Sentence examples for conditions of the solution from inspiring English sources

These structures were not etched out of a larger crystal, but were self-assembled on the atomic scale by actively modulating the conditions of the solution in which the mineral crystals precipitated.

In order to achieve spontaneous (electroless) and selective deposition at those patterns, conditions of the solution were optimized and the formation of metal nanostructures, such as Cu nanodot arrays and wires, has been achieved.

The equilibrium constant and the two binary interaction parameters are found to be independent of the conditions of the solution phase including concentration and the particular non-exchanging anionic species present in the solution.

We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit to the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation.

These tests are easily repeatable under different conditions of the solution, pH and contact time.

Bulatov and Chistyakov [11] gave the existence and uniqueness conditions of the solution for IAEs systems with convolution kernels and defined the index notion in analogy to Gear's approach.

To overcome this difficulty, an analytical method to determine the existence conditions of the solutions to revisit orbits is presented in this paper.

However, as far as we know the second-order optimality conditions of the solutions remain unstudied in set-valued vector equilibrium problems.

During the last two decades, many authors have considered the questions of existence, uniqueness, estimates of solutions, and dependence with respect to initial conditions of the solutions of differential and integral equations of two and three variables (see [15 19] and the references therein).

Testing various conditions of the solutions and two different application methods led to the conclusion that the outcome of the solution treatment depends on not only the chemical, but also how it is applied.

Then, it is important to give the optimality conditions for the solution of (VEPC) under conditions of generalized convexity.