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91.
Ervin Győri 《Combinatorica》1981,1(4):377-380
The problem is the following: How many questions are necessary in the worst case to determine whether a pointX in then-dimensional Euclidean spaceR
n
belongs to then-dimensional unit cubeQ
n, where we are allowed to ask which halfspaces of (n−1)-dimensional hyperplanes contain the pointX? It is known that ⌌3n/2⌍ questions are sufficient. We prove here thatcn questions are necessary, wherec≈1.2938 is the solution of the equationx log2
x−(x−1) log2 (x−1)=1. 相似文献
92.
93.
Jozef Ková und Ervin Sohler 《Fresenius' Journal of Analytical Chemistry》1965,208(3):201-204
Zusammenfassung Es wurde eine photometrische Methode zur Bestimmung von O,O-Dimethyl-O-(3-methyl-4-nitrophenyl)-thiophosphat-RückstÄnden in Obst und Gemüse entwickelt. Hierbei wird der PetrolÄtherextrakt mit Acetonitril ausgeschüttelt; die mitextrahierten Farbstoffe werden nach dem Abdampfen des Acetonitrils durch Dünnschichtchromatographie abgetrennt. Das Insecticid wird aus der Schicht isoliert und nach alkalischer Hydrolyse photometrisch bei 400 nm bestimmt.
Summary A photometric method for the determination of residues of O,O-dimethyl-O-(3-methyl-4-nitrophenyl)-phosphorothioate in fruit and vegetables was developed. In this method a petroleum-ether extract of the plant material is shaken with acetonitrile, the acetonitrile is evaporated and the coloured co-extractives are separated by thin-layer chromatography. The insecticide is isolated and its hydrolytic product determined photometrically at 400 nm.相似文献
94.
Vincent J. Ervin John Paul Roop 《Numerical Methods for Partial Differential Equations》2006,22(3):558-576
In this article a theoretical framework for the Galerkin finite element approximation to the steady state fractional advection dispersion equation is presented. Appropriate fractional derivative spaces are defined and shown to be equivalent to the usual fractional dimension Sobolev spaces Hs. Existence and uniqueness results are proven, and error estimates for the Galerkin approximation derived. Numerical results are included that confirm the theoretical estimates. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
95.
Dorin Ervin Dutkay Deguang Han Palle E.T. Jorgensen 《Journal of Functional Analysis》2009,257(9):2999-3019
We are concerned with an harmonic analysis in Hilbert spaces L2(μ), where μ is a probability measure on . The unifying question is the presence of families of orthogonal (complex) exponentials eλ(x)=exp(2πiλx) in L2(μ). This question in turn is connected to the existence of a natural embedding of L2(μ) into an L2-space of Bohr almost periodic functions on . In particular we explore when L2(μ) contains an orthogonal basis of eλ functions, for λ in a suitable discrete subset in ; i.e, when the measure μ is spectral. We give a new characterization of finite spectral sets in terms of the existence of a group of local translation. We also consider measures μ that arise as fixed points (in the sense of Hutchinson) of iterated function systems (IFSs), and we specialize to the case when the function system in the IFS consists of affine and contractive mappings in . We show in this case that if μ is then assumed spectral then its partitions induced by the IFS at hand have zero overlap measured in μ. This solves part of the Łaba–Wang conjecture. As an application of the new non-overlap result, we solve the spectral-pair problem for Bernoulli convolutions advancing in this way a theorem of Ka-Sing Lau. In addition we present a new perspective on spectral measures and orthogonal Fourier exponentials via the Bohr compactification. 相似文献
96.
V. J. Ervin William J. Layton 《Numerical Methods for Partial Differential Equations》1999,15(1):91-110
We propose and analyze a new relaxation scheme for the iterative solution of the linear system arising from the finite difference discretization of convection–diffusion problems. For problems that are convection dominated, the (nondimensionalized) diffusion parameter ϵ is usually several orders of magnitude smaller than computationally feasible mesh widths. Thus, it is of practical importance that approximation methods not degrade for small ϵ. We give a relaxation procedure that is proven to converge uniformly in ϵ to the solution of the linear algebraic system (i.e., “robustly”). The procedure requires, at each step, the solution of one 4 × 4 linear system per mesh cell. Each 4 × 4 system can be independently solved, and the result communicated to the neighboring mesh cells. Thus, on a mesh connected processor array, the communication requirements are four local communications per iteration per mesh cell. An example is given, which illustrates the robustness of the new relaxation scheme. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 91–110, 1999 相似文献
97.
Presliding and sliding frictional effects, limiting the performances of ultrahigh precision mechatronics devices, are studied in this work. The state-of-the-art related to frictional behavior in both motion regimes is, hence, considered, and the generalized Maxwell-slip (GMS) friction model is adopted to characterize frictional disturbances present in a micromanipulation device. All the parameters of the model are identified via experimental set-ups and included in the overall MATLAB/SIMULINK model. With the aim of compensating frictional effects, the modelled response of the system is thus compared to experimental results when using proportional-integral-derivative (PID) control, feed-forward model-based compensation and a self-tuning adaptive regulator. The adaptive regulator proves to be the most efficient and is, hence, used in the final repetitive point-to-point positioning tests allowing to achieve nanometric precision and accuracy. 相似文献
98.
We investigate convergence properties of generalized Walsh series associated with signals f∈L 1[0,1]. We also show how the dependence of the generalized Walsh bases on N×N unitary matrices allows for applications in signal encoding and encryption, provided the signals are piece-wise constant on N-adic subintervals of [0,1]. 相似文献
99.
100.