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20 May 2014, Volume 34 Issue 3 Previous Issue    Next Issue

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UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE NONLINEAR DIFFERENTIAL POLYNOMIALS SHARE ONE VALUE OR HAVE THE SAME FIXED POINTS IN AN ANGULAR DOMAIN LI Xiao-Min, YI Hong-Xun Acta mathematica scientia,Series B. 2014, 34 (3):  593-609.  DOI: 10.1016/S0252-9602(14)60032-1 Abstract ( 188 )   RICH HTML PDF (212KB) ( 627 )   Save In this article, we study the uniqueness question of nonconstant meromorphic functions whose nonlinear differential polynomials share 1 or have the same fixed points in an angular domain. The results in this article improve Theorem 1 of Yang and Hua [26], and improve Theorem 1 of Fang and Qiu [6]. References | Related Articles | Metrics

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POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE p-LAPLACIAN EQUATIONS Leszek GASINSKI, Nikolaos S. PAPAGEORGIOU Acta mathematica scientia,Series B. 2014, 34 (3):  610-618.  DOI: 10.1016/S0252-9602(14)60033-3 Abstract ( 178 )   RICH HTML PDF (171KB) ( 644 )   Save We consider a parametric Dirichlet problem driven by the p-Laplacian with a Carath´eodory reaction of equidiffusive type. Our hypotheses incorporate as a special case the equidiffusive p-logistic equation. We show that if λ1 > 0 is the principal eigenvalue of the Dirichlet negative p-Laplacian and λ > λ1 (λ being the parameter), the problem has a unique positive solution, while for λ ∈(0, λ1], the problem has no positive solution. References | Related Articles | Metrics

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APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES H. M. SRIVASTAVA, M. I. QURESHI, Kaleem A. QURAISHI, Ashish ARORA Acta mathematica scientia,Series B. 2014, 34 (3):  619-628.  DOI: 10.1016/S0252-9602(14)60034-5 Abstract ( 210 )   RICH HTML PDF (159KB) ( 562 )   Save Using series iteration techniques, we derive a number of general double series identities and apply each of these identities in order to deduce several hypergeometric reduc-tion formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon. References | Related Articles | Metrics

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PSEUDOHYPERBOLIC METRIC AND UNIFORMLY DISCRETE SEQUENCES IN THE REAL UNIT BALL REN Guang-Bin, Uwe KAHLER Acta mathematica scientia,Series B. 2014, 34 (3):  629-638.  DOI: 10.1016/S0252-9602(14)60035-7 Abstract ( 166 )   RICH HTML PDF (177KB) ( 498 )   Save We present an overview of the properties of the pseudohyperbolic metric in sev-eral real dimensions and study uniformly discrete sequences for the real unit ball in Rn. References | Related Articles | Metrics

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APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES Amir KHOSRAVI, Morteza MIRZAEE AZANDARYANI Acta mathematica scientia,Series B. 2014, 34 (3):  639-652.  DOI: 10.1016/S0252-9602(14)60036-9 Abstract ( 250 )   RICH HTML PDF (216KB) ( 898 )   Save In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction. References | Related Articles | Metrics

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ON THE DIFFERENCE COUNTERPART OF BRÜCK´S CONJECTURE CHEN Zong-Xuan Acta mathematica scientia,Series B. 2014, 34 (3):  653-659.  DOI: 10.1016/S0252-9602(14)60037-0 Abstract ( 155 )   RICH HTML PDF (142KB) ( 598 )   Save In this article, for a transcendental entire function f(z) of finite order which has a finite Borel exceptional value α we utilize properties of complex difference equations to prove the difference counterpart of Br¨uck´s conjecture, that is, if Δf(z) = f(z + η) − f(z) and f(z) share one value a (≠ ) CM, where η ∈ C is a constant such that f(z + η) ≠ f(z), then Δf(z) − a/f(z) − a =a/a −α. References | Related Articles | Metrics

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MATCHING PURSUITS AMONG SHIFTED CAUCHY KERNELS IN HIGHER-DIMENSIONAL SPACES QIAN Tao, WANG Jin-Xun, YANG Yan Acta mathematica scientia,Series B. 2014, 34 (3):  660-672.  DOI: 10.1016/S0252-9602(14)60038-2 Abstract ( 173 )   RICH HTML PDF (207KB) ( 535 )   Save Appealing to the Clifford analysis and matching pursuits, we study the adaptive decompositions of functions of several variables of finite energy under the dictionaries con-sisting of shifted Cauchy kernels. This is a realization of matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. It offers a method to process signals in arbitrary dimensions. References | Related Articles | Metrics

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CONVERGENCE ANALYSIS OF THE JACOBI SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS YANG Yin, CHEN Yan-Ping, HUANG Yun-Qing Acta mathematica scientia,Series B. 2014, 34 (3):  673-690.  DOI: 10.1016/S0252-9602(14)60039-4 Abstract ( 159 )   RICH HTML PDF (893KB) ( 1448 )   Save We propose and analyze a spectral Jacobi-collocation approximation for frac-tional order integro-differential equations of Volterra type. The fractional derivative is de-scribed in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L∞ norm and weighted L2-norm. The numerical examples are given to illustrate the theoretical results. References | Related Articles | Metrics

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SIGN-CHANGING SOLUTIONS FOR SCHRÖDINGER EQUATIONS WITH VANISHING AND SIGN-CHANGING POTENTIALS WU Yuan-Ze, HUANG Yi-Sheng, LIU Zeng Acta mathematica scientia,Series B. 2014, 34 (3):  691-702.  DOI: 10.1016/S0252-9602(14)60040-0 Abstract ( 163 )   RICH HTML PDF (208KB) ( 810 )   Save In this article, we study the existence of sign-changing solutions for the following Schr¨odinger equation −Δu + λV (x)u = K(x)|u|p−2u     x ∈RN, u →0 as |x| →+∞, where N ≥ 3, λ > 0 is a parameter, 2 < p < 2N/N−2 , and the potentials V (x) and K(x) satisfy some suitable conditions. By using the method based on invariant sets of the descending flow, we obtain the existence of a positive ground state solution and a ground state sign-changing solution of the above equation for small λ, which is a complement of the results obtained by Wang and Zhou in [J. Math. Phys. 52, 113704, 2011]. References | Related Articles | Metrics

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PERTURBATION METHODS IN SEMILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY-SOBOLEV EXPONENT LAN Yong-Yi, TANG Chun-Lei Acta mathematica scientia,Series B. 2014, 34 (3):  703-712.  DOI: 10.1016/S0252-9602(14)60041-2 Abstract ( 166 )   RICH HTML PDF (176KB) ( 615 )   Save In this article, we deal with a class of semilinear elliptic equations which are perturbations of the problems with the critical Hardy-Sobolev exponent. Some existence results are given via an abstract perturbation method in critical point theory. References | Related Articles | Metrics

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ON A KÄHLER VERSION OF CHEEGER-GROMOLL-PERELMAN´S SOUL THEOREM FU Xiao-Yong, GE Jian Acta mathematica scientia,Series B. 2014, 34 (3):  713-718.  DOI: 10.1016/S0252-9602(14)60042-4 Abstract ( 125 )   RICH HTML PDF (135KB) ( 516 )   Save In this note, we will prove a K¨ahler version of Cheeger-Gromoll-Perelman´s soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point. References | Related Articles | Metrics

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THE VALUE DISTRIBUTION AND UNIQUENESS OF ONE CERTAIN TYPE OF DIFFERENTIAL-DIFFERENCE POLYNOMIALS ZHANG Ke-Yu, YI Hong-Xun Acta mathematica scientia,Series B. 2014, 34 (3):  719-728.  DOI: 10.1016/S0252-9602(14)60043-6 Abstract ( 315 )   RICH HTML PDF (160KB) ( 780 )   Save In this article, we investigate the distribution of the zeros and uniqueness of differential-difference polynomials G(z) = (fn(fm(z) − 1)∏dj=1f(z + cj )vj )(k)− α(z), H(z) = (fn(f(z) − 1)m∏dj=1f(z + cj )vj )(k)− α(z), where f is transcendental entire function of finite order, cj(j = 1, 2, · · · , d), n, m, d, and vj (j = 1, 2, · · · , d) are integers, and obtain some theorems, which extended and improved many previous results. References | Related Articles | Metrics

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GENERAL DECAY FOR A DIFFERENTIAL INCLUSION OF KIRCHHOFF TYPE WITH A MEMORY CONDITION AT THE BOUNDARY Jum-Ran KANG Acta mathematica scientia,Series B. 2014, 34 (3):  729-738.  DOI: 10.1016/S0252-9602(14)60044-8 Abstract ( 164 )   RICH HTML PDF (167KB) ( 690 )   Save In this article, we consider a differential inclusion of Kirchhoff type with a memory condition at the boundary. We prove the asymptotic behavior of the corresponding solutions. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases. References | Related Articles | Metrics

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AREA INTEGRAL FUNCTIONS FOR SECTORIAL OPERATORS ON Lp SPACES CHEN Ze-Qan, SUN Mu Acta mathematica scientia,Series B. 2014, 34 (3):  739-747.  DOI: 10.1016/S0252-9602(14)60045-X Abstract ( 139 )   RICH HTML PDF (185KB) ( 455 )   Save Area integral functions are introduced for sectorial operators on Lp-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on Lp spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H1 functional calculus of sectorial operators on Lp-spaces hold true when the square functions are replaced by the area integral functions. References | Related Articles | Metrics

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PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL NONLINEAR DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION LI Yu-Huan, MI Yong-Sheng, MU Chun-Lai Acta mathematica scientia,Series B. 2014, 34 (3):  748-758.  DOI: 10.1016/S0252-9602(14)60046-1 Abstract ( 160 )   RICH HTML PDF (189KB) ( 903 )   Save This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses. References | Related Articles | Metrics

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GLOBAL EXISTENCE AND EXPONENTIAL STABILITY OF SOLUTIONS TO THE QUASILINEAR THERMO-DIFFUSION EQUATIONS WITH SECOND SOUND QIN Yu-Ming, LI Hai-Yan Acta mathematica scientia,Series B. 2014, 34 (3):  759-778.  DOI: 10.1016/S0252-9602(14)60047-3 Abstract ( 213 )   RICH HTML PDF (226KB) ( 769 )   Save This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially. References | Related Articles | Metrics

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ATOMIC DECOMPOSITION OF μ-BERGMAN SPACE IN Cn ZHANG Xue-Jun, XI Li-Hua, FAN Hai-Xia, LI Jun-Feng Acta mathematica scientia,Series B. 2014, 34 (3):  779-789.  DOI: 10.1016/S0252-9602(14)60048-5 Abstract ( 144 )   RICH HTML PDF (191KB) ( 384 )   Save Let μ be a normal function on [0, 1). The atomic decomposition of the μ-Bergman space in the unit ball B is given for all p > 0. References | Related Articles | Metrics

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ON COLEMAN OUTER AUTOMORPHISM GROUPS OF FINITE GROUPS HAI Jin-Ke, LI Zheng-Xing Acta mathematica scientia,Series B. 2014, 34 (3):  790-796.  DOI: 10.1016/S0252-9602(14)60049-7 Abstract ( 142 )   RICH HTML PDF (169KB) ( 634 )   Save Let G be a finite group and OutCol(G) the Coleman outer automorphism group of G(for the definition, see below). The question whether OutCol(G) is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime. In this article, some sufficient conditions for OutCol(G) to be a p′-group are obtained. Our results generalize some well-known theorems. References | Related Articles | Metrics

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SHARP BOUNDS FOR NEUMAN-SÁNDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS CHU Yu-Ming, ZhAO Tie-Hong, SONG Ying-Qing Acta mathematica scientia,Series B. 2014, 34 (3):  797-806.  DOI: 10.1016/S0252-9602(14)60050-3 Abstract ( 176 )   RICH HTML PDF (169KB) ( 551 )   Save In this article, we prove that the double inequality αP(a, b) + (1 − α)Q(a, b) < M(a, b) < βP(a, b) + (1 − β)Q(a, b) holds for any a, b > 0 with a ≠b if and only if α ≥ 1/2 and β ≤ [π(√2 log(1 + √2) −1)]/[(√2π−2) log(1+√2)] = 0.3595 · · · , where M(a, b), Q(a, b), and P(a, b) are the Neuman-S´andor, quadratic, and first Seiffert means of a and b, respectively. References | Related Articles | Metrics

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A NOTE ON COMPLETE MANIFOLDS WITH FINITE VOLUME DENG Hong-Cun Acta mathematica scientia,Series B. 2014, 34 (3):  807-813.  DOI: 10.1016/S0252-9602(14)60051-5 Abstract ( 130 )   RICH HTML PDF (153KB) ( 725 )   Save In this article, we concern on complete manifolds with finite volume. We prove that under some assumptions about scalar curvature and the Yamabe constant, the manifolds must be compact, and we also give the diameter estimates in terms of the scalar curvature and the Yamabe constant. References | Related Articles | Metrics

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GENERALIZED DERIVATIONS ON PARABOLIC SUBALGEBRAS OF GENERAL LINEAR LIE ALGEBRAS CHEN Zheng-Xin Acta mathematica scientia,Series B. 2014, 34 (3):  814-828.  DOI: 10.1016/S0252-9602(14)60052-7 Abstract ( 151 )   RICH HTML PDF (198KB) ( 404 )   Save Let P be a parabolic subalgebra of a general linear Lie algebra gl(n, F) over a field F, where n ≥ 3, F contains at least n different elements, and char(F) ≠ 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation. References | Related Articles | Metrics

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CYCLIC AND NEGACYCLIC CODES OF LENGTH 2ps OVER Fpm + uFpm LIU Xiu-Sheng, XU Xiao-Fang Acta mathematica scientia,Series B. 2014, 34 (3):  829-839.  DOI: 10.1016/S0252-9602(14)60053-9 Abstract ( 174 )   RICH HTML PDF (195KB) ( 893 )   Save In this article, we focus on cyclic and negacyclic codes of length 2ps over the ring R = Fpm + uFpm, where p is an odd prime. On the basis of the works of Dinh (in J.Algebra 324,940-950,2010), we use the Chinese Remainder Theorem to establish the alge-braic structure of cyclic and negacyclic codes of length 2ps over the ring Fpm +uFpm in terms of polynomial generators. Furthermore, we obtain the number of codewords in each of those cyclic and negacyclic codes. References | Related Articles | Metrics

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ON GROUND STATE SOLUTIONS FOR SUPERLINEAR DIRAC EQUATION ZHANG Jian, TANG Xian-Hua, ZHANG Wen Acta mathematica scientia,Series B. 2014, 34 (3):  840-850.  DOI: 10.1016/S0252-9602(14)60054-0 Abstract ( 193 )   RICH HTML PDF (197KB) ( 639 )   Save This article is concerned with the nonlinear Dirac equations -i∂t φ= ich φ −mc2β φ  + R φ(x, φ ) in R3. Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin andWeth.∑3k=1αk∂k References | Related Articles | Metrics

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LOCAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY YE Yu-Lin, DOU Chang-Sheng, JIU Quan-Sen Acta mathematica scientia,Series B. 2014, 34 (3):  851-871.  DOI: 10.1016/S0252-9602(14)60055-2 Abstract ( 204 )   RICH HTML PDF (248KB) ( 656 )   Save In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ(ρ) = ρβ with β ≥0. Note that the initial data can be arbitrarily large to contain vacuum states. References | Related Articles | Metrics

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A POD REDUCED-ORDER SPDMFE EXTRAPOLATING ALGORITHM FOR HYPERBOLIC EQUATIONS LUO Zhen-Dong, LI Hong Acta mathematica scientia,Series B. 2014, 34 (3):  872-890.  DOI: 10.1016/S0252-9602(14)60056-4 Abstract ( 170 )   RICH HTML PDF (2289KB) ( 695 )   Save In this article, a proper orthogonal decomposition (POD) method is used to study a classical splitting positive definite mixed finite element (SPDMFE) formulation for second-order hyperbolic equations. A POD reduced-order SPDMFE extrapolating algorithm with lower dimensions and sufficiently high accuracy is established for second-order hyperbolic equations. The error estimates between the classical SPDMFE solutions and the reduced-order SPDMFE solutions obtained from the POD reduced-order SPDMFE extrapolating algorithm are provided. The implementation for solving the POD reduced-order SPDMFE extrapolating algorithm is given. Some numerical experiments are presented illustrating that the results of numerical computation are consistent with theoretical conclusions, thus validating that the POD reduced-order SPDMFE extrapolating algorithm is feasible and efficient for solving second-order hyperbolic equations. References | Related Articles | Metrics

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BOUNDEDNESS OF STEIN´S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES YAN Xue-Fang Acta mathematica scientia,Series B. 2014, 34 (3):  891-904.  DOI: 10.1016/S0252-9602(14)60057-6 Abstract ( 164 )   RICH HTML PDF (225KB) ( 911 )   Save Let (X, d, μ) be a metric measure space endowed with a metric d and a nonneg-ative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L2(X). Assume that the semigroup e−tL generated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions, we show that Stein´s square function GδL) arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces HpL(X) to Lp(X) for all 0 < p ≤1. References | Related Articles | Metrics

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A QUASILINEAR SINGULAR ELLIPTIC SYSTEM WITHOUT COOPERATIVE STRUCTURE Dumitru MOTREANU, Abdelkrim MOUSSAOUI Acta mathematica scientia,Series B. 2014, 34 (3):  905-916.  DOI: 10.1016/S0252-9602(14)60058-8 Abstract ( 219 )   RICH HTML PDF (186KB) ( 842 )   Save In this article, we investigate the existence of positive solutions of a singular quasilinear elliptic system for which the cooperative structure is not required. The approach is based on the Schauder fixed point theorem combined with perturbation arguments that involve the singular terms. References | Related Articles | Metrics

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SPHERICAL SYMMETRIC SOLUTIONS FOR THE MOTION OF RELATIVISTIC MEMBRANES AND NULL MEMBRANES IN THE REISSNER-NORDSTRÖM SPACE-TIME LUO Shao-Ying, LIU Qi Acta mathematica scientia,Series B. 2014, 34 (3):  917-931.  DOI: 10.1016/S0252-9602(14)60059-X Abstract ( 164 )   RICH HTML PDF (278KB) ( 585 )   Save In this article, we concern the motion of relativistic membranes and null membranes in the Reissner-Nordstr¨om space-time. The equation of relativistic membranes moving in the Reissner-Nordstr¨om space-time is derived and some properties are discussed. Spherical symmetric solutions for the motion are illustrated and some interesting physical phenomena are discovered. The equations of the null membranes are derived and the exact solutions are also given. Spherical symmetric solutions for null membranes are just the two horizons of Reissner-Nordstr¨om space-time. References | Related Articles | Metrics

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ON A LEMMA OF BOWEN LI Ming-Tian, MA Ji-Hua Acta mathematica scientia,Series B. 2014, 34 (3):  932-940.  DOI: 10.1016/S0252-9602(14)60060-6 Abstract ( 244 )   RICH HTML PDF (174KB) ( 554 )   Save We are concerned with the sets of quasi generic points in finite symbolic space. We estimate the sizes of the sets by the Billingsley dimension defined by Gibbs measures. A dimension formula of such set is given, which generalizes Bowen´s result. An application is given to the level sets of Birkhoff average. References | Related Articles | Metrics

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BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT ZHANG Wei-Guo, LIU Qiang, LI Zheng-Ming, LI Xiang Acta mathematica scientia,Series B. 2014, 34 (3):  941-959.  DOI: 10.1016/S0252-9602(14)60061-8 Abstract ( 155 )   RICH HTML PDF (340KB) ( 495 )   Save This article studies bounded traveling wave solutions of variant Boussinesq equa-tion with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solutions for the above equation by the theory and method of planar dynamical systems, and obtain their existent conditions, number, and gen-eral shape. Secondly, we investigate the dissipation effect on the shape evolution of bounded traveling wave solutions. We find out a critical value r* which can characterize the scale of dissipation effect, and prove that the bounded traveling wave solutions appear as kink profile waves if |r| ≥ r*; while they appear as damped oscillatory waves if |r| < r*. We also obtain kink profile solitary wave solutions with and without dissipation effect. On the basis of the above discussion, we sensibly design the structure of the approximate damped oscillatory so-lutions according to the orbits evolution relation corresponding to the component u(ξ) in the global phase portraits, and then obtain the approximate solutions (u(ξ), H(ξ)). Furthermore, by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions. Finally, we discuss the dissipation effect on the amplitude, frequency, and energy decay of the bounded traveling wave solutions. References | Related Articles | Metrics

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TWO-LEVEL MULTISCALE FINITE ELEMENT METHODS FOR THE STEADY NAVIER-STOKES PROBLEM WEN Juan, HE Yin-Nian, WANG Xue-Min, HE Mi-Hui Acta mathematica scientia,Series B. 2014, 34 (3):  960-972.  DOI: 10.1016/S0252-9602(14)60062-X Abstract ( 141 )   RICH HTML PDF (1366KB) ( 790 )   Save In this article, on the basis of two-level discretizations and multiscale finite el-ement method, two kinds of finite element algorithms for steady Navier-Stokes problem are presented and discussed. The main technique is first to use a standard finite element dis-cretization on a coarse mesh to approximate low frequencies, then to apply the simple and Newton scheme to linearize discretizations on a fine grid. At this process, multiscale finite element method as a stabilized method deals with the lowest equal-order finite element pairs not satisfying the inf-sup condition. Under the uniqueness condition, error analyses for both algorithms are given. Numerical results are reported to demonstrate the effectiveness of the simple and Newton scheme. References | Related Articles | Metrics