicate that the generalizedβ-effect is the key factor inducing the evolution ofRossby solitary waves. 展开更多
关键词 planetary Rossby waves generalized beta effect derivative-expansion method nonlinear equation
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Underwater Image Enhancement Based on Depthwise Separable Convolution-Based Generative Adversarial Network
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作者 ZENG Jun-yang SI Zhan-jun 《印刷与数字媒体技术研究》 北大核心 2026年第1期60-66,共7页
The existence of absorption and reflection of light underwater leads to problems such as color distortion and blue-green bias in underwater images.In this study,a depthwise separable convolution-based generative adver... The existence of absorption and reflection of light underwater leads to problems such as color distortion and blue-green bias in underwater images.In this study,a depthwise separable convolution-based generative adversarial network(GAN)algorithm was proposed.Taking GAN as the basic framework,it combined a depthwise separable convolution module,attention mechanism,and reconstructed convolution module to realize the enhancement of underwater degraded images.Multi-scale features were captured by the depthwise separable convolution module,and the attention mechanism was utilized to enhance attention to important features.The reconstructed convolution module further extracts and fuses local and global features.Experimental results showed that the algorithm performs well in improving the color bias and blurring of underwater images,with PSNR reaching 27.835,SSIM reaching 0.883,UIQM reaching 3.205,and UCIQE reaching 0.713.The enhanced image outperforms the comparison algorithm in both subjective and objective metrics. 展开更多
关键词 Underwater image enhancement Generating adversarial network Depthwise separable convolution
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Further Generalizations of Opial’s Inequality
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作者 戚征 《Acta Mathematica Sinica,English Series》 SCIE 1985年第3期196-200,共5页
Let C1[a,b] denote the set of all continuously differentiable functions on theclosed finite interval [a,b],and Iet AC [a,b] be the set of all absolutely continuousfunctions on [a,b].Z.Opial proved that if f∈C1[O,h],f... Let C1[a,b] denote the set of all continuously differentiable functions on theclosed finite interval [a,b],and Iet AC [a,b] be the set of all absolutely continuousfunctions on [a,b].Z.Opial proved that if f∈C1[O,h],f(O)-f(h)=0 andf(x)>0 when x∈(O,h),then 展开更多
关键词 In Further generalizations of Opial’s Inequality AO
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Design of 400 V-10 kV Multi-Voltage Grades of Dual Winding Induction Generator for Grid Maintenance Vehicle
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作者 Tiankui Sun Shuyi Zhuang +3 位作者 Yongling Lu Wenqiang Xie Ning Guo Sudi Xu 《Energy Engineering》 2026年第1期356-372,共17页
To ensure an uninterrupted power supply,mobile power sources(MPS)are widely deployed in power grids during emergencies.Comprising mobile emergency generators(MEGs)and mobile energy storage systems(MESS),MPS are capabl... To ensure an uninterrupted power supply,mobile power sources(MPS)are widely deployed in power grids during emergencies.Comprising mobile emergency generators(MEGs)and mobile energy storage systems(MESS),MPS are capable of supplying power to critical loads and serving as backup sources during grid contingencies,offering advantages such as flexibility and high resilience through electricity delivery via transportation networks.This paper proposes a design method for a 400 V–10 kV Dual-Winding Induction Generator(DWIG)intended for MEG applications,employing an improved particle swarmoptimization(PSO)algorithmbased on a back-propagation neural network(BPNN).A parameterized finite element(FE)model of the DWIG is established to derive constraints on its dimensional parameters,thereby simplifying the optimization space.Through sensitivity analysis between temperature rise and electromagnetic loss of the DWIG,the main factors influencing the machine’s temperature are identified,and electromagnetic loss is determined as the optimization objective.To obtain an accurate fitting function between electromagnetic loss and dimensional parameters,the BPNN is employed to predict the nonlinear relationship between the optimization objective and the parameters.The Latin hypercube sampling(LHS)method is used for random sampling in the FE model analysis for training,testing,and validation,which is then applied to compute the cost function in the PSO.Based on the relationships obtained by the BPNN,the PSO algorithm evaluates the fitness and cost functions to determine the optimal design point.The proposed optimization method is validated by comparing simulation results between the initial design and the optimized design. 展开更多
关键词 Dual winding induction generator mobile emergency generator optimization design BP neural network
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Steady‑state microbunching based on transverse‑longitudinal coupling
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作者 Xiu‑Jie Deng Alexander Wu Chao +3 位作者 Wen‑Hui Huang Zi‑Zheng Li Zhi‑Long Pan Chuan‑Xiang Tang 《Nuclear Science and Techniques》 2026年第1期1-49,共49页
In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitud... In this study,three specific scenarios of a novel accelerator light source mechanism called steady-state microbunching(SSMB)were studied:longitudinal weak focusing,longitudinal strong focusing,and generalized longitudinal strong focusing(GLSF).At present,GLSF is the most promising method for realizing high-power short-wavelength coherent radiation with mild requirements on modulation laser power.Its essence is to exploit the ultrasmall natural vertical emittance of an electron beam in a planar storage ring for efficient microbunching formation,like a partial transverse-longitudinal emittance exchange in the optical laser wavelength range.Based on an in-depth investigation of related beam physics,a solution for a GLSF SSMB storage ring that can deliver 1 kW average-power EUV light is presented.The work in this paper,such as the generalized Courant–Snyder formalism,analysis of theoretical minimum emittances,transverse-longitudinal coupling dynamics,and derivation of the bunching factor and modulation strengths for laser-induced microbunching schemes,is expected to be useful not only for the development of SSMB but also for future accelerator light sources in general that demand increasingly precise electron beam phase space manipulations. 展开更多
关键词 Steady-state microbunching Extreme ultraviolet ARPES Generalized Courant-Snyder formalism Theoretical minimum emittances Longitudinal weak focusing Longitudinal strong focusing Generalized longitudinal strong focusing Transverse-longitudinal coupling Damping wiggler
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Transient Overcurrent Suppression and Fault Ride-through Strategy for Grid-forming DFIGs Based on Flux Linkage Tracking Control
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作者 Meng Huang Sirui Shu +3 位作者 Yufei Hu Zhen Tian Xiaoming Zha Wenhe Wang 《CSEE Journal of Power and Energy Systems》 2026年第1期71-83,共13页
Virtor(VSG)technology is widely investigated and applied for dual synchronous generatoubly-fed induction generators(DFIGs)to provide virtual inertia.However,under grid faults,the conventional VSG-based DFIG faces chal... Virtor(VSG)technology is widely investigated and applied for dual synchronous generatoubly-fed induction generators(DFIGs)to provide virtual inertia.However,under grid faults,the conventional VSG-based DFIG faces challenges of transient overcurrent and instability.The critical limitation for grid-forming DFIGs to withstand serious grid faults is the rotor-side converter(RSC)’s inability to quickly generate proper rotor voltage to counteract transient electromotive force(EMF),which results in transient overcurrent and damage to the RSC.To fill this gap,this study introduces a novel low-voltage ride-through(LVRT)control strategy for the grid-forming DFIG under symmetrical grid fault conditions.To mitigate transient overcurrent,the core mechanism is to regulate the rotor flux linkage to align with the stator flux linkage in an optimal proportion.Under the proposed control strategy,both post-fault rotor current and required rotor voltage are constrained within operational limits.Moreover,fluctuations in electromagnetic torque are efficiently suppressed during grid disturbances.Consequently,the dynamic stability and power support capacity of the DFIG system remain intact throughout the transient process.Finally,simulation studies and experimental results are provided to verify the feasibility of the proposed approach. 展开更多
关键词 Doubly-fed induction generator(DFIG) grid-forming converter low-voltage ride through(LVRT) transient current virtual synchronous generator(VSG)
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A Generative Steganography Based on Attraction-Matrix-Driven Gomoku Games
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作者 Yi Cao Kuo Zhang +2 位作者 Chengsheng Yuan Linglong Zhu Wentao Ge 《Computers, Materials & Continua》 2026年第2期939-962,共24页
Generative steganography uses generative stego images to transmit secret message.It also effectively defends against statistical steganalysis.However,most existing methods focus primarily on matching the feature distr... Generative steganography uses generative stego images to transmit secret message.It also effectively defends against statistical steganalysis.However,most existing methods focus primarily on matching the feature distribution of training data,often neglecting the sequential continuity between moves in the game.This oversight can result in unnatural patterns that deviate from real user behavior,thereby reducing the security of the hidden communication.To address this issue,we design a Gomoku agent based on the AlphaZero algorithm.The model engages in self-play to generate a sequence of plausible moves.These moves formthe basis of the stego images.We then apply an attractionmatrix at each step.It guides themove selection so that themoves appearmore natural.Thismethod helps maintain logical flow between moves.It also extends the game length,which increases the embedding capacity.Next,we filter and prioritize the generated moves.The selected moves are embedded into a move pool.Secret message is mapped to thesemoves.It is then embedded step by step as the game progresses.The finalmove sequence constitutes a complete steganographic game record.The receiver can extract the secret message using this record and a predefined mapping rule.Experiments show that our method reaches a maximum embedding capacity of 223 bits per carrier.Detection accuracy is 0.500 under XuNet and 0.498 under YeNet.These results are equal to random guessing,showing strong imperceptibility.The proposed method demonstrates superior concealment,higher embedding capacity,and greater robustness against common image distortions and steganalysis attacks. 展开更多
关键词 Generative steganography information hiding STEGANOGRAPHY steganalsis attraction matrix
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A Survey of Generative Adversarial Networks for Medical Images
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作者 Sameera V.Mohd Sagheer U.Nimitha +3 位作者 P.M.Ameer Muneer Parayangat MohamedAbbas Krishna Prakash Arunachalam 《Computer Modeling in Engineering & Sciences》 2026年第2期130-185,共56页
Over the years,Generative Adversarial Networks(GANs)have revolutionized the medical imaging industry for applications such as image synthesis,denoising,super resolution,data augmentation,and cross-modality translation... Over the years,Generative Adversarial Networks(GANs)have revolutionized the medical imaging industry for applications such as image synthesis,denoising,super resolution,data augmentation,and cross-modality translation.The objective of this review is to evaluate the advances,relevances,and limitations of GANs in medical imaging.An organised literature review was conducted following the guidelines of PRISMA(Preferred Reporting Items for Systematic Reviews and Meta-Analyses).The literature considered included peer-reviewed papers published between 2020 and 2025 across databases including PubMed,IEEE Xplore,and Scopus.The studies related to applications of GAN architectures in medical imaging with reported experimental outcomes and published in English in reputable journals and conferences were considered for the review.Thesis,white papers,communication letters,and non-English articles were not included for the same.CLAIM based quality assessment criteria were applied to the included studies to assess the quality.The study classifies diverse GAN architectures,summarizing their clinical applications,technical performances,and their implementation hardships.Key findings reveal the increasing applications of GANs for enhancing diagnostic accuracy,reducing data scarcity through synthetic data generation,and supporting modality translation.However,concerns such as limited generalizability,lack of clinical validation,and regulatory constraints persist.This review provides a comprehensive study of the prevailing scenario of GANs in medical imaging and highlights crucial research gaps and future directions.Though GANs hold transformative capability for medical imaging,their integration into clinical use demands further validation,interpretability,and regulatory alignment. 展开更多
关键词 Generative adversarial networks medical images DENOISING SEGMENTATION TRANSLATION
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