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Fractal Interpolation Functions: A Short Survey

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Applied Mathematics 2014年第12期5卷 1834-1841页

作者： María Antonia Navascués Arya Kumar Bedabrata Chand Viswanathan Puthan Veedu María Victoria Sebastián Centro Universitario de la defensa de Zaragoza Academia General Militar Zaragoza Spain departamento de matemática Aplicada EINA Universidad de Zaragoza Zaragoza Spain department of Mathematics Indian Institute of Technology Madras Chennai India

The object of this short survey is to revive interest in the technique of fractal interpolation. In order to attract the attention of numerical analysts, or rather scientific community of researchers applying various approximation techniques, the article is interspersed with comparison of fractal interpolation functions and diverse conventional interpolation schemes. There are multitudes of interpolation methods using several families of functions: polynomial, exponential, rational, trigonometric and splines to name a few. But it should be noted that all these conventional nonrecursive methods produce interpolants that are differentiable a number of times except possibly at a finite set of points. One of the goals of the paper is the definition of interpolants which are not smooth, and likely they are nowhere differentiable. They are defined by means of an appropriate iterated function system. Their appearance fills the gap of non-smooth methods in the field of approximation. Another interesting topic is that, if one chooses the elements of the iterated function system suitably, the resulting fractal curve may be close to classical mathematical functions like polynomials, exponentials, etc. The authors review many results obtained in this field so far, although the article does not claim any completeness. Theory as well as applications concerning this new topic published in the last decade are discussed. The one dimensional case is only considered.

关键词： Fractal Curves Fractal Functions Interpolation Approximation

A LOWER BOUND OF STABLE STATIONARY TRAJECTORIES

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Acta Mathematica Scientia 2007年第3期27卷 535-540页

作者： J.M. Soriano C. Ding departamento de Andlisis matemdtico Facultad de Matematicas Universidad de Sevilla Aptdo. 1160 Sevilla 41080 Spain department of Applied Mathematics Zhejiang University of Technology Hangzhou 310032 China

It is proven that an autonomous system verifying some conditions has at least one stable stationary trajectory and it is also given a lower bound to the number of unstable stationary trajectorlies.

关键词： Autonomous system continuation methods trajectory nondegenerate critical point zero point stationary trajectory stable trajectory asymptotically stable Morse inequalities

A citation iteration method for publications and scientists evaluation

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Data Science and Informetrics 2021年第2期1卷 100-109页

作者： Qiang Liu Jorge Gulín-González Yunwei Chen Scientometrics&Evaluation Research Center(SERC) Chengdu Library and Information Center of Chinese Academy of SciencesChengduChina Centro de Estudios de matemática Computacional(CEMC) Universidad de las Ciencias Informáticas(UCI)Carretera a San Antonio de los BanosKm 2^(1/2)TorrensLa LisaLa HabanaCuba department of Library Information and Archives ManagementSchool of Economics and ManagementUniversity of Chinese Academy of SciencesBeijingChina

In the last decades many methods have been developed for the evaluation of the quality and impact of both the scientific research papers and *** identifying,discovering,and evaluating high-impact papers using scientometric methods,and adopting reasonable evaluation procedures and methods are vital to stimulating scientists’creative *** of methods used for evaluating impact are:h-index and the cited frequency of articles and the number of highly cited *** we propose a new method to assess the scientist impact based on citation *** method was inspired in the Page Rank *** the present study,both the number of citations and the citing publications after each citation were *** to the obtained results,the proposal allows a more accurate measurement of the impact of scientific ***,the application of this method,it can greatly improve the judgment efficiency of high-impact *** have also conducted an empirical study at three levels in the discipline of mathematics,namely the comparisons of two publications,two scientists and eight *** show that indexes proposed in this dissertation designed for the publications’impacts evaluation and scientists’impact evaluation can be used to find the cause behind the number of cited frequencies resulting in the impact *** Q-index for publications’impacts evaluation and F-index for scientists’impacts evaluation proposed in this article can be used more accurately to check and evaluate the impact of ***,these new indexes can be used in the research management of departments at all levels,and can be useful by the states to find leading scientists in several fields.

关键词： Scientist Evaluation Citation network Algorithm Scientometric Method

On σ-Solubility Criteria for Finite Groups

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Communications in Mathematics and Statistics 2024年第3期12卷 563-571页

作者： A.Ballester-Bolinches S.F.Kamornikov V.Pérez-Calabuig V.N.Tyutyanov departament de matemàtiques University of ValènciaDr.Moliner 5046100 BurjassotValènciaSpain department of Mathematics Francisk Skorina State Gomel University104 Sovetskaya Str.246019 GomelBelarus Gomel Branch of International University“MITSO” 46 a October Ave.246029 GomelBelarus

In this paper,the structure of finite groups in whichmaximal subgroups of some Sylow subgroups have aσ-soluble orσ-nilpotent supplement,whereσis a partition of the set of all prime numbers,is *** solubility,σ-solu... 详细信息

关键词： Finite group Supplementation σ-Solubility σ-Nilpotency

Optomechanical feedback cooling of a 5 mm long torsional mode

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Photonics Research 2023年第12期11卷 2179-2184页

作者： DIANQIANG SU YUAN JIANG PABLO SOLANO LUIS A.OROZCO JOHN LAWALL YANTING ZHAO State Key Laboratory of Quantum Optics and Quantum Optics devices Institute of Laser SpectroscopyShanxi UniversityTaiyuan 030006China Collaborative Innovation Center of Extreme Optics Shanxi UniversityTaiyuan 030006China departamento de Fı´sica Facultad de Ciencias Fı´sicas y MatemáticasUniversidad de ConcepciónConcepciónChile CIFAR Azrieli Global Scholars Program CIFARTorontoOntario M5G 1M1Canada Joint Quantum Institute Department of Physics and NISTUniversity of MarylandCollege ParkMaryland 20742USA National Institute of Standards and Technology GaithersburgMaryland 20899USA

We report three orders of magnitude optical cooling of the fundamental torsional mode of a 5 mm long,550 nm diameter optical *** rotation of the nanofiber couples to the polarization of guided laser *** use a weak laser probe to monitor the rotation and use feedback to modulate the polarization of an auxiliary drive laser providing *** results present a tool for the optomechanical control of large-scale torsional resonators,with metrological applications and potential implications for studying macroscopic objects in quantum states.

关键词： polarization laser fiber

Quintom cosmology and modified gravity after deSI 2024

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Science Bulletin 2024年第17期69卷 2698-2704页

作者： Yuhang Yang Xin Ren Qingqing Wang Zhiyu Lu Dongdong Zhang Yi-Fu Cai Emmanuel N.Saridakis department of Astronomy School of Physical SciencesUniversity of Science and Technology of ChinaHefei 230026China CAS Key Laboratory for Researches in Galaxies and Cosmology School of Astronomy and Space ScienceUniversity of Science and Technology of ChinaHefei 230026China deep Space Exploration Laboratory Hefei 230088China department of Physics Tokyo Institute of TechnologyTokyo 152-8551Japan Kavli IPMU(WPI) UTIASThe University of TokyoChiba 277-8583Japan National Observatory of Athens Lofos Nymfon 11852Greece departamento de matemáticas Universidad Católica del NorteAntofagasta 1270398Chile

We reconstruct the cosmological background evolution under the scenario of dynamical dark energy through the Gaussian process approach,using the latest Dark Energy Spectroscopic Instrument(deSI)baryon acoustic oscillations(BAO)combined with other *** results reveal that the reconstructed dark-energy equation-of-state(EoS)parameter w(z)exhibits the so-called quintom-B behavior,crossing-1 from phantom to quintessence regime as the universe *** investigate under what situation this type of evolution could be achieved from the perspectives of field theories and modified *** particular,we reconstruct the corresponding actions for f(R),f(T),and f(Q)gravity,*** explicitly show that,certain modified gravity can exhibit the quintom dynamics and fit the recent deSI data efficiently,and for all cases the quadratic deviation from theΛCDM scenario is mildly favored.

关键词： deSI Dark energy Quintom cosmology Modified gravity

Almansi decomposition for Poly-Ultrahyperbolic Functions

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Acta Mathematica Sinica,English Series 2009年第9期25卷 1561-1566页

作者： Guang Bin REN Uwe KAHLER department of Mathematics University of Science and Technology of China Hefei 230026 P. R. China departamento de matemdtica Universidade de Aveiro P-3810-159 Aveiro Portugal

In this paper we construct Almansi decompositions for powers of the ultrahyperbolic operator. The construction will be done in a constructive way.

关键词： Almansi decompositions ultrahyperbolic operator

Evaluation of Two Highly Porous Microcrystalline Biphasic Calcium Phosphate-Based Bone Grafts for Bone Regeneration: An Experimental Study in Rabbits

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Journal of Materials Science and Chemical Engineering 2020年第6期8卷 8-30页

作者： Miguel Ángel Garcés-Villalá Sergio David Rico Sergio Gustavo Nazar Mariano Escudero-Pinel Víctor Galván-Josa José Luis Calvo-Guirado department of Implant and Biomaterial Research Fundación Corazón de Jesús San Juan Argentina Facultad de matemática Astronomía y Física Universidad Nacional de Córdoba Córdoba Argentina department of Oral Surgery and Implant dentistry Faculty of Health Sciences Universidad Católica San Antonio de Murcia Murcia Spain

A biphasic bone grafting biomaterial based on a mixture of calcium phosphates and beta-tricalcium phosphate (β-TCP) phases with high nanoporosity was synthesized. The synthesis route was based on calcium phosphate composition and the incorporation of glycolic acid as a pore former, giving a material composed of 97% β-TCP and 3% calcium orthophosphates (CaPO4). An in vitro study of the purity, microstructure, crystalline domain, and pores size for the material obtained was performed by SEM analysis as well as full structural characterization. The region of interest related to the surface was determined by the specific surface area measured with the BET method. In vivo evaluation of bone response was performed by implanting the new low-cost biphasic manufacturing material synthesized in this work, which was compared with a biphasic material of similar chemical and microstructural composition existing in the commercial market and with higher cost called Synergy Odontit® β-TCP. The materials were implanted separately into 5 mm diameter defects in the tibias of New Zealand White rabbits at 30, 60, and 90 days. The results obtained showed that the host tissue well accepted the new biphasic material;the presence of new bone formation was observed. A more complete resorption was observed for the new microcrystalline biphasic material compared to for a commercial β-TCP material.

关键词： Microcrystalline Beta-Tricalcium Phosphate Ceramic Bone Graft Glycolic Acid

IRREGULAR WAVELET FRAMES AND GABOR FRAMES

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Analysis in Theory and Applications 2001年第3期17卷 90-100页

作者： Ole Christensen Sergio Favier Felipe Zó department of Mathematics Technical University of DenmarkBuilding 3032800LyngbyDenmark Instituto de matemática Aplicada San Luis Universidad Nacional de San Luis Consejo Nacional de Investigaciones Científicasy TécnicasAvda.Ejercito de Los Andes950 5700San LuisArgentina

Given g∈L 2(R n ), we consider irregular wavelet for the form $\left\{ {\lambda ^{\frac{n}{2}} g\left( {\lambda _j x - kb} \right)} \right\}_{j\varepsilon zj\varepsilon z^n } ,where\;\lambda _j $ > 0 and b > 0. Sufficient conditions for the wavelet system to constitute a frame for L 2(R n ) are given. For a class of functions g∈L 22(R n ) we prove that certain growth conditions on {λ j } will frames, and that some other types of sequences exclude the frame property. We also give a sufficient condition for a Gabor system $\left\{ {e^{zrib\left( {j,x} \right)} g\left( {x - \lambda _k } \right)} \right\}_{j\varepsilon z^n ,k\varepsilon z} $ to be a frame.

关键词： sufficient condition Stability of Frames Wavelet Transforms Wavelet Frames Riesz Bases