Sentence examples for mathematical structure with from inspiring English sources

First, as we have seen, almost every set theoretically defined mathematical structure with the appropriate notion of homomorphism yields a category.

Such rudimentary methods are used either because there has historically been no suitable mathematical structure with which to represent the relevant grain boundary information, or, where there are existing methods they are extremely unintuitive and cumbersome to use.

Sharing the same mathematical structure with the original (reduced) systems, their numerical solution, is likewise efficiently performed.

This crucial step provides the mathematical structure with the capacity to reproduce a given data set, make predictions and discriminate among different model candidates.

The next step is to propose a mathematical structure with the necessary level of detail, which will in general include a number of unknown, non-measurable parameters.

Large scale metabolic network of the glycolysis, the pentose-phosphate-pathway, and the phosphotransferase system of E. coli K-12 W3110 [ 40] consists of a complex mathematical structure with 18 dynamic mass balance equations, (5) to (22) presented below, 7 additional algebraic equations, (A.1) to (A.7), and 30 kinetic rate expressions, (A.8) to (A.37) [ 2].

Mathematical structures with an addition operation but not a subtraction operation include commutative semigroups, commutative monoids and semirings.

In the language of category theory, they are group objects in a category, meaning that they are objects (that is, examples of another mathematical structure) which come with transformations (called morphisms) that mimic the group axioms.

In this study, we maintain the important physical requirements by employing a strategy based on the key concept that mathematical structures associated with conservative and nonconservative equations are preserved, even at the discrete level.

As a consequence, these sections define gIF model with more mathematical structure than the original paper [31] and mostly contain original results.

(2) The 'mixed tools' of dialectic are at the same time depicted as extended 'bands' that provide the soul with a mathematical structure through division in a complex set of proportions (35b 36b).