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20 April 2005, Volume 25 Issue 2 Previous Issue    Next Issue

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SINGULAR INTEGRAL EQUATIONS ALONG AN OPEN ARC WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER ZHONG Shou-Guo Acta mathematica scientia,Series B. 2005, 25 (2):  193-200.  Abstract ( 617 )   RICH HTML   PDF (128KB) ( 1065 )   Save In this paper, the difficulties on calculation in solving singular integral equa- tions are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for charac- teristic equations as well as the generalized Noether theorem for complete equations are given. References | Related Articles | Metrics

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ON THE SPH-DISTRIBUTION CLASS SHI Ding-Hua, GUO Jin-Li, LIU Li-Meng Acta mathematica scientia,Series B. 2005, 25 (2):  201-214.  Abstract ( 674 )   RICH HTML   PDF (157KB) ( 1120 )   Save Following up Neuts’ idea, the SPH-distribution class associated with bounded Q matrices for infinite Markov chains is defined. The main result in this paper is to characterize the SPH class through the derivatives of the distribution functions. Based on the characterization theorem, closure properties, the expansion, uniform approximation, and the matrix representations of the SPH class are also discussed by the derivatives of the distribution functions at origin. References | Related Articles | Metrics

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PROOF OF A CONJECTURE RELATED TO THE PARABOLIC CLASS NUMBERS OF SOME FUCHSIAN GROUPS Nihal Yilmaz ¨Ozg¨ur;Refik Keskin Acta mathematica scientia,Series B. 2005, 25 (2):  215-222.  Abstract ( 552 )   RICH HTML   PDF (116KB) ( 1060 )   Save This paper proves a conjecture given in [6], which is concerning with the parabolic class numbers of some Fuchsian groups. References | Related Articles | Metrics

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SLANT IMMERSIONS OF COMPLEX SPACE FORMS AND CHEN’S INEQUALITY LI Guang-Han, TUN Chuan-Chi Acta mathematica scientia,Series B. 2005, 25 (2):  223-232.  Abstract ( 639 )   RICH HTML   PDF (137KB) ( 1327 )   Save A submanifold in a complex space form is called slant if it has constant Wirtinger angles. B. Y. Chen and Y. Tazawa proved that there do not exist minimal proper slant surfaces in CP2 and CH2. So it seems that the slant immersion has some interesting properties. The authors have great interest to consider slant immersions sat- isfying some additional conditions, such as unfull first normal bundles or Chen’s equality holding. They prove that there do not exist n-dimensional Kaehlerian slant immersions in CPn and CHn with unfull first normal bundles. Next, it is seen that every Kaehlerian slant submanifold satisfying an equality of Chen is minimal which is similar to that of Lagrangian immersions. But in contrast, it is shown that a large class of slant immersions do not exist thoroughly. Finally, they give an application of Chen’s inequality to general slant immersions in a complex projective space, which generalizes a result of Chen. References | Related Articles | Metrics

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CONSTRUCTION OF COMPACTLY SUPPORTED BIVARIATE ORTHOGONAL WAVELETS BY UNIVARIATE ORTHOGONAL WAVELETS YANG Jian-Wei, LI La-Qing, TANG Yuan-Tan Acta mathematica scientia,Series B. 2005, 25 (2):  233-242.  Abstract ( 623 )   RICH HTML   PDF (130KB) ( 1073 )   Save After some permutation of conjugate quadrature filter, new conjugate quadra- ture filters can be derived. In terms of this permutation, an approach is developed for constructing compactly supported bivariate orthogonal wavelets from univariate orthog- onal wavelets. Non-separable orthogonal wavelets can be achieved. To demonstrate this method, an example is given. References | Related Articles | Metrics

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OPTIONS-GAME ANALYSIS FOR FIRM WITH INSURED DEBT MEI Zheng-Yang, LI Chu-Lin Acta mathematica scientia,Series B. 2005, 25 (2):  243-247.  Abstract ( 527 )   RICH HTML   PDF (97KB) ( 849 )   Save The strategic model for insured bond of firm is a new model which is developed based on options pricing model and game theory. When firm’s bond was insured against bankruptcy, some interesting results about endogenous bankruptcy and optimal capital structure are obtained. References | Related Articles | Metrics

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EMPIRICAL BAYES TEST PROBLEMS OF VARIANCE COMPONENTS IN RANDOM EFFECTS MODEL HUI Lai-Sheng, ZHANG Wei-Beng Acta mathematica scientia,Series B. 2005, 25 (2):  247-282.  Abstract ( 541 )   RICH HTML   PDF (143KB) ( 836 )   Save Bayes decision rule of variance components for one-way random effects model is derived and empirical Bayes (EB) decision rules are constructed by kernel estimation method. Under suitable conditions, it is shown that the proposed EB decision rules are asymptotically optimal with convergence rates near O(n−1/2). Finally, an example con- cerning the main result is given References | Related Articles | Metrics

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MAXIMAL ATTRACTORS OF CLASSICAL SOLUTIONS FOR REACTION DIFFUSION EQUATIONS WITH DISPERSION LI Yan-Ling, MA Yi-Chen Acta mathematica scientia,Series B. 2005, 25 (2):  248-258.  Abstract ( 559 )   RICH HTML   PDF (148KB) ( 871 )   Save The paper first deals with the existence of the maximal attractor of classical solution for reaction diffusion equation with dispersion, and gives the sup-norm estimate for the attractor. This estimate is optimal for the attractor under Neumann boundary condition. Next, the same problem is discussed for reaction diffusion system with uniformly contracting rectangle, and it reveals that the maximal attractor of classical solution for such system in the whole space is only necessary to be established in some invariant region. Finally, a few examples of application are given. References | Related Articles | Metrics

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LOCAL CLASSICAL SOLUTION OF FREE BOUNDARY PROBLEM FOR A COUPLED SYSTEM WANG Xiao-Hua, YI Fa-Huai, YANG Zhou Acta mathematica scientia,Series B. 2005, 25 (2):  259-273.  Abstract ( 600 )   RICH HTML   PDF (156KB) ( 808 )   Save This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-maintaining protocell in multidimensional case. The local classical solution of the problem with free boundary References | Related Articles | Metrics

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LOCATION OF THE BLOW UP POINT FOR POSITIVE SOLUTIONS OF A BIHARMONIC EQUATION INVOLVING NEARLY CRITICAL EXPONENT GENG Di Acta mathematica scientia,Series B. 2005, 25 (2):  283-295.  Abstract ( 641 )   RICH HTML   PDF (175KB) ( 1256 )   Save In this paper a semilinear biharmonic problem involving nearly critical growth with Navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point in the domain, which is also a critical point of the Robin’s function corresponding to the Green’s function of biharmonic operator with the same boundary condition. Similar conclusion has been obtained in [6] under the condition that the domain is strictly convex References | Related Articles | Metrics

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LIOUVILLE’S THEOREM FOR LPDO WITH CONSTANT COEFFICIENTS HAN E-Zhou, LUO Hua-Bao Acta mathematica scientia,Series B. 2005, 25 (2):  296-300.  Abstract ( 549 )   RICH HTML   PDF (106KB) ( 948 )   Save In this note, the authors consider a class of linear partial differential operators P(@) with constant coefficients and prove that the operator P(@) has Liouville property if and only if the polynomial P(i) doesn’t have roots in Rn\{0}. References | Related Articles | Metrics

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PROPERTIES OF FRACTIONAL k-FACTORS OF GRAPHS LIU Gui-Zhen, ZHANG Lan-Ju Acta mathematica scientia,Series B. 2005, 25 (2):  301-304.  Abstract ( 557 )   RICH HTML   PDF (93KB) ( 1165 )   Save In this paper the properties of some maximum fractional [0, k]-factors of graphs are presented. And consequently some results on fractional matchings and fractional 1-factors are generalized and a characterization of fractional k-factors is obtained.   References | Related Articles | Metrics

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LOCAL INEQUALITIES FOR SIDON SUMS AND THEIR APPLICATIONS FAN Ai-Hua, ZHANG Yi-Beng Acta mathematica scientia,Series B. 2005, 25 (2):  305-316.  Abstract ( 605 )   RICH HTML   PDF (154KB) ( 1100 )   Save The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere con- vergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor se- ries. Some of their results still hold for Sidon sets of second kind. References | Related Articles | Metrics

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THE EXPONENTIAL ATTRACTOR FOR THE EQUATIONS OF THERMOHYDRAULICS Guo Bolin;Du Xianyun Acta mathematica scientia,Series B. 2005, 25 (2):  317-325.  Abstract ( 557 )   RICH HTML   PDF (123KB) ( 900 )   Save In this paper, the existence of the exponential attractor for the thermohy- draulics equations is proved, and the estimates of its fractal dimensions are also given.  35B30, 35B45, 35K55 References | Related Articles | Metrics

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THE LAW OF ITERATED LOGARITHM FOR R/S STATISTICS LIN Zheng-Yan Acta mathematica scientia,Series B. 2005, 25 (2):  326-330.  Abstract ( 606 )   RICH HTML   PDF (96KB) ( 1350 )   Save A law of iterated logarithm for R/S statistics with the help of the strong approximations of R/S statistics by functions of a Wiener process is shown. References | Related Articles | Metrics

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GENERALIZED CIRCLES AND THEIR CONFORMAL MAPPING IN A SUBSPACE OF A WEYL SPACE G¨uler G¨urp?nar Arsan G¨ul?cin C? ivi Y?ld?r?m Acta mathematica scientia,Series B. 2005, 25 (2):  331-339.  Abstract ( 569 )   RICH HTML   PDF (115KB) ( 1143 )   Save The authors give the necessary and sufficient conditions for a generalized circle in a Weyl hypersurface to be generalized circle in the enveloping Weyl space. They then obtain the neccessary and sufficient conditions under which a generalized concircular transformation of one Weyl space onto another induces a generalized transformation on its subspaces. Finally, it is shown that any totally geodesic or totally umbilical hypersurface of a generalized concircularly flat Weyl space is also generalized concircularly flat. Weyl space, generalized circle, generalized concircular transformation, to- References | Related Articles | Metrics

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GLOBAL EXISTENCE OF SOLUTIONS FOR QUADRATIC QUASI-LINEAR KLEIN-GORDON SYSTEMS IN ONE SPACE DIMENSION XUE Ru-Yang, FANG Dao-Yuan Acta mathematica scientia,Series B. 2005, 25 (2):  340-358.  Abstract ( 697 )   RICH HTML   PDF (218KB) ( 848 )   Save Consider quadratic quasi-linear Klein-Gordon systems with eventually differ- ent masses for small, smooth, compactly supported Cauchy data in one space dimension. It is proved that the global existence holds when a convenient null condition is satisfied by nonlinearities. References | Related Articles | Metrics

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GLOBAL WEAK SHARP MINIMA AND COMPLETENESS OF METRIC SPACE HUANG Hui Acta mathematica scientia,Series B. 2005, 25 (2):  359-366.  Abstract ( 575 )   RICH HTML   PDF (115KB) ( 968 )   Save A sufficient condition on the existence of a global weak sharp minima for general function in metric space is established. A characterization for convex function to have global weak sharp minima is also presented, which generalized Burke and Ferris’ result[1] to infinite dimensional space. A characterization of the completeness of a metric space is given by the existence of global weak sharp minima. References | Related Articles | Metrics

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ON NEVANLINNA DIRECTIONS OF ALGEBROID FUNCTIONS LEI Qian, GU Yong-Xin Acta mathematica scientia,Series B. 2005, 25 (2):  367-375.  Abstract ( 559 )   RICH HTML   PDF (131KB) ( 1210 )   Save In this paper, a notation (!) is derived from the counting function N(r,!) of branch points of algebriod functions. With this notation, the authors give the definition of the Nevanlinna direction for algebriod functions and discuss its existence in certain condition. By this notation the authors also obtain the numbers of exceptional value of the Julia direction and Borel direction of algebriod functions are not more than 2+[(!)], here [x] implies an maximum integer number which does not exceed x. References | Related Articles | Metrics

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RANDOM SINGULAR INTEGRAL OF RANDOM PROCESS WITH SECOND ORDER MOMENT WANG Chuan-Rong Acta mathematica scientia,Series B. 2005, 25 (2):  376-384.  Abstract ( 534 )   RICH HTML   PDF (119KB) ( 1003 )   Save This paper discussses the random singular integral of random process with second order moment, establishes the concepts of the random singular integral and proves that it’s a linear bounded operator of space H (L)(m, s). Then Plemelj formula and some other properties for random singular integral are proved. References | Related Articles | Metrics