We present a survey of our recent work on generalized triangle inequalities in infinitesimal symmetric spaces, nonpositively curved symmetric spaces and Euclidean buildings. We also explain how these results can be used to analyze some basic problems of algebraic group theory including the problem of decomposition of tensor products of irreducible representations of complex reductive Lie groups...

A hypothesis is introduced under which a compact complex analytic space, X, viewed as a structure in the language of analytic sets, is essentially saturated. It is shown that this condition is met exactly when the irreducible components of the restricted Douady spaces of all the cartesian powers of X are compact. Some implications of saturation on Kähler-type spaces, which by a theorem of Fujik...

Let Detn denote the closure of the GLn2(C)-orbit of the determinant polynomial detn with respect to linear substitution. The highest weights (partitions) of irreducible GL n 2(C)-representations occurring in the coordinate ring of Detn form a finitely generated monoid S(Detn). We prove that the saturation of S(Detn) contains all partitions λ with length at most n and size divisible by n. This i...

[1] A Shan-Chen–type multiphase lattice Boltzmann (LB) model was applied to observed computed microtomography data from water-air and water-Soltrol displacement experiments in a glass bead porous medium. Analysis of the Bond, Reynolds, and Capillary numbers for these systems showed that capillary forces were dominant removing the need to model viscous, gravitational, and density effects. A nume...

in this work the likelihood of asphaltene deposition problems during dynamic displacement of oil by natural gas in unconsolidated porous media is experimentally inspected. the two different rock materials, limestone and sandstone, are used as a representative of porous media. dynamic flow experiments indicate that the increase of natural gas injection increases asphaltene deposition in the unco...

Microcracks are the main seepage channels and reservoir space for oil gas in dense sandstone reservoirs, degree of development dominates reservoir’s high stable production capacity. A new method has been devised to address lack quantitative identification characterization methods microcrack networks. The is based on core stress sensitivity, permeability anisotropy, two-phase rule testing. By im...

In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.