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For example, the d-d transitions for [Cr(NH 3) 5 Cl] 2+ are weak (ε < 100) even though the complex is only of C 4v symmetry. [5] The Laporte rule helps explain the intense colors often observed for the tetrahedral complexes. The tetrahedral point group lacks the inversion operation, so the Laporte rule does not apply. [6]
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?
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 ...
This is an energy balance which defines the position of the moving interface. Note that this evolving boundary is an unknown (hyper-)surface; hence, Stefan problems are examples of free boundary problems. Analogous problems occur, for example, in the study of porous media flow, mathematical finance and crystal growth from monomer solutions. [1]
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.
A simple example may help to explain how the Gillespie algorithm works. Consider a system of molecules of two types, A and B. In this system, A and B reversibly bind together to form AB dimers such that two reactions are possible: either A and B react reversibly to form an AB dimer, or an AB dimer dissociates into A and B.
The Newton and the Schrödinger equations in the absence of the macroscopic magnetic fields and in the inertial frame of reference are T-invariant: if X(t) is a solution then X(-t) is also a solution (here X is the vector of all dynamic variables, including all the coordinates of particles for the Newton equations and the wave function in the configuration space for the Schrödinger equation).
When it is completely settled, so that macroscopic change is no longer detectable, it is in its own thermal equilibrium. It is not implied that it is necessarily in other kinds of internal equilibrium. For example, it is possible that a body might reach internal thermal equilibrium but not be in internal chemical equilibrium; glass is an ...