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Branch and bound (BB, B&B, or BnB) is a method for solving optimization problems by breaking them down into smaller sub-problems and using a bounding function to eliminate sub-problems that cannot contain the optimal solution. It is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical ...
In numerical analysis, the shooting method is a method for solving a boundary value problem by reducing it to an initial value problem.It involves finding solutions to the initial value problem for different initial conditions until one finds the solution that also satisfies the boundary conditions of the boundary value problem.
The Hückel definition of bond order attempts to quantify any additional stabilization that the system enjoys resulting from delocalization. In a sense, the Hückel bond order suggests that there are four π-bonds in benzene instead of the three that are implied by the Kekulé-type Lewis structures.
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 sparsest cut problem is to bipartition the vertices so as to minimize the ratio of the number of edges across the cut divided by the number of vertices in the smaller half of the partition. This objective function favors solutions that are both sparse (few edges crossing the cut) and balanced (close to a bisection).
The steps for solving an Electromagnetic problem as a bond graph are as follows: Place an 0-junction at each node; Insert Sources, R, I, C, TR, and GY bonds with 1 junctions; Ground (both sides if a transformer or gyrator is present) Assign power flow direction; Simplify; These steps are shown more clearly in the examples below.
Ab initio quantum chemistry methods are a class of computational chemistry techniques based on quantum chemistry that aim to solve the electronic Schrödinger equation. [1] Ab initio means "from first principles" or "from the beginning", meaning using only physical constants [2] and the positions and number of electrons in the system as input.
In chemistry, bond order is a formal measure of the multiplicity of a covalent bond between two atoms. As introduced by Gerhard Herzberg, [1] building off of work by R. S. Mulliken and Friedrich Hund, bond order is defined as the difference between the numbers of electron pairs in bonding and antibonding molecular orbitals.