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20 January 2014, Volume 34 Issue 1 Previous Issue    Next Issue

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EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS CHEN Gui-Qang, XIAO Chang-Guo, ZHANG Yong-Qian Acta mathematica scientia,Series B. 2014, 34 (1):  1-38.  DOI: 10.1016/S0252-9602(13)60123-X Abstract ( 285 )   RICH HTML PDF (356KB) ( 991 )   Save We are concerned with the global existence of entropy solutions of the twodimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function (T) is assumed to have a positive lower bound. We first consider the Cauchy problem (the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is sufficiently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an additional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave (weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained. References | Related Articles | Metrics

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GLOBAL EXISTENCE OF CLASSICAL SOLUTION FOR A VISCOUS LIQUID-GAS TWO-PHASE MODEL WITH MASS-DEPENDENT VISCOSITY AND VACUUM WANG Zhen, ZHANG Hui Acta mathematica scientia,Series B. 2014, 34 (1):  39-52.  DOI: 10.1016/S0252-9602(13)60124-1 Abstract ( 203 )   RICH HTML PDF (181KB) ( 1203 )   Save In this work, we obtain the global existence and uniqueness of classical solu-tions to a viscous liquid-gas two-phase model with mass-dependent viscosity and vacuum in one dimension, where the initial vacuum is allowed. We get the upper and lower bounds of gas and liquid masses n and m by the continuity methods which we use to study the compressible Navier-Stokes equations. References | Related Articles | Metrics

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GENERALIZED FRACTIONAL TRACE VARIATIONAL IDENTITY AND A NEW FRACTIONAL INTEGRABLE COUPLINGS#br# OF SOLITON HIERARCHY WEI Han-Yu, XIA Tie-Cheng Acta mathematica scientia,Series B. 2014, 34 (1):  53-64.  DOI: 10.1016/S0252-9602(13)60125-3 Abstract ( 181 )   RICH HTML PDF (166KB) ( 972 )   Save Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy. References | Related Articles | Metrics

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QUASI-SURE CONVERGENCE RATE OF EULER SCHEME FOR STOCHASTIC DIFFERENTIAL EQUATIONS HUANG Wen-Liang, ZHANG Xi-Cheng Acta mathematica scientia,Series B. 2014, 34 (1):  65-72.  DOI: 10.1016/S0252-9602(13)60126-5 Abstract ( 158 )   RICH HTML PDF (165KB) ( 1012 )   Save Let Xt(x) be the solution of stochastic differential equations with smooth and bounded derivatives coefficients. Let Xnt (x) be the Euler discretization scheme of SDEs with step 2−n. In this note, we prove that for any R > 0 and γ∈ (0, 1/2), supt∈[0,1],|x|≤R|Xnt (x, ω) − Xt(x, ω)| ξ R, γ(ω)2−nγ, n > 1, q.e., where ξR, γ(ω) is quasi-everywhere finite. References | Related Articles | Metrics

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COMPOSITION OPERATORS BETWEEN BLOCH TYPE SPACES IN THE UNIT BALL Dai-Ji-Neng, OUYANG Cai-Heng Acta mathematica scientia,Series B. 2014, 34 (1):  73-81.  DOI: 10.1016/S0252-9602(13)60127-7 Abstract ( 234 )   RICH HTML PDF (156KB) ( 966 )   Save In this paper, we obtain some new necessary and sufficient conditions for the boundedness and compactness of composition operators CΦ between Bloch type spaces in the unit ball Bn. References | Related Articles | Metrics

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ON AN INFINITE FAMILY IN π*S LIU Xiu-Gui Acta mathematica scientia,Series B. 2014, 34 (1):  82-92.  DOI: 10.1016/S0252-9602(13)60128-9 Abstract ( 176 )   RICH HTML PDF (179KB) ( 832 )   Save In this paper, a new family of homotopy elements in the stable homotopy groups of spheres represented by h1hnhm˜ s in the Adams spectral sequence is detected, where n − 2 ≥ m ≥ 5 and 3 ≤ s < p. References | Related Articles | Metrics

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GLOBAL EXISTENCE AND CONVERGENCE RATES OF SMOOTH SOLUTIONS FOR THE 3-D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITHOUT HEAT CONDUCTIVITY GAO Zhen-Sheng, TAN Zhong, WU Guo-Chun Acta mathematica scientia,Series B. 2014, 34 (1):  93-106.  DOI: 10.1016/S0252-9602(13)60129-0 Abstract ( 200 )   RICH HTML PDF (195KB) ( 1262 )   Save In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations without heat conductivity, which is a hyperbolic-parabolic system. The global solutions are obtained by combining the local existence and a priori estimates if H3-norm of the initial perturbation around a constant states is small enough and its L1-norm is bounded. A priori decay-in-time estimates on the pressure, velocity and magnetic field are used to get the uniform bound of entropy. Moreover, the optimal convergence rates are also obtained. References | Related Articles | Metrics

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WELL-POSEDNESS OF A COMPRESSIBLE GAS-LIQUID MODEL FOR DEEPWATER OIL WELL OPERATIONS Helmer A. FRIIS, Steinar EVJE Acta mathematica scientia,Series B. 2014, 34 (1):  107-124.  DOI: 10.1016/S0252-9602(13)60130-7 Abstract ( 208 )   RICH HTML PDF (212KB) ( 948 )   Save The main purpose of this paper is two-fold: (i) to generalize an existence result for a compressible gas-liquid model with a friction term recently published by Friis and Evje [SIAM J. Appl. Math., 71 (2011), pp. 2014–2047]; (ii) to derive a uniqueness result for the same model. A main ingredient in the existence part is the observation that we can consider weaker assumptions on the initial liquid and gas mass, and still obtain an existence result. Compared to the above mentioned work, we rely on a more refined application of the estimates provided by the basic energy estimate. Concerning the uniqueness result, we borrow ideas from Fang and Zhang [Nonlinear Anal. TMA, 58 (2004), pp. 719–731] and derive a stability result under appropriate constraints on parameters that determine rate of decay toward zero at the boundary for gas and liquid masses, and growth rate of masses associated with the friction term and viscous coefficient. References | Related Articles | Metrics

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STABILITY OF DISPLACEMENT TO THE SECOND FUNDAMENTAL PROBLEM IN PLANE ELASTICITY LIN Juan, DU Jin-Yuan Acta mathematica scientia,Series B. 2014, 34 (1):  125-140.  DOI: 10.1016/S0252-9602(13)60131-9 Abstract ( 209 )   RICH HTML PDF (207KB) ( 932 )   Save In this article, by using the stability of Cauchy type integral when the smooth perturbation for integral curve and the Sobolev type perturbation for kernel density hap-pen, we discuss the stability of the second fundamental problem in plane elasticity when the smooth perturbation for the boundary of the elastic domain (unit disk) and the Sobolev type perturbation for the displacement happen. And the error estimate of the displacement between the second fundamental problem and its perturbed problem is obtained. References | Related Articles | Metrics

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ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES CHEN Zhen-Long Acta mathematica scientia,Series B. 2014, 34 (1):  141-161.  DOI: 10.1016/S0252-9602(13)60132-0 Abstract ( 179 )   RICH HTML PDF (264KB) ( 938 )   Save Let X(1) = {X(1)(s), s ∈ R+} and X(2) = {X(2)(t), t ∈ R+} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X(1) and X(2) are studied. More gener-ally, let E1, E2 ⊆ (0, ∞) and F ⊂ Rd be Borel sets. A necessary condition and a sufficient condition for P{X(1)(E1) ∩X(2)(E2) ∩F 6≠Φ} > 0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1×E2×F in the metric space (R+×R+×Rd, ρ), where ρ is an unsymmetric metric defined in R+ ×R+ ×Rd. Under reasonable conditions, results resembling those of Browian motion are obtained. References | Related Articles | Metrics

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NOTES ON THE RESCALED SASAKI TYPE METRIC ON THE COTANGENT BUNDLE Aydin GEZER, Murat ALTUNBAS Acta mathematica scientia,Series B. 2014, 34 (1):  162-174.  DOI: 10.1016/S0252-9602(13)60133-2 Abstract ( 178 )   RICH HTML PDF (197KB) ( 1451 )   Save Let (M, g) be an n-dimensional Riemannian manifold and T*M be its cotan-gent bundle equipped with the rescaled Sasaki type metric. In this paper, we firstly study the paraholomorphy property of the rescaled Sasaki type metric by using some compati-ble paracomplex structures on T*M. Second, we construct locally decomposable Golden Riemannian structures on T*M. Finally we investigate curvature properties of T*M. References | Related Articles | Metrics

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ON GENERALIZED ORDERS AND GENERALIZED TYPES OF DIRICHLET SERIES IN THE RIGHT HALF-PLANE HUO Ying-Ying, KONG Yin-Ying Acta mathematica scientia,Series B. 2014, 34 (1):  175-182.  DOI: 10.1016/S0252-9602(13)60134-4 Abstract ( 311 )   RICH HTML PDF (152KB) ( 1345 )   Save In the paper, generalized orders and generalized types of Dirichlet series in the right half-plane are given. Some interesting relationships on maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet series of in the right half-plane are obtained. References | Related Articles | Metrics

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HOMOGENIZATION OF THE INCOMPRESSIBLE NAVIER-STOKES FLUID WITH OSCILLATION COEFFICIENT ZHAO Hong-Xing Acta mathematica scientia,Series B. 2014, 34 (1):  183-193.  DOI: 10.1016/S0252-9602(13)60135-6 Abstract ( 200 )   RICH HTML PDF (171KB) ( 1088 )   Save We study the homogenization of the incompressible Navier-Stokes equations with periodic oscillating coefficient in a bounded non-homogeneous media. To do that, we introduce a generalized compensate compactness result and a suitable class of test function to this problem. By passing the limit, we obtain the homogenized model of this problem. References | Related Articles | Metrics

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A NOTE ON n-PERINORMAL OPERATORS ZUO Hong-Liang, ZUO Fei Acta mathematica scientia,Series B. 2014, 34 (1):  194-198.  DOI: 10.1016/S0252-9602(13)60136-8 Abstract ( 205 )   RICH HTML PDF (133KB) ( 1397 )   Save The study of operators satisfying σja(T) = σa(T) is of significant interest. Does σja(T) = σa(T) for n-perinormal operator T ∈B(H)? This question was raised by Mecheri and Braha [Oper. Matrices 6 (2012), 725–734]. In the note we construct a counterexample to this question and obtain the following result: if T is a n-perinormal operator in B(H), then σja(T)\{0} = σa(T)\{0}. We also consider tensor product of n-perinormal operators. References | Related Articles | Metrics

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LOCAL WELL-POSEDNESS IN SOBOLEV SPACES WITH NEGATIVE INDICES FOR A SEVENTH ORDER DISPERSIVE EQUATION WANG Hong-Wei Acta mathematica scientia,Series B. 2014, 34 (1):  199-208.  DOI: 10.1016/S0252-9602(13)60137-X Abstract ( 157 )   RICH HTML PDF (176KB) ( 1285 )   Save This paper is concerned with the Cauchy problem of a seventh order dispersive equation. We prove local well-posedness with initial data in Sobolev spaces Hs(R) for negative indices of s > −11/4 . References | Related Articles | Metrics

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THE MAXIMAL NUMBER OF Iπ-CHARACTERS OVER NORMAL SUBGROUPS ZHOU Fang, MI Fang, LIU He-Guo Acta mathematica scientia,Series B. 2014, 34 (1):  209-214.  DOI: 10.1016/S0252-9602(13)60138-1 Abstract ( 200 )   RICH HTML PDF (142KB) ( 866 )   Save Let G be a π-separable group for a set of primes, let N be a normal subgroup of G, and let θ be an Iπ-character (i.e., irreducible π-partial character) of N. We obtain a necessary and sufficient condition for the number of Iπcharacters of G over θ to take the possible maximum |G : N|π. Some applications are given. References | Related Articles | Metrics

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THE PROLONGATION STRUCTURES AND NONLOCAL SYMMETRIES FOR MODIFIED BOUSSINESQ SYSTEM CHENG Qiu-Sheng, HE Jin-Song Acta mathematica scientia,Series B. 2014, 34 (1):  215-227.  DOI: 10.1016/S0252-9602(13)60139-3 Abstract ( 192 )   RICH HTML PDF (181KB) ( 1246 )   Save The Wahlquist-Estabrook (WE) prolongation structures of modified Boussi-nesq (MB) system are studied from the coverings point of view. The realizations and classifications of one-dimensional coverings of this system are obtained completely. More-over the sufficient and necessary conditions for a vector field to be a nonlocal symmetry of this system are also demonstrated in the WE prolongation structures. References | Related Articles | Metrics

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ON THE COEFFICIENTS OF SEVERAL CLASSES OF BI-UNIVALENT FUNCTIONS PENG Zhi-Gang, HAN Qiu-Qiu Acta mathematica scientia,Series B. 2014, 34 (1):  228-240.  DOI: 10.1016/S0252-9602(13)60140-X Abstract ( 219 )   RICH HTML PDF (162KB) ( 1837 )   Save In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve or generalize the recent works of other authors. References | Related Articles | Metrics