We prove the consistency (modulo supercompact) of a negative answer to the Cantor discontinuum partition problem (i.e., some Hausdorff compact space cannot be partitioned to two sets not containing a closed copy of Cantor discontinuum). In this model we have CH. Without CH we get consistency results using a pcf assumption, close relatives of which are necessary for such results; so we try to de...

This paper raises important questions about the way we approach numerical analysis in rock engineering design. The application of advanced models is essential to adequately analyze and design different geotechnical aspects pit-to-cave transitions. We present a critical review methods centered around hypothesis that model not, cannot be, perfect imitation reality; therefore, modelling large-scal...

Stability analyses are routinely performed in order to assess the safe and functional design of an excavated slope (e.g. open pit mining, road cuts, etc.), and/or the equilibrium conditions of a natural slope. The analysis technique chosen depends on both site conditions and the potential mode of failure, with careful consideration being given to the varying strengths, weaknesses and limitation...

The stability of rock slopes is significance, as even the slightest slope failure can result in damage to infrastructure and catastrophes for human beings. Thus, this article focuses on review current techniques available analysis. be classified conventional methods numerical methods. advantages limitations method are briefly reviewed. mainly included three types, i.e., continuum methods, disco...

We prove the consistency (modulo supercompact) of a negative answer to the Cantor discontinuum partition problem (i.e., some Hausdorff compact space cannot be partitioned to two sets not containing a closed copy of Cantor discontinuum). In this model we have CH. Without CH we get consistency results using a pcf assumption, close relatives of which are necessary for such results; so we try to de...

Set constraints are inclusions between expressions denoting sets of ground terms They have been used extensively in program analysis and type inference In this paper we investigate the topological structure of the spaces of solutions to systems of set constraints We identify a family of topological spaces called rational spaces which formalize the notion of a topological space with a regular or...

It is well known that for all recursively enumerable sets X1, X2 there are disjoint recursively enumerable sets Y1, Y2 such that Y1 c X1, Y2 c X2 and Y1 U Y2 = X1 U X2. Alistair Lachlan called distributive lattices satisfying this property separated. He proved that the first-order theory of finite separated distributive lattices is decidable. We prove here that the first-order theory of all sep...

A combined finite-discrete element method (FDEM) is proposed to model the dynamic fracture, fragmentation, and resultant muck-piling process during mining production by blast in underground mine. The key component of method, that is, transition from continuum discontinuum through fracture introduced detail, which makes superior continuum-based finite discontinuum-based discrete method. FDEM cal...

An infinite binary word can be identified with a branch in the full binary tree. We consider sets of branches definable in monadic second-order logic over the tree, where we allow some extra monadic predicates on the nodes. We show that this class equals to the Boolean combinations of sets in the Borel class Σ 2 over the Cantor discontinuum. Note that the last coincides with the Borel complexit...