In high-consequence systems, there is a high cost associated with failure. Thus, there should be strong evidence that the systems will not fail in the field. Such evidence cannot be obtained by traditional verification methods such as testing. Transformation-oriented programming (TOP) is a promising formal software development technique. In TOP, a source file that represents a correct formal sp...

A unified methodology is presented for solving general global optimization problems. Based on the canonical dualitytriality theory, the nonconvex/nonsmooth/discrete problems from totally different systems are reformulated as a canonical min–max problem, which is equivalent to a monotone variational inequality problem over a convex cone. Therefore, a complementary-dual projection method is used ...

Quantum canonical transformations corresponding to the action of the unitary operator e √ f(x)p √ f(x) is studied. It is shown that for f(x) = x, the effect of this transformation is to rescale the position and momentum operators by e and e, respectively. This transformation is shown to lead to the identification of a previously unknown class of exactly solvable time-dependent harmonic oscillat...

The well-known classification of the Clifford algebrasCl(r, s) leads to canonical forms of complex and real representations which are essentially unique by virtue of the Wedderburn theorem. For s ≥ 1 representations of Cl(r, s) on R are obtained from representations on R by adding two new generators while in passing from a representation of Cl(p, 0) on R to a representation of Cl(r, 0) on R the...

The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic oscillator is solved in two different types of canonical transformations. The quantum form of the classical Hamiton-Jacobi theory is also employed to solve time d...

Canonical transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the ...

We consider the exact renormalization group for a non-canonical scalar field theory in which the field is coupled to the external source in a special non linear way. The Wilsonian action and the average effective action are then simply related by a Legendre transformation up to a trivial quadratic form. An exact mapping between canonical and non-canonical theories is obtained as well as the rel...