ON DIRECT METHOD OF SOLUTION FOR A CLASS OF SINGULAR INTEGRAL EQUATIONS

In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.     

The Generalized KKM Map and Its Applications to Variational Inequalities

In this paper,applying the concept of generalized KKM map,we study problems ofvariational inequalities.We weaken convexity(concavity)conditions for a functional of two variables■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth-od of acute angle principle about monotone operator as an application of these results.     

Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law

For independent identically distributed random vectors belonging to the generalized Domain of Attraction of the multivariate normal law, we define two partial sum processes analogous to that of Donsker's Theorem. We prove that each converges in distribution to a Brownian Motion in the space of continuous functions. One process uses nonrandom operator normalization, and the other is a studentization of the first, using normalization by the empirical covariance operator.     

Operator Matrix Forms of Positive Operators

If a 3-tuple (A:H1→H1,B:H2→H1,C:H2→H2）of operators on Hibert spaces is given,we proved that the operator ～↑A:=(↑A ↓B^*↑B ↓C) on H=H1 H2 is ≥0 is and only if A≥0,R(B)∪→R（A^1/2) and C≥B^* A^ b,where A^ is the generalized inverse of A.In general,A^ is a closed operator,but since R(B)∪→R(A^1/2,B^* A^ B is bounded yet.     

Variational inequalities for monotone operators in nonreflexive Banach spaces

The purpose of this paper is to study the existence problem of solutions and perturbation problem for some kind of variational inequalities with monotone operators in nonreflexive Banach spaces, and to obtain some results.     

广义分布空间中卷积算子可解之充要条件

Ｅｈｒｅｎｐｒｅｉｓ及Ｈｏｒｍａｎｄｅｒ在Ｓｃｈｗａｒｔｚ缓增分布空间中讨论了卷积算子的可解。本文充分利用Ｂｅｕｒｌｉｎｇ广义分布空间中的Ｆｏｕｒｉｅｒ－Ｌａｐｌａｃｅ变换的性质，在Ｂｅｕｒｌｉｎｇ广义分布空间中讨论了卷积算子可解的几个等价条件，进而导出了卷积算子可解的充要条件，并推广了Ｈｏｒｍａｎｄｅｒ的某些结果     

一个组合数学问题

讨论展开式（η＿１＋ｂη＿０）（η＿２＋ｂη＿０＋ｂη＿０）…（η＿ｎ＋ｂη＿（ｎ－１）…＋ｂ￣ｎη＿０）．引入个迅速求得Ａｆ（ｎ）的计算规则，以及系数的计算公式，这公式是牛顿二项式展开系数公式的推广。     

大型喷浆机器人的灵巧度分析

灵巧度是衡量机器人运动失真程度的重要参数。对机器人灵巧度评价指标进行了对比研究 ,结合大型喷浆机器人自由度较多的特点 ,用雅可比矩阵的条件数对喷浆机器人的灵巧度进行了分析。结果表明 ,大型喷浆机器人在不同形位下的条件数都很小 ,具有较好的运动灵巧度。     

The semiclassical limit of a quantum Fermi accelerator

A classical Fermi accelerator model (FAM) is known to show chaotic behavior. The FAM is defined by a free particle bouncing elastically from two rigid walls, one fixed and the other oscillating periodically in time. The central aim of this paper is to connect the quantum and the classical solutions to the FAM in the semiclassical limit. This goal is accomplished using a finite inverted parametric oscillator (FIPO), confined to a box withfixed walls, as an alternative representation of the FAM. In the FIPO representation, an explicit correspondence between classical and quantum limits is accomplished using a Husimi representation of the quasienergy eigenfunctions.     

Eigenvalue problem for arbitrary linear combinations of a boson annihilation and creation operator

The eigenvalue problem for arbitrary linear combinations kα + μα^? of a boson annihilation operator α and a boson creation operator α^? is solved. It is shown that these operators possess nondegenerate eigenstates to arbitrary complex eigenvalues. The expansion of these eigenstates into the basic set of number states | n >, (n = 0, 1, 2, …), is found. The eigenstates are normalizable and are therefore states of a Hilbert space for | ζ | < 1 with ζ ? μ/k and represent in this case squeezed coherent states of minimal uncertainty product. They can be considered as states of a rigged Hilbert space for | ζ | ? 1. A completeness relation for these states is derived that generalizes the completeness relation for the coherent states | α 〉. Furthermore, it is shown that there exists a dual orthogonality in the entire set of these states and a connected dual completeness of the eigenstates on widely arbitrary paths over the complex plane of eigenvalues. This duality goes over into a selfduality of the eigenstates of the hermitian operators kα + k* α^? to real eigenvalues. The usually as nonexistent considered eigenstates of the boson creation operator α^? are obtained by a limiting procedure. They belong to the most singular case among the considered general class of eigenstates with ζ ? μ/k as a parameter.