Sentence examples for various applied problems from inspiring English sources

Also, the numerical solution of (u_{xx}), in case of solution of (1) and the one-dimensional time-dependent Laplacian (u_{xx}-u_{t}) and in case of solution of (6), which are quite often of interest in various applied problems, are computed as a byproduct of the proposed methods.

Information of this kind creates a basis for solving various fundamental and applied problems of tectonics, mineral exploration, and engineering geology.

This principle provides a technique for solving a variety of applied problems in various branches of mathematics.

The integrals of integer order have clear physical interpretations in engineering and geometry and are features that help to solve applied problems in various scientific fields.

The weighted sums in the form ∑ k ≤ n a n, k X k can play an important role in various applied and theoretical problems, such as those of the least squares estimators (see Kafles and Bhaskara Rao [14]) and M-estimates (see Rao and Zhao [15]) in linear models, the nonparametric regression estimators (see Priestley and Chao [16]) etc.

The weighted sums ∑ k ≤ n a n, k X k can play an important role in various applied and theoretical problems, such as those of the least squares estimators (see Kafles and Bhaskara Rao [5]) and M-estimates (see Rao and Zhao [6]) in linear models, the nonparametric regression estimators (see Priestley and Chao [7]), etc.

There are many variations of the ant colony optimization applied on various classical problems.

This method was first presented by He [8, 9] and applied to various nonlinear problems [10 12].

Thus, as seen from the previous research, IGA has already been applied to various architectural problems.

The proposed method is applied to various test problems from the literature.

The Homotopy analysis method which provides an analytical approximate solution is applied to various nonlinear problems [8, 10, 12 14].