Yuan Wang's Technical Publications

Yuan Wang's Technical Publications

Books

The Numerical Evaluation of Integrals, Science Press, Beijing, 1961; 2nd edition: Numerical Integration and Its Applications, Science Press, Beijing, 1963. (with Hua Loo Keng).

Applications of Number Theory to Numerical Analysis, Springer Verlag and Science Press (Beijing), 1981. (with Hua Loo Keng).

Goldbach Conjecture (Edited), World Scientific Publishing Company, 1984.

Number Theory and Its Applications in China, Cont. Math; 77, 1988. (Edited with C.C. Yang and C.B. Pan).

Popularizing Mathematical Methods in the People's Republic of China, Birkhauser Boston, 1989. (with Hua Loo Keng).

Lecture Notes in Contemporary Mathematics, Science Press, 1990, (Edited with L. Yang)

Diophantine Equations and Inequalities in Algebraic Number Fields, Springer-Verlag, 1991.

International Symposium in Memory of Hua Loo Keng, Vol, I. Number Theory, Vol. II. Analysis, Springer-Verlag and Science Press, (Beijing), 1991. (Edited with S. Gong, Q. K. Lu and L. Yang)

Number-Theoretic Method in Statistics, Chapman and Hall, (with Fang Kai Tai), 1994

Hua Loo Keng, Kaiming Pub. Comp; Jiuzhang Pub. Comp; 1995.

Major Journal Articles

Sieve method and its applications

A note on some properties of the functions $\vp(n), \si(n)$ and $\the(n)$, Bull. de L'Acad. pol. des Sci; 4, 1956, 207--209. (with A. Schinzel).

On the representation of large even integer as a sum of a product of at most 3 primes and a product of at most 4 primes, Acta Math. Sin; 3, 1956, 500--513.

On the representation of large even integer as a sum of a prime and a product of at most 4 primes, Acta Math. Sin; 4, 1956, 565--582.

On some properties of integral polynomials, Shu Xue Jing Zhan, 3, 1957, 416--423.

On sieve methods and some of the related problems, Sci. Rec; 1, 1957, 9--12.

On sieve methods and some of their applications, Sci. Rec; 3, 1957, 1--5.

On the representation of large even number as a sum of two almost primes, Sci. Rec; 5, 1957, 15--19.

A note on some properties of the functions $\vp(n), \si(n)$ and $\the(n)$, Ann. Pol. Math; 8, 1958, 201--213. (with A. Schinzel). Corrigendum: 19, 1967.

A note on some properties of the arithmetic functions $\vp(n), \si(n)$ and $d(n)$, Acta Math. Sin; 1, 1958, 1--11.

A note on some properties of the Euler function $\vp(n)$, Proc. of Northwestern Univ. 1958, 15--23. (with Ren Jian Hua).

On sieve methods and some of their applications, Acta Math. Sin; 3, 1958, 413--429; also Sci. Sin; 4, 1959, 357--381.

A note on the least primitive root of a prime, Sci. Rec; 5, 1959, 174--179.

On sieve methods and some of their applications, Acta Math. Sin; 2, 1959, 87--100; also Sci. Sin; 12, 1962, 1607--1624.

On the least primitive root of a prime, Acta Math. Sin; 4, 1959, 432--441; also Sci. Sin; 1, 1961, 1--14.

On the representation of large integer as a sum of a prime and an almost prime, Acta Math. Sin; 2, 1960, 168--181; also Sci. Sin; 8, 1962, 1033--1054, (with a new appendix).

On the estimation of character sum and its applications, Shu Xue Jiang Zhan, 1, 1963, 78--81.

A note on the maximal number of pairwise orthogonal Latin squares of a given order, Sic. Sin; 5, 1964, 841--843.

Remarks on the difference of consecutive primes, Sci. Sin; 5, 1965, 786--788. (with Shieh Shen Kang and Yu Kun Rui).

On the maximal number of pairwise orthogonal Latin squares of order $s$, Acta Math. Sin; 3, 1966, 400--410.

A note on a theorem of Davenport, Acta Math. Sin; 4, 1875, 286--189.

On representation of large even integer as a sum of a prime and an almost prime, Kexue Tongbao, 8, 1975, 358--360. (with C.D. Pan and X.X. Ding).

On the representation of every large even integer as a sum of a prime and an almost prime, Sci. Sin; 5, 1975, 599-610. (with C.D. Pan and X.X. Ding).

Diophantine approximations and equations

A note on simultaneous diophantine approximations to algebraic integers, Sci. Sin; 5, 1977, 563--567. (with Hua Loo Keng).

Remarks concerning a transference theorem of linear forms, Acta Math. Sin; 2, 1979, 237-240. (with Yu Kun Rui and Zhu Yao Cheng).

A note on a transference theorem of linear forms, Sci, Sin; 3, 1979, 276--280. (with W.M. Schmidt).

A note on some metrical theorems in diophantine approximations, IHES/M/79/297; Chinese Ann. of Math; 2, 1981, 1--12. (with Yu Kun Rui).

A note on a transference theorem of the systems of linear congruences, Acta Math. Sin; 2, 1981, 303--307. (with Wang Lian Xiang and Ren Jian Hua).

On additive equations in an algebraic number field, Kexue Tongbao, 5, 1985, 583--587.

Bounds for solutions of additive equations in an algebraic number field I, Acta Arith; 48, 1987, 117--144; II, Acta Arith; 48, 1987, 307--323.

On a system of diophantine inequalities, Kexue Tongbao, 17, 1987, 1162--1165.

On homogeneous additive congruences, Sci. Sin; 5, 1989, 524--536.

Diophantine inequalities for forms in an algebraic number field, J. of number theory, 29, 1988, 324--344.

Diophantine equations and diophantine inequalities in algebraic number fields, Cont. Math; 77, AMS, 1988, 83--94.

On small zeros of quadratic forms over finite fields, J. of number theory, 31, 1989, 272--284.

On a generalized Waring's problem in algebraic number fields, in ``Number Theory'' in honor of Loo Keng Hua, Springer--Verlag, 1990. (with M. V. Subbarao).

Small solutions of congruences, J. of number theory, 45, 1993. 261--280.

On small zeros of quadratic forms over finite Fields II. Acta Math. Sin; 4, 1993, 382--389.

Applications of number theory

Remarks concerning numerical integration, Sci. Rec; 1, 1960, 8--11. (with Hua Loo Keng).

A note on interpolation of a certain class of functions, Sci. Sin; 6, 1960, 632--636.

On numerical integration and its applications, Shu Xue Jiang Zhan, 1, 1962, 1--44.

On diophantine approximations and numerical integrations I, Sci. Sin; 6, 1964, 1007--1008; II, Sci. Sin; 6, 1964, 1009--1010. (with Hua Loo Keng).

On numerical integration of periodic functions of several variables, Sci. Sin; 7, 1965, 964--978. (with Hua Loo Keng).

Remarks on the interpolation of a certain class of function, Sci. Sin; 4, 1965, 429--431.

Remarks on the number theoretic method in numerical analysis, J. Univ. Sci. Tech. China, 2, 1965, 213--218. (with Zhu Yao Cheng and Jian Yun Cui).

On interpolation of a certain class of functions, Kexue Tongbao, 9, 1966. 387--389.

On uniform distribution and numerical analysis (number theoretic method) I, Kexue Tongbao, 3, 1973, 112--114; II, Kexue Tongbao, 4, 1973, 165--166; III, Kexue Tongbao, 12, 1974, 559--560. (with Hua Loo Keng).

On uniform distribution and numerical analysis (number theoretic method) I, Sci. Sin; 4, 1973, 483--505; II, Sci. Sin; 3, 1974, 331--348; III, Sci. Sin; 2, 1975, 184--198. (with Hua Loo Keng).

On numerical integration and its applications for multi-dimensional functions of bounded variation, J. Univ. Sci. Tech. China 1, 1974, 39--67. (with Hua Loo Keng).

On number theoretic method in numerical integration of multi-dimensional space I, Acta Appl. Math. Sin; 2, 1978, 106--114; II, 4, 1982, 414--417. (with Xu Guang Shan and Zhang Rong Xiao).

A note on uniform distribution and experimental design, Kexue Tongbao, 6, 1981, 485--489. (with Fang Kai Tai).

Applications of number theory to numerical analysis, ``recent progress in analytic number theory'' Edited by H. Halberstam and C. Hooley, Vol. 2, Acad. Press, 1981, 111--118. (with Hua Loo Keng).

On diophantine approximation and approximate analysis, Kexue Tongbao, 5, 1982, 468--472.

On diophantine approximation and approximate analysis I, Acta Math. Sin; 2, 1982, 248--256; II, Acta Math. Sin; 3, 1982, 323--332.

A note on the approximate solution of the Cauchy problem by number--theoretic nets, Chin. Ann. of Math; 3, 1982, 451--456.

Number theoretic method in numerical analysis, Cont. Math; 77, AMS, 1988, 63--82.

Number theoretic methods in applied statistics. Chin. Ann. Math; 11B, 1990, 51--65; (ii) Chin. Ann. Math; 11B, 1990, 384--394. (with Fang Kai Tai).

A sequential algorithm for optimization and its applications to regression analysis, in Lecture Notes in Contemporary Mathematics, 1990 (with Fang Kai Tai).

Applications of quasirandom sequence in statistics, Proc. of the Asian Math. Conf. 1990, 135--139. (with K. T. Fang).

A sequential number-theoretic methods for optimization and its applications in statistics, in Development of Statistics: Recent contributions from China, 1991, Longman. (with Fang Kai Tai).

A sequential algorithm for solving a system of nonlinear equations, J. Computational Math., 9, 9--16, 1991 (with Fang Kai Tai)

A new method for generating the uniform distribution on the unit sphere, Tech. Rep. of the Hong Kong Baptist College, No. 15, 1992. (with K. T. Fang and H. L. Wong).

Some applications of number-theoretic methods in statistics, Statistical Science, 9--3, 1994, 416--428. (with Fang, Kai Tai and P .M. Bentler).

Uniform design of experiments with mixtures, Scientia Sinica, 1996. (with Fang Kai Tai).

Miscellaneous

On the calculation of mineral reserves and hillside areas on contour maps, Acta Math. Sin; 1, 1961, 29--40. (with Hua Loo Keng).

Finiteness and infinity, discrete and continuity, Kexue Tongbao, 1963, 4--21. (with Hua Loo Keng).

On Linnik's method concerning the Goldbach number, Sci. Sin; 1, 1977, 16--30.

On a set of independent units of cyclotomic field, Ziran Zazhi, 5, 1978, 6. (with Hua Loo Keng and Pei Ding Yi).

A conditional result on Goldbach problem, Acta Math. Sin; New Ser; 1, 1985, 72--78. (with Shan Zun).

Hua Loo Keng, a brief outline of his life and works, in ``Number Theory'' in honor of Loo-Keng Hua, Springer--Verlag, 1990.

Chen Jingrun, a brief outline of his life and works, Acta Math. Sin; 3, 1996, 225--233. (with C. D. Pan).