in an earlier work we showed that for ordered fields f not isomorphic to the reals r, there are continuous 1-1 unctions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 func...

In this paper, we propose a model for active contours to detect boundaries’ objects in given image. The curve evolution is based on Chan-Vese model implemented via binary variational level set formulation. The particularity of this model is the capacity to detect boundaries’ objects without need to use gradient of the image, this property gives its several advantages: it allows to detect both c...

Mechanical phenotyping of single cells is an emerging tool for cell classification, enabling assessment of effective parameters relating to cells' interior molecular content and structure. Here, we present iso-acoustic focusing, an equilibrium method to analyze the effective acoustic impedance of single cells in continuous flow. While flowing through a microchannel, cells migrate sideways, infl...

A ray-theoretic account of the passage of light through a radially inhomogeneous transparent sphere has been used to establish the existence of multiple primary rainbows for some refractive index profiles. The existence of such additional bows is a consequence of a sufficiently attractive potential in the interior of the drop, i.e., the refractive index gradient should be sufficiently negative ...

We prove the existence of globally injective weak solutions in mixed boundary-value problems of second-gradient nonlinear elastostatics via energy minimization. This entails the treatment of self-contact. In accordance with the classical (first-gradient) theory, the model incorporates the unbounded growth of the potential energy density as the local volume ratio approaches zero. We work in a cl...

In this paper, we study a gradient based method for general cone programming (CP) problems. In particular, we first consider four natural primal-dual convex smooth minimization reformulations for them, and then discuss a variant of Nesterov’s smooth (VNS) method recently proposed by Auslender and Teboulle [1] for solving these reformulations. The associated worst-case major arithmetic operation...

A typical example of the quadratic assignment problem (QAP) is the facility location problem, in which a set of n facilities are to be assigned, at minimum cost, to an equal number of locations. Between each pair of facilities, there is a given amount of flow, contributing a cost equal to the product of the flow and the distance between locations to which the facilities are assigned. Proving op...

The constant-density Charney model describes the simplest unstable basic state with a planetary-vorticity gradient, which is uniform and positive, and baroclinicity that is manifest as a negative contribution to the potential-vorticity (PV) gradient at the ground and positive vertical wind shear. Together, these ingredients satisfy the necessary conditions for baroclinic instability. In Part I ...

One of the most efficient interior-point methods for some classes of block-angular structured problems solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for, respectively, the block and linking constraints. In this work we show that the choice of a good preconditioner depends on geometrical properties of the constraints structure. In p...

We examine the tectonic geomorphology of La Sila, Calabria, southern Italy, a high-standing (1500 m) plateau surrounded by crustal extension, with map, DEM, and field data. These data are used to constrain a simple geodynamic model that describes short-wavelength deformation of the plateau rim. Topographic metrics including drainage patterns, river longitudinal profiles, and swath profiles are ...