Matroidal Entropy Functions: A Quartet of Theories of Information, Matroid, Design and Coding

In this paper, we study the entropy functions on extreme rays of the polymatroidal region which contain a matroid, i.e., matroidal entropy functions. We introduce variable strength orthogonal arrays indexed by a connected matroid M and positive integer v which can be regarded as expanding the classic combinatorial structure orthogonal arrays. It is interesting that they are equivalent to the partition-representations of the matroid M with degree v and the (M,v) almost affine codes. Thus, a synergy among four fields, i.e., information theory, matroid theory, combinatorial design, and coding theory is developed, which may lead to potential applications in information problems such as network coding and secret-sharing. Leveraging the construction of variable strength orthogonal arrays, we characterize all matroidal entropy functions of order n≤5 with the exception of log10·U2,5 and logv·U3,5 for some v.

Understanding deformation of cratons in presence of mid-lithospheric discontinuity

<p>The recent discovery of mid-lithospheric discontinuity (MLD) within most cratons has added a new dimension in the understanding of cratonic survival. The MLD shows up as a seismic discontinuity at ~80-160 km depth. However, there is controversy regarding the strength of this layer. While some studies suggest that this layer is as strong as the craton itself, others advocate that under some special conditions (e.g. metasomatism) MLD can become weak and aid in the delamination of cratons. In this study, we develop 3-D full spherical mantle convection models to understand the effect of MLD in the survival of cratons. In our models, we incorporate MLDs of variable strength, depth and thickness. Along with varying the strength of MLDs, we use different combinations of craton and asthenosphere viscosity to quantitatively estimate how deformation pattern varies. Results obtained from the models suggest that in the presence of a weak MLD stress magnitudes decrease but strain-rates increase  ~2-3 times. This could potentially lead to delamination of cratons. To constrain the present-day strength of MLDs, we predict deviatoric stresses from these different models and compare them to the observed SH<sub>max</sub> directions obtained from the World Stress Map. The deviatoric stress pattern changes as the viscosity, depth and thickness of MLD changes.</p>

CONCEPT OF A SEGMENTED PENETRATOR MADE OF TUNGSTEN HEAVY ALLOYS WITH VARIABLE STRENGTH PARAMETERS

The paper describes a concept of increasing the penetration capacities of kinetic antitank projectiles, having a penetrator made of a tungsten based sinter, through the application of materials with variable mechanical characteristics for penetrator’s particular segments. The influence of alloy additions on some strength parameters for the tung-sten based sinters were assessed by using the literature data, and in the next step by numerical analyses of steel plate penetration process calculated for selected configurations of structural materials of penetrator segments. The summary describes some possibilities for modification of the structure of tungsten based sinters which may decisively improve the penetrating capacities.