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61.
Wolfgang M. Ruppert 《manuscripta mathematica》1998,96(1):17-22
If K is a number field of degree n over Q with discriminant D
K
and if α∈K generates K, i.e. K=Q(α), then the height of α satisfies with . The paper deals with the existence of small generators of number fields in this sense. We show: (1) For each $n$ there are
infinitely many number fields K of degree $n$ with a generator α such that . (2) There is a constant d
2 such that every imaginary quadratic number field has a generator α which satisfies .?(3) If K is a totally real
number field of prime degree n then one can find an integral generator α with .
Received: 10 January 1997 / Revised version: 13 January 1998 相似文献
62.
Hiroshi Sawai 《Topology and its Applications》2007,154(18):3125-3134
The purpose in this paper is to prove that there exists a lattice on certain solvable Lie groups and to construct a symplectic solvmanifold with the Hard Lefschetz property, and a locally conformal Kähler solvmanifold. We see that minimal models for these solvmanifolds are formal. 相似文献
63.
We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations. 相似文献
64.
We give a simple proof that everyk-connected bipartite tournament has a cycle through every set ofk vertices. This was conjectured in [4].This research was done while the first author was visiting Laboratoire de Recherche en Informatique, universite Paris-Sud whose hospitality and financial support is gratefully acknowledged 相似文献
65.
B. Abramovitz 《Acta Appl Math》1994,36(3):211-226
In this work, we consider the regularization method for linear ill-posed problems. For operators and approximating subspaces satisfying certain conditions and for a specific form of the regularization parameter, upper and lower bounds are given for the condition number of the corresponding discrete problem. 相似文献
66.
Resistivity and low field ac susceptibility measurements are made on R: 123 superconducting samples with different rare earth elements R. The order parameter dimensionality OPD is deduced from resistivity versus temperature plot using the Aslamazov and Larkin expression, while the analysis of the temperature dependence of ac susceptibility is done employing Beans’ critical state model and with the help of the Ravi expression. With increasing R, the critical temperatures Tc are nearly kept constant (∼90 K), while the crossover temperatures To are shifted to lower values. Moreover, the superconducting order parameter OPD is shifted toward 2D behavior. On the other hand, the values of superconducting volume fraction fg decrease with increasing ac field amplitude Hm for all samples and it is higher in Er: 123 sample than in Nd: 123 sample. Although the values of critical current density Jc at the peak temperature Tm are nearly unchanged with increasing R, the values of Jc(T), at T<Tm and T>Tm, are found to be dependent on the chosen R. The correlation between the above calculated parameters against R is also mentioned. 相似文献
67.
The first object of this paper is to introduce a new evolution equation for the characteristic function of the boundary Γ
of a Lipschitzian domain Ω in the N-dimensional Euclidean space under the influence of a smooth time-dependent velocity field. The originality of this equation is that the evolution takes place in an Lp-space with respect to the (N − 1)-Hausdorff measure. A second more speculative objective is to discuss how that equation can be relaxed to rougher velocity
fields via some weak formulation. A candidate is presented and some of the technical difficulties and open issues are discussed.
Continuity results in several metric topologies are also presented. The paper also specializes the results on the evolution
of the oriented distance function to initial sets with zero N-dimensional Lebesgue measure. 相似文献
68.
Toshiyuki Oyama Akira Kitamura Eiichi Sato Masao Tomoi 《Journal of polymer science. Part A, Polymer chemistry》2006,44(8):2694-2706
The factors affecting pattern‐forming properties in reaction development patterning were examined with polyarylates with various bisphenol moieties. The developability of the photosensitive polyarylates was dependent on the properties of the subtituent (R) in the bisphenol moieties. The development time decreased in the following order: R?C(CH3)2 > fluorenyl unit ? phenolphthalein unit > C(CF3)2 > SO2. This order agreed with that of the reactivity between the polyarylates and ethanolamine, and these orders can be explained by pKa of the bisphenol used to prepare the polyarylates. The development with NH2? R′? OH resulted in successful positive‐tone pattern formation. However, pattern formation with the developers containing NH2? R′? OCH3 was unsuccessful. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2694–2706, 2006 相似文献
69.
In this paper we study the stability of transonic shocks in steady supersonic flow past a wedge. We take the potential flow equation as the mathematical model to describe the compressible flow. It is known that in generic case such a problem admits two possible location of shock, connecting the flow ahead it and behind it. They can be distinguished as supersonic-supersonic shock and supersonic-subsonic shock (or transonic shock). Both these possible shocks satisfy the Rankine-Hugoniot conditions and entropy condition. In this paper we prove that the transonic shock is also stable under perturbation of the coming flow provided the pressure at infinity is well controlled. 相似文献
70.
Yue Liu Masahito Ohta Grozdena Todorova 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2007
We study here instability problems of standing waves for the nonlinear Klein–Gordon equations and solitary waves for the generalized Boussinesq equations. It is shown that those special wave solutions may be strongly unstable by blowup in finite time, depending on the range of the wave's frequency or the wave's speed of propagation and on the nonlinearity. 相似文献