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Protein folding problem: Is it possible to predict the secondary, tertiary and quaternary structure of a polypeptide sequence based solely on the sequence and environmental information? Inverse protein-folding problem: Is it possible to design a polypeptide sequence which will adopt a given structure under certain environmental conditions?
In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables.. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics for these deductive systems) and connected ...
Mathematical chemistry [1] is the area of research engaged in novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena. [2] Mathematical chemistry has also sometimes been called computer chemistry , but should not be confused with computational chemistry .
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
Since there are continuously infinite number of elements, the translation group is a continuous group. Moreover, the translation operators commute among themselves, i.e. the product of two translation (a translation followed by another) does not depend on their order. Therefore, the translation group is an abelian group.
The free and bound variable occurrences in a formula are defined inductively as follows. Atomic formulas If φ is an atomic formula, then x occurs free in φ if and only if x occurs in φ. Moreover, there are no bound variables in any atomic formula. Negation x occurs free in ¬φ if and only if x occurs free in φ.
In chemistry, topology provides a way of describing and predicting the molecular structure within the constraints of three-dimensional (3-D) space. Given the determinants of chemical bonding and the chemical properties of the atoms, topology provides a model for explaining how the atoms ethereal wave functions must fit together.
This the algebraic translation of the preceding definition. The difference between n and the maximal length of the regular sequences contained in I. This is the algebraic translation of the fact that the intersection of n – d general hypersurfaces is an algebraic set of dimension d. The degree of the Hilbert polynomial of A.