Abstract:
this article explores several territorial dynamics, based on their symbolic and social importance. it asks for the role the sacred plays in the construction of the territory and the ways in which, from this starting point, a set of associations and belongings to a determined group is created. to this end, the work studies several places that are considered sacred inside gotshezhi, a wiwa village located in the lower river basin of the guachaca river, in the northeast of the sierra nevada of santa martha.

Abstract:
Hepatic encephalopathy is a frequent and serious complication of liver cirrhosis; the pathophysiology of this complication is not fully understood although great efforts have been made during the last years. There are few prospective studies on the epidemiology of this complication; however, it is known that it confers with high short-term mortality. Hepatic encephalopathy has been classified into different groups depending on the degree of hepatic dysfunction, the presence of portal-systemic shunts, and the number of episodes. Due to the large clinical spectra of overt EH and the complexity of cirrhotic patients, it is very difficult to perform quality clinical trials for assessing the efficacy of the treatments proposed. The physiopathology, clinical manifestation, and the treatment of HE is a challenge because of the multiple factors that converge and coexist in an episode of overt HE. 1. Introduction Hepatic encephalopathy (HE) is a disturbance in the central nervous system (CNS) function due to hepatic insufficiency or portal-systemic shunting. HE causes a spectrum of neurologic manifestations that develop in association with different liver diseases [1]. A common link is the potential reversibility of the neurologic manifestations once the abnormality of liver function is corrected. The shunting of blood from the portal venous bed into the systemic circulation is considered a key element of HE. There are a series of neurological disorders associated with liver disease that are not considered HE. This disorders may share a common pathogenetic mechanism, for example, brain and liver damage caused by alcohol or copper (Wilson’s disease). HE must also be differentiated from neurologic disturbances caused directly by bilirubin accumulation (kernicterus), cerebral hemorrhage secondary to disorders of coagulation caused by the liver disease, or other abnormalities that are not secondary to liver failure. The nomenclature that several authors have used for HE is confusing. For this reason several efforts have been made to reach a consensus, especially for the design of clinical trials [2]. Despite this limitation, from a clinical perspective, HE is generally classified according to the underlying liver disease and the evolution of the neurological manifestations (Table 1). The most frequent liver disease is cirrhosis, usually accompanied by extrahepatic portal-systemic shunts (spontaneous or surgical). HE also can be seen in acute liver failure, where it constitutes the hallmark of the disease. In rare cases, HE develops in the absence of any sign of

Abstract:
The problem we are concerned with is whether singularities form in finite time in incompressible fluid flows. It is well known that the answer is ``no'' in the case of Euler and Navier-Stokes equations in dimension two. In dimension three it is still an open problem for these equations. In this paper we focus on a two-dimensional active scalar model for the 3D Euler vorticity equation. Constantin, Majda and Tabak suggested, by studying rigorous theorems and detailed numerical experiments, a general principle: ``If the level set topology in the temperature field for the 2D quasi-geostrophic active scalar in the region of strong scalar gradients does not contain a hyperbolic saddle, then no finite time singularity is possible.'' Numerical simulations showed evidence of singular behavior when the geometry of the level sets of the active scalar contain a hyperbolic saddle. There is a naturally associated notion of simple hyperbolic saddle breakdown. The main theorem we present in this paper shows that such breakdown cannot occur in finite time. We also show that the angle of the saddle cannot close in finite time and it cannot be faster than a double exponential in time. Using the same techniques, we see that analogous results hold for incompressible 2D and 3D Euler.

Abstract:
We study a 1D transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the finite time singularity is prevented and the solutions exist globally in time.

Abstract:
We study the dynamics of the interface between two incompressible 2-D flows where the evolution equation is obtained from Darcy's law. The free boundary is given by the discontinuity among the densities and viscosities of the fluids. This physical scenario is known as the two dimensional Muskat problem or the two-phase Hele-Shaw flow. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in the normal direction has the proper sign, an assumption which is also known as the Rayleigh-Taylor condition.

Abstract:
We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in the normal direction has the proper sign, an assumption which is also known as the Rayleigh-Taylor condition. The well-posedness of the full water wave problem was first obtained by Wu \cite{Wu}. The methods introduced in this paper allows us to consider multiple cases: with or without gravity, but also a closed boundary or a periodic boundary with the fluids placed above and below it. It is assumed that the initial interface does not touch itself, being a part of the evolution problem to check that such property prevails for a short time, as well as it does the Rayleigh-Taylor condition, depending conveniently upon the initial data. The addition of the pressure equality to the contour dynamic equations is obtained as a mathematical consequence, and not as a physical assumption, from the mere fact that we are dealing with weak solutions of Euler's equation in the whole space.

Abstract:
The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3-D the relevance of the Rayleigh-Taylor condition, and the topology of the initial interface, in order to prove its local existence in Sobolev spaces.

Abstract:
Se desarrolla un modelo matem′atico para analizar el auto confinamiento de un haz de forma cuadrada, propag′andose a lo largo entre la frontera entre un cristal fotorefractivo en contacto con un metal ideal. Se muestra que el haz es auto-deflectado y que puede ser balanceado por la reflexi′on interna en la superficie interna del cristal photorefractivo, resultando en la formaci′on de la onda superficial. Se da evidencia te′orica.

Abstract:
We present the exact solution to the non linear Monge differential equation lambda(x, t)lambdax(x, t) = lambdat(x, t). It is widely accepted that the Monge equation is equivalent to the ODE d2X/dt2= 0 of free motion for particular conditions. Furthermore, the Monge Type equations are connected with X = F(dX/dt, X; t), which can be integrated with quadratures [1]. Other asymptotic solutions are discussed, see e.g. [2]. The solution was reached with calculations that depend upon dimensional representation, which is given by (x, t) coordinates. We present this analytical solution to the Monge differential equation as an implicit solution.

Abstract:
We consider the fluid interface problem given by two incompressible fluids with different densities evolving by Darcy's law. This scenario is known as the Muskat problem for fluids with the same viscosities, being in two dimensions mathematically analogous to the two-phase Hele-Shaw cell. We prove in the stable case (the denser fluid is below) a maximum principle for the $L^\infty$ norm of the free boundary.