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101.
In the introduction of the Arithmetica Diophantus says that in order to solve arithmetical problems one has to “follow the way he (Diophantus) will show.” The present paper has a threefold objective. Firstly, the meaning of this sentence is discussed, the conclusion being that Diophantus had elaborated a program for handling various arithmetical problems. Secondly, it is claimed that what is analyzed in the introduction is definitions of several terms, the exhibition of their symbolism, the way one may operate with them, but, most significantly, the main stages of the program itself. And thirdly, it is argued that Diophantus' intention in the Arithmetica is to show the way the stages of his program should be practically applied in various arithmetical problems. 相似文献
102.
The possible defect models of Y^3+:PbWO4 crystals are discussed by defect chemistry and the most possible substituting positions of the impurity Y^3+ ions are studied by using the general utility lattice program (GULP). The calculated results indicate that in the lightly doped Y^3+ :PWO crystal, the main compensating mechanism is [2Ypb^+ + VPb^2-], and in the heavily doped Y^3+ :PWO crystal, it will bring interstitial oxygen ions to compensate the positive electricity caused by YPb^+, forming defect clusters of [2Ypb^+ +Oi^2-] in the crystal. The electronic structures of Y3+ :PWO with different defect models are calculated using the DV-Xα method. It can be concluded from the electronic structures that, for lightly doped cases, the energy gap of the crystal would be broadened and the 420nm absorption band will be restricted; for heavily doped cases, because of the existence of interstitial oxygen ions, it can bring a new absorption band and reduce the radiation hardness of the crystal. 相似文献
103.
Jan J. Dijkstra 《Topology and its Applications》2006,153(15):2948-2951
In 1988 A. Gutek proved that there exist one-point connectifications of hereditarily disconnected spaces that do not have the fixed point property. We improve on this result by constructing a one-point connectification of a totally disconnected space without the fixed point property. 相似文献
104.
C. Praagman 《Aequationes Mathematicae》1987,33(1):251-259
In this paper it is proved that having a logarithm is equivalent to having roots of arbitrary order in the group of automorphisms of a formal power series ring, and in algebraic subgroups too 相似文献
105.
F. García 《Topology and its Applications》2006,153(15):2886-2892
In this paper we characterize the class of uniform Eberlein compact spaces through a network condition and also in terms of covering properties for the square of the space. 相似文献
106.
Debora Di Caprio 《Topology and its Applications》2006,153(14):2680-2702
We introduce and study some completeness properties for systems of open coverings of a given topological space. A Hausdorff space admitting a system of cardinality κ satisfying one of these properties is of type Gκ. Hence, we define several new variants of the ?ech number and use elementary submodels to determine further results. We introduce M-hulls and M-networks, for M elementary submodel. As an application, we give estimates for both the tightness and the Lindelöf number of a generic upper hyperspace. Two recent results of Costantini, Holá and Vitolo on the tightness of co-compact hyperspaces follow from ours as corollaries. 相似文献
107.
J. -P. Kauthen 《Numerische Mathematik》1989,56(5):409-424
Summary Integral equations of mixed Volterra-Fredholm type arise in various physical and biological problems. In the present paper we study continuous time collocation, time discretization and their global and discrete convergence properties. 相似文献
108.
The problem of analytic representation of integrable CR functions on hypersurfaces with singularities is treated. The nature of singularities does not matter while the set of singularities
has surface measure zero. For simple singularities like cuspidal points, edges, corners, etc., also the behaviour of representing
analytic functions near singular points is studied.
Received: 8 December 2000; in final form: 24 June 2001/Published online: 1 February 2002 相似文献
109.
In this paper, we establish some new nonlinear integral inequalities of the Gronwall–Bellman–Ou-Iang-type in two variables. These on the one hand generalizes and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of differential equations. We illustrate this by applying our new results to certain boundary value problem. 相似文献
110.
We prove that a for a mapping f of finite distortion , the -Hausdorff measure of any point preimage is zero provided is integrable, with , and the multiplicity function of f is essentially bounded. As a consequence for we obtain that the mapping is then open and discrete.
Received: 18 June 2001 / Revised version: 31 January 2002 / Published online: 27 June 2002 相似文献