ﻻ يوجد ملخص باللغة العربية
1) We identify new parameter branches for the ultra-local boundary Poisson bracket in d spatial dimension with a (d-1)-dimensional spatial boundary. There exist 2^{r(r-1)/2} r-dimensional parameter branches for each d-box, r-row Young tableau. The already known branch (hep-th/9912017) corresponds to a vertical 1-column, d-box Young tableau. 2) We consider a local distribution product among the so-called boundary distributions. The product is required to respect the associativity and the Leibnitz rule. We show that the consistency requirements on this product correspond to the Jacobi identity conditions for the boundary Poisson bracket. In other words, the restrictions on forming a boundary Poisson bracket can be related to the more fundamental distribution product construction. 3) The definition of the higher functional derivatives is made independent of the choice of integral kernel representative for a functional.
The minimum rate needed to accurately approximate a product distribution based on an unnormalized informational divergence is shown to be a mutual information. This result subsumes results of Wyner on common information and Han-Verd{u} on resolvabili
The choice of a star product realization for noncommutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as integration measur
Using the recently introduced boundary form factor bootstrap equations, we map the complete space of their solutions for the boundary version of the scaling Lee-Yang model and sinh-Gordon theory. We show that the complete space of solutions, graded b
In recent years, there are many attempts to understand popular heuristics. An example of such a heuristic algorithm is the ID3 algorithm for learning decision trees. This algorithm is commonly used in practice, but there are very few theoretical work
We propose a Monte Carlo simulation method to generate stress tests by VaR scenarios under Solvency II for dependent risks on the basis of observed data. This is of particular interest for the construction of Internal Models and requirements on evalu