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SSRN 2023年

作者： Cui, Manjun Zhang, Zhichao School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China

Convolution theorems for the free metaplectic transformation (FMT) have great significance in the fields of fractional domain non-stationary signal processing theory and method. The existing results have found many applications in high-dimensional non-stationary signal sampling and filtering. However, a widely accepted closed-form expression has not yet been established. In this paper, we introduce the definitions of generalized convolution and product operators in the FMT domain, and use them to formulate the generalized convolution and product theorems for the FMT. The derived results include particular cases the existing convolution and product theorems for the FMT and also the convolution and product theorems for the Fourier transform, the fractional Fourier transform, and the linear canonical transform. We employ the generalized convolution theorem for the FMT in designing an optimal filter in the FMT domain. We also validate the correctness and effectiveness of the theoretical analysis through numerical experiments, demonstrating the superiority of the proposed optimal filtering method over the conventional ones. © 2023, The Authors. All rights reserved.

关键词： Convolution

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Numerical Investigations of low Reynolds number Aerodynamics of Bio-Inspired 3D wings

Numerical Investigations of low Reynolds number Aerodynamics...

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International Conference on Recent Advances in Space Technologies (RAST)

作者： Smail Boughou Ashraf A. Omar Radouan Boukharfane Omer A. Elsayed Renewable Energies and Advanced Materials Lab (LERMA) Université Internationale de Rabat (UIR) Rabat Morocco School of Aerospace and Automotive Engineering Université Internationale de Rabat (UIR) Rabat Morocco Modeling Simulation and Data Analysis (MSDA) group Mohammed VI Polytechnic University (UM6P) Benguerir Morocco

The silent flight of owls is a result of unique physical features and adaptations, which has been studied by both biologists and engineers to enhance the design of unmanned aerial vehicles (UAVs). This study investigates the flight mechanics and aerodynamics of UAVs with a wing of aspect ratio of four and varying swept angles and taper ratios, using bio-inspired wing. Different configurations are tested by varying the swept angle and taper ratio to optimize design and ensure peak performance under different conditions and angles of attack. The behavior of the wings in various flying scenarios is used to research the aerodynamics and mechanics of flight. Although simulating folding bio-inspired wings is a thrilling field with revolutionary potential for UAV design, wingtips are identified as a source of three-dimensional flow that slightly lowers pressure towards the wingtip regions. This work enhances our understanding of aerodynamics and mechanics, leading to improved UAV design.

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Multi-dimensional graph linear canonical transform

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Digital Signal Processing: A Review Journal 2025年 165卷

作者： Li, Na Zhang, Zhichao School of Mathematics and Statistics Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China Key Laboratory of System Control and Information Processing Ministry of Education Shanghai200240 China Key Laboratory of Computational Science and Application of Hainan Province Haikou571158 China

Multi-dimensional (M-D) graph signals represent fundamental data structures in various practical applications, including digital imaging systems, sensor network telemetry, and meteorological observation records. The development of efficient transformation methodologies for processing such M-D graph signals within the linear canonical transform domain continues to present significant challenges. This paper introduces two novel transforms: the two-dimensional graph linear canonical transform based on central discrete dilated Hermite functions (2-D CDDHFs-GLCT) and the two-dimensional graph linear canonical transform based on chirp multiplication-chirp convolution-chirp multiplication decomposition (2-D CM-CC-CM-GLCT). These foundational constructs are extended to the multi-dimensional domain, resulting in M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT. In terms of computational complexity, additivity and reversibility, M-D CDDHFs-GLCT and M-D CM-CC-CM-GLCT are compared. Theoretical analyses reveal that the M-D CM-CC-CM-GLCT algorithm achieves substantial computational complexity reduction compared to its CDDHFs-based counterpart. Numerical simulations further establish that while maintaining comparable additivity performance, the M-D CM-CC-CM-GLCT exhibits enhanced reversibility characteristics. To validate practical applicability, the proposed M-D GLCT framework is implemented in data compression scenarios. Experimental results demonstrating superior algorithmic efficiency and implementation effectiveness compared to multi-dimensional graph fractional Fourier transform. © 2025 Elsevier Inc.

关键词： Linear transformations

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TYDI QA: A benchmark for information-seeking question answering in typologically diverse languages

arXiv

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arXiv 2020年

作者： Clark, Jonathan H. Choi, Eunsol Collins, Michael Garrette, Dan Kwiatkowski, Tom Nikolaev, Vitaly Palomaki, Jennimaria Google Research Project Design Modeling Linguistic Analysis Data Quality

Confidently making progress on multilingual modeling requires challenging, trustworthy evaluations. We present TYDI QA -a question answering dataset covering 11 typologically diverse languages with 204K question-answer pairs. The languages of TYDI QA are diverse with regard to their typology-the set of linguistic features each language expresses-such that we expect models performing well on this set to generalize across a large number of the world's languages. We present a quantitative analysis of the data quality and example-level qualitative linguistic analyses of observed language phenomena that would not be found in English-only corpora. To provide a realistic information-seeking task and avoid priming effects, questions are written by people who want to know the answer, but don't know the answer yet, and the data is collected directly in each language without the use of translation. Copyright © 2020, The Authors. All rights reserved.

关键词： Information use

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The Gamma/Weibull Customer Lifetime Model

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Communications in Mathematics and Statistics 2019年第1期7卷 33-59页

作者： Gen Ye Songjian Wang Key Lab of Statistical Modeling and Data Analysis of Yunnan Province Yunnan UniversityKunming 650091People’s Republic of China

This paper proposes a new customer lifetime model:the Gamma/Weibull distribution(G/W).Similar to the Pareto/NBD model,we propose a G/W/NBD model by combining the G/W distribution with a negative binomial distribution(NBD)and study its properties such as(i)the probability that a customer to be alive at a time point;(ii)the expectation and variance of the number of transactions for a customer during a fixed time period;(iii)the conditional expectation and conditional variance of the number of future transactions for a customer during a fixed time *** simulation studies are conducted to investigate the forecasting accuracy and flexibility of the proposed model.A CDNOW data set is analyzed by the proposed model.

关键词： Customer lifetime Gamma distribution Negative binomial distribution Purchase history Weibull distribution

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modeling Arctic Boundary Layer Cloud Streets at Grey-zone Resolutions

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Advances in Atmospheric Sciences 2020年第1期37卷 42-56页

作者： Hui-Wen LAI Fuqing ZHANG Eugene E.CLOTHIAUX David R.STAUFFER Brian J.GAUDET Johannes VERLINDE Deliang CHEN Department of Meteorology and Atmospheric Science and Center for Advanced Data Assimilation and Predictability TechniquesThe Pennsylvania State UniversityUniversity ParkPennsylvania 16802USA Department of Earth Sciences University of GothenburgGothenburg 40530Sweden Earth Systems Analysis and Modeling Pacific Northwest National LaboratoryRichlandWashington 99354USA

To better understand how model resolution affects the formation of Arctic boundary layer clouds,we investigated the influence of grid spacing on simulating cloud streets that occurred near Utqiaġvik(formerly Barrow),Alaska,on 2 May 2013 and were observed by MODIS(the Moderate Resolution Imaging Spectroradiometer).The Weather Research and Forecasting model was used to simulate the clouds using nested domains with increasingly fine resolution ranging from a horizontal grid spacing of 27 km in the boundary-layer-parameterized mesoscale domain to a grid spacing of 0.111 km in the large-eddy-permitting *** investigated the model-simulated mesoscale environment,horizontal and vertical cloud structures,boundary layer stability,and cloud properties,all of which were subsequently used to interpret the observed roll-cloud *** model resolution led to a transition from a more buoyant boundary layer to a more shear-driven turbulent boundary *** clouds were stratiform-like in the mesoscale domain,but as the model resolution increased,roll-like structures,aligned along the wind field,appeared with ever smaller wavelengths.A stronger vertical water vapor gradient occurred above the cloud layers with decreasing grid *** fixed model grid spacing at 0.333 km,changing the model configuration from a boundary layer parameterization to a large-eddy-permitting scheme produced a more shear-driven and less unstable environment,a stronger vertical water vapor gradient below the cloud layers,and the wavelengths of the rolls decreased *** this study,only the large-eddy-permitting simulation with gird spacing of 0.111 km was sufficient to model the observed roll clouds.

关键词： cloud streets large eddy simulation grey zone Arctic clouds model resolution

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A new estimator for the number of high-dimensional signals using ratio of higher-order moments

A new estimator for the number of high-dimensional signals u...

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IET International Radar Conference (IRC 2023)

作者： Lewen Zhang Yao Rong Mengjiao Tang Xiaolin Du Fan Li Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University Kunming People's Republic of China School of Computer and Control Engineering Yantai University Yantai People's Republic of China CAAC Key Laboratory of Flight Techniques and Flight Safety Civil Aviation Flight University of China Guanghan People's Republic of China

ISBN: (数字)9781837240982

This paper provides a novel estimation procedure for determining the number of high-dimensional complex-valued signals embedded in Gaussian white noise. Initially, this problem is formulated as a sequence of nested hypothesis tests. To enhance the decision performance, we introduce new test statistics based on the ratio of the fourth- and square second-order moments of the population covariance eigenvalues. This enables us to leverage higher-order moments information in the observed data, distinguishing it from conventional tests that rely solely on the first and second order moments. In the context of high-dimensional, complex-valued data and within a sub-sphericity testing framework, unbiased and consistent estimates are derived for these two higher-order moments. Subsequently, we conduct an asymptotic analysis to incoporate these estimates into the construction of the test statistics and the design of our proposed estimation scheme for determining the number of sources. Finally, numerical examples are presented to show its effectiveness and superiority over several classical estimation methods.

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Cohomology and Deformation Theory of O-Operators on Hom-Lie Conformal Algebras

SSRN

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SSRN 2024年

作者： Asif, Sania Wang, Yao Mosbahi, Bouzid Basdouri, Imed School of Mathematics and Statistics Nanjing University of Information Science and Technology Jiangsu Nanjing210044 China Center for Applied Mathematics of Jiangsu Province Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Jiangsu Nanjing210044 China University of Sfax Faculty of Sciences of Sfax BP 1171 Sfax3038 Tunisia University of Gafsa Faculty of Sciences of Gafsa Gafsa2112 Tunisia

In the present paper, we aim to introduce the cohomology of $\mathcal{O}$-operators defined on the Hom-Lie conformal algebra concerning the given representation. To obtain the desired results, we describe three different cochain complexes and discuss the interrelation of their coboundary operators. And show that differential maps on the graded Lie algebra can also be defined by using the Maurer-Cartan element. We further find out that, the $\mathcal{O}$-operator on the given Hom-Lie conformal algebra serves as a Maurer-Cartan element and it leads to acquiring the notion of a differential map in terms of $\mathcal{O}$-operator $\delta_\T$. Next, we provide the notion of Hom-pre-Lie conformal algebra, that induces a sub-adjacent Hom-Lie conformal algebra structure. The differential $\delta_{\b,\a}$ of this sub-adjacent Hom-Lie conformal algebra is related to the differential $\delta_\T$. Finally, we provide the deformation theory of $\mathcal{O}$-operators on the Hom-Lie conformal algebras as an application to the cohomology theory, where we discuss linear and formal deformations in detail. © 2024, The Authors. All rights reserved.

关键词： Algebra

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Graph Linear Canonical Transform Based on CM-CC-CM Decomposition

arXiv

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arXiv 2024年

作者： Li, Na Zhang, Zhichao Han, Jie Chen, Yunjie Cao, Chunzheng School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Nanjing University of Information Science and Technology Nanjing210044 China School of Remote Sensing and Geomatics Engineering Nanjing University of Information Science and Technology Nanjing210044 China

The graph linear canonical transform (GLCT) is presented as an extension of the graph Fourier transform (GFT) and the graph fractional Fourier transform (GFrFT), offering more flexibility as an effective tool for graph signal processing. In this paper, we introduce a GLCT based on chirp multiplication-chirp convolution-chirp multiplication decomposition (CM-CCCM- GLCT), which irrelevant to sampling periods and without oversampling operation. Various properties and special cases of the CM-CC-CM-GLCT are derived and discussed. In terms of computational complexity, additivity, and reversibility, we compare the CM-CC-CM-GLCT and the GLCT based on the central discrete dilated Hermite function (CDDHFs-GLCT). Theoretical analysis demonstrates that the computational complexity of the CM-CC-CM-GLCT is significantly reduced. Simulation results indicate that the CM-CC-CM-GLCT achieves similar additivity to the CDDHFs-GLCT. Notably, the CM-CC-CM-GLCT exhibits better reversibility. Copyright © 2024, The Authors. All rights reserved.

关键词： Chirp modulation

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Simulating the Peculiar Periphery of the Cygnus Loop

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天文和天体物理学研究 2024年第12期24卷 192-206页

作者： Jun-Yu Shen Bi-Wen Bao Li Zhang Department of Astronomy Key Laboratory of Astroparticle Physics of Yunnan ProvinceYunnan UniversityKunming 650091China Department of Astronomy Key Laboratory of Astroparticle Physics of Yunnan ProvinceYunnan UniversityKunming 650091China Key Laboratory of Statistical Modeling and Data Analysis of Yunnan Province Yunnan UniversityKunming 650091China

The middle-aged Galactic supernova remnant(SNR)-the Cygnus Loop(CL)-displays a peculiar morphology in X-rays,featuring a blowout in the southern *** underlying process accounting for the formation of the peculiar periphery remains a *** this end,we conduct hydrodynamical simulations to investigate the SNR evolution coupled with a tailored stellar-wind model:a bipolar stellar wind emanating from a runaway red supergiant progenitor,excavating a wind-blown cavity elongated along *** simulation results reveal that the forward shock of the consequent SNR sweeps up the modified ambient media,shaping the overall morphology with a blowout comparable to that of ***,a series of simulation runs are performed to assess the impacts of different model parameters and the projection effect(observational angle θobs)on the final SNR *** physical quantities are extracted from simulation results to characterize the simulated SNR and make a direct comparison with the X-ray observations of *** find that the final SNR morphology is sensitive to both stellar-wind properties and θobs.A Cygnus-Loop-like SNR could be reproduced under appropriate parameter combinations at θobs=0°.While for θobs＜30°,the projected morphology akin to CL could be also generated under specific conditions.

关键词： hydrodynamics methods:numerical ISM:supernova remnants

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