相关论文: Some Ropelength-Critical Clasps
We consider importance sampling as well as other properly weighted samples with respect to a target distribution $\pi$ from a different point of view. By considering the associated weights as sojourn times until the next jump, we define…
We discuss a possible characterization, by means of forbidden configurations, of posets which are embeddable in a product of finitely many scattered chains.
We prove rigorously the convergence of the Cahn-Larch\'e system, which is a Cahn-Hilliard system coupled with the system of linearized elasticity, to a modified Hele-Shaw problem as long as a classical solution of the latter system exists.…
A question relating the critical probability for percolation, the critical probability for a unique infinite cluster and graph limits is presented, together with some partial results.
The problem of fitting concentric ellipses is a vital problem in image processing, pattern recognition, and astronomy. Several methods have been developed but all address very special cases. In this paper, this problem has been investigated…
Following a recent paper by N. Mandache (Inverse Problems 17 (2001), pp. 1435-1444), we establish a general procedure for determining the instability character of inverse problems. We apply this procedure to many elliptic inverse problems…
We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the…
This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the…
This review-style article presents an overview of recent progress in constructing and studying critical Gaussian multiplicative chaos. A proof that the critical measure in any dimension can be obtained as a limit of subcritical measures is…
This paper considers critical points of the length-penalized elastic bending energy among planar curves whose endpoints are fixed. We classify all critical points with an explicit parametrization. The classification strongly depends on a…
In this short note we provide a proof of the importance of the connectedness assumption in the statement of the optimal $p$-compliance problem with length penalization and in the statement of the constrained form of this problem for the…
A model of correlated random networks is examined, i.e. networks with correlations between the degrees of neighboring nodes. These nodes do not necessarily have to be direct neighbors, the maximum range of the correlations can be…
An analytic solution for Bragg grating with linear chirp in the form of confluent hypergeometric functions is analyzed in the asymptotic limit of long grating. Simple formulas for reflection coefficient and group delay are derived. The…
The stability bounds and error estimates for a compact higher order Numerov-Crank-Nicolson scheme on non-uniform space meshes for the 1D time-dependent Schr\"odinger equation have been recently derived. This analysis has been done in $L^2$…
Hyperfinite knots, or limits of equivalence classes of knots induced by a knot invariant taking values in a metric space, were introduced in a previous article by the author. In this article, we present new examples of hyperfinite knots…
A long standing open conjecture states that if a link $\mathcal{K}$ is alternating, then its ropelength $L(\mathcal{K})$ is at least of the order $O(Cr(\mathcal{K}))$. A recent result shows that the maximum braid index of a link bounds the…
In this note, we study the Gehring link problem in the round sphere, which motives our study of the width of a band in positively curved manifolds. Using the same idea, we are able to get a sphere theorem for hypersurface in in the round…
In this paper the number and lengths of minimal length lattice knots confined to slabs of width $L$, is determined. Our data on minimal length verify the results by Sharein et.al. (2011) for the similar problem, expect in a single case,…
We calculate the ground state entanglement entropy between two heterogeneous parts of a free fermion chain. The two parts could be XX chains with different parameters or an XX half chain connected with a quantum Ising half chain. It is…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.