We prove that every cyclically 6-edge-connected cubic graph with oddness at most 4 has a nowhere-zero 5-flow. Therefore, a possible minimum counterexample to the 5-flow conjecture has oddness at least 6.

We present a new representation of the string vertices of the cubic open string field theory. By using this three-string vertex, we attempt to identify open string fields as huge-sized matrices by following Witten's idea. By using these huge matrices, we obtain some results about the construction of partial isometries in the algebra of open string fields.

Geometric modelling of several intricate and complex structures such as trees, mountains, clouds, ferns, geographic topography, coastlines is challenging in computer graphics. Traditional splines astrigonometric, polynomial, exponential, rational fail to simulate this significant class structures, which are highly irregular nature. For purpose, research develops a novel cutting-edgemethod for s...

In this paper, a cubic objective programming problem (COPP) is defined. Introduced new modification to solve problem. Suggested an algorithm for its solution. Also reported the of usual simplex method. Application talks about how developed can be used unravel non-linear. The proposed technique, with constructed numerical examples illustrative problems are given demonstrate algorithms.