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New Generalized Transformation Method and Its Application in Higher-Dimensional Soliton Equation 被引量:2
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作者 BAI Cheng-Lin GUO Zong-Lin ZHAO Hong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第3期447-451,共5页
A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the (3+1)-dimensional breaking soliton equati... A new generalized transformation method is differential equation. As an application of the method, we presented to find more exact solutions of nonlinear partial choose the (3+1)-dimensional breaking soliton equation to illustrate the method. As a result many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic function solutions, and rational solutions, are obtained. The new method can be extended to other nonlinear partial differential equations in mathematical physics. 展开更多
关键词 new generalized transformation method exact solution (3+1)-dimensional breaking soliton equation KdV equation mKdV equation cubic nonlinear Klein-Gordon equation
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The Significance of Generalized Gauge Transformation across Fundamental Interactions
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作者 Bi Qiao 《Journal of Modern Physics》 CAS 2023年第5期604-622,共19页
The author of this paper has put forward a unified program of gauge field from the mathematical and physical picture of the principal associated bundles: thinking that our universe may have more fundamental interactio... The author of this paper has put forward a unified program of gauge field from the mathematical and physical picture of the principal associated bundles: thinking that our universe may have more fundamental interactions than the four fundamental interactions, and these basic interaction gauge fields are only the projection components to the base manifold, that is our universe, from a unified gauge potential or connection of the principal associated bundle manifold on the base manifold. These components can satisfy the transformation of gauge potential, and can even be transformed from one basic interaction gauge potential to another basic interaction gauge potential, and can be summarized into a unified equation, that is, the generalized gauge Equation (GGE), but the gauge potential or connection on the principal bundle is invariant, corresponding to the invariance of gauge transformation [1]. In this paper, we will continue to discuss this aspect concretely, and specifically construct a spatiotemporal model with the frame bundle as the principal bundle, and the tensor bundle as the associated bundle, so that the four fundamental interactions, especially the electromagnetic interaction and the gravitational interaction, can be reflected in the bottom manifold, that is, the regional distributions in our universe. Furthermore, this paper studies the existence of gauge transformation across basic interactions by establishing a model of gauge transformation of basic interaction field;it is found that the unified expression formula is GGE and the expression relation on the curvature of space-time. Therefore, the author discusses the feasibility of the generalized gauge transformation across the basic electromagnetic interaction and the basic gravitational interaction, and on this basis, specifically determines a method or way to find the generalized gauge transformation, so as to try to realize the last step of the “unification” of the four fundamental interactions in physics, that is, the “unification” of electromagnetism and gravity. 展开更多
关键词 generalized Gauge transformation Unification of Fundamental Interactions Principal Bundle Connection and Curvature
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Generalized Darboux Transformation and Rational Solutions for the Nonlocal Nonlinear Schrodinger Equation with the Self-Induced Parity-Time Symmetric Potential 被引量:1
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作者 Jian Chen 《Journal of Applied Mathematics and Physics》 2015年第5期530-536,共7页
In this paper, I construct a generalized Darboux transformation for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time symmetric potential. The N-order rational solution is derived by the it... In this paper, I construct a generalized Darboux transformation for the nonlocal nonlinear Schrodinger equation with the self-induced parity-time symmetric potential. The N-order rational solution is derived by the iterative rule and it can be expressed by the determinant form. In particular, I calculate first-order and second-order rational solutions and obtain their figures according to different parameters. 展开更多
关键词 generalized Darboux transformation Rational Solutions Nonlocal Nonlinear Schrodinger Equation
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Generalized Canonical Transformations for Fractional Birkhoffian Systems
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作者 ZHANG Yi 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2022年第4期499-506,共8页
This paper presents fractional generalized canonical transformations for fractional Birkhoffian systems within Caputo derivatives.Firstly,based on fractional Pfaff-Birkhoff principle within Caputo derivatives,fraction... This paper presents fractional generalized canonical transformations for fractional Birkhoffian systems within Caputo derivatives.Firstly,based on fractional Pfaff-Birkhoff principle within Caputo derivatives,fractional Birkhoff’s equations are derived and the basic identity of constructing generalized canonical transformations is proposed.Secondly,according to the fact that the generating functions contain new and old variables,four kinds of generating functions of the fractional Birkhoffian system are proposed,and four basic forms of fractional generalized canonical transformations are deduced.Then,fractional canonical transformations for fractional Hamiltonian system are given.Some interesting examples are finally listed. 展开更多
关键词 fractional Birkhoffian system generalized canonical transformation fractional Pfaff-Birkhoff principle generating function
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A generalized Hadamard transformation from new entangled state
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作者 徐兴磊 徐世民 +2 位作者 张运海 李洪奇 王继锁 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第1期105-109,共5页
A new entangled state |η 0) is proposed by the technique of integral within an ordered product. A generalized Hadamaxd transformation is derived by virtue of η; θ), which plays a role of Hadamard transformation ... A new entangled state |η 0) is proposed by the technique of integral within an ordered product. A generalized Hadamaxd transformation is derived by virtue of η; θ), which plays a role of Hadamard transformation for (a1 sinθ - a2 cosθ) and (a1 cosθ + a2 sin θ). 展开更多
关键词 generalized Hadamard transformation entangled state technique of integral within an ordered product
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A Generalized Hankel Transformation Derived by Parametrized Entangled State Representations
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作者 FAN Hong-Yi HU Li-Yun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第7期85-88,共4页
Using the parametrized entangled state representations we have found a generalized Hankel transformationwith the integral kernel being a combination of Bessel functions.This generalized Hankel transformation correspon... Using the parametrized entangled state representations we have found a generalized Hankel transformationwith the integral kernel being a combination of Bessel functions.This generalized Hankel transformation corresponds tothe appropriate quantum mechanical representation transformation. 展开更多
关键词 parametrized bipartite entangled state generalized Hankel transformation
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Doubling Algorithm for Nonsymmetric Algebraic Riccati Equations Based on a Generalized Transformation
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作者 Bo Tang Yunqing Huang Ning Dong 《Advances in Applied Mathematics and Mechanics》 SCIE 2018年第6期1327-1343,共17页
We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with M-matrix.It is well known that such equations can be efficiently solved via the structure-preserving doubling ... We consider computing the minimal nonnegative solution of the nonsymmetric algebraic Riccati equation with M-matrix.It is well known that such equations can be efficiently solved via the structure-preserving doubling algorithm(SDA)with the shift-and-shrink transformation or the generalized Cayley transformation.In this paper,we propose a more generalized transformation of which the shift-and-shrink transformation and the generalized Cayley transformation could be viewed as two special cases.Meanwhile,the doubling algorithm based on the proposed generalized transformation is presented and shown to be well-defined.Moreover,the convergence result and the comparison theorem on convergent rate are established.Preliminary numerical experiments show that the doubling algorithm with the generalized transformation is efficient to derive the minimal nonnegative solution of nonsymmetric algebraic Riccati equation with M-matrix. 展开更多
关键词 Shift-and-shrink transformation generalized Cayley transformation doubling algorithm nonsymmetric algebraic Riccati equation
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Linearization of Emden Differential Equation via the Generalized Sundman Transformations
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作者 Joel Mvendaga Orverem Yusuf Haruna +1 位作者 Bala Ma’aji Abdulhamid Magaji Yunbunga Adamu 《Advances in Pure Mathematics》 2021年第3期163-168,共6页
The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanic... The Emden differential equation is one of the most widely studied and challenging nonlinear dynamics equations in literature. It finds applications in various areas of study such as celestial mechanics, fluid mechanics, Steller structure, isothermal gas spheres, thermionic currents and so on. Because of the importance of the equation, the method of generalized Sundman transformation (GST) as proposed by Nakpim and Meleshko is used for linearizing the Emden differential equation. The Emden differential equation considered here is a modification of the equation given by Berkovic. The results obtained in this paper imply that the Emden equation cannot be linearized by a point transformation. The general solution of the modified Emden equation is also obtained. 展开更多
关键词 Emden Differential Equation Second Order Ordinary Differential Equation generalized Sundman transformation LINEARIZATION
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Amplitude spectrum compensation and phase spectrum correction of seismic data based on the generalized S transform 被引量:6
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作者 周怀来 王峻 +3 位作者 王明春 沈铭成 张听锟 梁平 《Applied Geophysics》 SCIE CSCD 2014年第4期468-478,510,511,共13页
We propose a method for the compensation and phase correction of the amplitude spectrum based on the generalized S transform. The compensation of the amplitude spectrum within a reliable frequency range of the seismic... We propose a method for the compensation and phase correction of the amplitude spectrum based on the generalized S transform. The compensation of the amplitude spectrum within a reliable frequency range of the seismic record is performed in the S domain to restore the amplitude spectrum of reflection. We use spectral simulation methods to fit the time-dependent amplitude spectrum and compensate for the amplitude attenuation owing to absorption. We use phase scanning to select the time-, space-, and frequencydependent phases correction based on the parsimony criterion and eliminate the residual phase effect of the wavelet in the S domain. The method does not directly calculate the Q value; thus, it can be applied to the case of variable Q. The comparison of the theory model and field data verify that the proposed method can recover the amplitude spectrum of the strata reflectivity, while eliminating the effect of the residual phase of the wavelet. Thus, the wavelet approaches the zero-phase wavelet and, the seismic resolution is improved. 展开更多
关键词 generalized S transform amplitude spectra phase spectra seismic resolution phase correction
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May ChatGPT be a tool producing medical information for common inflammatory bowel disease patients’questions?An evidencecontrolled analysis 被引量:2
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作者 Antonietta Gerarda Gravina Raffaele Pellegrino +6 位作者 Marina Cipullo Giovanna Palladino Giuseppe Imperio Andrea Ventura Salvatore Auletta Paola Ciamarra Alessandro Federico 《World Journal of Gastroenterology》 SCIE CAS 2024年第1期17-33,共17页
Artificial intelligence is increasingly entering everyday healthcare.Large language model(LLM)systems such as Chat Generative Pre-trained Transformer(ChatGPT)have become potentially accessible to everyone,including pa... Artificial intelligence is increasingly entering everyday healthcare.Large language model(LLM)systems such as Chat Generative Pre-trained Transformer(ChatGPT)have become potentially accessible to everyone,including patients with inflammatory bowel diseases(IBD).However,significant ethical issues and pitfalls exist in innovative LLM tools.The hype generated by such systems may lead to unweighted patient trust in these systems.Therefore,it is necessary to understand whether LLMs(trendy ones,such as ChatGPT)can produce plausible medical information(MI)for patients.This review examined ChatGPT’s potential to provide MI regarding questions commonly addressed by patients with IBD to their gastroenterologists.From the review of the outputs provided by ChatGPT,this tool showed some attractive potential while having significant limitations in updating and detailing information and providing inaccurate information in some cases.Further studies and refinement of the ChatGPT,possibly aligning the outputs with the leading medical evidence provided by reliable databases,are needed. 展开更多
关键词 Crohn’s disease Ulcerative colitis Inflammatory bowel disease Chat Generative Pre-trained Transformer Large language model Artificial intelligence
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THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS
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作者 黄先勇 邓勋环 王其如 《Acta Mathematica Scientia》 SCIE CSCD 2024年第3期925-946,共22页
In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existe... In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results. 展开更多
关键词 nonlinear delay dynamic equations NONOSCILLATION asymptotic behavior Philostype oscillation criteria generalized Riccati transformation
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Unlocking the Potential:A Comprehensive Systematic Review of ChatGPT in Natural Language Processing Tasks
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作者 Ebtesam Ahmad Alomari 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第10期43-85,共43页
As Natural Language Processing(NLP)continues to advance,driven by the emergence of sophisticated large language models such as ChatGPT,there has been a notable growth in research activity.This rapid uptake reflects in... As Natural Language Processing(NLP)continues to advance,driven by the emergence of sophisticated large language models such as ChatGPT,there has been a notable growth in research activity.This rapid uptake reflects increasing interest in the field and induces critical inquiries into ChatGPT’s applicability in the NLP domain.This review paper systematically investigates the role of ChatGPT in diverse NLP tasks,including information extraction,Name Entity Recognition(NER),event extraction,relation extraction,Part of Speech(PoS)tagging,text classification,sentiment analysis,emotion recognition and text annotation.The novelty of this work lies in its comprehensive analysis of the existing literature,addressing a critical gap in understanding ChatGPT’s adaptability,limitations,and optimal application.In this paper,we employed a systematic stepwise approach following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses(PRISMA)framework to direct our search process and seek relevant studies.Our review reveals ChatGPT’s significant potential in enhancing various NLP tasks.Its adaptability in information extraction tasks,sentiment analysis,and text classification showcases its ability to comprehend diverse contexts and extract meaningful details.Additionally,ChatGPT’s flexibility in annotation tasks reducesmanual efforts and accelerates the annotation process,making it a valuable asset in NLP development and research.Furthermore,GPT-4 and prompt engineering emerge as a complementary mechanism,empowering users to guide the model and enhance overall accuracy.Despite its promising potential,challenges persist.The performance of ChatGP Tneeds tobe testedusingmore extensivedatasets anddiversedata structures.Subsequently,its limitations in handling domain-specific language and the need for fine-tuning in specific applications highlight the importance of further investigations to address these issues. 展开更多
关键词 Generative AI large languagemodel(LLM) natural language processing(NLP) ChatGPT GPT(generative pretraining transformer) GPT-4 sentiment analysis NER information extraction ANNOTATION text classification
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Evaluating the role of large language models in inflammatory bowel disease patient information
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作者 Eun Jeong Gong Chang Seok Bang 《World Journal of Gastroenterology》 SCIE CAS 2024年第29期3538-3540,共3页
This letter evaluates the article by Gravina et al on ChatGPT’s potential in providing medical information for inflammatory bowel disease patients.While promising,it highlights the need for advanced techniques like r... This letter evaluates the article by Gravina et al on ChatGPT’s potential in providing medical information for inflammatory bowel disease patients.While promising,it highlights the need for advanced techniques like reasoning+action and retrieval-augmented generation to improve accuracy and reliability.Emphasizing that simple question and answer testing is insufficient,it calls for more nuanced evaluation methods to truly gauge large language models’capabilities in clinical applications. 展开更多
关键词 Crohn’s disease Ulcerative colitis Inflammatory bowel disease Chat generative pre-trained transformer Large language model Artificial intelligence
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Classification of Conversational Sentences Using an Ensemble Pre-Trained Language Model with the Fine-Tuned Parameter
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作者 R.Sujatha K.Nimala 《Computers, Materials & Continua》 SCIE EI 2024年第2期1669-1686,共18页
Sentence classification is the process of categorizing a sentence based on the context of the sentence.Sentence categorization requires more semantic highlights than other tasks,such as dependence parsing,which requir... Sentence classification is the process of categorizing a sentence based on the context of the sentence.Sentence categorization requires more semantic highlights than other tasks,such as dependence parsing,which requires more syntactic elements.Most existing strategies focus on the general semantics of a conversation without involving the context of the sentence,recognizing the progress and comparing impacts.An ensemble pre-trained language model was taken up here to classify the conversation sentences from the conversation corpus.The conversational sentences are classified into four categories:information,question,directive,and commission.These classification label sequences are for analyzing the conversation progress and predicting the pecking order of the conversation.Ensemble of Bidirectional Encoder for Representation of Transformer(BERT),Robustly Optimized BERT pretraining Approach(RoBERTa),Generative Pre-Trained Transformer(GPT),DistilBERT and Generalized Autoregressive Pretraining for Language Understanding(XLNet)models are trained on conversation corpus with hyperparameters.Hyperparameter tuning approach is carried out for better performance on sentence classification.This Ensemble of Pre-trained Language Models with a Hyperparameter Tuning(EPLM-HT)system is trained on an annotated conversation dataset.The proposed approach outperformed compared to the base BERT,GPT,DistilBERT and XLNet transformer models.The proposed ensemble model with the fine-tuned parameters achieved an F1_score of 0.88. 展开更多
关键词 Bidirectional encoder for representation of transformer conversation ensemble model fine-tuning generalized autoregressive pretraining for language understanding generative pre-trained transformer hyperparameter tuning natural language processing robustly optimized BERT pretraining approach sentence classification transformer models
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The Similarity Transformation of Regularizing Functionals and Simularity Property of Their Fourier Transformations
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作者 祝同江 《Journal of Beijing Institute of Technology》 EI CAS 1995年第2期105+99-105,共8页
Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.
关键词 Fourier transform generalized functions/similarity transformation regularizing functionals
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Controlled teleportation of high-dimension quantumstates with generalized Bell-state measurement 被引量:2
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作者 詹佑邦 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第9期2557-2562,共6页
In this paper a scheme for controlled teleportation of arbitrary high-dimensional unknown quantum states is proposed by using the generalized Bell-basis measurement and the generalized Hadamard transformation. As two ... In this paper a scheme for controlled teleportation of arbitrary high-dimensional unknown quantum states is proposed by using the generalized Bell-basis measurement and the generalized Hadamard transformation. As two special cases, two schemes of controlled teleportation of an unknown single-qutrit state and an unknown two-qutrit state are investigated in detail. In the first scheme, a maximally entangled three-qutrit state is used as the quantum channel, while in the second scheme, an entangled two-qutrit state and an entangled three-qutrit state are employed as the quantum channels. In these schemes, an unknown qutrit state can be teleported to either one of two receivers, but only one of them can reconstruct the qutrit state with the help of the other. Based on the case of qutrits, a scheme of controlled teleportation of an unknown qudit state is presented. 展开更多
关键词 controlled teleportation high-dimensional quantum state generalized Bell-basis measurement generalized Hadamard transformation
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High-frequency compensation for seismic data based on adaptive generalized S transform 被引量:2
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作者 Li Hui-Feng Wang Jin +1 位作者 Wei Zheng-Rong Yang Fei-Long 《Applied Geophysics》 SCIE CSCD 2020年第5期747-755,902,共10页
The low-pass fi ltering eff ect of the Earth results in the absorption and attenuation of the high-frequency components of seismic signals by the stratum during propagation.Hence,seismic data have low resolution.Consi... The low-pass fi ltering eff ect of the Earth results in the absorption and attenuation of the high-frequency components of seismic signals by the stratum during propagation.Hence,seismic data have low resolution.Considering the limitations of traditional high-frequency compensation methods,this paper presents a new method based on adaptive generalized S transform.This method is based on the study of frequency spectrum attenuation law of seismic signals,and the Gauss window function of adaptive generalized S transform is used to fi t the attenuation trend of seismic signals to seek the optimal Gauss window function.The amplitude spectrum compensation function constructed using the optimal Gauss window function is used to modify the time-frequency spectrum of the adaptive generalized S transform of seismic signals and reconstruct seismic signals to compensate for high-frequency attenuation.Practical data processing results show that the method can compensate for the high-frequency components that are absorbed and attenuated by the stratum,thereby eff ectively improving the resolution and quality of seismic data. 展开更多
关键词 seismic data time-frequency analysis adaptive generalized S transform high-frequency compensation
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s-parameterized Weyl transformation and the corresponding quantization scheme 被引量:2
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作者 王继锁 孟祥国 范洪义 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第1期265-268,共4页
By extending the usual Weyl transformation to the s-parameterized Weyl transformation with s being a real parameter,we obtain the s-parameterized quantization scheme which includes P–Q quantization, Q–P quantization... By extending the usual Weyl transformation to the s-parameterized Weyl transformation with s being a real parameter,we obtain the s-parameterized quantization scheme which includes P–Q quantization, Q–P quantization, and Weyl ordering as its three special cases. Some operator identities can be derived directly by virtue of the s-parameterized quantization scheme. 展开更多
关键词 generalized Wigner transformation s-parameterized quantization scheme
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GENERALIZED WAVELETS AND INVERSION OF THE RADON TRANSFORM ON THE LAGUERRE HYPERGROUP 被引量:1
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作者 Bai Linglan He Jianxun (Nanjing Normal University, China) 《Approximation Theory and Its Applications》 2002年第4期55-69,共15页
Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Usin... Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X. 展开更多
关键词 MATH generalized WAVELETS AND INVERSION OF THE RADON TRANSFORM ON THE LAGUERRE HYPERGROUP
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On the generalized Cauchy function and new Conjecture on its exterior singularities 被引量:1
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作者 Theodore Yaotsu Wu 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2011年第2期135-151,共17页
This article studies on Cauchy’s function f (z) and its integral, (2πi)J[ f (z)] ≡ ■C f (t)dt/(t z) taken along a closed simple contour C, in regard to their comprehensive properties over the entire z =... This article studies on Cauchy’s function f (z) and its integral, (2πi)J[ f (z)] ≡ ■C f (t)dt/(t z) taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x + iy plane consisted of the simply connected open domain D + bounded by C and the open domain D outside C. (1) With f (z) assumed to be C n (n ∞-times continuously differentiable) z ∈ D + and in a neighborhood of C, f (z) and its derivatives f (n) (z) are proved uniformly continuous in the closed domain D + = [D + + C]. (2) Cauchy’s integral formulas and their derivatives z ∈ D + (or z ∈ D ) are proved to converge uniformly in D + (or in D = [D +C]), respectively, thereby rendering the integral formulas valid over the entire z-plane. (3) The same claims (as for f (z) and J[ f (z)]) are shown extended to hold for the complement function F(z), defined to be C n z ∈ D and about C. (4) The uniform convergence theorems for f (z) and F(z) shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle |z| = 1 such that the four general- ized Hilbert-type integral transforms are proved. (5) Further, the singularity distribution of f (z) in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . (6) A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. (7) Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. (8) Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f (z) in domain D , based on the continuous numerical value of f (z) z ∈ D + = [D + + C], is presented for resolution as a conjecture. 展开更多
关键词 Uniform continuity of Cauchy’s function · Uni- form convergence of Cauchy’s integral formula · generalized Hilbert-type integral transforms · Functional properties and singularity distributions
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