Sentence examples for distinct solutions which from inspiring English sources

Then there exist and such that, for every, problem (1.1) admits at least three distinct solutions which belong to.

Assume that (f2), (f4), and (f5) hold; then there exist and such that, for every, problem (1.1) admits at least three distinct solutions which belong to.

Our results identified multiple distinct solutions by which the monogenic trait could be suppressed, including genetic and nongenetic mechanisms as well as frequent aneuploidy.

An application of Lemma 3.2 leads to two distinct solutions of (1 - 3) which satisfy d 1 ⩽ ∥ y 1 ¯ ∥ ⩽ l 1, l 2 ⩽ ∥ y 2 ¯ ∥ ⩽ d 2. □.

This paper presents a new algorithm, the Multi-objective Niching Co-evolutionary Algorithm (MNCA) that identifies distinct sets of non-dominated solutions which are maximally different in their decision vectors and are located in the same non-inferior regions of a Pareto front.

Jung and Choi [2] proved that (1.1) has at least m weak solutions, which are geometrically distinct and nonconstant under some jumping nonlinearity.

In this section, we derive some conditions under which system (1.2) admits infinitely many distinct solutions.

In this section, we derive some sufficient conditions under which the functional φ admits at least two distinct critical points; consequently, (1.1) admits at least two distinct solutions.

BASS tetramer was concentrated to 25 mg/ml for crystallization trials, which were performed using a mosquito robot (TTPlabtech) by mixing 100 nL drops with equal amounts of 2500 distinct solutions of home-made and commercial crystallization screens (Qiagen).

admits at least three distinct solutions.

Suppose that are distinct solutions to (3.3).