Showing papers in "Science in China Series A-Mathematics, Physics, Astronomy & Technological Science in 1989"

On intrinsic rigidity for minimal submanifolds in a sphere

Abstract: In this paper, some intrinsic rigidity theorems are given for compact minimal submanifolds in a sphere. In particular, the pinching constant of J. Simons is improved for higher codimensions.

On estimations of trigonometric sums over primes in short intervals(i)

Abstract: Let α be a real number,x≥A≥2, e(θ) = e~(2πiθ), Λ(n) be Mangoldt's function, andS(α; x, A) = sum from x-An≤x (Λ(n)e(nα).In this paper, the two following results are proved by a purely analytic method. (i) Let e bean arbitrarily small positive number and x~(91/96+e)≤A≤x. Then for any given positive c,there exist positive c_1 and c_2 such that S(α/q +λ; x,A)?A(logx)~(-c), provided that (α,q) = 1,1≤q≤log~(c_1)x, and A~(-1)log~(c_2)x| λ |≤(qlog~(c_1)x)~(-1); (ii) Let N be a sufficiently large odd integer, andU = N~(91/96+e). Then the Diophantine equation with prime variables N = p_1 + p_2 + p_3 is solv-able for N/3 - Up_j≤N/3 + U, j= 1, 2, 3, and there is an asymptotic formula for thenumber of its solutions.

Necessary and sufficient conditions for absolute stability of lurie indirect control systems

Abstract: In this paper, we transform the Lurie indirect control systems into a nonlinear system with separating variables by a topological transformation and introduce a definition of absolute stability for partial variables The necessary and sufficient conditions (NASC) for the absolute stability of Lurie indirect control systems are given and some sufficient conditions are obtained

General variational principle family for fully 3-d unsteady transonic flow with shocks around oscillating wings

Abstract: Based on the author's previous work, a general form of generalized variational princi-ples (VPs) together with its derived VP family is established for 3-D unsteady' transonicpotential flow with shocks past arbitrary wings oscillating periodically. To facilitate thenumerical handling, full use is made of functional variations with variable domain and natu-ral boundary conditions (BC) so that almost all boundary/interface conditions, including theRankine-Hugoniot shock relations and slip conditions across free trailing vortex sheets, havebeen converted into natural ones. Also distributed suction/blowing along the wing surfacefor the boundary layer control is accounted for. This theory aims at rendering a general,rigorous theoretical basis for the finite element metbod and other direct variational methods,and it can be generalized to both wing-body combinations and 3-D rotating bladings, includ-ing the subsonic flow as a special case.

Physicochemical and mechanical properties of saline soils during temperature change

Abstract: A series of important changes in physicochemical and physicomechanical properties ofsaline soils occurs during cooling, i. e. the parts of solute migrate towards the colder endof soil column and the parts of the sodium sulphate recrystallize from the soil solution, caus-ing the soil expension in volume or salt heave, which makes the soil decrease in compres-sive strength. The ratio of salt heave of soils decreases with the increase in the coolingrate, surcharge. initial density and the cohesion between soil particles, but increases with anincrease in water content. The fact that soil volume does not reduce obviously during re-warming shows the nonreversibility of salt heave process. During the repeated cycles ofcooling and warming, the salt heave accumulates and the compressive strength of soil de-creases gradually.

On kronecker limit formula for real quadratic fields (ii)

Abstract: In this paper, the Kronecker limit formula with Dirichlet characters for real quadratic fields is discussed and some class number formulae for certain imaginary quadratic fields are deduced.

Quaternary cmos circuits based on transmission function theory

Abstract: The transmission function theory is proposed, the quaternary and logic variables are distinguished, and three kinds of new operations (ie the threshold comparison operation, transmission operation and union operation) are introduced Since these operations describe the action principle of metal-oxide semiconductor (MOS) transistors, the transmission functions expressed by using them and logic operations can direct the realization of quaternary complementary metal-oxide semiconductor (CMOS) circuits In this paper the design of CMOS circuits for some basic transmission functions is proposed The computer simulation has confirmed that these circuits have correct logic and desirable DC transfer characteristics Furthermore, the synthesis technique for a quaternary CMOS transmission network is also proposed here

Investigation of deformations,stresses and stability of circular corrugated diaphragms under concentrated load at the center

Abstract: This paper deals with the deformations, stresses and stability of circular corrugateddiaphragm under a concentrated load at the center on the basis of the large-deflection theoryof shallow shells of revolution. By using the Newton-spline method the nonlinear equationsof the shell for circular corrugated diaphragm with sine-shaped shallow waves are solved.Solutions for both unbuckled and buckled states are obtained. Numerical results are yieldedby digital computer for some circular corrugated diaphragms with a given form of corrugations.