A study of the one loop dilatation operator in the scalar sector of N = 4 SYM is presented. The dilatation operator is analyzed from the point of view of Hamiltonian matrix models. A Lie algebra underlying operator mixing in the planar large N limit is presented, and its role in understanding the integrability of the planar dilatation operator is emphasized. A classical limit of the dilatation ...

In the recent preprint [1] S. Parrott proves the equality between the Arveson's curvature and the Fredholm index of a " pure " contraction with finite defect numbers. In the present note one derives a similar formula in the " non-pure " case. The notions of d-contraction T = (T 1 , T 2 ,. .. , T d) and its curvature was introduced by W. Arveson in a series of papers (see [2], [3], and [4]). In ...

Revision of a description logic-based ontology deals with the problem of incorporating newly received information consistently. In this paper, we propose a general operator for revising terminologies in description logic-based ontologies. Our revision operator relies on a reformulation of the kernel contraction operator in belief revision. We first define our revision operator for terminologies...

A study of the one loop dilatation operator in the scalar sector of N = 4 SYM is presented. The dilatation operator is analyzed from the point of view of Hamiltonian matrix models. A Lie algebra underlying operator mixing in the planar large N limit is presented, and its role in understanding the integrability of the planar dilatation operator is emphasized. A classical limit of the dilatation ...

The paper deals with a risk averse dynamic programming problem infinite horizon. First, the required assumptions are formulated to have well defined. Then Bellman equation is derived, which may be also seen as standalone reinforcement learning problem. fact that operator contraction proved, guaranteeing convergence of various solution algorithms used for problems, we demonstrate on value iterat...

In this paper, we present results of $\omega$-order preserving partial contraction mapping generating a wave equation. We use the theory semigroup to generate equation by showing that operator $ \begin{pmatrix} 0 & I\\ \Delta \end{pmatrix}, which is $A,$ infinitesimal generator $C_0$-semigroup operators in some appropriately chosen Banach functions. Furthermore show $A$ closed, unique and

We find characterization for the distinguished varieties in symmetrized polydisc $\mathbb G_n \; (n\geq 2)$ and thus generalize work [\textit{J. Funct. Anal.}, 266 (2014), 5779 -- 5800] on G_2$ by author Shalit. show that a variety $\Lambda$ G_n$ is part of an algebraic curve, which set-theoretic complete intersection, can be represented Taylor joint spectrum $n-1$ commuting scalar matrices sat...

we investigated contraction to noradrenaline (na) and kc1 and sensitivity of na at the level of larger vessels (thoracic aorta and vena cava; left renal artery and left renal vein; lateral saphenous artery and lateral saphenous vein and finally central ear artery and marginal ear vein) in a model devised to mimic heart failure. the model presented here is the rabbit coronary ligation model in w...

In this note, a general class of contractive inequality, namely, admissible hybrid H − α ϕ contraction, is proposed in metric space endowed with graph, and new criteria for which the mapping Picard operator are examined. The ...