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81.
82.
A self-avoiding polygon (SAP) on a graph is an elementary cycle. Counting SAPs on the hypercubic lattice ℤ
d
withd≥2, is a well-known unsolved problem, which is studied both for its combinatorial and probabilistic interest and its connections
with statistical mechanics. Of course, polygons on ℤ
d
are defined up to a translation, and the relevant statistic is their perimeter.
A SAP on ℤ
d
is said to beconvex if its perimeter is “minimal”, that is, is exactly twice the sum of the side lengths of the smallest hyper-rectangle containing
it. In 1984, Delest and Viennot enumerated convex SAPs on the square lattice [6], but no result was available in a higher
dimension.
We present an elementar approach to enumerate convex SAPs in any dimension. We first obtain a new proof of Delest and Viennot's
result, which explains combinatorially the form of the generating function. We then compute the generating function for convex
SAPs on the cubic lattice. In a dimension larger than 3, the details of the calculations become very cumbersome. However,
our method suggests that the generating function for convex SAPs on ℤ
d
is always a quotient ofdifferentiably finite power series. 相似文献
83.
84.
Sans résumé
相似文献
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85.
Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4]. 相似文献
86.
The main aim of this paper is the calculation of the dimension of certain atomic amalgams. These consist of finite Boolean algebras (blocks) pasted together in such a way that a pair of blocks intersects either trivially in the bounds, or the intersection consists of the bounds, an atom, and its complement. 相似文献
87.
The stability of Ochratoxin A during its extraction using different extraction techniques has been evaluated. Microwave-assisted extraction and pressurised liquid extraction, in addition to two other reference methods of extraction, i.e. ultrasound-assisted and magnetic stirring-assisted extraction, were evaluated. The effect of extraction temperature using the cited techniques was checked.The results show that Ochratoxin A can be extracted using microwave-assisted extraction at temperatures up to 150 °C without degradation. Pressurised liquid extraction can be used at temperatures up to 100 °C, for extraction times of less than 30 min. Further, both ultrasound-assisted extraction and magnetic stirring extraction can be applied at temperatures up to 65 °C.High-performance liquid chromatography combined with fluorescence detection using a Chromolith RP-18e column at a flow rate of 5 mL min−1 was used to quantify the Ochratoxin A. The retention time for the Ochratoxin A was 1.3 min. The limits of detection (LOD) and of quantification (LOQ) were 0.03 and 0.10 μg L−1, respectively. 相似文献
88.
Let Λ be a smooth Lagrangian submanifold of a complex symplectic manifold X. We construct twisted simple holonomic modules along Λ in the stack of deformation-quantization modules on X. 相似文献
89.
Helly and Hadwiger type theorems for transversal m-flats to families of flats and, respectively, convex sets of dimension n are proved in the case of general position. The proofs rely on Helly type theorems for “linear partitions” and “convex partitions,” so that a general theory of Helly numbers is also developed. 相似文献
90.
Lévy processes in matrix Lie groups are studied. Subordination (random time change) is used to show that quasi-invariance of the Brownian motion in a Lie group induces absolute continuity of the laws of the corresponding pure jump processes. These results are applied to several examples which are discussed in detail. 相似文献