We study interior operators and interior structures in a fuzzy setting.We investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.

Abstract In this paper, we analyze some properties of a sixth-order elliptic operator arising in the framework strain gradient linear elasticity theory for nanoplates flexural deformation. We first rigorously deduce weak formulation underlying Neumann problem as well its posedness. Under suitable smoothness assumptions on coefficients and geometry, derive interior boundary regularity estimates ...

Logistic regression with l1 regularization has been proposed as a promising method for feature selection in classification problems. Several specialized solution methods have been proposed for l1-regularized logistic regression problems (LRPs). However, existing methods do not scale well to large problems that arise in many practical settings. In this paper we describe an efficient interior-poi...

Self-concordant functions are a special class of convex functions in Euclidean space introduced by Nesterov. They are used in interior point methods, based on Newton iterations, where they play an important role in solving efficiently certain constrained optimization problems. The concept of self-concordant functions has been defined on Riemannian manifolds by Jiang et al. and a damped Newton m...

Bicoid (Bcd) protein distributes in a concentration gradient that organizes the anterior/ posterior axis of the Drosophila embryo. It has been understood that bcd RNA is sequestered at the anterior pole during oogenesis, is not translated until fertilization, and produces a protein gradient that functions in the syncytial blastoderm after 9–10 nuclear divisions. However, technical issues limite...

Bicoid (Bcd) protein distributes in a concentration gradient that organizes the anterior/posterior axis of the Drosophila embryo. It has been understood that bcd RNA is sequestered at the anterior pole during oogenesis, is not translated until fertilization, and produces a protein gradient that functions in the syncytial blastoderm after 9-10 nuclear divisions. However, technical issues limited...

The white rot fungus, Phanerochaete chrysosporium, is one of the few organisms with documented ability to degrade lignin. Protoplasts from P. chrysosporium were disrupted by osmotic shock and membrane vesicles were isolated from the cell debris. The vesicles exhibit active glucose transport that is consistent with a glucose/H+ symport mechanism. An artificial gradient of H+ (outside greater tha...

A continuous interior penalty hp-finite element method that penalizes the jump of the gradient of the discrete solution across mesh interfaces is introduced. Error estimates are obtained for advection and advection-diffusion equations. The analysis relies on three technical results that are of independent interest: an hp-inverse trace inequality, a local discontinuous to continuous hp-interpola...

In this work, a recovery technique for the intermediate nite element family of the second type is proposed and analyzed on a second-order elliptic model problem. It is shown that when the pollution error is properly controlled, the convergent rate of the recovered gradient is of two orders higher than the optimal global rate on an interior sub-domain where rectangular meshes of regular type are...

For stationary harmonic maps between Riemannian manifolds, we provide a necessary and sufficient condition for the uniform interior and boundary gradient estimates in terms of the total energy of maps. We also show that if analytic target manifolds do not carry any harmonic S2, then the singular sets of stationary maps are m ≤ n− 4 rectifiable. Both of these results follow from a general analys...