The phrase "and thus the solution" is correct and usable in written English.
It can be used to indicate a conclusion or result that follows logically from the preceding statements or arguments.
Example: "After analyzing the data and considering all possible outcomes, we reached a consensus, and thus the solution was proposed."
Alternatives: "therefore the solution" or "hence the solution".
Under μG the solutes dissolved at the seed interface were not able to move up to the feed interface unlike the 1G condition, due to the absence of convection, and thus the solution at the seed interface gets locally supersaturated.
In particular it is shown that this extensibility average measure, and thus the solution spinnability, is primarily determined by the extensibility of the highest molecular weight fractions.
The warmth of Earth and Mars during their early periods (and thus the solution to the faint young Sun problem) can be attributed to the presence of abundant greenhouse gases in their atmospheres, with carbon dioxide, water, and possibly ammonia and methane playing major roles.
Named complex-length finite element method (CFEM), the technique is linked to Padé approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain.
namely,, and thus the solution is constant state formed as (5.17).
namely,, and thus the solution is rarefaction wave formed as (5.15).
As VLSI technology advances, the number of modules on a chip multiplies and thus the solutions for on-chip communication are evolving to support the new paradigm in inter-module communication on System on Chip (SOC).
However, if energy research is not undertaken in an interdisciplinary way, researchers 'are not likely to grasp the problems, and thus the solutions to this challenging (energy) research space'([44], p.247).
In the presence of the magnetic-electric potentials, the wavevector satisfies k x 2 + ( k y + A y ) 2 = ( E - V ) 2 - ( g μ B B ) 2. Note that the translational invariance along the y direction gives rise to conservation of k y, and thus the solutions can be written as ψ ( x, y ) = ψ ( x ) e i k y y.
Existing sampling-based path planners on manifolds focus on finding a feasible solution, but they do not optimize the quality of the path in any sense and, thus, the returned solution is usually not adequate for direct execution.
Therefore, appropriate shading must be applied and thus the optimum solution is achieved in regard to the building's cumulative yearly energy consumption.
