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, ...

We establish that every cyclically 4-connected cubic planar graph of order at most 40 is hamiltonian. Furthermore, this bound is determined to be sharp and we present all nonhamiltonian such graphs of order 42. In addition we list all nonhamiltonian cyclically 5-connected cubic planar graphs of order at most 52 and all nonhamiltonian 3-connected cubic planar graphs of girth 5 on at most 46 vert...

In this paper a piece of a conic section is approximated by a cubic or piecewise cubic polynomial. The main tool is to define the two inner control points of the cubic as an affine combination, defined by λ ∈ [0, 1], of two control points of the conic. If λ is taken to depend on the weight w of the latter, a function λ(w) results which is used to distinguish between different algorithms and to ...

In this study, we presented the concept of neutrosophic cubic set by extending the concept of cubic set to neutrosophic set. We also defined internal neutrosophic cubic set (INCS) and external neutrosophic cubic set (ENCS). Then, we proposed some new type of INCS and ENCS is called 1 3 -INCS (or 2 3 -ENCS ), 2 3 -INCS(or 1 3 -ENCS). Then we study some of their relevant properties. Finally, we i...

Jorgensen, L.K., Nonexistence of certain cubic graphs with small diameters, Discrete Mathematics 114 (1993) 2655273. We consider the maximum number of vertices in a cubic graph with small diameter. We show that a cubic graph of diameter 4 has at most 40 vertices. (The Moore bound is 46 and graphs with 38 vertices are known.) We also consider bipartite cubic graphs of diameter 5, for which the M...

In a previous paper analytical equations were derived for the packing fraction of crystalline structures consisting of bimodal randomly placed hard spheres [H. J. H. Brouwers, Phys. Rev. E 76, 041304 (2007)]. The bimodal packing fraction was derived for the three crystalline cubic systems: viz., face-centered cubic, body-centered cubic, and simple cubic. These three equations appeared also to b...

In 1954, Tutte conjectured that every bridgeless graph has a nowherezero 5-flow. Let ω be the minimum number of odd cycles in a 2-factor of a bridgeless cubic graph. Tutte’s conjecture is equivalent to its restriction to cubic graphs with ω ≥ 2. We show that if a cubic graph G has no edge cut with fewer than 5 2ω − 1 edges that separates two odd cycles of a minimum 2-factor of G, then G has a n...

We establish some stability results concerning the general cubic functional equation f(x+ ky)− kf(x+ y) + kf(x− y)− f(x− ky) = 2k(k − 1)f(y) for fixed k ∈ N\{1} in the fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately cubic function can be approximated by a cubic mapping in a fuzzy sense and we establish that the existence of a solution for any ap...

In this study we produced a new method for solving regular differential equations with step size h and Taylor series. This method analyzes a regular differential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coeffcients and cubic and second-level equations.

3/— Abstract. To calculate R, the regulator of a pure cubic field Q(\Jd), a complete period of Voronoi's continued fraction algorithm over Q(\JD) is usually generated. In this paper it is shown how, in certain pure cubic fields, R can be determined by generating only about one third of this period. These results were used on a computer to find R and 3 — then the class number for all pure cubic ...