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An Attempt to Make Non-Elementary Functions That Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs 被引量:2
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作者 Magne Stensland 《Journal of Applied Mathematics and Physics》 2022年第1期56-67,共12页
In this paper, we define an exponential function whose exponent is the product of a real number and the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, desc... In this paper, we define an exponential function whose exponent is the product of a real number and the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of functions. Differentiating these functions twice give second-order nonlinear ODEs that have the defined set of functions as solutions. 展开更多
关键词 non-elementary functions Second-Order Nonlinear Autonomous ODE
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On Two New Groups of Non-Elementary Functions That Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs
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作者 Magne Stensland 《Journal of Applied Mathematics and Physics》 2022年第3期703-713,共11页
In this paper, we define a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We will also define a group of solutions x(t) that are ... In this paper, we define a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We will also define a group of solutions x(t) that are equal to the amplitude. This is a generalized amplitude function. We are using Abel’s methods, described by Armitage and Eberlein. And finally, we define an exponential function whose exponent is the product of a complex number and the upper limit of integration in a non-elementary integral that can be arbitrary. At least three groups of non-elementary functions are special cases of this complex function. 展开更多
关键词 non-elementary functions Second-Order Nonlinear Autonomous ODE
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The Extended Non-Elementary Amplitude Functions as Solutions to the Damped Pendulum Equation, the Van der Pol Equation, the Damped Duffing Equation, the Lienard Equation and the Lorenz Equations
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作者 Magne Stensland 《Journal of Applied Mathematics and Physics》 2023年第11期3428-3445,共18页
In this paper, we define some non-elementary amplitude functions that are giving solutions to some well-known second-order nonlinear ODEs and the Lorenz equations, but not the chaos case. We are giving the solutions a... In this paper, we define some non-elementary amplitude functions that are giving solutions to some well-known second-order nonlinear ODEs and the Lorenz equations, but not the chaos case. We are giving the solutions a name, a symbol and putting them into a group of functions and into the context of other functions. These solutions are equal to the amplitude, or upper limit of integration in a non-elementary integral that can be arbitrary. In order to define solutions to some short second-order nonlinear ODEs, we will make an extension to the general amplitude function. The only disadvantage is that the first derivative to these solutions contains an integral that disappear at the second derivation. We will also do a second extension: the two-integral amplitude function. With this extension we have the solution to a system of ODEs having a very strange behavior. Using the extended amplitude functions, we can define solutions to many short second-order nonlinear ODEs. 展开更多
关键词 non-elementary functions Second-Order Nonlinear Autonomous ODE Damped Pendulum Equation Van der Pol Equation Damped Duffing Equation Lienard Equation Lorenz System
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Six New Sets of the Non-Elementary Jef-Family-Functions that Are Giving Solutions to Some Second-Order Nonlinear Autonomous ODEs
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作者 Magne Stensland 《Journal of Applied Mathematics and Physics》 2023年第4期1077-1097,共21页
In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are usi... In this paper, we define some new sets of non-elementary functions in a group of solutions x(t) that are sine and cosine to the upper limit of integration in a non-elementary integral that can be arbitrary. We are using Abel’s methods, described by Armitage and Eberlein. The key is to start with a non-elementary integral function, differentiating and inverting, and then define a set of three functions that belong together. Differentiating these functions twice gives second-order nonlinear ODEs that have the defined set of functions as solutions. We will study some of the second-order nonlinear ODEs, especially those that exhibit limit cycles. Using the methods described in this paper, it is possible to define many other sets of non-elementary functions that are giving solutions to some second-order nonlinear autonomous ODEs. 展开更多
关键词 non-elementary functions Second-Order Nonlinear Autonomous ODE Limit Cycle
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Na^(+)/K^(+)-ATPase:ion pump,signal transducer,or cytoprotective protein,and novel biological functions 被引量:2
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作者 Songqiang Huang Wanting Dong +1 位作者 Xiaoqian Lin Jinsong Bian 《Neural Regeneration Research》 SCIE CAS CSCD 2024年第12期2684-2697,共14页
Na^(+)/K^(+)-ATPase is a transmembrane protein that has important roles in the maintenance of electrochemical gradients across cell membranes by transporting three Na^(+)out of and two K^(+)into cells.Additionally,Na^... Na^(+)/K^(+)-ATPase is a transmembrane protein that has important roles in the maintenance of electrochemical gradients across cell membranes by transporting three Na^(+)out of and two K^(+)into cells.Additionally,Na^(+)/K^(+)-ATPase participates in Ca^(2+)-signaling transduction and neurotransmitter release by coordinating the ion concentration gradient across the cell membrane.Na^(+)/K^(+)-ATPase works synergistically with multiple ion channels in the cell membrane to form a dynamic network of ion homeostatic regulation and affects cellular communication by regulating chemical signals and the ion balance among different types of cells.Therefo re,it is not surprising that Na^(+)/K^(+)-ATPase dysfunction has emerged as a risk factor for a variety of neurological diseases.However,published studies have so far only elucidated the important roles of Na^(+)/K^(+)-ATPase dysfunction in disease development,and we are lacking detailed mechanisms to clarify how Na^(+)/K^(+)-ATPase affects cell function.Our recent studies revealed that membrane loss of Na^(+)/K^(+)-ATPase is a key mechanism in many neurological disorders,particularly stroke and Parkinson's disease.Stabilization of plasma membrane Na^(+)/K^(+)-ATPase with an antibody is a novel strategy to treat these diseases.For this reason,Na^(+)/K^(+)-ATPase acts not only as a simple ion pump but also as a sensor/regulator or cytoprotective protein,participating in signal transduction such as neuronal autophagy and apoptosis,and glial cell migration.Thus,the present review attempts to summarize the novel biological functions of Na^(+)/K^(+)-ATPase and Na^(+)/K^(+)-ATPase-related pathogenesis.The potential for novel strategies to treat Na^(+)/K^(+)-ATPase-related brain diseases will also be discussed. 展开更多
关键词 ANTIBODY biological functions cellular communication electrochemical gradient ion balance ion channels Na^(+)/K^(+)-ATPase neurological diseases neurotransmitter release signal transduction
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BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED K-HOLOMORPHIC FUNCTIONS IN C^(2)
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作者 Yanyan CUI Chaojun WANG +1 位作者 Yonghong XIE Yuying QIAO 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1837-1852,共16页
In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems a... In this paper,conjugate k-holomorphic functions and generalized k-holomorphic functions are defined in the two-dimensional complex space,and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders.By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate k-holomorphic kernels,the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion,and the integral expressions of the solutions are obtained. 展开更多
关键词 several complex variables k-holomorphic functions partial difference equations polyanalytic functions
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Evaluation of the Pharmacological Potential of Strychnos camptoneura Trunk Bark Hydroethanol Extract on Reproductive Functions in Male Guinea Pigs (Cavia porcellus) Exposed to Cypermethrin
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作者 Akassa Herman Moukouma Constantin +5 位作者 Diakouka Diambalou Rancia Colombe Njilo Tchatchouang Didier Gestil Mouzita Judicaël Ferry Mpika M’boko Etou Ossibi Arnaud Wilfrid Abena Ange Antoine 《American Journal of Plant Sciences》 CAS 2024年第10期884-898,共15页
The main objective of this study was to evaluate the pharmacological potential of the hydroethanol extract of Strychnos camptoneura trunk bark on reproductive functions in male guinea pigs exposed to cypermethrin. The... The main objective of this study was to evaluate the pharmacological potential of the hydroethanol extract of Strychnos camptoneura trunk bark on reproductive functions in male guinea pigs exposed to cypermethrin. The results showed that administration of the hydroethanolic extract (100 and 250 mg/kg) of Strychnos camptoneura trunk bark after exposure of the animals to cypermethrin induced a highly significant (p Strychnos camptoneura trunk bark produced a highly significant (p Strychnos camptoneura trunk bark may have protective effects against cypermethrin-induced male infertility due to its androgenic, spermatogenic and antiradical properties. 展开更多
关键词 Strychnos Camptoneura Guinea Pig Males CYPERMETHRIN Reproductive function
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Neuropeptide cholecystokinin:a key neuromodulator for hippocampal functions
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作者 Fengwen Huang Stephen Temitayo Bello 《Neural Regeneration Research》 SCIE CAS 2025年第7期1991-1992,共2页
Spatial memory is crucial for survival within external surroundings and wild environments.The hippocampus,a critical hub for spatial learning and memory formation,has received extensive investigations on how neuromodu... Spatial memory is crucial for survival within external surroundings and wild environments.The hippocampus,a critical hub for spatial learning and memory formation,has received extensive investigations on how neuromodulators shape its functions(Teixeira et al.,2018;Zhang et al.,2024).However,the landscape of neuromodulations in the hippocampal system remains poorly understood because most studies focus on classical monoamine neuromodulators,such as acetylcholine,serotonin,dopamine,and noradrenaline.The neuropeptides,comprising the most abundant neuromodulators in the central nervous system,play a pivotal role in neural information processing in the hippocampal system.Cholecystokinin(CCK),one of the most abundant neuropeptides,has been implicated in regulating various physiological and neurobiological statuses(Chen et al.,2019).CCK-A receptor(CCK-AR)and CCK-B receptors(CCK-BR)are two key receptors mediating the biological functions of CCK,both of which belong to class-A sevenfold transmembrane G protein-coupled receptors(Nishimura et al.,2015).CCK-AR preferentially reacts to sulfated CCK,whereas CCK-BR binds both CCK and gastrin with similar affinities(Ding et al.,2022).The expression patterns of CCK-AR and CCK-BR are distinct,implying that CCK has various functions in target regions.For instance,CCK-AR is widely expressed in the GI and brain subregions and is hence implicated in the control of digestive function and satiety regulation.Conversely,CCK-BR is abundantly and widely distributed in the central nervous system,which majorly regulates anxiety,learning,and memory(Ding et al.,2022).However,the roles of endogenous CCK and CCK receptors in regulating hippocampal function at electrophysiological and behavioral levels have received less attention. 展开更多
关键词 abundant functions MODULATOR
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A Set of Almost Automorphic Functions and Applications
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作者 William Dimbour Vincent Valmorin 《Applied Mathematics》 2024年第1期9-21,共13页
For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-al... For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem. 展开更多
关键词 Almost Automorphic functions S-Almost Automorphic functions Differential Equation with Piecewise Constant Argument of Generalized Type
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On the Weyl’s Lemma for Triharmonic Functions
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作者 ZHENG Run-jie ZENG Jia-min FANG Yi 《Chinese Quarterly Journal of Mathematics》 2024年第3期288-294,共7页
In this paper,by choosing some appropriate test functions,we prove the Weyl’s lemma for triharmonic functions based on the new type of mean value formulas.
关键词 Weyl’s lemma Harmonic functions Triharmonic functions Test functions Mean value formulas
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Bioactive material promotes longdistance regeneration of optic nerve to restore visual functions
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作者 Kai Liu 《Neural Regeneration Research》 SCIE CAS CSCD 2024年第1期160-160,共1页
Visual system is vital to human beings.Unfortunately,the optic nerve lacks the ability to regenerate after injury.Therefo re,long-distance regeneration of the optic nerve is a major unsolved medical problem in the wor... Visual system is vital to human beings.Unfortunately,the optic nerve lacks the ability to regenerate after injury.Therefo re,long-distance regeneration of the optic nerve is a major unsolved medical problem in the world(Laha et al.,2017).Recently,Li and So groups' study showed that the bioactive material(ciliary neurotrophic factor[CNTF]-chitosan) could promote long-distance regeneration of the completely transected optic nerve in adult rats and partially restored the visual functions(Liu et al.,2023).This study sheds light on the clinical potential for repairing the severely injured optic nerve. 展开更多
关键词 VISUAL VISUAL functions
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The biological functions and metabolic pathways of valine in swine
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作者 Chuni Wang Yao Peng +4 位作者 Yiru Zhang Juan Xu Sheng Jiang Leli Wang Yulong Yin 《Journal of Animal Science and Biotechnology》 SCIE CAS CSCD 2024年第1期20-34,共15页
Valine is an essential amino acid and a type of branched-chain amino acid. Due to the involvement of branchedchain amino acids in various metabolic pathways, there has been a surge of interests in valine nutrition and... Valine is an essential amino acid and a type of branched-chain amino acid. Due to the involvement of branchedchain amino acids in various metabolic pathways, there has been a surge of interests in valine nutrition and its role in animal physiology. In pigs, the interactions between valine and other branched-chain amino acids or aromatic amino acids are complex. In this review, we delve into the interaction mechanism, metabolic pathways, and biological functions of valine. Appropriate valine supplementation not only enhances growth and reproductive performances, but also modulates gut microbiota and immune functions. Based on past observations and interpretations, we provide recommended feed levels of valine for weaned piglets, growing pigs, gilts, lactating sows, barrows and entire males. The summarized valine nutrient requirements for pigs at different stages offer valuable insights for future research and practical applications in animal husbandry. 展开更多
关键词 Additional dosage Biological function Metabolic pathway PIG VALINE
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Extraction of Acoustic Normal Mode Depth Functions Using Range-Difference Method with Vertical Linear Array Data
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作者 GAO Siyu LI Weilu +2 位作者 ZHANG Yinquan LI Xiaolei WANG Ning 《Journal of Ocean University of China》 SCIE CAS CSCD 2024年第4期871-882,共12页
Data-derived normal mode extraction is an effective method for extracting normal mode depth functions in the absence of marine environmental data.However,when the corresponding singular vectors become nonunique when t... Data-derived normal mode extraction is an effective method for extracting normal mode depth functions in the absence of marine environmental data.However,when the corresponding singular vectors become nonunique when two or more singular values obtained from the cross-spectral density matrix diagonalization are nearly equal,this results in unsatisfactory extraction outcomes for the normal mode depth functions.To address this issue,we introduced in this paper a range-difference singular value decomposition method for the extraction of normal mode depth functions.We performed the mode extraction by conducting singular value decomposition on the individual frequency components of the signal's cross-spectral density matrix.This was achieved by using pressure and its range-difference matrices constructed from vertical line array data.The proposed method was validated using simulated data.In addition,modes were successfully extracted from ambient noise. 展开更多
关键词 range difference depth function extraction normal mode
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Dynamical distribution of continuous service time model involving non-Maxwellian collision kernel and value functions
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作者 Minfang Zhao Lingting Kong +1 位作者 Miao Liu Shaoyong Lai 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第9期340-348,共9页
The distribution of continuous service time in call centers is investigated.A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of conti... The distribution of continuous service time in call centers is investigated.A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of continuous service time,respectively.Using the statistical mechanical and asymptotic limit methods,Fokker–Planck equations are derived from the corresponding Boltzmann-type equations with non-Maxwellian collision kernels.The steady-state solutions of the Fokker–Planck equation are obtained in exact form.Numerical experiments are provided to support our results under different parameters. 展开更多
关键词 kinetic theory service time Fokker-Planck equation value function
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THE(p,q)-ANALOG OF MULTIVALENT BAZILEVIC FUNCTIONS ASSOCIATED WITH A LIMACON
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作者 HUANG An LONG Pin-hong +1 位作者 LIU Jin-lin Gangadharan Murugusundaramoorthy 《数学杂志》 2024年第6期471-484,共14页
This paper studies the problem of functional inequalities for analytic functions in classical geometric function theory.Using the di erential subordination principle and(p,q)-derivative operator,it introduces(p,q)-ana... This paper studies the problem of functional inequalities for analytic functions in classical geometric function theory.Using the di erential subordination principle and(p,q)-derivative operator,it introduces(p,q)-analog of a class of multivalently Bazilevic functions as-sociated with a limacon function,and obtains the corresponding coefficient estimates and the Fekete-Szego inequality,which extend and improve the related results for starlike functions,even q-starlike functions. 展开更多
关键词 Fekete-Szego inequality symmetric Toeplitz determinant multivalent function Bazilevic function (p q)-derivative operator
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QUASIPERIODICITY OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS
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作者 刘新玲 刘凯 +1 位作者 Risto KORHONEN Galina FILIPUK 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期161-172,共12页
This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities... This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity. 展开更多
关键词 QUASIPERIODICITY meromorphic functions complex delay-differential polynomials Nevanlinna theory
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Bibliographical Review on Rehabilitation of Executive Functions in Patients With Developmental Coordination Disorder(DCD)
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作者 Keiko da Costa Oikawa Fabrício Bruno Cardoso +3 位作者 Filipe M.Bonone Samuel Pereira de Souza Vitor da Silva Loureiro Alfred Sholl-Franco 《Psychology Research》 2024年第2期45-56,共12页
The present study aims to establish a literature review on intervention programs for executive functions(EFs)through the use of fundamental motor skills,from a neuropsychopedagogical perspective in subjects with Devel... The present study aims to establish a literature review on intervention programs for executive functions(EFs)through the use of fundamental motor skills,from a neuropsychopedagogical perspective in subjects with Developmental Coordination Disorder(DCD).An exploratory study was carried out through an integrative literature review.The research was carried out in the Scientific databases Electronic Library Online(SciELO),Latin American and Caribbean Literature in Health Sciences(LILACS),Virtual Health Library-Psychology Brazil(BVSPSI),Electronic Journals of Psychology(PePSIC),in the periodicals available in the Brazilian Digital Library of Theses and Dissertations(BDTD)and on the website of the Coordination for the Improvement of Higher Education Personnel(CAPES).The covering publications took place from 2018 to 2023,14 articles were selected for analysis.This literature review made it possible to create strategies for stimulating EF and Visuomotor Functions so that educators and other professionals can better deal with students with DCD.It was perceived the need to carry out and develop more empirical research regarding the intervention of EFs and Visuomotor Functions by educators and professionals,with a greater sampling amplitude,to increase the number of studies that enable interventions both in children and in teenagers with DCD. 展开更多
关键词 developmental coordination disorder executive functions school neuropsychology stimulation of executive functions
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Image Splicing Forgery Detection Using Feature-Based of Sonine Functions and Deep Features
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作者 Ala’a R.Al-Shamasneh Rabha W.Ibrahim 《Computers, Materials & Continua》 SCIE EI 2024年第1期795-810,共16页
The growing prevalence of fake images on the Internet and social media makes image integrity verification a crucial research topic.One of the most popular methods for manipulating digital images is image splicing,whic... The growing prevalence of fake images on the Internet and social media makes image integrity verification a crucial research topic.One of the most popular methods for manipulating digital images is image splicing,which involves copying a specific area from one image and pasting it into another.Attempts were made to mitigate the effects of image splicing,which continues to be a significant research challenge.This study proposes a new splicing detectionmodel,combining Sonine functions-derived convex-based features and deep features.Two stages make up the proposed method.The first step entails feature extraction,then classification using the“support vector machine”(SVM)to differentiate authentic and spliced images.The proposed Sonine functions-based feature extraction model reveals the spliced texture details by extracting some clues about the probability of image pixels.The proposed model achieved an accuracy of 98.93% when tested with the CASIA V2.0 dataset“Chinese Academy of Sciences,Institute of Automation”which is a publicly available dataset for forgery classification.The experimental results show that,for image splicing forgery detection,the proposed Sonine functions-derived convex-based features and deep features outperform state-of-the-art techniques in terms of accuracy,precision,and recall.Overall,the obtained detection accuracy attests to the benefit of using the Sonine functions alongside deep feature representations.Finding the regions or locations where image tampering has taken place is limited by the study.Future research will need to look into advanced image analysis techniques that can offer a higher degree of accuracy in identifying and localizing tampering regions. 展开更多
关键词 Image forgery image splicing deep learning Sonine functions
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A General Analytic Approximation Technique for the Modified Bessel Functions with Fractional Order Iv (x), Applied to I1/6(x) and I1/7(x)
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作者 Jorge Olivares Pablo Martín Maria T. Veliz 《Advances in Pure Mathematics》 2024年第9期768-777,共10页
A general technique to obtain simple analytic approximations for the first kind of modified Bessel functions. The general procedure is shown, and the parameter determination is explained through the applications to th... A general technique to obtain simple analytic approximations for the first kind of modified Bessel functions. The general procedure is shown, and the parameter determination is explained through the applications to this particular case I1/6(x)and I1/7(x). In this way, it shows how to apply the technique to any particular orderν, in order to obtain an approximation valid for any positive value of the variable x. In the present method power series and asymptotic expansion are simultaneously used. The technique is an extension of the multipoint quasirational approximation method, MPQA. The main idea is to look for a bridge function between the power and asymptotic expansion of the I1/6(x), and similar procedure for I1/7(x). To perform this, rational functions are combined with hyperbolic ones and fractional powers. The number of parameters to be determined for each case is four. The maximum relative errors are 0.0049 for ν=1/6, and 0.0047 for ν=7. However, these relative errors decrease outside of the small region of the variables, wherein the maximum relative errors are reached. There is a clear advantage of this procedure compared with any other ones. 展开更多
关键词 Bessel functions Power Series Asymptotic Expansion MPQA Technique
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Approximation Properties of Vectorial Exponential Functions
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作者 Christophe Buet Bruno Despres Guillaume Morel 《Communications on Applied Mathematics and Computation》 EI 2024年第3期1801-1831,共31页
This contribution is dedicated to the celebration of Rémi Abgrall’s accomplishments in Applied Mathematics and Scientific Computing during the conference“Essentially Hyperbolic Problems:Unconventional Numerics,... This contribution is dedicated to the celebration of Rémi Abgrall’s accomplishments in Applied Mathematics and Scientific Computing during the conference“Essentially Hyperbolic Problems:Unconventional Numerics,and Applications”.With respect to classical Finite Elements Methods,Trefftz methods are unconventional methods because of the way the basis functions are generated.Trefftz discontinuous Galerkin(TDG)methods have recently shown potential for numerical approximation of transport equations[6,26]with vectorial exponential modes.This paper focuses on a proof of the approximation properties of these exponential solutions.We show that vectorial exponential functions can achieve high order convergence.The fundamental part of the proof consists in proving that a certain rectangular matrix has maximal rank. 展开更多
关键词 Trefftz method Transport equation Vectorial exponential functions
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