General Travelling Notes

Heuristics for sparse general travelling salesman problems

The well-known travelling salesman problem can be expressed in graphtheoretic terms as follows : find a minimum-weight Hamiltonian cycle in a connected edge-weighted graph G(N, A). vVe concentrate here on the problem where G is large and sparse, i.e., where INI is 500 or more and IAI is O( INI). Such graphs arise frequently in practice, where G represents a road network, and each node (city) is...

General Inorganic Nmr Notes

The signal intensity S is given by: S = γB0NB1g(v)/T Where N is the number of nuclei sampled, B1 is the field due to the applied radiofrequency radiation, and g(v) is the lineshape function. Hence, • S ∝ N (large sample and desirability of high isotopic abundance). • S ∝ γ (signals due to nuclei with large γ easiest to observe). • S ∝ B0 (advantage of maximum B0). • S ∝ 1/T (low temperatures gi...

Notes on General Topology

Part of the rigorization of analysis in the 19th century was the realization that notions like convergence of sequences and continuity of functions (e.g. f : R → R) were most naturally formulated by paying close attention to the mapping properties between subsets U of the domain and codomain with the property that when x ∈ U , there exists > 0 such that ||y− x|| < implies y ∈ U . Such sets are ...

Lecture notes for General Insurance

i Contents Contents ii 1 Utility theory 1 1.

Lecture Notes on General Relativity