We demonstrate that complex point transformations can be used to construct non-Hermitian first integrals, time-dependent Dyson maps and metric operators for quantum systems. Initially we identify a transformation as map from an exactly solvable time-independent system explicitly Hamiltonian system. Subsequently employ the invariant latter Exploiting fact this is pseudo-Hermitian, corresponding ...

An adjoint model for a 2D finite element Galerkin shallow water model is developed using the Independent Set Perturbation (ISP, [46]) sensitivity analysis. Its performance in a full 4-D Var setup with a limited area is assessed by comparing with the adjoint model derived by the automatic differentiation approach, where it is used for optimising the initial conditions. It is shown that the ISP s...

Given, on the Hilbert space H0, the self-adjoint operator B and the skew-adjoint operators C1 and C2, we consider, on the Hilbert space H ≃ D(B)⊕H0, the skew-adjoint operator

A neural net based development of multi-adjoint logic programming is presented. Transformation rules carry programs into neural networks, where truth-values of rules relate to output of neurons, truth-values of facts represent input, and network functions are determined by a set of general operators; the output of the net being the values of propositional variables under its minimal model. Some...

The procedural semantics of multi-adjoint logic programming is used for providing a model-theoretic semantics for a data model. A translation method for deductive logic databases is presented for obtaining a relational algebra with classical projection and enriched parametric join operator with aggregations. The use of non-commutative conjunctors allows for a model of different degrees of granu...

The structure of the paper is as follows. In Section 2, we introduce the preliminary concepts necessary for the definition of the syntax and semantics of sorted multi-adjoint logic programs, presented in Section 3. In Section 4, we state the basic results regarding the termination properties of our semantics, which are extended later in Section 5. The paper finishes with some conclusions and po...

Common velocity analysis is based on the invariance of migrated images with respect to the experiment index (shot number, plane-wave take-off angle, etc.) or extension parameters (reflection angle, correlation lags in extended images, etc.). All the information available, i.e. the entire survey, is used for assessing the quality of the model used for imaging. This approach is effective but forc...

This paper deals with the application of the adjoint transport theory in order to optimize Monte Carlo based radiotherapy treatment planning. The technique is applied to Boron Neutron Capture Therapy where most often mixed beams of neutrons and gammas are involved. In normal forward Monte Carlo simulations the particles start at a source and lose energy as they travel towards the region of inte...

We consider one-dimensional steady-state conservation laws with discontinuous solutions. Giles and Pierce [7] realized that a shock leads to a new term in the adjoint error representation for target functionals. This term disappears if and only if the adjoint solution satisfies an internal boundary condition. Curiously, most computer codes implementing adjoint error estimation ignore the new te...