Chinese Quarterly Journal of Mathematics

On the Sum of Powers of Natural Numbers

CHEN Jing-run, LI Jian-yu

1987, 2(1): 1-18.

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Riemann Manifolds and Harmonic Maps

XIN Yuan-long

1987, 2(1): 19-36.

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In this paper we will give a survey of varyous developments of related topics harmonic maps. The results which have been given since 1978are important points.

Paracompactness in Generalized Topology

HE Ming, LIU Ying-ming

1987, 2(1): 37-42.

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A Posterior Error Estimimates of the Finite Elements Methods for One Dimensional Boundary Value Problems

HUANG Hong-ci, E Wei-nan

1987, 2(1): 43-48.

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An alternative approach to the a posterior error estimates of the finite element methods for one-dimensional boundary
value problems is presented, This approach grealty simplifies the proofs of available results for linear element and naturally gives results on high order elements at the same time.

Hierarchies of a Subclass of Total Recursive Functions

QIAO Hai-yan, XU Shu-run

1987, 2(1): 49-58.

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In this paper an increasing sequence \mathcal{B}_{0},\mathcal{B}_{1},...of the classesoftotal recursive functiond is examined. Each class \mathcal{B}_{N} is closed under the operation of substituion, the operation of recursion and the operationof limited minimum.

On the Cauchy Problem of Nonlinear Heat Equation, Solution and Existence Interval

YU Xin

1987, 2(1): 59-72.

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In this paper, we construct a specisl space which incarates the estimate of decay of solutions, and use Banach fixed point theorem to directly prove the existence and uniqueness of the generalized solution of nonlinear heat equation.

Some Mathematical Problems in Cryptology

TAO Ren-ji

1987, 2(1): 73-90.

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It is wellknown th at mathematics is very important in crytology. Among others, in this paper we discuss Shift register sequences and finite automata and their application in cryptology.

On the Diophantine Eguation X²ⁿ-Dy²=1

CAO Zhen-fu

1987, 2(1): 91-98.

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Note on the Multiple Values and Unigueness of Meromorphic Funtions

YI Hong-xun

1987, 2(1): 99-104.

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In this paper we prove the following theorems:
Theorem 1 and Theorem 2.

Real Projective Algebraic Manifolds with a Fliation

LI Zi-sheng

1987, 2(1): 105-108.

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In this paper,we introcduce a real projective algebeaic manifold which is the product manifold p^m\times p^q embeds into pⁿ,
n=(m+1)(q+1)-1, where pm,pq and pn are all the real projective space with m, q and n dimension respectively.This embeding submanifold in pⁿ has a foliation with codimension q, all of its leaves are compact.

Some Results on the Product of \delta Functions

WANG Zhi-qing

1987, 2(1): 109-110.

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