Chinese Quarterly Journal of Mathematics

A Generalized Schwarz Lemma

ZHAO Lian-kun, LI Hong-yi

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.

Existence of Positive Solutions for Eigenvalue Problems of Fourth-order Elastic Beam Equations

LU Hai-xia

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.

Mean Values of the Hardy Sum

WANG Xiao-ying, YUE Xia-xia

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.

The Generalization on Inequalities of Hermite-Hadamard's Integration

LIAN Tie-yan, TANG Wei

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].

L\acute{e}vy-Prohorov Metric on the Measure Space

QU Li-min, ZHU Ji-yun

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.

Existence and Uniqueness of Solutions to Singular Higher Order Two-point BVPs on Time Scales

TENG Nan, MA Fu-bo, YU Tong, MO Ran

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.

The Translational Hull of Strongly Inverse Wrpp Semigroups

QIU Shu-ming

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.

Option Pricing and Hedging under a Markov Switching Lévy Process Model

SONG Rui-li, WANG Bo

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.

Bloch Constant on \alpha-Bloch Mappings of the Unit Ball

XU Qing, LIU Zhi-bin, WANG Jian-fei

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.

A Second Order Nonconforming Triangular Mixed Finite Element Scheme for the Stationary Navier-Stokes Equations

WANG Zhi-jun, HAO Xiao-bin, SHI Dong-yang

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.

Solvable Lie Algebras with Nilradical \tilde{Q}_{2n+1} and Their Casimir Invariants

LI Xiao-chao, JIN Quan-qin

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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