Sentence examples for problems of continuum from inspiring English sources

A mixed topology optimization algorithm is implemented and presented for the compliance minimization problems of continuum structures with material volume constraints.

The ant colony optimization (ACO) algorithm, a relatively recent bio-inspired approach to solve combinatorial optimization problems mimicking the behavior of real ant colonies, is applied to problems of continuum structural topology design.

This paper presents a novel methodology, fuzzy tolerance multilevel programming approach, for applying fuzzy set theory and sequence multilevel method to multi-objective topology optimization problems of continuum structures undergoing multiple loading cases.

Numerical results show that the proposed BESO method is efficient, and convergent solid-void or bi-material optimal solutions can be achieved for a variety of frequency optimization problems of continuum structures.

The particle swarm optimization (PSO) algorithm, a relatively recent bio-inspired approach to solve combinatorial optimization problems mimicking the social behavior of birds flocking, is applied to problems of continuum structural topology design for the purpose of investigating optimal topologies and automatically creating innovative solutions.

This led to the famous problem of the continuum hypothesis, namely, that there are no cardinal numbers between aleph-null and the cardinal number of the points on a line.

This made it possible to formulate much more precisely the problem of the continuum; Cantor's conjecture became the hypothesis that card(R) = ℵ1.

We also offer case studies to illustrate practical applications of the methods for structural problems, including a coupled problem of a continuum with molecular dynamics.

Gödel stressed the fact that his approach to the problem of the continuum hypothesis was not constructive, since it needs the uncountable ordinal ω1, and it was natural to study the ramified hierarchy along constructive ordinals.

In regard to the problem of the continuum, the focus shifted away from metaphysics to technique, from the problem of "what indivisibles were, or whether they composed magnitudes" to "the new marvels one could accomplish with them" (see Murdoch [1957], p. 325) through the emerging calculus and mathematical analysis.

Leibniz, however, thought that he had found the way out of each labyrinth, and his solution to the problem of the continuum is related ultimately to a maxim or law that he employs not only in his mathematical writings but also in his metaphysics.