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The energy and iota energy of signed digraphs are respectively defined by $E(S) = $ $\sum_{k = 1}^n|{\rm Re}(\rho_k)|$ and $E_c(S) = \sum_{k = 1}^n|{\rm Im }(\rho_k)|$, where $\rho_1, \dots, \rho_n$ are eigenvalues of $S$, and ${\rm Re}(\rho_k)$ and ${\rm Im}(\rho_k)$ are respectively real and imaginary values of the eigenvalue $\rho_k$. Recently, Yang and Wang (2018) found the energy and iota energy ordering of digraphs in $\mathcal{D}_n$ and computed the maximal energy and iota energy, where $\mathcal{D}_n$ denotes the set of vertex-disjoint bicyclic digraphs of a fixed order $n$. In this paper, we investigate the energy ordering of signed digraphs in $\mathcal{D}_n^s$ and find the maximal energy, where $\mathcal{D}_n^s$ denotes the set of vertex-disjoint bicyclic sidigraphs of a fixed order $n$.

On the basis of universal scaling properties, we claim that in Au+Au collisions at RHIC, the QCD critical point is within reach. The signal turns out to be an extended plateau of net baryons in rapidity with approximate height of the net-baryon rapidity density approximately 15 and a strong intermittency pattern with index s_2=1/6 in rapidity fluctuations. A window also exists, to reach the critical point at the SPS, especially in Si+Si collisions at maximal energy. 8 pages, 3 figures

Various quantum thermodynamic bounds are shown to stem from a single tighter and more general inequality, consequence of the operator concavity of the logarithmic function. Such an inequality, which we call the "thermodynamic reverse bound", is compactly expressed as a quantum relative entropy, from which it inherits mathematical properties and meaning. As concrete examples, we apply our bound to evaluate the thermodynamic length for open processes, the heat exchange in erasure processes, and the maximal energy outflow in general quantum evolutions. v2: added six colorful plots for the heat exchanged in erasure processes, accepted in PRA; v1: 6 pages, two-column

In this note we establish estimates for the harmonic map heat flow from $S^1$ into a closed manifold, and use it to construct sweepouts with the following good property: each curve in the tightened sweepout, whose energy is close to the maximal energy of curves in the sweepout, is itself close to a closed geodesic. Comment: 7 pages; added reference; corrected typos

We consider the extremal pointset configuration problem of maximizing a kernel-based energy subject to the geometric constraints that the points are contained in a fixed set, the pairwise distances are bounded below, and that every closed ball of fixed radius contains at least one point. We also formulate an extremal density problem, whose solution provides an upper bound for the pointset configuration problem in the limit as the number of points tends to infinity. Existence of solutions to both problems is established and the relationship between the parameters in the two problems is studied. Several examples are studied in detail, including the density problem for the $d$-dimensional ball and sphere, where the solution can be computed exactly using rearrangement inequalities. We develop a computational method for the density problem that is very similar to the Merriman-Bence-Osher (MBO) diffusion-generated method. The method is proven to be increasing for all non-stationary iterations and is applied to study more examples. Comment: 24 pages, 6 figures

In this paper we study the distribution of scattering resonances for a multidimensional semi-classical Schr\"odinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea. Comment: 55 pages, 2 figures, to be published in Arkiv f\"or Matematik

The present work draws on the understanding how notions of general potential theory - as set up, e.g., by Fuglede - explain existence and some basic results on the "magical" rendezvous numbers. We aim at a fairly general description of rendezvous numbers in a metric space by using systematically the potential theoretic approach. In particular, we generalize and explain results on invariant measures, hypermetric spaces and maximal energy measures, when showing how more general proofs can be found to them. Comment: 10 pages