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20 October 2008, Volume 28 Issue 4 Previous Issue    Next Issue

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SOME REMARKS ON HOLOMORPHIC FUNCTIONS AND TAYLOR SERIES IN Cn Yu Jiarong Acta mathematica scientia,Series B. 2008, 28 (4):  721-726.  DOI: 10.1016/S0252-9602(08)60073-9 Abstract ( 932 )   RICH HTML PDF (137KB) ( 1452 )   Save Some previous results on convergence of Taylor series in Cn [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy--Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in Cn are constructed and the Taylor series expansion is deduced. Related Articles | Metrics

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ZERO DISSIPATION LIMIT OF THE COMPRESSIBLE HEAT-CONDUCTING NAVIER-STOKES EQUATIONS IN THE PRESENCE OF THE SHOCK Wang Yi Acta mathematica scientia,Series B. 2008, 28 (4):  727-748.  DOI: 10.1016/S0252-9602(08)60074-0 Abstract ( 934 )   RICH HTML PDF (246KB) ( 1568 )   Save The zero dissipation limit of the compressible heat-conducting Navier--Stokes equations in the presence of the shock is investigated. It is shown that when the heat conduction coefficient κ and the viscosity coefficient ε satisfy κ=O(ε), κ/ε ≥ c ＞ 0, as ε → 0 (see (1.3)), if the solution of the corresponding Euler equations is piecewise smooth with shock wave satisfying the Lax entropy condition, then there exists a smooth solution to the Navier--Stokes equations, which converges to the piecewise smooth shock solution of the Euler equations away from the shock discontinuity at a rate of ε. The proof is given by a combination of the energy estimates and the matched asymptotic analysis introduced in [3]. Related Articles | Metrics

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LOWER BOUNDS FOR SUP+INF AND SUP*INF AND AN EXTENSION OF CHEN-LIN RESULT IN DIMENSION 3 Samy Skander Bahoura Acta mathematica scientia,Series B. 2008, 28 (4):  749-758.  DOI: 10.1016/S0252-9602(08)60075-2 Abstract ( 932 )   RICH HTML PDF (180KB) ( 1296 )   Save We give two results about Harnack type inequalities. First, on Riemannian surfaces, we have an estimate of type sup +inf. The second result concern the solutions of prescribed scalar curvature equation on the unit ball of Rn with Dirichlet condition. Next, we give an inequality of type (supKu)2s-1× inf Ωu ≤ c for positive solutions of △u=Vu5 on Ω ∈R3 , where K is a compact set of Ω and V is s-Hölderian, s ∈]-1/2,1] . For the case s=1/2 and Ω= S3, we prove that, if minΩu > m > 0 (for some particular constant m > 0), and the Hölderian constant A of V tends to 0 (in certain meaning), we have the uniform boundedness of the supremum of the solutions of the previous equation on any compact set of Ω. Related Articles | Metrics

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THE NORMAL FAMILITY OF MERMORPHIC FUNCTIONS Han Minghua; Gu Yongxing Acta mathematica scientia,Series B. 2008, 28 (4):  759-762.  DOI: 10.1016/S0252-9602(08)60076-4 Abstract ( 883 )   RICH HTML PDF (121KB) ( 1345 )   Save Let F be a family of mermorphic functions in a domain D, and let a, b, c be complex numbers, a ≠ b. If for each f ∈F, the zeros of f-c are of multiplicity ≥ k+1, and Ef(k)(a) ∈Ef(a), Ef(k)(b) ∈ Ef(b), then F is normal in D. Related Articles | Metrics

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AN OPERATORIAL APPROACH TO SINGULAR INTEGRAL EQUATIONS 0F A MODIFIED TYPE He Fuli; Du Jinyuan Acta mathematica scientia,Series B. 2008, 28 (4):  763-769.  DOI: 10.1016/S0252-9602(08)60077-6 Abstract ( 978 )   RICH HTML PDF (140KB) ( 904 )   Save In this article, the authors discuss a kind of modified singular integral quations on a disjoint union of closed contours or a disjoint union of open arcs. The authors introduce some singular integral operators associated with this kind of singular integral equations, and obtain some useful properties for them. An operatorial approach is also given together with some illustrated examples. Related Articles | Metrics

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A RELAXATION RESULT OF FUNCTIONALS IN THE SPACE SBD(Ω) Lü Zhongxue; Yang Xiaoping Acta mathematica scientia,Series B. 2008, 28 (4):  770-778.  DOI: 10.1016/S0252-9602(08)60078-8 Abstract ( 884 )   RICH HTML PDF (182KB) ( 900 )   Save In this article, the authors obtain an integral representation for the relaxation of the functional F(x, u, Ω):={∫Ω f(x, u(x), εu(x))dx if u ∈ W1, 1(Ω, RN), +∞ otherwise, in the space of functions of bounded deformation, with respect to L1-convergence. Here εu represents the absolutely continuous part of the symmetrized distributional derivative εu.f(x, p, ξ) satisfying weak convexity assumption. Related Articles | Metrics

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INTERSECTIONS AND POLAR FUNCTIONS OF FRACTIONAL BROWNIAN SHEETS Chen Zhenlong Acta mathematica scientia,Series B. 2008, 28 (4):  779-796.  DOI: 10.1016/S0252-9602(08)60079-X Abstract ( 870 )   RICH HTML PDF (234KB) ( 1240 )   Save Let BH={BH(t), t ∈ R+N} be a real-valued (N, d) fractional Brownian sheet with Hurst index H=(H1, …, HN). The characteristics of the polar functions for BH are discussed. The relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar-functions of BH is obtained. The Hausdorff dimension about the fixed points and the inequality about the Kolmogorov’s entropy index for BH are presented. Furthermore, it is proved that any two independent fractional Brownian sheets are nonintersecting in some conditions. A problem proposed by LeGall about the existence of no-polar continuous functions satisfying the Hölder condition is also solved. Related Articles | Metrics

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A SHORT NOTE ABOUT EXPOSED POINTS IN REAL BANACH SPACES Antonio Aizpuru; Francisco J Garc Acta mathematica scientia,Series B. 2008, 28 (4):  797-800.  DOI: 10.1016/S0252-9602(08)60080-6 Abstract ( 788 )   RICH HTML PDF (126KB) ( 1989 )   Save We express the set of exposed points in terms of rotund points and non-smooth points. As long as we have Banach spaces each time "bigger", we consider sets of non-smooth points each time "smaller". Related Articles | Metrics

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COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY, VACUUM AND GRAVITATIONAL FORCE IN THE CASE OF GENERAL PRESSURE Yao Lei; Wang Wenjun Acta mathematica scientia,Series B. 2008, 28 (4):  801-817.  DOI: 10.1016/S0252-9602(08)60081-8 Abstract ( 1201 )   RICH HTML PDF (198KB) ( 1283 )   Save This is a continuation of the article (Comm. Partial Differential Equations 26 (2001) 965). In this article, the authors consider the one-dimensional compressible isentropic Navier--Stokes equations with gravitational force, fixed boundary condition, a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density. Precisely, the viscosity coefficient μ is proportional to ρθ and 0 < θ < 1/2, where ρ is the density, and the pressure P=P(ρ) is a general pressure. The global existence and the uniqueness of weak solution are proved. Related Articles | Metrics

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SUPPORTING AND SEPARATING SUBSETS FOR INVEX BODIES H.K. El-Sayied Acta mathematica scientia,Series B. 2008, 28 (4):  818-822.  DOI: 10.1016/S0252-9602(08)60082-X Abstract ( 742 )   RICH HTML PDF (200KB) ( 996 )   Save Invex bodies represent an important class of bodies which are considered as a generalization of convex bodies. In this article, the author studies the supporting for this class of bodies as well as the separating subsets of two bodies. Related Articles | Metrics

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A NOTE ON KLEIN-GORDON-SCHRöDINGER EQUATIONS WITH HOMOGENEOUS DIRICHLET BOUNDARY CONDITION Zhao Caidi; Zhou Shengfan; Li Yongsheng Acta mathematica scientia,Series B. 2008, 28 (4):  823-833.  DOI: 10.1016/S0252-9602(08)60083-1 Abstract ( 1033 )   RICH HTML PDF (175KB) ( 1293 )   Save This note discusses the long time behavior of solutions for nonautonomous weakly dissipative Klein-Gordon-Schrödinger equations with homogeneous Dirichlet boundary condition. The authors prove the existence of compact kernel sections for the associated process by using a suitable decomposition of the equations. Related Articles | Metrics

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A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS Shi Wei Acta mathematica scientia,Series B. 2008, 28 (4):  834-842.  DOI: 10.1016/S0252-9602(08)60084-3 Abstract ( 902 )   RICH HTML PDF (210KB) ( 1649 )   Save In this article, the author extends the validity of a uniform asymptotic expansion of the Hermite polynomials Hn(2n+1α) to include all positive values of α. His method makes use of the rational functions introduced by Olde Daalhuis and Temme (SIAM J. Math. Anal., (1994), 25: 304-321). A new estimate for the remainder is given. Related Articles | Metrics

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THE TANGENT CONES ON CONSTRAINT QUALIFICATIONS IN OPTIMIZATION PROBLEMS Huang Longguang Acta mathematica scientia,Series B. 2008, 28 (4):  843-850.  DOI: 10.1016/S0252-9602(08)60085-5 Abstract ( 830 )   RICH HTML PDF (141KB) ( 1867 )   Save This article proposes a few tangent cones, which are relative to the constraint qualifications of optimization problems. With the upper and lower directional derivatives of an objective function, the characteristics of cones on the constraint qualifications are presented. The interrelations among the constraint qualifications, a few cones involved, and level sets of upper and lower directional derivatives are derived. Related Articles | Metrics

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MULTIPLE POSITIVE SOLUTIONS BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER SINGULAR WITH DERIVATIVE DEPENDENCE Yan Baoqiang Acta mathematica scientia,Series B. 2008, 28 (4):  851-864.  DOI: 10.1016/S0252-9602(08)60086-7 Abstract ( 911 )   RICH HTML PDF (191KB) ( 1087 )   Save The existence of at least two positive solutions is presented for the singular second-order boundary value problem {(p(t)/1 (p(t)x’(t))′+Φ(t)f(t, x(t), p(t)x′(t))=0, 0 ＜t ＜1, limt→0 p(t)x′(t)=0, x(1)=0. by using the fixed point index, where f may be singular at x=0 and px’=0. Related Articles | Metrics

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LIMIT CYCLES AND INVARIANT PARABOLA IN A KUKLES SYSTEM OF DEGREE THREE Liu Zhenhai; E. Sáez; I. Szántó Acta mathematica scientia,Series B. 2008, 28 (4):  865-869.  DOI: 10.1016/S0252-9602(08)60087-9 Abstract ( 850 )   RICH HTML PDF (124KB) ( 1288 )   Save In this article, the authors consider a class of Kukles planar polynomial differential system of degree three having an invariant parabola. For this class of second-order differential systems, it is shown that for certain values of the parameters the invariant parabola coexists with a center. For other values it can coexist with one, two or three small amplitude limit cycles which are constructed by Hopf bifurcation. This result gives an answer for the question given in [4], about the existence of limit cycles for such class of system. Related Articles | Metrics

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SYMMETRIES IN YETTER-DRINFELD CATEGORIES OVER WEAK HOPF ALGEBRAS Gao Nan Acta mathematica scientia,Series B. 2008, 28 (4):  870-876.  DOI: 10.1016/S0252-9602(08)60088-0 Abstract ( 824 )   RICH HTML PDF (137KB) ( 1120 )   Save This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak Hopf algebra.It generalizes the corresponding results in Hopf algebras. Related Articles | Metrics

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PARTIAL REGULARITY FOR WEAK SOLUTIONS OF STATIONARY NAVIER-STOKES SYSTEMS Chen Shuhong; Tan Zhong Acta mathematica scientia,Series B. 2008, 28 (4):  877-894.  DOI: 10.1016/S0252-9602(08)60089-2 Abstract ( 762 )   RICH HTML PDF (221KB) ( 1473 )   Save This article is concerned with the partial regularity for the weak solutions of stationary Navier-Stokes system under the controllable growth condition. By A-harmonic approximation technique, the optimal regularity is obtained. Related Articles | Metrics

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THE UNIFORMLY BOUNDEDNESS OF THE RIESZ TRANSFORMS ON THE CAYLEY HEISENBERG GROUPS Luan Jingwen; Zhu Fuliu Acta mathematica scientia,Series B. 2008, 28 (4):  895-914.  DOI: 10.1016/S0252-9602(08)60090-9 Abstract ( 931 )   RICH HTML PDF (221KB) ( 949 )   Save In this article, the authors estimate some functions by using the explicit expression of the heat kernels for the Cayley Heisenberg groups, and then prove the uniform boundedness of the Riesz transforms on these nilpotent Lie groups. Related Articles | Metrics

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VERSAL UNFOLDING OF EQUIVARIANT BIFURCATION PROBLEMS IN MORE GENERAL CASE UNDER TWO EQUIVALENT GROUPS Li Yangcheng; He Wei Acta mathematica scientia,Series B. 2008, 28 (4):  915-923.  DOI: 10.1016/S0252-9602(08)60091-0 Abstract ( 752 )   RICH HTML PDF (164KB) ( 1354 )   Save For the unfolding of equivariant bifurcation problems with two types of state variables in the presence of parameter symmetry, the versal unfolding theorem with respect to left-right equivalence is obtained by using the related methods and techniques in the singularity theory of smooth map-germs. The corresponding results in [4, 9] can be considered as its special cases. A relationship between the versal unfolding w.r.t. left-right equivalence and the versal deformation w.r.t. contact equivalence is established. Related Articles | Metrics

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THE ASYMPTOTIC LIMIT FOR A COMBUSTION MODEL IN REGARD TO INFINITE REACTION RATE Ying Longan Acta mathematica scientia,Series B. 2008, 28 (4):  924-932.  DOI: 10.1016/S0252-9602(08)60092-2 Abstract ( 862 )   RICH HTML PDF (158KB) ( 911 )   Save The Zeldovich-von Neumann-Doring model and the Chapman-Jouguet model for a simplified combustion model--Majda’s model is studied. The author proves a uniform maximum norm estimate, then proves that as the rate of chemical reaction tends to infinity the solutions to the Zeldovich-von Neumann-Doring model tend to that of the Chapman-Jouguet model. The type of combustion waves is studied. This result is compared with the result of the projection and finite difference method for the same model. Related Articles | Metrics

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DERIVATIONS AND EXTENSIONS OF LIE COLOR ALGEBRA Zhang Qingcheng; Zhang Yongzheng Acta mathematica scientia,Series B. 2008, 28 (4):  933-948.  DOI: 10.1016/S0252-9602(08)60093-4 Abstract ( 765 )   RICH HTML PDF (200KB) ( 1624 )   Save In this article, the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer(L) and central extension H2(L, F) on some Lie color algebras. Meanwhile, they generalize the notion of double extension to quadratic Lie color algebras, a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given. Related Articles | Metrics

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BOUND ON THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS FOR 2n-(n-k) DESIGNS Zhao Shengli; Zhang Runchu Acta mathematica scientia,Series B. 2008, 28 (4):  949-954.  DOI: 10.1016/S0252-9602(08)60094-6 Abstract ( 841 )   RICH HTML PDF (151KB) ( 878 )   Save Clear effects criterion is an important criterion for selecting fractional factorial designs [1]. Tang et al. [2] derived upper and lower bounds on the maximum number of clear two-factor interactions (2fi’s) in 2n-(n-k) designs of resolution III and IV by constructing 2n-(n-k) designs. But the method in [2] does not perform well sometimes when the resolution is III. This article modifies the construction method for 2n-(n-k) designs of resolution III in [2]. The modified method is a great improvement on that used in [2]. Related Articles | Metrics

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THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL Zhang Weiping; Wei Laisheng Acta mathematica scientia,Series B. 2008, 28 (4):  955-962.  DOI: 10.1016/S0252-9602(08)60095-8 Abstract ( 714 )   RICH HTML PDF (151KB) ( 1531 )   Save In this article, the empirical Bayes (EB) estimators are constructed for the estimable functions of the parameters in partitioned normal linear model. The superiorities of the EB estimators over ordinary least-squares (LS) estimator are investigated under mean square error matrix (MSEM) criterion. Related Articles | Metrics

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HOMOGENIZATION OF A STATIONARY NAVIER-STOKES FLOW IN POROUS MEDIUM WITH THIN FILM Yao Zhengan; Zhao Hongxing Acta mathematica scientia,Series B. 2008, 28 (4):  963-974.  DOI: 10.1016/S0252-9602(08)60096-X Abstract ( 936 )   RICH HTML PDF (181KB) ( 1407 )   Save The article studies the homogenization of a stationary Navier-Stokes fluid in porous medium with thin film under Dirichlet boundary condition. At the end of the article, "Darcy’s law" is rigorously derived from this model as the parameter ε tends to zero, which is independent of the coordinates towards the thickness. Related Articles | Metrics

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THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS SATISFYING (F) OR (B) Hu Dihe; Hu Xiaoyu Acta mathematica scientia,Series B. 2008, 28 (4):  975-988.  DOI: 10.1016/S0252-9602(08)60097-1 Abstract ( 988 )   RICH HTML PDF (194KB) ( 1041 )   Save This article is a continuation of [9]. Based on the discussion of random Kolmogorov forward (backward) equations, for any given q-matrix in random environment, Q(θ)=(q(θ; x, y), x, y∈ χ), an infinite class of q-processes in random environments satisfying the random Kolmogorov forward (backward) equation is constructed. Moreover, under some conditions, all the q-processes in random environments satisfying the random Kolmogorov forward (backward) equation are constructed. Related Articles | Metrics

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EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES Zhang Riquan; Li Guoying Acta mathematica scientia,Series B. 2008, 28 (4):  989-997.  DOI: 10.1016/S0252-9602(08)60098-3 Abstract ( 872 )   RICH HTML PDF (197KB) ( 1092 )   Save In this article, a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined. First step, by the local linear technique and the averaged method, the initial estimates of the coefficient functions are given. Second step, based on the initial estimates, the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure. The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions. Two simulated examples show that the procedure is effective. Related Articles | Metrics

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AN ORDER PRESERVING INEQUALITY FOR THREE OPERATORS VIA FURUTA INEQUALITY Yang Changsen Acta mathematica scientia,Series B. 2008, 28 (4):  998-002.  DOI: 10.1016/S0252-9602(08)60099-5 Abstract ( 786 )   RICH HTML PDF (142KB) ( 897 )   Save Furuta showed that if A ≥ B ≥0, then for each r≥0, f(p)=(Ar/2BpAr/2)t+r/p+r is decreasing for p≥t≥0. Using this result, the following inequality (Cr/2AB2A)δCr/2)p-1+r/4δ+r≤Cp-1+r is obtained for 0<p≤1, r≥1, 1/4≤δ≤1 and three positive operators A, B, C satisfy (A1/2 B A1/2)p/2 ≤ Ap, (B1/2 AB1/2)p/2 ≥ Bp, (C1/2 AC1/2)p/2 ≤Cp, (A1/2 CA1/2)p/2≥Ap. Related Articles | Metrics