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Sizing or size is a substance that is applied to, or incorporated into, other materials—especially papers and textiles—to act as a protective filler or glaze. Sizing is used in papermaking and textile manufacturing to change the absorption and wear characteristics of those materials.
Solving topology optimization problems in a discrete sense is done by discretizing the design domain into finite elements. The material densities inside these elements are then treated as the problem variables. In this case material density of one indicates the presence of material, while zero indicates an absence of material.
Industrial applications of cutting-stock problems for high production volumes arise especially when basic material is produced in large rolls that are further cut into smaller units (see roll slitting). This is done e.g. in paper and plastic film industries but also in production of flat metals like steel or brass.
In granulometry, the particle-size distribution (PSD) of a powder, or granular material, or particles dispersed in fluid, is a list of values or a mathematical function that defines the relative amount, typically by mass, of particles present according to size. [1]
A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems .
The satisfiability problem, also called the feasibility problem, is just the problem of finding any feasible solution at all without regard to objective value. This can be regarded as the special case of mathematical optimization where the objective value is the same for every solution, and thus any solution is optimal.
According to the classical theories of elastic or plastic structures made from a material with non-random strength (f t), the nominal strength (σ N) of a structure is independent of the structure size (D) when geometrically similar structures are considered. [1] Any deviation from this property is called the size effect.
The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, [3] linguistics, [4] and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different ...