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...

By minimizing free energy density, we show that the stellar core of a hydrogen burning star is not in a global thermodynamical equilibrium unless density, temperature, mass and composition assume given values. The core (as the solar interior) may be viewed more appropriately as a metastable state with very long lifetime. Slightly non-extensive distribution function could be the natural distribu...

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuri...

In this paper, an anisotropic nonlinear diffusion equation for image restoration is presented. The model has two terms: the diffusion and the forcing term. The balance between these terms is made in a selective way, in which boundary points and interior points of the objects that make up the image are treated differently. The optimal smoothing time concept, which allows for finding the ideal st...

Let M be the interior of a compact, orientable 3–manifold with non-empty boundary a disjoint union of tori, and T be an ideal triangulation of M . The affine algebraic set D(M ; T ), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T , is defined and compactified by adding projective classes of transversely measured singular codimension–one foliations of (M...

in this paper, we introduce a new generalization of weakly prime ideals called $i$-prime. suppose $r$ is a commutative ring with identity and $i$ a fixed ideal of $r$. a proper ideal $p$ of $r$ is $i$-prime if for $a, b in r$ with $ab in p-ip$ implies either $a in p$ or $b in p$. we give some characterizations of $i$-prime ideals and study some of its properties.  moreover, we give conditions  ...

The anterior maxilla presents a challenging milieu interior for ideal placement of implants because of the compromised bone quality. With the advent of intraoral bone harvesting and augmentation techniques, immediate implant placement into fresh extraction sockets have become more predictable. Immediate implant placement has numerous advantages compared to the delayed procedure including superi...

A two-dimensional unstructured elliptic smoothing method is described where the Winslow equations are discretized using a finite volume approach. Virtual control volumes for each node are constructed with element shapes that are nearly ideal. Green-Gauss theorem is used to formulate gradients over an element or a collection of elements for a node, which ultimately leads to a coupled non-linear ...

The properties of hydrogen-helium mixtures at high pressure are crucial to address important questions about the interior of Giant planets e.g. whether Jupiter has a rocky core and did it emerge via core accretion? Using path integral Monte Carlo simulations, we study the properties of these mixtures as a function of temperature, density and composition. The equation of state is calculated and ...

Let M be the interior of a compact 3–manifold with boundary, and let T be an ideal triangulation of M. This paper describes necessary and sufficient conditions for the existence of angle structures, semi–angle structures and generalised angle structures on (M ;T ) respectively in terms of a generalised Euler characteristic function on the solution space of the normal surface theory of (M ; T )....