Sentence examples for continuum of solutions from inspiring English sources

For each integer,, there exists a continuum of solutions of (3.8) joining to infinity in.

By a continuum of solutions of (1.1) we mean C ⊂ T which is closed and connected.

For each integer, there exists a continuum of solutions of (3.8) joining to infinity in Moreover, Proof of Theorem 1.5.

The constraint x²+y² = 1 has a continuum of solutions forming a shape, in this case a circle of radius 1.

For orthogonal designs, the relaxed Lasso provides a continuum of solutions that include both soft- and hard-thresholding of estimators.

The results of Rabinowitz [13] for (3.8) can be stated as follows: for each integer,, there exists a continuum of solutions of (3.8), joining to infinity in.

We use the abstract bifurcation theorems concerning the bifurcation of continua of solutions from infinity for the operator equation z = λ L z + H ( λ, z ).

By figuring the shape of unbounded continua of solutions, we show the existence and multiplicity of positive solutions with respect to the parameter λ, and especially, we obtain the existence of at least three distinct positive solutions for λ being in a certain interval.

By figuring the shape of unbounded continua of solutions, we show the existence and multiplicity of positive solutions with respect to parameter λ, and especially, we obtain the existence of three distinct positive solutions for λ being in a certain interval.

This constructive approach enables useful design-oriented capabilities: a graphical control of multiple solutions, the direct switching of the dependencies hierarchy, the execution of dynamic conditional statements using static constraints, the computation of interdependencies, and coordinate-free methods for ensuring consistency between certain continuums of solutions.

Here are just a few examples of steps that leaders can take immediately: Consider using a collective impact approach to building cradle-to-career continua of solutions in low-income areas.