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Estimation of optimum sample size allocation:An illustration with body mass index for evaluating the effect of a dietetic supplement

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International Journal of Biomathematics 2019年第8期12卷 75-86页

作者： Carlos N.Bouza-Herrera Sira M.Allende-Alonso Gajendra K.Vishwakarma Neha Singh departamento de matemdtica Aplicada Universidad de La Habana Cuba department of Mathematics and Computing Indian Institute of Technology Dhanbad India

In many medical researches,it is needed to determine the optimal sample size allocation in a heterogeneous *** paper proposes the algorithm for optimal sample size *** consider the optimal allocation problem as an optimization problem and the solution is obtained by using Bisection,Secant,Regula-Falsi and other numerical *** performance of the algorithm for different numerical methods are analyzed and evaluated in terms of computing time,number of iterations and gain in accuracy using *** efficacy of algorithm is evaluated for the response in terms of body mass index(BMI)to the dietetic supplement with diabetes mellitus,HIV/AIDS and cancer post-operatory recovery patients.

关键词： Optimal sample allocation Body Mass Index diabetes HIV/AIDS cancer

The Quotient Category of a Graded Morita-Takeuchi Context

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Acta Mathematica Sinica,English Series 2006年第1期22卷 123-130页

作者： F. CASTANO IGLESIAS C. NASTASESCU departamento de Estadistica y matemdtica Aplicada Universidad de Almeria 04120 Almeria Spain Facultatea de Matematica Str. Academiei 14 RO-70109 Bucharest Romania

In this paper, we offer a graded equivalence between the quotient categories defined by any graded Morita-Takeuchi context via certain modifications of the graded cotensor functors. As a consequence, we show a commutative diagram that establish the relation between the closed objects of the categories gr^c and M^C, where C is a graded coalgebra.

关键词： Graded coalgebra Graded Morita context Quotient category

Global Phase Portraits of Quadratic Systems with a Complex Ellipse as Invariant Algebraic Curve

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Acta Mathematica Sinica,English Series 2018年第5期34卷 801-811页

作者： Jaume LLIBRE Claudia VALLS departament de Mateatiques Universitat Autonoma de Barcelona 08193 Bellaterra Barcelona Catalonia Spain departamento de matemdtica Instituto Superior Tecnico Universidade de Lisboa 1049-001 Lisboa Portugal

In this paper, we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x^2 ＋ y^2 ＋ 1 = 0 as invariant algebraic curve. We provide all the different topological phase portraits that this class exhibits in the Poincare disc.

关键词： Quadratic system complex ellipse invariant algebraic curves phase portrait Poincare disc

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

STABILITY AND RESONANCES OF MULTISTEP COSINE METHODS

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Journal of Computational Mathematics 2012年第5期30卷 517-532页

作者： B. Cano M.J. Moreta departamento de matemdtica Aplicada IMUVA. Facultad de Ciencias. Paseo Belen 7 CP 47011 Valladolid Spain departamento de Fundamentos del Andlisis Econdmico I. Universidad Complutense de Madrid. Campus de Somosaguas Pozuelo de Alarcdn 28223 Madrid Spain

In a previous paper, some particular multistep cosine methods were constructed which proved to be very efficient because of being able to integrate in a stable and explicit way linearly stiff problems of second-order in time. In the present paper, the conditions which guarantee stability for general methods of this type are given, as well as a thorough study of resonances and filtering for symmetric ones （which, in another paper, have been proved to behave very advantageously with respect to conservation of invariants in Hamiltonian wave equations）. What is given here is a systematic way to analyse and treat any of the methods of this type in the mentioned aspects.

关键词： Exponential integrators Multistep cosine methods Second-order partial dif-ferential equations Stability Resonances

Chaotic dynamics and coexistence in a three species interaction model

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International Journal of Biomathematics 2015年第2期8卷 135-159页

作者： Eduardo Saez Eduardo Stange Ivan Szanto Eduardo Gonzalez-Olivares Manuel Falconi departamento de Matematica Universidad Tecnica Federico Santa Maria Valparaiso Chile Instituto de matemdticas Universidad de Valparaiso Valparaiso Chile departamento de matemdtica Universidad Tdcnica Federico Santa Maria Valparaiso Chile departamento de matemdticas Facultad de Ciencias Universidad Nacional Autonoma de Mdxico Ciudad de Mexico Mexico

This work deals with a three-dimensional system, which describes a food web model consisting of a prey, a specialist predator and a top predator which is generalist as it consumes the other two species. Using tools of dynamical systems we prove that the trajectories of system are bounded and that open subsets of parameters exist, such that the system in the first octant has at most two singularities. For an open subset of the parameters space, the system is shown to have an invariant compact set and this is a topologically transitive attractor set. Finally, we find another open set in the parameters space, such that the system has two limit cycles each contained in different invariant planes. The work is completed with a numeric simulation showing the attractor is a strange attractor.

关键词： Food chain functional response bifurcation behavior dynamic separatrix curve stability.

A Maschke Type Theorem for Weak Hopf Algebras

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Acta Mathematica Sinica,English Series 2008年第12期24卷 2065-2080页

作者： J.N.ALONSOLVAREZ J.M.FERNNdeZVILABOA R.GONZLEZRODRíGUEZ A.B.RODRíGUEZRAPOSO departamento de Matemáticas Universidad de Vigo. Lagoas-Marcosende Vigo. E-36200 Spain departamento de lxebra. Universidad de Santiago de Compostela Santiago de Compostela. E-15771 Spain departamento de matemdtica Aplicada Ⅱ. Universidad de Vigo. Lagoas-Marcosende Vigo. E-36310 Spain departamento delxebra Universidad de Santiago de CompostelaSantiago de Compostela E-15771 Spain

In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. Also, from these results, we deduce a version of Maschke＇s Theorem for （H, B）-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B.

关键词： Monoidal category weak Hopf algebra Hopf modules Maschke Theorem

Topological Minors in Bipartite Graphs

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Acta Mathematica Sinica,English Series 2011年第11期27卷 2085-2100页

作者： Camino BALBUENA Martin CERA Pedro GARCIA-VAZQUEZ Juan Carlos VALENZUELA departament de Matematica Aplicada III Universitat Politecnica de Catalunya C/ Jordi Girona 1-3 （ Edifici C2 Despatx 302） 08034 Barcelona Spain departamento de matemdtica Aplicada I Universidad de SeviUa EUIT Agrlcola Ctra. Utrera Kin. 1 41013 Sevilla Spain departamento de matemdtica Aplicada I Universidad de Sevilla ETS Arquitectura Avda. Reina Mercedes 2 41012 Sevilla Spain departamento de matemdticas Universidad de Cddiz EPS Algeciras Avda. Ramdn Puyol s/n 11202 Algeciras Spain

For a bipartite graph G on m and n vertices, respectively, in its vertices classes, and for integers s andt such that 2≤ s ≤ t, 0≤ m-s ≤ n-t, andre＋n≤ 2s＋t-1, we prove that if G has at least mn- （2（m - s）＋ n - t） edges then it contains a subdivision of the complete bipartite K（s,t） with s vertices in the m-class and t vertices in the n-class. Furthermore, we characterize the corresponding extremal bipartite graphs with mn- （2（m - s）＋ n - t ＋ 1） edges for this topological Turan type problem.

关键词： Bipartite graphs extremal graph theory topological minor

Fixed points of n-valued maps on surfaces and the Wecken property a configuration space approach

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Science China Mathematics 2017年第9期60卷 1561-1574页

作者： GONCALVES Daciberg Lima GUASCHI John departamento de matemdtica&IME Universidade de Sao PauloSdo Paulo 05508-090Brazil Laboratoire de Mathematiques Nicolas Oresme UMR CNRS 6139 UNICAENNormandie UniversiteCS 1403214032 Caen Cedex 5France

Abstract In this paper, we explore the fixed point theory of n-vaiued maps using configuration spaces and braid groups, focusing on two fundamental problems, the Wecken property, and the computation of the Nielsen number. We show that the projective plane （resp. the 2-sphere S2） has the Wecken property for n-valued maps for all n ∈N （resp. all n ≥ 3）. In the case n = 2 and S2, we prove a partial result about the Wecken property. We then describe the Nielsen number of a non-split n-valued map φ ： X → X of an orientable, compact manifold without boundary in terms of the Nielsen coincidence numbers of a certain finite covering q：）→ X with a subset of the coordinate maps of a lift of the n-valued split map → q ： →X.

关键词： multivalued maps fixed points Wecken property Nielsen numbers braids configuration space