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| 1 | Modifid Interpolatory Projection Method for Weakly Singular Integral Equation Eigenvalue Problems显示文摘This paper deals with eigenvalue problems for linear Fredholm integral equations of the second kind with weakly singular kernels. A new discrete method is proposed for the approximation of eigenvalues.Compactness of the integral operator in L^1[0, 1] space is obtained. This method is based on the approximation of the integral operator by modified interpolatory projection. Different from traditional methods, norm convergence of operator approximation is proved theoretically. Further, convergence of eigenvalue approximation is obtained by analytical tools. Numerical examples are presented to illustrate the theoretical results and the efficiency of the method. | Xin ZHANG Yun-hui HE | 2019 | Acta Mathematicae Applicatae Sinica2019，35，2： | 18 |
| 2 | SPECTRAL METHOD FOR SOLVING TWODIMENSIONAL NEWTON-BOUSSINESQ EQUATIONS显示文摘In this paper, the spectral method for solving two-dimensional Newton-Boussinesq equations hasbeen proposed. The existence and uniqueness of global generalized solution for this equations, and theerror estimates and convergence of approximate solutions also have been obtained. | 郭柏灵 | 1989 | Acta Mathematicae Applicatae Sinica1989，5，3： | 13 |
| 3 | Some open questions in the theory of generalized permutable subgroups显示文摘A subgroup H of a group G is said to be weakly s-supplemented in G if H has a supplement T in G such that H ∩ T HsG, where HsG is the largest s-permutable subgroup of G contained in H. This paper constructs an example to show that the open questions 6.3 and 6.4 in J Algebra, 315: 192–209 (2007) have negative solutions, and shows that in many cases Question 6.4 is positive. A series of known results are unified and generalized. | GUO WenBin XIE FengYan LI BaoJun | 2009 | Science China Mathematics2009，52，10： | 11 |
| 4 | WEAKLY ALMOST PERIODIC POINT AND ERGODIC MEASURE显示文摘Let X be a compact metric space and f: X→X be continuous.This pape introduces the notion of weakly almost periodic point, which is a generalization of the notion of almost periodic point, proves that each of f-invariant ergodic measures can be generated by a weakly almost periodic point of f and gives some equivalent conditions for that f has an invariant ergodic measure whose support is X and ones for that f has no non-atomic invariant ergodic measure, the latter is a generalization of the Blokh’s work on self-maps of the interval. Also two formulae for calculating the togological entropy are obtained. | 周作领 | 1992 | Chinese Annals of Mathematics,Series B1992，13，2： | 11 |
| 5 | Weakly Almost Periodic Point and Measure Centre显示文摘In studying a dynamical system, one finds that there frequently exist some kinds of disturbance or false phenomenon. In order to remove them, we introduce a concept of the measure centre and in order to determine the structure of the measure centre, we also introduce another concept of the weakly almost periodic point. We totally determine the structure of the measure centre and exhibit an example to show that the measure centre may be contained properly in the motion centre and there is a system which is chaotic on the nonwandering set but has zero topological entropy. | 周作领 | 1993 | Science China Mathematics1993，36，2： | 10 |
| 6 | Multiplier ideal sheaves in complex and algebraic geometry显示文摘The application of the method of multiplier ideal sheaves to effective problems in algebraic geometry is briefly discussed. Then its application to the deformational invariance of plurigenera for general compact algebraic manifolds is presented and discussed.Finally its application to the conjecture of the finite generation of the canonical ring is explored, and the use of complex algebraic geometry in complex Neumann estimates is discussed. | Yum-Tong Siu | 2005 | Science China Mathematics2005，48，z1： | 7 |
| 7 | 3-D NUMERICAL SIMULATION OF FLOW THROUGH AN ORIFICE SPILLWAY TUNNEL显示文摘A Large Eddy Simulation (LES) approach based on the weakly compressible hydrodynamic equation with a single plase fluid model for the cavitation flow has been developed and employed in simulating 3 D unsteady viscous flow through an orifice type spillwy tunnel. The finite volume approach in space and the predictor corrector method in time have been used to the numerical discretization, and the 'Law of wall' is applied at the solid boundary. The velocity, pressure fields and the cavitation phenomenon are obtained, the computational results show that 3 D LES approach can give more realistic flow field prediction of the orifice type spillway tunnel. | Zhang Chang bing, Yang Yong quan Hydraulics and Hydroelectric Engineering College, Sichuan University, Chengdu 610065, China | 2002 | Journal of Hydrodynamics2002，14，3： | 6 |
| 8 | A Modified Form of Mild-Slope Equation with Weakly Nonlinear Effect显示文摘Nonlinear effect is of importance to waves propagating from deep water to shallow water.Thenon-linearity of waves is widely discussed due to its high precision in application.But there are still someproblems in dealing with the nonlinear waves in practice.In this paper,a modified form of mild-slope equa-tion with weakly nonlinear effect is derived by use of the nonlinear dispersion relation and the steady mild-slope equation containing energy dissipation.The modified form of mild-slope equation is convenient to solvenonlinear effect of waves.The model is tested against the laboratory measurement for the case of a submergedelliptical shoal on a slope beach given by Berkhoff et al,The present numerical results are also comparedwith those obtained through linear wave theory.Better agreement is obtained as the modified mild-slope e-quation is employed.And the modified mild-slope equation can reasonably simulate the weakly nonlinear ef-fect of wave propagation from deep water to coast. | 李瑞杰 王厚杰 | 1999 | China Ocean Engineering1999，14，3： | 5 |
| 9 | Hydrodynamic Coefficients for a 3-D Uniform Flexible Barge UsingWeakly Compressible Smoothed Particle Hydrodynamics显示文摘The numerical modelling of the interactions between water waves and floating structures is significant for different areas of the marine sector, especially seakeeping and prediction of wave-induced loads. Seakeeping analysis involving severe flow fluctuations is still quite challenging even for the conventional RANS method. Particle method has been viewed as alternative for such analysis especially those involving deformable boundary, wave breaking and fluid fragmentation around hull shapes. In this paper, the weakly compressible smoothed particle hydrodynamics(WCSPH), a fully Lagrangian particle method, is applied to simulate the symmetric radiation problem for a stationary barge treated as a flexible body. This is carried out by imposing prescribed forced simple harmonic oscillations in heave, pitch and the two-and three-node distortion modes. The resultant,radiation force predictions, namely added mass and fluid damping coefficients, are compared with results from 3-D potential flow boundary element method and 3-D RANS CFD predictions, in order to verify the adopted modelling techniques for WCSPH.WCSPH were found to be in agreement with most results and could predict the fluid actions equally well in most cases. | Muhammad Zahir Ramli P.Temarel M.Tan | 2018 | Journal of Marine Science and Application2018，17，3： | 4 |
| 10 | Further improvement of weakly nonlinear theory of hydrodynamic stability显示文摘The problems of the weakly nonlinear theory of hydrodynamic stability has been re addressed; namely, (i) why is the radius of convergence of its solution too small? (ii) it is not appropriate to use it to deal with the evolution problem of disturbances; the main reason is that the way of calculating the mean flow distortion is inappropriate, (iii) it cannot be used to deal with the initial value problem. Ways of its improvement were proposed. Its correctness was confirmed by its comparison with the results of numerical simulations. | 周恒 | 1998 | Science China Mathematics1998，41，1： | 4 |
| 11 | ON PROBLEMS IN THE WEAKLY NONLINEAR THEORY OF HYDRODYNAMIC STABILITY AND ITS IMPROVEMENT显示文摘There are three main problems in the weakly nonlinear theory of hydrodynamic stability:(1)The ra-dius of convergence with respect to the perturbation parameter is too small and there is no concrete estimationfor it.(2)The solution has a special structure, thus in general, it can not satisfy the initial condition posed bymany practical problems.(3) When the linear part of its solution does not correspond to a neutral case. thereare more than one way in determining the Landau constants, and practically no one knows which is the bestway. In this paper, problems(1)and(2)are solved theoretically, and ways for its improvement have been proposed.By comparing the theoretical results with those obtained by numerical simulations, problem(3)has also been clari-fied. | 周恒 尤学一 | 1993 | Acta Mechanica Sinica1993，9，1： | 4 |
| 12 | Antidiabetic principles of Loranthus micranthus Linn.parasitic on Persea americana显示文摘Objective:To explore antidiabetic principles of the Eastern Nigeria mistletoe,Loranlhus micranthus Linn,parasitic on Persea Americana.Methods:The weakly acidic fraction of the aqueous methanol extract of the leaves of Loranlhus micranthus(Linn.) was isolated and tested for its antidiabetic activities.The isolation of the weakly acidic fraction was carried out following established physico-chemical based procedures.Furthermore,alloxan-induced diabetic rats were treated intraperitoneally(ip) with 250 mg/kg and 400 mg/kg of the weakly acidic fraction, glibenclamide 10 mg/kg(positive control) and 2 mg/kg of 3%v/v tween 20(negative control).The sugar levels of the treated and untreated animals were determined by withdrawing the blood at regular intervals and testing them with an automated glucometer.The phytochemical analysis of the acidic fraction was carried out using standard procedures.Chromatographic techniques were employed in the subsequent isolation and purification of the constituents of the weakly acidic fraction.Results:It was shown that the maximum effect of the weakly acidic fraction was obtained at 24 hours after administration and was found to be statistically comparable with that of the positive control.The phytochemical analysis revealed the presence of steroids,terpenoids, alkaloids,flavonoids,glycosides,carbohydrates,saponins,and acidic compounds in the crude extract and carbohydrates,flavonoids.terpenoids and oil in the weakly acidic fraction.Further purification of the weakly acidic fraction of the methanol extract using thin layer chromatography shows that toluene:methanol:diethyl amine(3:1:1) and chloroform:methanol:diethyl amine (9:1:1) are the best solvent system for the isolation of the various components of the weakly acidic fraction of the crude methanol extract of Loranlhus micranthus.Conclusions:The present study has led to the conclusion that the weakly acidic fraction of the plant under study has the potent antidiabetic activity and that the various components can be isolated using basic chromatographic techniques. | Patience Ogoamaka Osadebe Edwin Ogechukwu Omeje Sylvester Chukwuemeka Nworu Charles Okechukwu Esimone Philip Felix Uzor Ernest kenechukwu David John Uchechukwu Uzoma | 2010 | Asian Pacific Journal of Tropical Medicine2010，3，8： | 4 |
| 13 | Weakly repelling fixed points and multiply-connected wandering domains of meromorphic functions显示文摘We consider the dynamics of a transcendental meromorphic function f(z) with only finitely many poles and prove that if f has only finitely many weakly repelling fixed points,then there is no multiply-connected wandering domain in its Fatou set. | QIU Ling WU Shengjian | 2006 | Science China Mathematics2006，49，2： | 3 |
| 14 | ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SECOND ORDER NONLINEAR ELLIPTIC DIFFERENTIAL EQUATIONS显示文摘In this paper, the second order nonlinear elliptic differential equations are considered in an exterior Ω Rn , where q(x) is allowed to change sign. Some sufficient conditions for any solutions y(x) of (E) to be satisfied |y(x)| = 0 are obtained. Particularly, these results improve the previous results for second order ordinary differential equations. | 徐志庭 | 2001 | Acta Mathematica Scientia2001，21，1： | 3 |
| 15 | Asymptotic properties for median cross-validated nearest neighbor median estimate in nonparametric regression显示文摘Consider the nonparametric regression model Yni = g(xni) + eni, 1≤i≤n, where g is an unknown function to be estimated on [0,1], xni (1≤i≤n) are the fixed design points in the interval [0,1] and {eni,1≤i≤n} is a triangular array of row iid random variables having median zero. The nearest neighbor median estimator gn. h (xni )=m (Yi(1)(n)…Yi(h)(n) is taken as the estimator of the unknown function g(x). Median cross validation (mcv) criterion is employed to select the smoothing parameter h . Let hn * be the smoothing parameter chosen by mcv criterion. Under mild regularity conditions, the upper and lower bounds of hn* , the rate of convergence and the weak consistency of the median cross-validated estimate gn,hn* (xni) are obtained. | 杨瑛 郑忠国 | 1997 | Science China Mathematics1997，40，6： | 3 |
| 16 | Investigation of cell mechanics using single-beam acoustic tweezers as a versatile tool for the diagnosis and treatment of highly invasive breast cancer cell lines: an in vitro study显示文摘Advancements in diagnostic systems for metastatic cancer over the last few decades have played a significant role in providing patients with effective treatment by evaluating the characteristics of cancer cells.Despite the progress made in cancer prognosis,we still rely on the visual analysis of tissues or cells from histopathologists,where the subjectivity of traditional manual interpretation persists.This paper presents the development of a dual diagnosis and treatment tool using an in vitro acoustic tweezers platform with a 50MHz ultrasonic transducer for label-free trapping and bursting of human breast cancer cells.For cancer cell detection and classification,the mechanical properties of a single cancer cell were quantified by single-beam acoustic tweezers(SBAT),a noncontact assessment tool using a focused acoustic beam.Cell-mimicking phantoms and agarose hydrogel spheres(AHSs)served to standardize the biomechanical characteristics of the cells.Based on the analytical comparison of deformability levels between the cells and the AHSs,the mechanical properties of the cells could be indirectly measured by interpolating the Young’s moduli of the AHSs.As a result,the calculated Young’s moduli,i.e.,1.527kPa for MDA-MB-231(highly invasive breast cancer cells),2.650kPa for MCF-7(weakly invasive breast cancer cells),and 2.772 kPa for SKBR-3(weakly invasive breast cancer cells),indicate that highly invasive cancer cells exhibited a lower Young’s moduli than weakly invasive cells,which indicates a higher deformability of highly invasive cancer cells,leading to a higher metastasis rate.Single-cell treatment may also be carried out by bursting a highly invasive cell with high-intensity,focused ultrasound. | Hae Gyun Lim Hsiao-Chuan Liu Chi Woo Yoon Hayong Jung Min Gon Kim Changhan Yoon Hyung Ham Kim KKirk Shung | 2020 | Microsystems & Nanoengineering2020，6，1： | 3 |
| 17 | THE EXISTENCE AND NODAL CHARACTER OF THE SOLUTIONS IN R^n FOR SEMILINEAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV EXPONENT显示文摘This paper is concerned with the existence and the nodal character of the nontrivial solutions in the entire space for some semilinear elliptic equation involving critical Sobolev exponent. | 邓引斌 | 1989 | Acta Mathematica Scientia1989，9，4： | 3 |
| 18 | Random duality显示文摘The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably difierent from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants. | GUO TieXin CHEN XinXiang | 2009 | Science China Mathematics2009，52，10： | 3 |
| 19 | PP-Rings of Generalized Power Series | Javed Ahsan | 2000 | Acta Mathematica Sinica,English Series2000，16，4： | 2 |
| 20 | Measure Centre and Minimal Centre of Attraction显示文摘In this note, we give the definition of the minimal centre of attraction for self-mapping on a compact metrizable space (for the case of flow, see Ref. [1]) and prove that the minimal centre of attraction coincides with the measure centre. Let (X, d) be a compact metrizable space and f: X→X be continuous. | 周作领 | 1993 | Chinese Science Bulletin1993，38，7： | 2 |
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