Solving equations exactly
نویسندگان
چکیده
منابع مشابه
Quasi - Exactly - Solvable Differential Equations
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a representation as a polynomial element of the universal enveloping algebra of the algebra of differential (difference) operators in finitedimensional represent...
متن کاملQuasi Exactly Solvable Difference Equations
Several explicit examples of quasi exactly solvable ‘discrete’ quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known quasi exactly solvable systems, the harmonic oscillator (with/without the centrifugal potential) deformed by a sextic potential and the 1/ sin x potential de...
متن کاملExactly solving packing problems with fragmentation
In packing problems with fragmentation a set of items of known weight is given, together with a set of bins of limited capacity; the task is to find an assignment of items to bins such that the sum of items assigned to the same bin does not exceed its capacity. As a distinctive feature, items can be split at a price, and fractionally assigned to different bins. Arising in diverse application fi...
متن کاملSolving MAP Exactly using Systematic Search
MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network, given some partial evidence about the complement of that set. Unlike posterior probabilities, or MPE (a special case of MAP), the time and space complexity of structure–based algorithms for MAP are not only exponential in the network treewidth, but in a larger parameter known as the constrai...
متن کاملQuasi-Exactly Solvable One-Dimensional Equations
Quasi-exactly solvable one-dimensional Schrödinger equations can be specified in order to exhibit supplementary analytic eigenstates. While the usual solutions are preserved by the sl(2,R) generators, the additional ones are stabilized at the level of the universal enveloping algebra of this Lie structure. We discuss the square-integrability, the orthogonality of these supplementary solutions a...
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ژورنال
عنوان ژورنال: Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics
سال: 1967
ISSN: 0022-4340
DOI: 10.6028/jres.071b.023