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221.
222.
By using a more efficient way of almost diagonalizing,known results on small fractional parts of general real cubicforms in a small number of variables, are improved. In particular,for ternary forms the method gives a bound superior to thatarising from simply reducing to a cubic form in one variable.2000 Mathematics Subject Classification 11D75, 11E76, 11J54. 相似文献
223.
Rainer Buckdahn Marc Quincampoix Catherine Rainer Aurel Răşcanu 《Applied Mathematics and Optimization》2004,49(2):99-112
We study the existence of a
solution of controlled stochastic
differential equations remaining in a given set of constraints
at any time smaller than the exit time of a given open set.
We also investigate the small time attainability of a given closed
set K, i.e., the property that, for all arbitrary small time horizon T
and for all initial condition in a sufficiently small
neighborhood of K,
there exists
a solution to the controlled stochastic
differential equation which reaches K before T. 相似文献
224.
A high-power, low-noise photodetector, in conjunction with a current shunt actuator, is used in an ac-coupled servo to stabilize the intensity of a 10-W cw Nd:YAG laser. A relative intensity noise of 1 x 10(-8) Hz(-1/2) at 10 Hz is achieved. 相似文献
225.
Hydrodynamic flow and electric currents through model porous media were investigated. The transport rates through the individual pathways of the pore network are determined by the local width of the pore channels and by the driving mechanism. The model objects represent quasi two-dimensional random site percolation clusters. The calculated design was realized by milling the structure in polystyrene sheets. Velocity maps of stationary flow and current density maps of stationary currents through the cluster were acquired by magnetic resonance imaging methods. The findings were compared to the results of numerical simulations based on the same structure. Since the difference in the transport patterns of the different driving mechanisms are expected to be more pronounced in smaller pore spaces, ultra deep X-ray lithography has been used for the fabrication of downsized model objects with a spatial resolution of better than 50 microm and an aspect ratio as large as 20. First results obtained with these objects are reported. 相似文献
226.
We consider quadratic diophantine equations of the shape
for a polynomial Q(X1, ..., Xs) Z[X1, ..., Xs] of degree 2.Let H be an upper bound for the absolute values of the coefficientsof Q, and assume that the homogeneous quadratic part of Q isnon-singular. We prove, for all s 3, the existence of a polynomialbound s(H) with the following property: if equation (1) hasa solution x Zs at all, then it has one satisfying
For s = 3 and s = 4 no polynomial bounds s(H) were previouslyknown, and for s 5 we have been able to improve existing boundsquite significantly. 2000 Mathematics Subject Classification11D09, 11E20, 11H06, 11P55. 相似文献
227.
We study the relationship of two incidence geometric convexity notions, namely, ovoids in real affine spaces and compact unitals of codimension 1 in topological affine translation planes. In [3] we showed that every ovoid in a translation plane is a unital, and we asked if the converse is true. Here we introduce the notion of a shell, which is distinctly weaker than that of an ovoid and still implies the unital property if the translation plane is properly chosen (and the shell is not too degenerate). We give an explicit example of a shell that is not an ovoid. The question remains whether or not conversely, every compact unital of codimension 1 in a translation plane is a shell.This paper was written while the third author was supported by a grant from DFG and TÜBITAK.Received March 12, 2002
Published online November 18, 2002 相似文献
228.
Valentina?CasarinoEmail author Klaus-Jochen?Engel Rainer?Nagel Gregor?Nickel 《Integral Equations and Operator Theory》2003,47(3):289-306
In this paper we convert a (linear abstract) initial boundary value
problem into an abstract Cauchy problem on some product space and use
semigroup methods to solve it. In particular, we apply spectral theory in
order to discuss stability under boundary feedback. 相似文献
229.
Let φ be a Whitney jet on a closed set F ? ?. By Whitney’s extension theorem φ can be extended to an infinitely differentiable function f on ? which is real analytic on ? F. The main purpose of this article is to show that f can be chosen in such a way that f¦?F has a holomorphic continuation to the open set (? F) × i? ? ?. In the special case that F is a compact interval or a single point we can even achieve that f¦?F has a holomorphic continuation to all of $\hat {\rm C}\setminus F$ . In particular, this implies an improvement of the well-known theorem of E. Borel. We also investigate the question when such extensions are given by a so-called extension operator. 相似文献
230.
Rainer H. Kaenders 《Proceedings of the American Mathematical Society》2001,129(5):1271-1281
Given a compact Riemann surface of genus and distinct points and on , we consider the non-compact Riemann surface with basepoint . The extension of mixed Hodge structures associated to the first two steps of is studied. We show that it determines the element in , where represents the canonical divisor of as well as the corresponding extension associated to . Finally, we deduce a pointed Torelli theorem for punctured Riemann surfaces.