The ladder operator formalism of a general quantum state for su(1,1) Lie algebra is obtained. The state bears the generally deformed oscillator algebraic structure. It is found that the Peremolov’s coherent state is a su(1,1) nonlinear coherent state. The expansion and the exponential form of the nonlinear coherent state are given. We obtain the matrix elements of the su(1,1) displacement opera...

We propose a formal approach to the problem of prediction based on the following steps: First, a mental-level model is constructed based on the agent’s previous actions; Consequently, the model is updated to account for any new observations by the agent, and finally, we predict the optimal action w.r.t, the agent’s mental state as its next action. This paper formalizes this prediction process. ...

The Hankel operator of the system with single control input delay is established by using state-space formulation in this paper. In general, this type of operator is not a compact one. Singular values of this type of operator are studied. Two examples are used to illustrate the computation of Hankel singular value by the theoretical method proposed in this paper.

This paper presents CO3L, a compact, expressive and easy to use language for ontology representation. CO3L reflects the O3F model of ontology representation proposed elsewhere. The proposed language enables the representation of basic ontological entities, their relationships, and arbitrary axioms of the domain. Ontological entities include classes, properties, methods, facets and types. Relati...

We perform a comparison between different lattice regularizations of the Dirac operator for massless fermions in the framework of the single and two flavor Schwinger model. We consider a) the Wilson-Dirac operator at the critical value of the hopping parameter; b) Neuberger's overlap operator; c) the fixed point operator. We test chiral properties of the spectrum, dispersion relations and rotat...

Optimal control is formulated based on a noncommutative calculus of operator derivatives. The use of optimal control methods in the design of quantum systems relies on the differentiation of an operator-valued function with respect to the relevant operator. Noncommutativity between the operator and its derivative leads to a generalization of the conventional method of control for classical syst...

We use the theory of quantization to introduce non-commutative versions of metric on state space and Lipschitz seminorm. We show that a lower semicontinuous matrix Lipschitz seminorm is determined by their matrix metrics on the matrix state spaces. A matrix metric comes from a lower semicontinuous matrix Lip-norm if and only if it is convex, midpoint balanced, and midpoint concave. The operator...

A relativistic and non-local model for the coherent photoproduction of pions on spin-zero nuclei is presented. The production operator is derived from an effective Lagrangian model that contains all the degrees of freedom known to contribute to the elementary process. Using the framework of DWIA, the matrix elements of this operator are evaluated using relativistic bound state wave functions. F...

Semi-classical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semiclassical (coherent) state is obtained by solving the eigen-equation of that operator. Moreover, we use these coherent states to analyze the semiclassical limit of the quantum dynamics. It ...

A relativistic and non-local model for the coherent photoproduction of pions on nuclei is presented. The production operator is derived from an effective Lagrangian model that contains all the degrees of freedom known to contribute to the elementary process. Using the framework of DWIA, the matrix elements of this operator are evaluated using relativistic bound state wave functions. Final state...