Abstract:In this paper，two location problems have been put forward. A necessary and sufficient condition of local optimality is established. On the basis of this analysis，an efficient algorithm to solve these location problems is proprosed.

Abstract:This paper reveals the inner relationship between the characteristic vectors of Lanchester equations and fire indexes with the help of the property of positive matrixes. By way of examples the paper further shows that the fire indexes are the extension of the notion of power coefficients in Lanchester equations. It is pointed out that the fire indexes are not only related to the weapons，but also depend on the disposition of troops in a whole battle. When some kinds of weapons are destroyed the fire indexes will change with situation. The fire indexes also depend on the principles of weapon assignment. Thus the relationship between fire indexes and tactical principles is set up.

Abstract:Let there be a heap of beans with total number N(odd) and an integer s，we difine a 2-person game Γ(N，s) as follows: The first player P_Ⅰ takes some beans from the heap, at least one bean and at most s beans. Player two，P_II now picks some beans under the same constraint. The play then reverts to P_II and continues in the same way until all beans have been removed. The player with odd number of beans at hand wins. In this paper，We completely solve the game. At first，we give the winning strategy (if exists) for P_Ⅰ. Theorem Let r be the number of beans P_Ⅰ leaving to P_II at any step，and q be the number p_Ⅰ have at the end of the step. Then p_Ⅰ will win if r=1 or 0(mod(2s+2)) if q is odd ,and r=s+1 or s+2(mod(2s+2)) if q is even when s is odd and r=1 or 0 (mod(s+2)) if q is odd,and r=s+1(mod(s+2)) if q is even when s is even. The theorem can be proved by induction. As a by-product of the theorem we have Corollary Γ(n，s) is a win for P_II iff n=S十1 (mod(2s+2)) when s is odd and n=s+1 (mod(s+2)) when s is even.

Abstract:In this paper，the window paralle1 algorithms for solving general three-level schemes On MIMD machines are proposed，the WBJ schemes are given，and the convergence for three-level schemes is proved. The conclusions of the paper show that the convergence for the window parallel algorithms is independent of the size of the window，Which has influence on the efficiency of each processor.

Abstract:A few useful properties of the support function of the convex set C are discussed in the paper. They are also applied to the study of the subdifferential of a function. Some interesting results about the subdifferential of a function are obtained.

Abstract:In this paper，the projection theory of Lg-smoothing splines is discussed. Based on it a recursive algorithm is derived for Lg-smoothing splines. The method for the construction of Lg-smootbing splines in paper [1] is simplified by a special basis.

Abstract:In this paper，we described a shape preserving spline function with Hermite interpolation condition. A spline function of monotone perserving q(x) is constructed，and q(x) satisfies 1) q(x_i)=y_i，i=0，1，…，n，n+1， 2) q'(x_i)= y'_i i=0，1 ，…，n，n+1. Similar spline functions have a1so been studied for convex sequences {y_i}_i=0ⁿ⁺¹.

Abstract:This paper deals with the optimal stopping problem for Markov chains with non-discounted total payment. Paper [2] proves a sufficient condition: The value function of the optimal stopping problem for discrete finite Markov chains exists if the corresponding linear programming has a solution. This paper also shows that this condition is also necessary.

Abstract:In this paper，1inear models with p variance components are considered and the explicit and easy computable expressions for Bayes invariant quadratic unbiased estimates (BAIQUE's) are presented. The class of BAI-QUE's is proved to form the entire class of admissible invariant quadratic unbiased estimates. A necessary and sufficient condition for the existence of admissible nonegative definte quadratic unbiased estimates is given.

Abstract:Assume that (X_n，?_n)^∞₁ is an adapted reward sequence， (γ_n）^∞₁) is snell's envelope of X_n，(A_n) is a predictable increased process with A₀=0 in Doob-Meyer's decomposition of (γ_n). In this paper，from J. Klass，we prove that σ₁=inf{K≥1:Xk₁≥γ_k} is the smallest semi-optimal and the largest strong regular generalized rule，and K₀?sup{n≥0:A_n=0}<∞ is the largest reqular generalized rule. Hence another expression of the uniqueness of optimal generalized rule is given.

Abstract:This paper discusses the problem of fast computation of convolutions in rings. The adaptability of the well-known Winograd algorithm，FPT algorithm and FFT algorithm which are proposed for computing convolutions in complex fields is studied in the case of rings. Especially，fast algorithms for computing multiplication of matrix polynomial，matrix convolution and polynomial convolution are proposed. They are of wide practical usage.

Abstract:The paper gives a new method for solving the transportation problem-the dual algorithm for the transportation problem (on the table work). Finally，the author gives one examples which show that the algorithm is simpler for solving some problems than the method in [1].

Abstract:A new fast computer algorithm for the transposing of an n×n data matrix，which requires more internal storage than the available to a certain computer，is given in this paper. The required computation time is much less than the conventional algorithm.

Abstract:In this paper，the unified definition of divergence，cur1 and gradient independent of the coordinate system is given by the extended divergence theorem. Stressed on using a common model which is a volume element enclosed by the three pairs of coordinate surfaces，a11 the divergence，curl and gradient are denoted uniformly in the form of the limiting value of a differential quantity. So the known expressions of these three quantities in tensor analysis can be derived directly.

Abstract:This paper describes a new interpolation method with the convex combination of two operators，the interpolation function is simple to construct and easy to calculate，and the error of interpolation functions is estimated. The error order is O(h⁴)，which is better that of [4].

Abstract:Let S(p，α)，C(p，α) and K(p，α) denote the classes of p-valent starlike，convex and close-to-convex functions of order α respectively. In this paper the extreme points and support points of these classes are studied and a series of results have been obtained as follows: Theorem 1.(l) SuppS(p，α)=EHS'(p,α); (2) SuppC(p，α)=EHC(p，α); (3) SuppK(p，α)?EHK(p，α). Theorem 2.(1)EHs(S(p,α))={xz^p/(1?yz)^2(1?α)p,│x│=│y│=1}(0≤α≤1/2). （2）Supp{s(S(p,α))J}=EHs(S(p,α))(0≤α<1/2). Where J is a continuous linear functional on which does not have the form J(h)=ΣA_nh⁽ⁿ⁾(0) for each h belonging to.

Abstract:In this paper，we derive a rule endeavouring to increase the accuracy of the estimate of parameters. Corresponding compu-tational methods are given.

Abstract:Combining the Markov process with target planning method，two concepts for manpower structure system analysis-monoterm control and multiterm control are presented in this paper. Based on monoterm control models，multiterm control models are developed，hence the models are more convincible and more general.

Abstract:This paper presents a selection system scheme with the aid of a microcomputer for sifting graduate students. It is a direct application of fuzzy mathematics, the paper constructs two fuzzy operators conducted from the selection process of graduate students，and some matrixs which are composed of many evaluations about their po1itical attitudes，moral characters，prefessional ability and physical level. Taking a number of statistics and calculations，the system wi1l provide some selection informations and a scheme with relatively credible level for the dean's office.