90,823 research outputs found
Rigidity of infinite disk patterns
Let P be a locally finite disk pattern on the complex plane C whose
combinatorics are described by the one-skeleton G of a triangulation of the
open topological disk and whose dihedral angles are equal to a function
\Theta:E\to [0,\pi/2] on the set of edges. Let P^* be a combinatorially
equivalent disk pattern on the plane with the same dihedral angle function. We
show that P and P^* differ only by a euclidean similarity.
In particular, when the dihedral angle function \Theta is identically zero,
this yields the rigidity theorems of B. Rodin and D. Sullivan, and of O.
Schramm, whose arguments rely essentially on the pairwise disjointness of the
interiors of the disks. The approach here is analytical, and uses the maximum
principle, the concept of vertex extremal length, and the recurrency of a
family of electrical networks obtained by placing resistors on the edges in the
contact graph of the pattern.
A similar rigidity property holds for locally finite disk patterns in the
hyperbolic plane, where the proof follows by a simple use of the maximum
principle. Also, we have a uniformization result for disk patterns.
In a future paper, the techniques of this paper will be extended to the case
when 0 \le \Theta < \pi. In particular, we will show a rigidity property for a
class of infinite convex polyhedra in the 3-dimensional hyperbolic space.Comment: 33 pages, published versio
Variations in radiocarbon ages of various organic fractions in core sediments from Erhai Lake, SW China
Radiocarbon dating was performed for the extracted organic fractions (cellulose-rich and humic acid fractions of plant fragment; fulvic acid, humic acid and humin fractions of humus substance) and shell from core sediments of the Erhai Lake, SW China. The C-14 dating results reveal that there are considerable differences, but there apparently is a humic acid less than or equal to humin < fulvic acid fraction sequence of C-14 age increase. The variability in radiocarbon ages of organic fraction of lake sediment suggests that special caution is necessary when radiocarbon ages of bulk sediments are used.
The linear correlation between C-14 age of allochthonous terrestrial macrofossil (plant fragment and shell) and depth indicates roughly a constant sedimentation rate of ca. 0.7 rum yr(-1) in central Erhai Lake since 4500 yr BP. The C-14 ages of the autochthonous humic acid fraction are 210similar to4800 yr shift from "the true C-14 age" obtained by interpolating the corresponding horizontal level to the above C-14 age-depth correlation. Such age difference may be alternatively attributed to a uniform reservoir effect (most likely ca. 300 yr). The period with large C-14 age shift synchronizes with the period of changes in (delta(13)C and ARM intensity and ARM/susceptibility values
Basket Options Valuation for a Local Volatility Jump-Diffusion Model with the Asymptotic Expansion Method
In this paper we discuss the basket options valuation for a jump-diffusion
model. The underlying asset prices follow some correlated local volatility
diffusion processes with systematic jumps. We derive a forward partial integral
differential equation (PIDE) for general stochastic processes and use the
asymptotic expansion method to approximate the conditional expectation of the
stochastic variance associated with the basket value process. The numerical
tests show that the suggested method is fast and accurate in comparison with
the Monte Carlo and other methods in most cases.Comment: 16 pages, 4 table
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