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Two different models of the liquid phase were considered: an associate and a random solution model.
Assuming random perturbations with known k moments, we derive, to leading order in the random perturbationʼs amplitude, deterministic equations for k moments of the random solution.
Based on the decay of the random fluctuations of the layer's thickness, we prove rates of decay of the derivatives of the random solution with respect to this parameter y which are robust in the scale parameter ε.
Multicomponent alloys with high entropy of mixing, e.g., high entropy alloys (HEAs) and/or multiprincipal-element alloys (MEAs), are attracting increasing attentions, because the materials with novel properties are being developed, based on the design strategy of the equiatomic ratio, multicomponent, and high entropy of mixing in their liquid or random solution state.
Random solution created can be.
Then problem (6.1) has a unique random solution.
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Issues relating to measurability of solutions, probabilistic and statistical aspects of random solutions have arisen due to the introduction of randomness.
Arnold was also an early contributor to what is popularly known as "chaos theory", the branch of dynamics that deals with apparently random solutions to non-random equations.
The GA fits a population of random solutions to the optimized solution of a specific problem.
Jump Step can produce a number of random solutions to escape from poor local minima.
It is initialized with a population of random solutions and searches for optima by updating generations.
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