This paper presents solutions of some selected problems that can be easily solved by the projective space representation. If the principle of duality is used, quite surprising solutions can be found and new useful theorems can be generated as well. There are many algorithms based on computation of intersection of lines, planes, barycentric coordinates etc. Those algorithms are based on represen...

We construct a homogeneous subspace of 2ω whose complement is dense in 2ω and rigid. Using the same method, assuming Martin’s Axiom, we also construct a countable dense homogeneous subspace of 2ω whose complement is dense in 2ω and rigid.

It is well known that no infinite homogeneous space is both compact and extremally disconnected. (Since there are infinite compact homogeneous spaces and infinite extremally disconnected homogeneous spaces, it is the combination of compactness and extremal disconnectedness that brings about this result.) The following question then arises naturally: How “close to compact” can a homogeneous, ext...

Consider a closed manifold M immersed in Rm. Suppose that the trivial bundle M × Rm = TM ⊗ νM is equipped with an almost metric connection ∇̃ which almost preserves the decomposition of M × Rm into the tangent and the normal bundle. Assume moreover that the difference Γ = ∂ − ∇̃ with the usual derivative ∂ in Rm is almost ∇̃-parallel. Then M admits an extrinsically homogeneous immersion into Rm.

The advance in the global environment, rapidly changing markets, and information technology has created a new stage for design. In such an environment, one strategy for success is the Collaborative Product Development (CPD). Organizing people effectively is the goal of Collaborative Product Development, and it solves the problem with certain foreseeability. The development group activities are ...

Vibration behavior of different types of porous functionally graded (FG) conical sandwich shells are investigated based on a modified high order sandwich shells theory for the first time. Sandwich shell includes FG face sheets covering a homogeneous core and the second one includes homogeneous face sheets and a FG core. Power law rule modified by considering two types of porosity distributions ...

What happens to the entropy increase principle as the Universe evolve to form the bigcrunch singularity? What happens to the uncertainity relations along the process of gravitational collapses? What is the quantum mechanical description of a Radon atom in a rigid box when the distance of consecutive nodes and antinodes of ψ is equal to or less than the diameter of the atom? What is the position...

What happens to the entropy increase principle as the Universe evolve to form the big-crunch singularity? What happens to the uncertainity relations along the process of grav-itational collapses? What is the quantum mechanical description of a Radon atom in a rigid box when the distance of consecutive nodes and antinodes of ψ is equal to or less than the diameter of the atom? What is the positi...

What happens to the entropy increase principle as the Universe evolve to form the big-crunch singularity? What happens to the uncertainity relations along the process of grav-itational collapses? What is the quantum mechanical description of a Radon atom in a rigid box when the distance of consecutive nodes and antinodes of ψ is equal to or less than the diameter of the atom? What is the positi...