It is shown that the BRST operator of twisted N = 4 Yang-Mills theory in four dimensions is locally the same as the BRST operator of a fully decomposed non-Abelian gerbe. Using locally defined Yang-Mills theories we describe non-perturbative backgrounds that carry a novel magnetic flux. Given by elements of the crossed module G ⋉ AutG, these nongeometric fluxes can be classified in terms of the...

We present several results concerning non-commutative instantons and the Seiberg–Witten map. Using a simple ansatz we find a large new class of instanton solutions in arbitrary even dimensional non-commutative Yang–Mills theory. These include the two dimensional “shift operator” solutions and the four dimensional Nekrasov–Schwarz instantons as special cases. We also study how the Seiberg–Witten...

The near-horizon properties of a black hole are studied within an algebraic framework, using a scalar field as a simple probe to analyze the geometry. The operator H governing the near-horizon dynamics of the scalar field contains an inverse square interaction term. It is shown that the operators appearing in the corresponding algebraic description belong to the representation space of the Vira...

The theory of measures of noncompactness has many applications on topology, functional analysis, and operator theory. In this paper, we consider one axiomatic approach to this notion which includes the most important classical definitions. We give some results concerning a certain class of semi-Fredholm and Fredholm operators via the concept of measures of noncompactness. Moreover, we establish...

An operator formalism is developed for a description of charged electron-hole complexes in magnetic fields. A unitary transformation of the Hamiltonian that allows one to separate partially the center-of-mass and internal motions is proposed. We study an operator algebra that leads to the appearance of effective particles, electrons, and holes with modified interparticle interactions, and their...

We describe how CiPF 2.0, a propositional constructive learner, can cope with both noise and representation mismatch in training examples simultaneously. CiPF 2.0 abilities stem from coupling the robust selective learner C4.5 (and its production rule generator) with a sophisticated constructive induction component. An important new general constructive operator incorporated into CiPF 2.0 is the...

A Poincaré-invariant description of mesonic baryon resonance decays is presented following the point form of relativistic quantum mechanics. In this contribution we focus on pionic decay modes. It is found that the theoretical results in general underestimate the experimental ones considerably. Furthermore, the problem of a nontrivial normalization factor appearing in the definition of the deca...

Nonlinear dynamic systems with positive solutions and the parametric problem of entropy maximization (entropy operator) are considered. The continuity, differentiability and boundedness of the entropy operator and the boundedness of the solutions of the dynamic system are derived using the global implicit function theorem. The technique of positive dynamic systems is applied to modelling of the...

We consider a spin coherent states description of a general quantum spin system. It is shown that it is possible to use the spin-1/2 representation to study the general spin-J case. We identify the 1/2 spinor components as the homogeneous coordinates of the projective space associated to the complex variable that labels the coherent states and establish a relation between the two-component spin...

Abstract. In this paper we present a generalized description of the Grover operator, employed in a quantum database search algorithm. Our purpose is to employ an operator to find the proper solution(s) originated from an arbitrary initial state in the two dimensional vector space, where the orthogonal basis vector system are rotated in such a way where the result is obtained with a probability ...