In this paper, we consider the ranks of four real matrices Gi(i = 0, 1, 2, 3) in M†, where M = M0 +M1i+M2j+M3k is an arbitrary quaternion matrix, and M† = G0 + G1i + G2j + G3k is the Moore-Penrose inverse of M . Similarly, the ranks of four real matrices in Drazin inverse of a quaternion matrix are also presented. As applications, the necessary and sufficient conditions for M† is pure real or p...

1. Pure natural science and pure psychology. 2. The purely psychical in self experience and community experience. The universal description of intentional experiences. 3. The self contained field of the purely psychical. Phenomenological reduction and true inner experience. 4. Eidetic reduction and phenomenological psychology as an eidetic science. 5. The fundamental function of pure phenomenol...

Solid electrolytes based on doped cerium oxide, Ce(M)O2-δ (M = rare-earth cations), are of considerable interest for potential use in low temperature solid oxide fuel cells (LTSOFCs) due to its higher ionic conductivity than YSZ based solid electrolyte.  In this research work, crystalline, pure Ce1-xMxO2-δ (where M = Gd or Sm, x = 0.10 or 0.20) based nanoparticles were prepared by chemical prec...

In an m 3 m bimatrix game, consider the case where payoffs to each player are randomly 1 2 drawn without replacement, independently of payoffs to the other player, from the set of integers 1,2, . . . ,m m . Thus each player’s payoffs represent ordinal rankings without ties. In such ‘ordinal 1 2 randomly selected’ games, assuming constraints on the relative sizes of m and m and ignoring 1 2 any ...

For a ring R, call a class C of R-modules (pure-) mono-correct if for any M,N ∈ C the existence of (pure) monomorphisms M → N and N → M implies M ' N . Extending results and ideas of Rososhek from rings to modules, it is shown that, for an R-module M , the class σ[M ] of all M -subgenerated modules is mono-correct if and only if M is semisimple, and the class of all weakly M -injective modules ...

We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay. By using new delayed matrix functions and the method variation, we obtain a representation their solutions. As an application, derive finite time stability result solutions norm estimation functions. The obtained results are new, they extend improve some existing ones. Finally, example is pr...