BILINEAR

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Periodic solutions,breather,lump and interaction solutions of a generalized(2+1)-dimensional Hirota bilinear equation via the bilinear neural network method
《Communications in Theoretical Physics》2025年第3期1-11,共11页Zhao Zhao Bo Ren 
supported by the National Natural Science Foundation of China under Grant No.12375006;the Weimu Technology Company Limited of Hangzhou of China under Grant No.KYY-HX-20240495。
The main focus of this paper is to address a generalized(2+1)-dimensional Hirota bilinear equation utilizing the bilinear neural network method.The paper presents the periodic solutions through a single-layer model of...
关键词：bilinear transformation BNNM double-layer model exact analytical solution 
Bilinear magnetoelectric resistance induced by spin Hall effect
《Science China Materials》2025年第2期687-688,共2页Ruiyue Chu Cheng Song 
Magnetoresistance(MR)is a fundamental transport phenomenon crucial for reading magnetic states.It also plays a key role in understanding how time-reversal symmetry breaking affects electrical resistance.Landmark disco...
关键词：BREAKING SYMMETRY LINEARLY 
In an Ocean or a River:Bilinear Auto-Backlund Transformations and Similarity Reductions on an Extended Time-Dependent(3+1)-Dimensional Shallow Water Wave Equation
《China Ocean Engineering》2025年第1期160-165,共6页GAO Xin-yi 
financially supported by the Scientific Research Foundation of North China University of Technology(Grant Nos.11005136024XN147-87 and 110051360024XN151-86).
With respect to oceanic fluid dynamics,certain models have appeared,e.g.,an extended time-dependent(3+1)-dimensional shallow water wave equation in an ocean or a river,which we investigate in this paper.Using symbolic...
关键词：OCEAN RIVER extended time-dependent(3+1)-dimensional shallow water wave equation bilinear auto-Bäcklund transformation similarity reduction symbolic computation 
Bilinear Exotic Calderón–Zygmund Operators
《Acta Mathematica Sinica,English Series》2025年第1期355-377,共23页Jin Bai Jinsong Li Kangwei Li 
Supported by National Key R&D Program of China(Grant No.2021YFA1002500);NNSF of China(Grant Nos.12222114 and 12001400)。
We introduce a bilinear extension of the so-called exotic Calderón–Zygmund operators.These kernels arise naturally from the bilinear singular integrals associated with Zygmund dilations.We show that such a class of ...
关键词：Bilinear Calderón–Zygmund operators weighted inequalities sparse bounds 
On Weighted Compactness of Commutators of Bilinear Vector-valued Singular Integral Operators and Applications
《Acta Mathematica Sinica,English Series》2025年第1期169-190,共22页Zhengyang Li Liu Lu Fanghui Liao Qingying Xue 
supported by the National Natural Science Foundation of China(Grant No.12101222);National Natural Science Foundation of China(Grant No.12271041);Scientific Research Fund of Hunan Provincial Education Department(Grant No.23B0458);supported by the Scientific Research Fund of Hunan Provincial Education Department(Grant No.22B0155);partly supported by the National Key R&D Program of China(Grant No.2020YFA0712900)。
Let T be a bilinear vector-valued singular integral operator satisfies some mild regularity conditions,which may not fall under the scope of the theory of standard Calder¬on–Zygmund classes.For anyb^(→)=(b_(1),b_(2)...
关键词：Weighted compactness COMMUTATORS multilinear square functions Fourier multiplier operator 
Message Verification Protocol Based on Bilinear Pairings and Elliptic Curves for Enhanced Security in Vehicular Ad Hoc Networks
《Computers, Materials & Continua》2024年第10期1029-1057,共29页Vincent Omollo Nyangaresi Arkan A.Ghaib Hend Muslim Jasim Zaid Ameen Abduljabbar Junchao Ma Mustafa A.Al Sibahee Abdulla J.Y.Aldarwish Ali Hasan Ali Husam A.Neamah 
supported by Teaching Reform Project of Shenzhen University of Technology under Grant No.20231016.
Vehicular ad hoc networks(VANETs)provide intelligent navigation and efficient route management,resulting in time savings and cost reductions in the transportation sector.However,the exchange of beacons and messages ov...
关键词：ATTACKS BILINEAR elliptic curve cryptography(ECC) PRIVACY SECURITY vehicular ad hoc network(VANET) 
Double-Pole Solution and Soliton-Antisoliton Pair Solution of MNLSE/DNLSE Based upon Hirota Method
《Wuhan University Journal of Natural Sciences》2024年第5期430-438,共9页LUO Runjia ZHOU Guoquan 
Supported by the National Natural Science Foundation of China (12074295)。
Hirota method is applied to solve the modified nonlinear Schrodinger equation/the derivative nonlinear Schrodinger equation(MNLSE/DNLSE) under nonvanishing boundary conditions(NVBC) and lead to a single and double-pol...
关键词：nonlinear partial differential equation integrable system Hirota's bilinear derivative method soliton solution the derivative Schrodinger equation nonlinear optics 
Sharp bilinear decomposition for products of both anisotropic Hardy spaces and their dual spaces with its applications to endpoint boundedness of commutators
《Science China Mathematics》2024年第9期2091-2152,共62页Jun Liu Dachun Yang Mingdong Zhang 
supported by National Natural Science Foundation of China(Grant Nos.12001527,11971058 and 12071197);the Natural Science Foundation of Jiangsu Province(Grant No.BK20200647);the Postdoctoral Science Foundation of China(Grant No.2021M693422)。
Let a:=(a_(1),...,a_(n))2[1,∞)^(n),p∈(0,1),andα:=1/p-1.For any x∈R^(n)and t∈[0,∞),letΦ_(p)(x,t):={t/1+(t[x]_(a)^(ν))^(1-p)if να■N,t/1+(t[x]_(a)^(ν))^(1-p)[log(e+|x|a)]^(p)if να∈N,let where [·]a:=1+|·|...
关键词：anisotropic Euclidean space bilinear decomposition Hardy space Campanato space Musielak-Orlicz Hardy space commutator wavelet 
BACNN: Multi-scale feature fusion-based bilinear attention convolutional neural network for wood NIR classification被引量：1
《Journal of Forestry Research》2024年第4期202-214,共13页Zihao Wan Hong Yang Jipan Xu Hongbo Mu Dawei Qi 
This study was supported by the Fundamental Research Funds for the Central Universities(No.2572023DJ02).
Effective development and utilization of wood resources is critical.Wood modification research has become an integral dimension of wood science research,however,the similarities between modified wood and original wood...
关键词：Wood classification Near infrared spectroscopy Bilinear network SE module Anti-noise algorithm 
Alleviating limit cycling in training GANs with an optimization technique被引量：2
《Science China Mathematics》2024年第6期1287-1316,共30页Keke Li Liping Tang Xinmin Yang 
supported by the Major Program of National Natural Science Foundation of China(Grant Nos.11991020 and 11991024);the Team Project of Innovation Leading Talent in Chongqing(Grant No.CQYC20210309536);NSFC-RGC(Hong Kong)Joint Research Program(Grant No.12261160365);the Scientific and Technological Research Program of Chongqing Municipal Education Commission(Grant No.KJQN202300528)。
In this paper,we undertake further investigation to alleviate the issue of limit cycling behavior in training generative adversarial networks(GANs)through the proposed predictive centripetal acceleration algorithm(PCA...
关键词：GANs general bilinear game predictive centripetal acceleration algorithm lower and upper complexity bounds PCAA-Adam 
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