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The examples "is greater than", "is at least as great as", and "is equal to" are transitive relations on various sets. As are the set of real numbers or the set of natural numbers: whenever x > y and y > z, then also x > z whenever x ≥ y and y ≥ z, then also x ≥ z whenever x = y and y = z, then also x = z. More examples of transitive ...
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?
Le Chatelier–Braun principle analyzes the qualitative behaviour of a thermodynamic system when a particular one of its externally controlled state variables, say , changes by an amount , the 'driving change', causing a change , the 'response of prime interest', in its conjugate state variable , all other externally controlled state variables remaining constant.
For example, a construction by transfinite recursion frequently will not specify a unique value for A α+1, given the sequence up to α, but will specify only a condition that A α+1 must satisfy, and argue that there is at least one set satisfying this condition. If it is not possible to define a unique example of such a set at each stage ...
For example, if two systems of ideal gases are in joint thermodynamic equilibrium across an immovable diathermal wall, then P 1 V 1 / N 1 = P 2 V 2 / N 2 where P i is the pressure in the ith system, V i is the volume, and N i is the amount (in moles, or simply the number of atoms) of gas.
The classical Stefan problem aims to describe the evolution of the boundary between two phases of a material undergoing a phase change, for example the melting of a solid, such as ice to water. This is accomplished by solving heat equations in both regions, subject to given boundary and initial conditions.
The lone pairs on transition metal atoms are usually stereochemically inactive, meaning that their presence does not change the molecular geometry. For example, the hexaaquo complexes M(H 2 O) 6 are all octahedral for M = V 3+, Mn 3+, Co 3+, Ni 2+ and Zn 2+, despite the fact that the electronic configurations of the central metal ion are d 2, d ...
An example of such a reaction is the ring closure of cyclopentane biradicals generated from the gas-phase thermal decomposition of 2,3-diazabicyclo[2.2.1]hept-2-ene. [ 20 ] [ 21 ] Transition state theory is also based on the assumption that atomic nuclei behave according to classical mechanics . [ 22 ]