We study the 3-Coloring problem in graphs with small diameter. In 2013, Mertzios and Spirakis showed that for $n$-vertex diameter-2 this can be solved subexponential time $2^{\mathcal{O}(\sqrt{n \log n})}$. Whether polynomial remains a well-known open question area of algorithmic graph theory. paper we present an algorithm solves $2^{\mathcal{O}(n^{1/3} \log^{2} n)}$. This is first improvement ...

Two-phase flow regimes are affected by conduit position, alignment, geometry, flow direction, physical characteristics, and flow rate of each phase as well as the heat flux toward the boundaries. Due to the importance of two-phase flow, numerous regimes have been identified. The first step in studying micro-bubble formation inside a venturi tube is to recognize the type of flow regimes. In this...

INTRODUCTION The discharge ofliquids from vertical tubes with various con­ traction geometries was studied via the unsteady Bernoulli equa­ tion. The temporal variations of the exit velocity and fluid level in the tube were found from the numerical integration of nonlin­ ear differential equations. Sudden, quadratic, and exponential contraction geometries were considered. For inlet to exit area...

Solar energy is a good solution for energy-deficiency problems, especially in regions such as rural areas in the Middle East that have not been electrified yet or are under electrification. In this paper, with the aid of a Computational Fluid Dynamics simulation, we propose a system that comprises a trough solar concentrator and a pipe—with flowing water—that is set in the concentrator focus. T...