The Chernobyl Disaster : reflection after 25 years = 切爾諾貝爾核災難25年後的反思

The adverse technogenic impact of industrial accidents that have gripped the world in recent decades definitely testifies to the problem-ridden character of contemporary economic and technological development. This is especially evident on the example of nuclear industry, which proved to be a source of dangerous pollution in case of potential (and real) catastrophes, as recently borne out by the Fukushima disaster. In this regard, the issues of Chernobyl disaster once again become the part of the discourse centered on the analysis of global nuclear industry problems. Likewise, current situation in Ukraine demands deeper investigation of the problems of technological development, as the gradual decay of industrial infrastructure inherited from the period of the USSR presents ever greater threat to the prospects of the nation’s further development. Therefore the examination of the consequences of the Chernobyl catastrophe is of a great importance for the purpose of more complex understanding of the situation of modern Ukraine

The variational principle and effective action for a spherical dust shell

The variational principle for a spherical configuration consisting of a thin spherical dust shell in gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions''. These conditions and the field equations following from the variational principle are used for performing of the reduction of this system. The equations of motion for the shell follow from the obtained reduced action. The transformation of the variational formula for the reduced action leads to two natural variants of the effective action. One of them describes the shell from a stationary interior observer's point of view, another from the exterior one. The conditions of isometry of the exterior and interior faces of the shell lead to the momentum and Hamiltonian constraints.Comment: 16 pages, LaTe

From Laplacian Transport to Dirichlet-to-Neumann (Gibbs) Semigroups

The paper gives a short account of some basic properties of \textit{Dirichlet-to-Neumann} operators $\Lambda_{\gamma,\partial\Omega}$ including the corresponding semigroups motivated by the Laplacian transport in anisotropic media ($\gamma \neq I$) and by elliptic systems with dynamical boundary conditions. For illustration of these notions and the properties we use the explicitly constructed \textit{Lax semigroups}. We demonstrate that for a general smooth bounded convex domain $\Omega \subset \mathbb{R}^d$ the corresponding {Dirichlet-to-Neumann} semigroup $\left\{U(t):= e^{-t \Lambda_{\gamma,\partial\Omega}}\right\}_{t\geq0}$ in the Hilbert space $L^2(\partial \Omega)$ belongs to the \textit{trace-norm} von Neumann-Schatten ideal for any $t>0$. This means that it is in fact an \textit{immediate Gibbs} semigroup. Recently Emamirad and Laadnani have constructed a \textit{Trotter-Kato-Chernoff} product-type approximating family $\left\{(V_{\gamma, \partial\Omega}(t/n))^n \right\}_{n \geq 1}$ \textit{strongly} converging to the semigroup $U(t)$ for $n\to\infty$. We conclude the paper by discussion of a conjecture about convergence of the \textit{Emamirad-Laadnani approximantes} in the the {\textit{trace-norm}} topology

Large NN Limits in Tensor Models: Towards More Universality Classes of Colored Triangulations in Dimension d≥2d\geq 2

We review an approach which aims at studying discrete (pseudo-)manifolds in dimension $d\geq 2$ and called random tensor models. More specifically, we insist on generalizing the two-dimensional notion of $p$-angulations to higher dimensions. To do so, we consider families of triangulations built out of simplices with colored faces. Those simplices can be glued to form new building blocks, called bubbles which are pseudo-manifolds with boundaries. Bubbles can in turn be glued together to form triangulations. The main challenge is to classify the triangulations built from a given set of bubbles with respect to their numbers of bubbles and simplices of codimension two. While the colored triangulations which maximize the number of simplices of codimension two at fixed number of simplices are series-parallel objects called melonic triangulations, this is not always true anymore when restricting attention to colored triangulations built from specific bubbles. This opens up the possibility of new universality classes of colored triangulations. We present three existing strategies to find those universality classes. The first two strategies consist in building new bubbles from old ones for which the problem can be solved. The third strategy is a bijection between those colored triangulations and stuffed, edge-colored maps, which are some sort of hypermaps whose hyperedges are replaced with edge-colored maps. We then show that the present approach can lead to enumeration results and identification of universality classes, by working out the example of quartic tensor models. They feature a tree-like phase, a planar phase similar to two-dimensional quantum gravity and a phase transition between them which is interpreted as a proliferation of baby universes

Distances between composition operators

The norm distance between two composition operators is calculated in select cases