Operations of cubic soft sets including "AND" operation and "OR" operation based on P-orders and R-orders are introduced and some related properties are investigated. An example is presented to show that the R-union of two internal cubic soft sets might not be internal. A sufficient condition is provided, which ensure that the R-union of two internal cubic soft sets is also internal. Moreover, ...

Since fluctuations can be magnified due to internal interactions under a certain condition, the equal-probability does not hold. The entropy would be defined as ∑ − = r r r t P t P k t S ) ( ln ) ( ) ( . From this or Ω = ln k S in an internal condensed process, possible decrease of entropy is calculated. Internal interactions, which bring about inapplicability of the statistical independence, c...

This paper extends the analysis of the choice between internal and external R&D to consider the costs of internal R&D. The underlying hypothesis is that the choice of R&D mode is determined by their relative costs. Rather than merely estimating a reduced form probit model for R&D mode, we employ the Heckman two-stage estimator to estimate in addition the determinants of internal R&D unit cost (...

We prove the following main theorem of the theory of (r, q)-polycycles. Suppose a nonseparable plane graph satisfies the following two conditions: (1) each internal face is an r-gon, where r ≥ 3 ; (2) the degree of each internal vertex is q , where q ≥ 3 , and the degree of each boundary vertex is at most q and at least 2 . Then it also possesses the following third property: (3) the vertices, ...