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20 January 2015, Volume 35 Issue 1 Previous Issue    Next Issue

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ON LOCAL STRUCTURAL STABILITY OF ONE-DIMENSIONAL SHOCKS IN RADIATION HYDRODYNAMICS TANG PingFan, FANG BeiXiang, WANG YAGuang Acta mathematica scientia,Series B. 2015, 35 (1):  1-44.  DOI: 10.1016/S0252-9602(14)60137-5 Abstract ( 157 )   RICH HTML PDF (394KB) ( 956 )   Save In this paper, we are concerned with the local structural stability of one-dimensional shock waves in radiation hydrodynamics described by the isentropic Euler-Boltzmann equa-tions. Even though in this radiation hydrodynamics model, the radiative effects can be understood as source terms to the isentropic Euler equations of hydrodynamics, in general the radiation field has singularities propagated in an angular domain issuing from the initial point across which the density is discontinuous. This is the major difficulty in the stability analysis of shocks. Under certain assumptions on the radiation parameters, we show there ex-ists a local weak solution to the initial value problem of the one dimensional Euler-Boltzmann equations, in which the radiation intensity is continuous, while the density and velocity are piecewise Lipschitz continuous with a strong discontinuity representing the shock-front. The existence of such a solution indicates that shock waves are structurally stable, at least local in time, in radiation hydrodynamics. References | Related Articles | Metrics

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EXISTENCE AND STABILITY OF STANDING WAVES FOR A COUPLED NONLINEAR SCHR¨|ODINGER SYSTEM ZENG XiaoYu,ZHANG Yi Ming, ZHOU Huang Song Acta mathematica scientia,Series B. 2015, 35 (1):  45-70.  DOI: 10.1016/S0252-9602(14)60138-7 Abstract ( 141 )   RICH HTML PDF (294KB) ( 484 )   Save We study the existence and stability of the standing waves of two coupled Schr¨odinger equations with potentials |x|bi (bi 2 R, i = 1, 2). Under suitable conditions on the growth of the nonlinear terms, we first establish the existence of standing waves of the Schr¨odinger system by solving a L2-normalized minimization problem, then prove that the set of all minimizers of this minimization problem is stable. Finally, we obtain the least energy solutions by the Nehari method and prove that the orbit sets of these least energy solutions are unstable, which generalizes the results of [11] where b1 = b2 = 2. References | Related Articles | Metrics

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ON THE VALIRON’S THEOREM IN THE POLYDISK WANG Gang,DENG FangWen Acta mathematica scientia,Series B. 2015, 35 (1):  71-78.  DOI: 10.1016/S0252-9602(14)60139-9 Abstract ( 114 )   RICH HTML PDF (163KB) ( 928 )   Save In this paper, we discuss the Valiron’s theorem in the unit polydisk DN. We prove that for a holomorphic map ' : DN → DN satisfying some regular conditions, there exists a holomorphic map  : DN → H and a constant > 0 such that  ? ' = 1  . It is based on the extension of Julia-Wolff-Carath´eodory (JWC) theorem of D in the polydisk References | Related Articles | Metrics

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RATE OF CONVERGENCE AND EXPANSION OF RÉNYI ENTROPIC CENTRAL LIMIT THEOREM SUN Jian Qiang, DING Yi Ming Acta mathematica scientia,Series B. 2015, 35 (1):  79-88.  DOI: 10.1016/S0252-9602(14)60140-5 Abstract ( 143 )   RICH HTML PDF (179KB) ( 508 )   Save We obtain the expansion of R´enyi divergence of order α (0 <α < 1) between the normalized sum of IID continuous random variables and the Gaussian limit under minimal moment conditions via Edgeworth-type expansion. The rate is faster than that of Shannon case, which can be used to improve the rate of convergence in total variance norm. References | Related Articles | Metrics

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A NOTE ON SCHWARZ LEMMA FOR THE MODULUS OF HOLOMORPHIC MAPPINGS ON D LIU Yang, DAI ShaoYu Acta mathematica scientia,Series B. 2015, 35 (1):  89-94.  DOI: 10.1016/S0252-9602(14)60141-7 Abstract ( 142 )   RICH HTML PDF (144KB) ( 1116 )   Save In this note, we consider a holomorphic mapping f from the unit disk D in C to p-ball Bp = z ∈ Cn : n Pi=1 |zi|p < 1 , 1 < p < +∞. It is proved that for such f, |∇||f||(z)| ≤ 1 − ||f(z)||2 1 − |z|2 , z ∈ D. The extremal problem is also discussed when p is an even number. This result extends some related results on Schwarz lemma. References | Related Articles | Metrics

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EVOLUTIONARY DYNAMICS ON ONE-DIMENSIONAL CYCLE WITH SHIFTING MECHANISM AND TINY MUTATION RATE WANG XianJia,LAN Jun,DONG QianJin, LEI GuoLiang Acta mathematica scientia,Series B. 2015, 35 (1):  95-104.  DOI: 10.1016/S0252-9602(14)60142-9 Abstract ( 132 )   RICH HTML PDF (166KB) ( 1041 )   Save In this paper we study the impact of tiny mutation on the evolutionary dynamics on one-dimensional cycle with shifting mechanism. The evolutionary success is evaluated by investigating the stationary distribution of the ergodic process with the idea of viscosity solutions. The cooperative behaviors in ecosystem and social system are briefly discussed by applying the results to the prisoner’s dilemma game. References | Related Articles | Metrics

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GROWTH OF MEROMORPHIC SOLUTIONS OF SOME ALGEBRAIC DIFFERENTIAL EQUATIONS LI Ye Zhou, QI Jian Ming, YUAN Wen Jun Acta mathematica scientia,Series B. 2015, 35 (1):  105-111.  DOI: 10.1016/S0252-9602(14)60143-0 Abstract ( 117 )   RICH HTML PDF (157KB) ( 975 )   Save In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give some examples to show that our results occur in some special cases. References | Related Articles | Metrics

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A NOTE ON GLOBAL WELL-POSEDNESS OF SOLUTIONS TO BOUSSINESQ EQUATIONS WITH FRACTIONAL DISSIPATION YE Zhuan Acta mathematica scientia,Series B. 2015, 35 (1):  112-120.  DOI: 10.1016/S0252-9602(14)60144-2 Abstract ( 136 )   RICH HTML PDF (172KB) ( 576 )   Save The goal of this paper is to consider the global well-posedness to n-dimensional (n  3) Boussinesq equations with fractional dissipation. More precisely, it is proved that there exists a unique global regular solution to the Boussinesq equations provided the real parameter satisfies  1 2 + n 4 . References | Related Articles | Metrics

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THE NORMALITY OF ALGEBROID MULTIFUNCTIONS AND THEIR COEFFICIENT FUNCTIONS CAI FuJie GAO Zong Sheng Acta mathematica scientia,Series B. 2015, 35 (1):  121-132.  DOI: 10.1016/S0252-9602(14)60145-4 Abstract ( 203 )   RICH HTML PDF (188KB) ( 748 )   Save In this paper, we investigate the normality relationship between algebroid mul-tifunctions and their coefficient functions. We prove that the normality of a k-valued entire algebroid multifunctions family is equivalent to their coefficient functions in some conditions. Furthermore, we obtain some new normality criteria for algebroid multifunctions families based on these results. We also provide some examples to expound that some restricted conditions of our main results are necessary. References | Related Articles | Metrics

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ON THE GENERALIZED ORDER OF DIRICHLET SERIES HUO YingYing, KONG YinYing Acta mathematica scientia,Series B. 2015, 35 (1):  133-139.  DOI: 10.1016/S0252-9602(14)60146-6 Abstract ( 146 )   RICH HTML PDF (188KB) ( 772 )   Save By the method of Knopp-Kojima, the generalized order of Dirichlet series is studied and some interesting relations on the maximum modulus, the maximum term and the coefficients of entire function defined by Dirichlet series of slow growth are obtained, which briefly extends some results of paper [1]. References | Related Articles | Metrics

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GLOBAL CLASSICAL SOLUTIONS FOR QUANTUM KINETIC FOKKER-PLANCK EQUATIONS LUO Lan, ZHANG XinPing Acta mathematica scientia,Series B. 2015, 35 (1):  140-156.  DOI: 10.1016/S0252-9602(14)60147-8 Abstract ( 141 )   RICH HTML PDF (212KB) ( 1039 )   Save We consider a class of nonlinear kinetic Fokker-Planck equations modeling quantum particles which obey the Bose-Einstein and Fermi-Dirac statistics, respectively. We establish the existence and convergence rate to the steady state of global classical solution to such kind of equations around the steady state. References | Related Articles | Metrics

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ON THE EXISTENCE OF LOCAL CLASSICAL SOLUTION FOR A CLASS OF ONE-DIMENSIONAL COMPRESSIBLE NON-NEWTONIAN FLUIDS FANG Li,LI ZiLai Acta mathematica scientia,Series B. 2015, 35 (1):  157-181.  DOI: 10.1016/S0252-9602(14)60148-X Abstract ( 128 )   RICH HTML PDF (263KB) ( 989 )   Save In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero. References | Related Articles | Metrics

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TOEPLITZ OPERATORS ASSOCIATED WITH SEMIFINITE VON NEUMANN ALGEBRA YAN Cheng,BEKJAN Turdebek N Acta mathematica scientia,Series B. 2015, 35 (1):  182-188.  DOI: 10.1016/S0252-9602(14)60149-1 Abstract ( 169 )   RICH HTML PDF (167KB) ( 415 )   Save Let H2(M) be a noncommutative Hardy space associated with semifinite von Neumann algebra M , we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H2(M), and the norm of Toeplitz operator Tt is equivalent to ktk when t is hyponormal operator in M. References | Related Articles | Metrics

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A REMARK ON LIMINF SETS IN DIOPHANTINE APPROXIMATION LIU Jia,SUN Yu Acta mathematica scientia,Series B. 2015, 35 (1):  189-194.  DOI: 10.1016/S0252-9602(14)60150-8 Abstract ( 96 )   RICH HTML PDF (142KB) ( 912 )   Save Let Q be an infinite set of positive integers,  > 1 be a real number and let  (Q) = x 2 R : x − q q− for infinitely many (p, q) 2 Z × Q. For any given positive integer m, set Q(m) = {n 2 N : (n,m) = 1}. If m is divisible by at least two prime factors, Adiceam [1] showed that W (N) \ W (Q(m)) contains uncountably many Liouville numbers, and asked if it contains any non-Liouville numbers? In this note, we give an affirmative answer to Adiceam’s question. References | Related Articles | Metrics

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MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPLEX DIFFERENTIAL-DIFFERENCE EQUATIONS LI Hai Chou,GAO Ling Yun Acta mathematica scientia,Series B. 2015, 35 (1):  195-206.  DOI: 10.1016/S0252-9602(14)60151-X Abstract ( 148 )   RICH HTML PDF (185KB) ( 1041 )   Save Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form nPj=1 j (z)f (j1)1 (z + cj ) = R2(z, f2(z)), n Pj=1 j (z)f (j2) 2 (z + cj ) = R1(z, f1(z)). () where ij (j = 1, 2, · · · , n; i = 1, 2) are finite non-negative integers, and cj (j = 1, 2, · · · , n) are distinct, nonzero complex numbers, j(z), j(z) (j = 1, 2, · · · , n) are small functions relative to fi(z) (i = 1, 2) respectively, Ri(z, f(z)) (i = 1, 2) are rational in fi(z) (i = 1, 2) with coefficients which are small functions of fi(z) (i = 1, 2) respectively. References | Related Articles | Metrics

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MULTI-DIMENSIONAL MARKOV CHAIN–BASED ANALYSIS OF CONFLICT PROBABILITY FOR SPECTRUM RESOURCE SHARING ZHANG Yi,Yu Li, ZHANG Li Wei Acta mathematica scientia,Series B. 2015, 35 (1):  207-215.  DOI: 10.1016/S0252-9602(14)60152-1 Abstract ( 112 )   RICH HTML PDF (871KB) ( 946 )   Save In this paper, we consider the optimal problem of channels sharing with het- erogeneous traffic (real-time service and non-real-time service) to reduce the data conflict probability of users. Moreover, a multi-dimensional Markov chain model is developed to analyze the performance of the proposed scheme. Meanwhile, performance metrics are de- rived. Numerical results show that the proposed scheme can effectively reduce the forced termination probability, blocking probability and spectrum utilization References | Related Articles | Metrics

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TIME PERIODIC SOLUTIONS OF NON-ISENTROPIC COMPRESSIBLE MAGNETOHYDRODYNAMIC SYSTEM XU Qiu Ju,CAI Hong,TAN Zhong Acta mathematica scientia,Series B. 2015, 35 (1):  216-234.  DOI: 10.1016/S0252-9602(14)60153-3 Abstract ( 165 )   RICH HTML PDF (248KB) ( 877 )   Save In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in Rn. Under the condition that the optimal time decay rates are obtained by spectral analysis, we show that the existence, uniqueness and time-asymptotic stability of time periodic solutions when the space dimension n  5. Our proof is based on a combination of the energy method and the contraction mapping theorem. References | Related Articles | Metrics

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THE GAUSS–GREEN THEOREM IN CLIFFORD ANALYSIS AND ITS APPLICATIONS LUO Wei Yu,DU Jin Yuan Acta mathematica scientia,Series B. 2015, 35 (1):  235-254.  DOI: 10.1016/S0252-9602(14)60154-5 Abstract ( 124 )   RICH HTML PDF (258KB) ( 512 )   Save In this article, we establish the Gauss–Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very gen- eral by using the geometric measure theoretic method. The Cauchy–Pompeiu formula for Clifford-valued functions under the weak condition will be derived as their simple applica- tion. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy–Pompeiu formula. References | Related Articles | Metrics

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GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE MASS-CRITICAL HARTREE EQUATION IN HIGH DIMENSIONS XIA Hong Qiang Acta mathematica scientia,Series B. 2015, 35 (1):  255-274.  DOI: 10.1016/S0252-9602(14)60155-7 Abstract ( 120 )   RICH HTML PDF (240KB) ( 638 )   Save We obtain global well-posedness and scattering, and global L2(d+2)dt,x spacetimebounds for solutions to the defocusing mass-critical Hartree equation in Rt × Rdx, d  5. References | Related Articles | Metrics

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SOME FURTHER NOTES ON THE MATRIX EQUATIONS ATXB + BTXTA = C ANDATXB + BTXA = C G.SOARES Acta mathematica scientia,Series B. 2015, 35 (1):  275-280.  DOI: 10.1016/S0252-9602(14)60156-9 Abstract ( 156 )   RICH HTML PDF (138KB) ( 876 )   Save Dehghan and Hajarian, [4], investigated the matrix equations ATXB+BTXTA = C and ATXB + BTXA = C providing inequalities for the determinant of the solutions of these equations. In the same paper, the authors presented a lower bound for the product of the eigenvalues of the solutions to these matrix equations. Inspired by their work, we give some generalizations of Dehghan and Hajarian results. Using the theory of the numerical ranges, we present an inequality involving the trace of C when A,B,X are normal matrices satisfying ATB = BAT References | Related Articles | Metrics