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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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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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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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Na^(+)/K^(+)-ATPase:ion pump,signal transducer,or cytoprotective protein,and novel biological functions
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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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FROM WAVE FUNCTIONS TO TAU-FUNCTIONS FOR THE VOLTERRA LATTICE HIERARCHY
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作者 付昂 李明金 杨迪 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期405-419,共15页
For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functio... For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators. 展开更多
关键词 volterra lattice hierarchy matrix-resolvent method wave functions even GUE correlators
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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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AGGREGATE SPECIAL FUNCTIONS TO APPROXIMATE PERMUTING TRI-HOMOMORPHISMS AND PERMUTING TRI-DERIVATIONS ASSOCIATED WITH A TRI-ADDITIVEψ-FUNCTIONAL INEQUALITY IN BANACH ALGEBRAS
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作者 Safoura Rezaei ADERYANI Azam AHADI +1 位作者 Reza SAADATI Hari M.SRIVASTAVA 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期311-338,共28页
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better... In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem. 展开更多
关键词 permuting tri-homomorphism in Banach algebra permuting tri-derivation on C*-algebra fixed point theorem Ulam-Hyers-Rassias stability aggregate special functions tri-additiveψ-functional inequality
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Crustal and uppermost mantle structure of the northeastern Qinghai-Xizang Plateau from joint inversion of surface wave dispersions and receiver functions with P velocity constraints
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作者 Pei Zhang Xiaodong Song +2 位作者 Jiangtao Li Xingchen Wang Xuezhen Zhang 《Earthquake Science》 2024年第2期93-106,共14页
Lithospheric structure beneath the northeastern Qinghai-Xizang Plateau is of vital significance for studying the geodynamic processes of crustal thickening and expansion of the Qinghai-Xizang Plateau. We conducted a j... Lithospheric structure beneath the northeastern Qinghai-Xizang Plateau is of vital significance for studying the geodynamic processes of crustal thickening and expansion of the Qinghai-Xizang Plateau. We conducted a joint inversion of receiver functions and surface wave dispersions with P-wave velocity constraints using data from the Chin Array Ⅱ temporary stations deployed across the Qinghai-Xizang Plateau. Prior to joint inversion, we applied the H-κ-c method(Li JT et al., 2019) to the receiver function data in order to correct for the back-azimuthal variations in the arrival times of Ps phases and crustal multiples caused by crustal anisotropy and dipping interfaces. High-resolution images of vS, crustal thickness, and vP/vSstructures in the Qinghai-Xizang Plateau were simultaneously derived from the joint inversion. The seismic images reveal that crustal thickness decreases outward from the Qinghai-Xizang Plateau. The stable interiors of the Ordos and Alxa blocks exhibited higher velocities and lower crustal vP/vSratios. While, lower velocities and higher vP/vSratios were observed beneath the Qilian Orogen and Songpan-Ganzi terrane(SPGZ), which are geologically active and mechanically weak, especially in the mid-lower crust.Delamination or thermal erosion of the lithosphere triggered by hot asthenospheric flow contributes to the observed uppermost mantle low-velocity zones(LVZs) in the SPGZ. The crustal thickness, vS, and vP/vSratios suggest that whole lithospheric shortening is a plausible mechanism for crustal thickening in the Qinghai-Xizang Plateau, supporting the idea of coupled lithospheric-scale deformation in this region. 展开更多
关键词 joint inversion receiver functions surface waves crustal thickness vP/vS ratio NE Qinghai-Xizang Plateau
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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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Enhancing Proficiency in Quadratic Equations and Functions Through the MILAPlus Strategy
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作者 Rolando S.Merle 《Journal of Contemporary Educational Research》 2024年第1期221-232,共12页
This study investigates the efficacy of the Mathematics Independent Learning Activity Practice and Play Unite Scheme(MILAPlus)as an instructional strategy to improve the proficiency levels of Grade 9 students in quadr... This study investigates the efficacy of the Mathematics Independent Learning Activity Practice and Play Unite Scheme(MILAPlus)as an instructional strategy to improve the proficiency levels of Grade 9 students in quadratic equations and functions through a study carried out at Quezon National High School.The research involved 116 Grade 9 students and utilized a quantitative approach,incorporating both pre-assessment and post-assessment measures.The research utilizes a quasi-experimental design,examining the academic performance of students before and after the introduction of MILAPlus.The pre-assessment establishes a baseline,and the subsequent post-assessment measures the impact of the instructional strategy.Statistical analyses,including t-tests,assess the significance of differences in mean scores and mean percentage scores,providing quantitative insights into the effectiveness of MILAPlus.Findings from the study revealed a statistically significant improvement in both mean scores and mean percentage scores after the utilization of MILAPlus,indicating enhanced proficiency in quadratic equations and functions.The Mean Proficiency Scores(MPS)also showed a substantial increase,demonstrating a marked improvement in overall proficiency levels among Grade 9 students.In light of the results,recommendations were given including the continued utilization of MILAPlus as an instructional strategy and aligning its development with prescribed learning competencies.Emphasizing the consistent adherence to policies and guidelines for MILAPlus implementation is suggested for sustaining positive effects on students’long-term performance in mathematics.This research contributes valuable insights into the practical application and effectiveness of MILAPlus within the context of Grade 9 mathematics education at Quezon National High School. 展开更多
关键词 Mathematics Independent Learning Activity Practice and Play Unite Scheme PROFICIENCY Quadratic equations and 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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Quantum control based on three forms of Lyapunov functions
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作者 俞国慧 杨洪礼 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期216-222,共7页
This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.S... This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors.In this paper, the specific control laws under the three forms are given.Stability is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test system.The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm.Finally, a unified form of the control laws under the three forms is given. 展开更多
关键词 quantum system Lyapunov function particle swarm optimization simulated annealing algorithms quantum control
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Crustal structure in the Anyuan Coal Mine and its adjacent areas of Jiangxi Province by P-wave receiver functions
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作者 Xingmian Zhang Meng Gong +5 位作者 Jian Lü Hongxing Li Jie Hu Junwen He Jianhua Peng Bingyue Liu 《Earthquake Research Advances》 CSCD 2024年第1期47-58,共12页
We collected high-quality teleseismic events recorded by 12 broadband seismographs deployed in the Anyuan Coal Mine and its adjacent areas in Pingxiang City,Jiangxi Province for nearly two years.The H-κ-c stacking me... We collected high-quality teleseismic events recorded by 12 broadband seismographs deployed in the Anyuan Coal Mine and its adjacent areas in Pingxiang City,Jiangxi Province for nearly two years.The H-κ-c stacking method was employed to obtain the crustal thickness and Poisson's ratio distribution,then the characteristics of crustal structure below the stations were obtained by using the time-domain linear inversion method.The crustal thickness in the Anyuan Coal Mine and its adjacent areas ranges from approximately 32~35 km,with an average thickness of 33 km,which is consistent with the crustal thickness results in South China from previous studies using the receiver function method.The average Poisson's ratio of the crustal bulk composition in the study area varies between 0.22 and 0.25,which is lower than the global value with a 0.27 average,indicating a predominantly intermediate-acidic or felsic crustal composition.There is a weak negative correlation between Poisson's ratio and crustal thickness estimates in the Anyuan Coal Mine and its adjacent areas,suggesting that the absence of mafic-ultramafic materials in the lower crust is associated with the process of crustal delamination.The velocity inversion results indicate that the crustal structure including three velocity discontinuity interfaces,with the first at a depth of approximately 1.5 km,the second at about 10~15 km,and the third being the Moho.The study also indicates that the results obtained by the H-κ-c stacking method are significantly better than those obtained by the H-κmethod,effectively reducing the standard deviation and dispersion of crustal thickness and vP/vSratio. 展开更多
关键词 Anyuan Coal Mine Receiver function H-κ-c stacking Crustal thickness Poisson's ratio
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Duality between Bessel Functions and Chebyshev Polynomials in Expansions of Functions
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作者 Alfred Wünsche 《Advances in Pure Mathematics》 2023年第8期504-536,共16页
In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and fo... In expansions of arbitrary functions in Bessel functions or Spherical Bessel functions, a dual partner set of polynomials play a role. For the Bessel functions, these are the Chebyshev polynomials of first kind and for the Spherical Bessel functions the Legendre polynomials. These two sets of functions appear in many formulas of the expansion and in the completeness and (bi)-orthogonality relations. The analogy to expansions of functions in Taylor series and in moment series and to expansions in Hermite functions is elaborated. Besides other special expansion, we find the expansion of Bessel functions in Spherical Bessel functions and their inversion and of Chebyshev polynomials of first kind in Legendre polynomials and their inversion. For the operators which generate the Spherical Bessel functions from a basic Spherical Bessel function, the normally ordered (or disentangled) form is found. 展开更多
关键词 Spherical Bessel functions Chebyshev Polynomials Legendre Polynomials Hermite Polynomials Derivatives of Delta functions Normally and Anti-Normally Ordered Operators
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Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces
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作者 Akachukwu Offia Ugochukwu Osisiogu +4 位作者 Theresa Efor Friday Oyakhire Monday Ekhator Friday Nkume Sunday Aloke 《Open Journal of Optimization》 2023年第3期99-108,共10页
In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K  ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Su... In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K  ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K  ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces. 展开更多
关键词 Real Banach Spaces Pseudo-Convex functions Pseudo-Monotone Maps Sub-Differentials Lower Semi-Continuous functions and Approximate Mean Value Inequality
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Vertical impedance functions of pile groups under low-to-high loading amplitudes:numerical simulations and experimental validation 被引量:1
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作者 Usama Zafar Chandra Shekhar Goit +1 位作者 Masato Saitoh Riku Fukuda 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2023年第3期647-666,共20页
Piles in a group experience additional displacements in soil due to pile-to-pile interactions apart from those resulting from the external loading.The effect of these interactions determined assuming soil as an elasti... Piles in a group experience additional displacements in soil due to pile-to-pile interactions apart from those resulting from the external loading.The effect of these interactions determined assuming soil as an elastic and/or viscoelastic material on pile head impedance functions of the pile group is studied by relating the group stiffness to the static stiffness of a single pile.However,the prevailing elastic solutions may misestimate the resulting pile group response due to the lack of consideration for either soil(material)and/or soil-pile interface nonlinearities.It is well established that soil behaves nonlinearly under moderate-to-high loading amplitudes,and besides,the soil-pile interface nonlinearity can exist even at small loading amplitudes.This study addresses the effects of these nonlinearities on the vertical impedance functions of a 3×3-pile group using numerical methods by direct analyses and superposition using pile-to-pile interaction factors.The numerical results are validated using scaled model tests under 1 g conditions.The results highlight the overestimation of pile-to-pile interactions in the pile group when assuming elastic soil conditions.The cases either by direct analyses or superposition approach involving soil and soil-pile interface nonlinearities agree well with the experimental pile group responses under close-to-elastic and nonlinear conditions. 展开更多
关键词 impedance functions numerical simulations model-scale experiment superposition approach soil-pile interface nonlinearity
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The Theory of Higher-Order Types of Asymptotic Variation for Differentiable Functions. Part II: Algebraic Operations and Types of Exponential Variation 被引量:2
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作者 Antonio Granata 《Advances in Pure Mathematics》 2016年第12期817-867,共52页
In this second part, we thoroughly examine the types of higher-order asymptotic variation of a function obtained by all possible basic algebraic operations on higher-order varying functions. The pertinent proofs are s... In this second part, we thoroughly examine the types of higher-order asymptotic variation of a function obtained by all possible basic algebraic operations on higher-order varying functions. The pertinent proofs are somewhat demanding except when all the involved functions are regularly varying. Next, we give an exposition of three types of exponential variation with an exhaustive list of various asymptotic functional equations satisfied by these functions and detailed results concerning operations on them. Simple applications to integrals of a product and asymptotic behavior of sums are given. The paper concludes with applications of higher-order regular, rapid or exponential variation to asymptotic expansions for an expression of type f(x+r(x)). 展开更多
关键词 Higher-Order Regularly-Varying functions Higher-Order Rapidly-Varying functions Smoothly-Varying functions Exponentially-Varying functions Asymptotic Functional Equations Asymptotic Expansions
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The Theory of Higher-Order Types of Asymptotic Variation for Differentiable Functions. Part I: Higher-Order Regular, Smooth and Rapid Variation 被引量:2
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作者 Antonio Granata 《Advances in Pure Mathematics》 2016年第12期776-816,共42页
Motivated by a general theory of finite asymptotic expansions in the real domain for functions f of one real variable, a theory developed in a previous series of papers, we present a detailed survey on the classes of ... Motivated by a general theory of finite asymptotic expansions in the real domain for functions f of one real variable, a theory developed in a previous series of papers, we present a detailed survey on the classes of higher-order asymptotically-varying functions where “asymptotically” stands for one of the adverbs “regularly, smoothly, rapidly, exponentially”. For order 1 the theory of regularly-varying functions (with a minimum of regularity such as measurability) is well established and well developed whereas for higher orders involving differentiable functions we encounter different approaches in the literature not linked together, and the cases of rapid or exponential variation, even of order 1, are not systrematically treated. In this semi-expository paper we systematize much scattered matter concerning the pertinent theory of such classes of functions hopefully being of help to those who need these results for various applications. The present Part I contains the higher-order theory for regular, smooth and rapid variation. 展开更多
关键词 Higher-Order Regularly-Varying functions Higher-Order Rapidly-Varying functions Smoothly-Varying functions Exponentially-Varying functions Asymptotic Functional Equations
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ON THE GRAPHS OF PRODUCTS OF CONTINUOUS FUNCTIONS AND FRACTAL DIMENSIONS
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作者 刘佳 石赛赛 张远 《Acta Mathematica Scientia》 SCIE CSCD 2023年第6期2483-2492,共10页
In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C... In this paper,we consider the graph of the product of continuous functions in terms of Hausdorff and packing dimensions.More precisely,we show that,given a real number 1≤β≤2,any real-valued continuous function in C([0,1])can be decomposed into a product of two real-valued continuous functions,each having a graph of Hausdorff dimensionβ.In addition,a product decomposition result for the packing dimension is obtained.This work answers affirmatively two questions raised by Verma and Priyadarshi[14]. 展开更多
关键词 Hausdorff dimension packing dimension graph of function product of functions
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Numerical modelling of resonance mechanisms in jointed rocks using transfer functions
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作者 Harry Holmes Chrysothemis Paraskevopoulou +2 位作者 Mark Hildyard Krishna Neaupane David P.Connolly 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2023年第5期1076-1089,共14页
Resonance effects in parallel jointed rocks subject to stress waves are investigated using transfer functions,derived from signals generated through numerical modelling.Resonance is important for a range of engineerin... Resonance effects in parallel jointed rocks subject to stress waves are investigated using transfer functions,derived from signals generated through numerical modelling.Resonance is important for a range of engineering situations as it identifies the frequency of waves which will be favourably transmitted.Two different numerical methods are used for this study,adopting the finite difference method and the combined discrete element-finite difference method.The numerical models are validated by replicating results from previous studies.The two methods are found to behave similarly and show the same resonance effects;one operating at low frequency and the other operating at relatively high frequency.These resonance effects are interpreted in terms of simple physical systems and analytical equations are derived to predict the resonant frequencies of complex rock masses.Low frequency resonance is shown to be generated by a system synonymous with masses between springs,described as spring resonance,with an equal number of resonant frequencies as the number of blocks.High frequency resonance is generated through superposition of multiple reflected waves developing standing waves within intact blocks,described as superposition resonance.While resonance through superposition has previously been identified,resonance based on masses between springs has not been previously identified in jointed rocks.The findings of this study have implications for future analysis of multiple jointed rock masses,showing that a wave travelling through such materials can induce other modes of propagation of waves,i.e.spring resonance. 展开更多
关键词 RESONANCE Jointed rocks Finite difference method Discrete element Transfer functions Wave propagation
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