数学季刊

一个Schwarz引理的推广

赵连坤 , 李红裔

2017, 32(1): 1-6. doi:10.13371/j.cnki.chin.q.j.m.2017.01.001

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In this paper, we establish a boundary Schwarz Lemma for holomorphic mapping on the generalized complex ellipsoid in C~n.

四阶弹性梁方程特征值问题正解的存在性

陆海霞

2017, 32(1): 7-15. doi:10.13371/j.cnki.chin.q.j.m.2017.01.002

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In this paper, we investigate the positive solutions of fourth-order elastic beam equations with both end-points simply supported. By using the approximation theorem of completely continuous operators and the global bifurcation techniques, we obtain the existence of positive solutions of elastic beam equations under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, when the nonlinear term is non-singular or singular, and allowed to change sign.

关于Hardy和的均值

王晓瑛 , 岳霞霞

2017, 32(1): 16-33. doi:10.13371/j.cnki.chin.q.j.m.2017.01.003

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Let p≥5 be a prime. For any integer h, the Hardy sum is defined by H（h,p）=sum(（-1）^{j+1+[（hj）/p]})from （p-1） to （j=1） which is related to the classical Dedekind sum. The mean values of the Hardy sum in short intervals are studied by using the mean value theorems of Dirichlet L-functions.

关于Hermite-Hadamard积分不等式的推广

连铁艳, 汤伟

2017, 32(1): 34-41. doi:10.13371/j.cnki.chin.q.j.m.2017.01.004

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Some new inequalities of Hermite-Hadamard’s integration are established. As for as inequalities about the righthand side of the classical Hermite-Hadamard’s integral inequality refined by S Qaisar in [3], a new upper bound is given. Under special conditions,the bound is smaller than that in [3].

测度空间上的Lévy-Prohorov距离

曲立敏 , 朱季云

2017, 32(1): 42-48. doi:10.13371/j.cnki.chin.q.j.m.2017.01.005

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Under the premise of infinitely many pure strategies, by defining the new LP* metric, striking an equivalence of topology and weak* topology, we prove that the existence of the essential component.

时间测度上奇异高阶两点边值问题解的存在性与唯一性

滕南, 马扶博, 于童, 莫冉

2017, 32(1): 49-58. doi:10.13371/j.cnki.chin.q.j.m.2017.01.006

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This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method.The theorems obtained are very general. For the different time scale, the problem may be the corresponding continuous or discrete boundary value problem.

强逆Wrpp半群的平移包

邱书明

2017, 32(1): 59-65. doi:10.13371/j.cnki.chin.q.j.m.2017.01.007

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In this paper, we obtain some characterizations of the translational hull of strongly inverse wrpp semigroups. And we prove that the translational hull of a strongly inverse wrpp semigroup is still of the same type.

马尔可夫交换Lévy过程模型下的期权定价及其对冲

宋瑞丽, 王波

2017, 32(1): 66-78. doi:10.13371/j.cnki.chin.q.j.m.2017.01.008

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In this paper, we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging. In this model, the market interest rate, the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process. We use the MEMM（minimal entropy martingale measure） as the equivalent martingale measure. The option price using this model is obtained by the Fourier transform method. We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging.

单位球上α-Bloch映照的Bloch常数

许青, 刘智斌, 王建飞

2017, 32(1): 79-87. doi:10.13371/j.cnki.chin.q.j.m.2017.01.009

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This note is denoted to establishing sharp distortion theorems for subclasses of α-Bloch mappings defined in the unit ball of Cn with critical points. Furthermore, the estimates of Bloch constant with respect to these subclasses are given.

定常Navier-Stokes方程的一个二阶非协调三角型混合元格式

王志军, 郝晓斌, 石东洋

2017, 32(1): 88-98. doi:10.13371/j.cnki.chin.q.j.m.2017.01.010

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In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure. The convergence analysis is presented and optimal error estimates of both broken H¹-norm and L²-norm for velocity as well as the L²-norm for the pressure are derived.

幂零根基为Q_2n+1的可解李代数及其Casimir不变量

李小朝, 靳全勤

2017, 32(1): 99-110. doi:10.13371/j.cnki.chin.q.j.m.2017.01.011

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The finite-dimensional indecomposable solvable Lie algebras s with Q_2n+1 as their nilradical are studied and classified and their Casimir invariants are calculated. It turns out that the dimension of s is at most dim Q_2n+1+2.

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