We analyze the eeects of random local linker length variability on the global morphology of a very long, linear, homogeneous chromatin ber that is modelled as a diiusion process that is parametrized by arclength under a suitable spatial re-scaling. We obtain Fokker-Planck equation for the process whose solution, a probability density function describes the folding.

1. A comparison theorem for complete Riemannian manifolds with sectional curvatures ≥ k says that distance functions in such manifolds are more concave than in the model space Sk of constant curvature k. In other words, the restriction of any distance function distp to any geodesic γ (always parametrised by the arclength) satisfies a certain concavity condition (∗)k. For example, the condition ...

This paper proves that classical minimal surfaces of arbitrary topological type with total boundary curvature at most 4 must be smoothly embedded. Related results are proved for varifolds and for soap lm surfaces. In a celebrated paper N3] of 1973, Nitsche proved that if ? is an analytic simple closed curve in R 3 with total curvature at most 4, then ? bounds exactly one minimal disk M. Further...

the aim of this paper is to generalize the‎‎notion of pseudo-almost valuation domains to arbitrary‎ ‎commutative rings‎. ‎it is shown that the classes of chained rings‎ ‎and pseudo-valuation rings are properly contained in the class of‎ ‎pseudo-almost valuation rings; also the class of pseudo-almost‎ ‎valuation rings is properly contained in the class of quasi-local‎ ‎rings with linearly ordere...

in this paper, some results of the chebyshev type integral inequality for the pseudo-integral are proven. the obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. finally, we applied our results  to the case of comonotone functions.

Some Definitions and Notations. In this section α : [0, L] → R will denote a curve in R that is parametrized by arclength and is of class C, k ≥ 2. We recall that the unit tangent to α at s is defined by −→t (s) := α′(s). (That it is a unit vector is just the definition of α being parametrized by arclength.) The curvature of α is the non-negative real-valued function k : [0, L] → R defined by k...

Correspondence: youngwoo@ajou. ac.kr Department of Mathematics, Ajou University, Suwon 443-749, South Korea Abstract Based on a uniform estimate of convolution operators with measures on a family of plane curves, we obtain optimal L-L boundedness of convolution operators with affine arclength measures supported on space curves satisfying a suitable condition. The result generalizes the previous...

Hydrostatically pressurized circular rings confined to two dimensions (or cylinders constrained to have only z -independent deformations) undergo Euler-type buckling when the outside pressure exceeds a critical value. We perform a stability analysis of rings with arclength-dependent bending moduli and determine how weakened bending modulus segments affect the buckling critical pressure. Rings w...