Related papers: Composite operators and algebra constraints: a for…
The properties of gauge-invariant composite operators and their correlation functions in N=4 SYM are discussed in the analytic superspace formalism. A complete classification of the different types of operators in the theory is given.…
The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel…
We study the phenomenon of composite operator renormalization and mixing in systems where time-translational invariance is broken and the evolution is out-of-equilibrium. We show that composite operators mix also through non-local memory…
Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…
This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(\mu) \). Within the framework of \( A \)-adjoint operators, we characterize…
Theoretical and computational frameworks of modern science are dominated by binary structures. This binary bias, seen in the ubiquity of pair-wise networks and formal operations of two arguments in mathematical models, limits our capacity…
The ability to combine known skills to create new ones may be crucial in the solution of complex reinforcement learning problems that unfold over extended periods. We argue that a robust way of combining skills is to define and manipulate…
The aim of this work is to propose a meta-algorithm for automatic classification in the presence of discrete binary classes. Classifier learning in the presence of overlapping class distributions is a challenging problem in machine…
The objectives of this research work which is intimately related to pattern discovery and management are threefold: (i) handle the problem of pattern manipulation by defining operations on patterns, (ii) study the problem of enriching and…
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
The present article is primarily a review of the projection-operator approach to quantize systems with constraints. We study the quantization of systems with general first- and second-class constraints from the point of view of…
A bialgebra is a structure which is simultaneously an algebra and a coalgebra, such that the algebraic and coalgebraic parts are "compatible". Bialgebras are normally studied over a field or commutative ring. In this paper, we show how to…
Computational devices combining two or more different parts, one controlling the operation of the other, for example, derive their power from the interaction, in addition to the capabilities of the parts. Non-classical computation has…
Hamiltonian of a parametric process describing the interaction of a finite number of optical cavity modes, with the microwave field is proposed. Three-boson interaction is due to electro-optical effect. Analysis of the model is based on the…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
In this paper, the possibility to construct a path integral formalism by using the Hubbard operators as field dynamical variables is investigated. By means of arguments coming from the Faddeev-Jackiw symplectic Lagrangian formalism as well…