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LetRo andR1 be two KempfNess sets arising from moment maps induced by strictly plurisubharmonic,Kinvariant, proper functions.


It is shown here that there are proper subsets of ${\cal M}$ that also form a complete set of translation invariants, and these subsets are characterized.


The existence and uniqueness of optional and predictable projections of setvalued measurable processes are proved under proper circumstances.


Benson proper efficiency in the nearly conesubconvexlike vector optimization with setvalued functions


Under the assumption of nearly conesubconvexlikeness, a Lagrangian multiplier theorem on Benson proper efficiency is presented.

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 Abstract—We have calculated the binding energies of atomic nuclei by using the theory of density matrices. Treating the binding energies of atomic nuclei as functionals of density matrices and applying the variational principle, we obtain the proper values of nuclear binding energies and nuclear radii. If the nucleonic interaction potential is taken as a Gaussian well of purely central fore with its interaction constants determined by low energy experiments and its exchange interaction double the ordinary... Abstract—We have calculated the binding energies of atomic nuclei by using the theory of density matrices. Treating the binding energies of atomic nuclei as functionals of density matrices and applying the variational principle, we obtain the proper values of nuclear binding energies and nuclear radii. If the nucleonic interaction potential is taken as a Gaussian well of purely central fore with its interaction constants determined by low energy experiments and its exchange interaction double the ordinary interaction, it is able to obtain theoretical results in resonable agreement with the empirical data. The nuclear radii are 1.2×10~(13) A~(1/3) cm, and the nuclear binding energies are eveneven nuclei,odd mass nuclei, oddodd nuclei.  本文运用密度矩阵理论对原子核的结合能进行了计算,把原子核的能量看做密度矩阵的泛西,用变分原理求出原子核的能量和相应的核半径,假定核子间的作用势阱为高斯势阱,从低能实验数据来确定势阱参数,并假定交换作用为普通作用的二倍,则所得理论结果与实验结果大体相符。原子核的半径为1.2×10~(13)A~(1/3)Cm,原子核的能量为(E/A)=10.73+17.40A~(1/3)+(46.7034.94A~(1/3))((2/A))~2+0.728~(Z~2/A(4/3))0.556(Z~(4/3)/A~(4/3))+(0 偶一偶核 (69.040.9A~(1/3))1/A~2 奇数A核 (125.969.5A(1/3)) 奇—奇核)  The paper presents a generalized theory for thin elastic shallow shells in general orthogonal coordinates. Both tangential surface forces as well as normal surface load are considered in the present theory, provided that these tangential forces can be derivable from a load potential. The basic equations are reduced likewise to two simultaneous forthorder differential equations in normal deflection w and stress function F, and they are further combined into a single complex differential equation. The theory... The paper presents a generalized theory for thin elastic shallow shells in general orthogonal coordinates. Both tangential surface forces as well as normal surface load are considered in the present theory, provided that these tangential forces can be derivable from a load potential. The basic equations are reduced likewise to two simultaneous forthorder differential equations in normal deflection w and stress function F, and they are further combined into a single complex differential equation. The theory is then specialized to the shallow shells of revolution as a special case. With this simplified theory, the axisymmetrical bending of a paraboloidal shell is investigated. A general solution of such a problem is given in terms of the wellknown Thomson functions, presumably applicable to all paraboloidal shells. In addition, detailed analyses on various types of shells are made, so as to provide the designers the means to an optimum design of structure under the given load. In order to demonstrate the proper procedure of design, the paper has also included a simple example of uniform normal load. Through numerical comparison, it reveals that the paraboloidal shell of second degree i.e. the shallow spherical shell is a most favorable design among all under this particular loading.  本文首先对扁壳的基本方程作了新的改进,将它表达为一般正交曲线坐标的普遍形式,同时还包括有势的切向表面载荷的情况。文中结合旋转扁壳,建立了这类壳体的简化复数微分方程。根据这一简化理论,对抛物旋转扁壳的轴对称弯曲问题作了研究,并给出以Thomson函数形式表示的普遍解。它将适用于所有类型的抛物旋转扁壳。文中还针对各类壳体的具体情况作了比较深入的分析,使设计者便于在给定载荷的情况下进行壳体最佳线型的选择。最后作者以简单法向均布载荷为例,示范其设计方法。通过数值计算的比较表明,球面扁壳乃是在这类载荷形式之下具有最佳承载性能的壳体。  We shall attempt to study an interesting phenomenon in the theory of best approximation. We begin by some concepts which will be used below. 1. Let be a Hilbert space, h_n∈, and let (h_,h_k)=η_r),n,k=0,1,2,...; (1) (ⅰ) If η_(nk)=1 (n=0,1,2…), (2) η_(nk)→0 (for n≠k, as n,k→∞) (3) and η_(nk)→0 (for any fixed k, as n→∞; for any fixed n, as k→∞),(4) then we say that the sequence {h_n} is a quasiorthonormal system (QONS)of 1st kind. (ⅱ) If (2) and (4) are satisfied, we say that {h_n} is a QONS of 2nd klnd. (ⅲ) If... We shall attempt to study an interesting phenomenon in the theory of best approximation. We begin by some concepts which will be used below. 1. Let be a Hilbert space, h_n∈, and let (h_,h_k)=η_r),n,k=0,1,2,...; (1) (ⅰ) If η_(nk)=1 (n=0,1,2…), (2) η_(nk)→0 (for n≠k, as n,k→∞) (3) and η_(nk)→0 (for any fixed k, as n→∞; for any fixed n, as k→∞),(4) then we say that the sequence {h_n} is a quasiorthonormal system (QONS)of 1st kind. (ⅱ) If (2) and (4) are satisfied, we say that {h_n} is a QONS of 2nd klnd. (ⅲ) If (2) and (3) are satisfied, we say that {h_m} is a QONS of 3rd kind. 2. Let f(x)∈C_(1,1), p(x)∈C_(1,1) be a nonnegative weight function, and let P_n(x)=P_n(f,x) be the (nth) best approximation polynomials or simply the minimum polynomials of f with the weight p on [—1,1. We say simply that ψ_n(x)=f(x)p_m(x) is the minimum sequence of functions for f. 3. Let f∈C_(1,1)~′ (the class of functions with 1st derivative belonging to C_(1,1), L_n=‖(f—P_n)p‖y_n=(f—P_n)P, where P_n are the minimum polynomials, the functions Q_n(x)=(y_n~(′2))/(L_n~2y_n~2) (5) are called the (nth) associate functions of f. Concerning these definitions and reserving the sense of the above symbols, we proved the following theorems. Let A be a certain class of real irreducible proper fractions and let the positive weight p(x) take the form Ⅰ. {C_0+…+c_vx~v}~(1/2) or Ⅱ. {C_0+…+c_vx~v}~(1/2); Then under certain restrictions (see the begInning of §2) we have THEOREM 1. Let R_n(x)={Q_m(x)((1x~2)/((n±v/2)~2))}~(1) where="±" corespond to p taking Ⅰ or Ⅱ, respectively. (ⅰ) If L_m=O(1),‖1—R_m‖=o(1/n), ‖R_n~′‖=o(1/n), then the normal minimum sequence of functions λ_n {f—P_n} is a QONS of 1st kind in space L_(1,1)~2((p~2(x)/(1x~2)~(1/2)) (ⅱ) If L_m=o(1),‖1—R_m‖=O(1/n), ‖R_n~′‖=O(1/n), the conclusion of (ⅰ) also holds. (ⅲ) If L_m=O(1), ‖1—R_n‖=o(1), ‖R_n~′‖=o(1), the same sequence λ_n{f—P_n} is a QONS of 2nd kind in L_(1,1)~2((p~2(x)/(1x~2)~(1/2)). THEOREM 2. Let p(x) be of the form Ⅱ, the associate functions of f be of the form Q_n(x)=((nv/2)~2)/(1x~2){1+sum from n=1 to 1,μ B_l/(xβ_l)+sum from n=1 to 1,v C_j/(xy)}~2 (U_(μ1)~2)/(V_(2μ2)), where B,C,β,γ are constants, U,V are some μ—1 th and 2μ—2 th order polynomials, respectively. If (ⅰ) (?) (U_(μ1)~2(x))/(V_(2μ2)(x))=1 (—∞  文中引进伪直交性(quasiorthogonality)概念,它是平常直交性概念的一种推广。受到了古典切彼曉夫多項式等的提示,我們指出对於連續函数的某一子类,其最小元列在某內积空間中具有第一种、第二种或第三种伪直交性。这些結果可以看成一种嵌入性质(embedding property)。文中有若干例子說明伪直交系的存在,还給出定理的特例,即在某些情形最小元列具有(真)直交性。   << 更多相关文摘 
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