Related papers: The two membranes problem in a regular tree
The finite strain theory is reformulated in the frame of the Tangential Differential Calculus (TDC) resulting in a unification in a threefold sense. Firstly, ropes, membranes and three-dimensional continua are treated with one set of…
We establish a generic weak uniqueness result and partial regularity of the free boundary and of minimizers for the composite membrane problem.
We use a bifurcation theory due to Crandall and Rabinowitz to show the existence of a symmetry breaking bifurcation of a specific one parameter family of axially symmetric disc type solutions of a membrane equation with fixed boundary. In…
We consider special cases of the two tree degree sequences problem. We show that if two tree degree sequences do not have common leaves then they always have edge-disjoint caterpillar realizations. By using a probabilistic method, we prove…
This paper studies the effect of boundary value conditions on consensus networks. Consider a network where some nodes keep their estimates constant while other nodes average their estimates with that of their neighbors. We analyze such…
Using a microscopic phase-space model of the membrane system, the boundary condition at a membrane is derived. According to the condition, the substance flow across the membrane is proportional to the difference of the substance…
We present a method of deriving two boundary conditions at a thin membrane for diffusion from experimental data. This method can be really useful in complex membrane systems in which we do not know mechanisms of processes occurring within…
The occurrence and the distribution of patterns of trees associated to natural numbers are investigated. Bounds from above and below are proven for certain natural quantities.
Using the topological membrane approach to string theory, we suggest a geometric origin for the heterotic string. We show how different membrane boundary conditions lead to different string theories. We discuss the construction of closed…
We investigate the recently developed theory of multiple membranes. In particular, we consider open membranes, i.e. the theory defined on a membrane world volume with a boundary. We first restrict our attention to the gauge sector of the…
This paper focuses on the initial- and boundary-value problem for the two-dimensional micropolar equations with only angular velocity dissipation in a smooth bounded domain. The aim here is to establish the global existence and uniqueness…
The boundary value problems for linear and nonlinear singular degenerate differential-operator equations are studied. We prove a well-posedeness of linear problem and optimal regularity result for the nonlinear problem which occur in fluid…
We show NP-completeness for various problems about the existence of arithmetic expression trees. When given a set of operations, inputs, and a target value does there exist an expression tree with those inputs and operations that evaluates…
The cellular tree classifier model addresses a fundamental problem in the design of classifiers for a parallel or distributed computing world: Given a data set, is it sufficient to apply a majority rule for classification, or shall one…
We study protected nodes in $m$-ary search trees, by putting them in context of generalised P\'olya urns. We show that the number of two-protected nodes (the nodes that are neither leaves nor parents of leaves) in a random ternary search…
In this paper we introduce a variation on the multidimensional segment tree, formed by unifying different interpretations of the dimensionalities of the data structure. We give some new definitions to previously well-defined concepts that…
The discrete membrane model is a Gaussian random interface whose inverse covariance is given by the discrete biharmonic operator on a graph. In literature almost all works have considered the field as indexed over $\mathbb{Z}^d$, and this…
The many-normal-means problem is a classic example that motivates the development of many important inferential procedures in the history of statistics. In this short note, we consider a further special case of the problem, which involves…
This is a continuation of the paper 'Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes' by S. Chanillo, D. Grieser, M. Imai, K. Kurata, and I. Ohnishi. Again, we consider the following…
Inspired by the numerical immersed boundary method, we introduce regularized Stokes immersed boundary problems in two dimensions to describe regularized motion of a 1-D closed elastic string in a 2-D Stokes flow, in which a regularized…