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Systems biology can be considered from a number of different aspects. As a field of study, particularly, the study of the interactions between the components of biological systems, and how these interactions give rise to the function and behavior of that system (for example, the enzymes and metabolites in a metabolic pathway or the heart beats).
In mathematical analysis, the Minkowski inequality establishes that the L p spaces are normed vector spaces.Let be a measure space, let < and let and be elements of (). Then + is in (), and we have the triangle inequality
Bernstein inequalities (probability theory) Boole's inequality; Borell–TIS inequality; BRS-inequality; Burkholder's inequality; Burkholder–Davis–Gundy inequalities; Cantelli's inequality; Chebyshev's inequality; Chernoff's inequality; Chung–Erdős inequality; Concentration inequality; Cramér–Rao inequality; Doob's martingale inequality
Instead, the inequalities must be solved independently, yielding x < 1 / 2 and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < 1 / 2 . Occasionally, chained notation is used with inequalities in different directions, in which case the meaning is the logical conjunction of the inequalities ...
A biological system is a complex network which connects several biologically relevant entities. Biological organization spans several scales and are determined based different structures depending on what the system is. [1] Examples of biological systems at the macro scale are populations of organisms.
Following Antman (1983, p. 283), the definition of a variational inequality is the following one.. Given a Banach space, a subset of , and a functional : from to the dual space of the space , the variational inequality problem is the problem of solving for the variable belonging to the following inequality:
The rearrangement inequality can be regarded as intuitive in the following way. Imagine there is a heap of $10 bills, a heap of $20 bills and one more heap of $100 bills.
The ideas of this theory were developed by Kenneth Ferraro and colleagues as an integrative or middle-range theory.Originally specified in five axioms and nineteen propositions, cumulative inequality theory incorporates elements from the following theories and perspectives, several of which are related to the study of society:
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