This paper discusses two combinatorial problems in stability theory. First we prove a partition result for subsets of stable models: for any A and B, we can partition A into |B | ) pieces, 〈Ai | i < |B | 〉, such that for each Ai there is a Bi ⊆ B where |Bi| < κ(T ) and Ai |̂ Bi B. Second, if A and B are as above and |A | > |B |, then we try to find A′ ⊂ A and B′ ⊂ B such that |A′| is as large as...

This paper presents a comparative study on the application of different numerical methods for the solution of the dynamic bi-variate population balance equation (PBE) in batch particulate systems. Specifically, particulate processes operating under the combined action of particle aggregation and/or particle growth are examined. In order to solve the bi-variate PBE the Galerkin finite element me...

The influence of both photochromic doping and photochromic transitions on the effect of magnetooptical rotation (Farady effect FE) of undoped and doped with Cr, Mn and Cu Bi 12 SiO 20 (BSO) and Bi 12 TiO 20 (BTO) crystals is studied. The present results show, that Cr, Mn and Cu increase the FE. The influence of Cr, whose affect on the optical activity (OA) of BSO is most significant, here is to...

Bi-stable mechanisms can remain in two positions without a power input or locking system. These achieve large displacements with low energy, requiring only during switching. However, their design and analysis are challenging due to the non-linear behavior of flexible members. Researchers commonly use experimental approaches study validate bi-stability, which demands efficient affordable setups....

The structural, mechanical, electronic, and optical characteristics of Alkali chalcogenide oxychalcogenides, i.e., A2O2B2Se3 (A = Sr, Ba; B Bi, Sb), were investigated using density functional theory (DFT). After full relaxation, the obtained structural parameters are in good agreement with experimental parameters. Furthermore, calculated elastic stiffness Cij shows that all studied compounds fo...