Descent c-Wilf Equivalence

Let $S_n$ denote the symmetric group. For any $\sigma \in S_n$, we let $\mathrm{des}(\sigma)$ denote the number of descents of $\sigma$, $\mathrm{inv}(\sigma)$ denote the number of inversions of $\sigma$, and $\mathrm{LRmin}(\sigma)$ denote the number of left-to-right minima of $\sigma$. For any sequence of statistics $\mathrm{stat}_1, \ldots \mathrm{stat}_k$ on permutations, we say two permutations $\alpha$ and $\beta$ in $S_j$ are $(\mathrm{stat}_1, \ldots \mathrm{stat}_k)$-c-Wilf equivalent if the generating function of $\prod_{i=1}^k x_i^{\mathrm{stat}_i}$ over all permutations which have no consecutive occurrences of $\alpha$ equals the generating function of $\prod_{i=1}^k x_i^{\mathrm{stat}_i}$ over all permutations which have no consecutive occurrences of $\beta$. We give many examples of pairs of permutations $\alpha$ and $\beta$ in $S_j$ which are $\mathrm{des}$-c-Wilf equivalent, $(\mathrm{des},\mathrm{inv})$-c-Wilf equivalent, and $(\mathrm{des},\mathrm{inv},\mathrm{LRmin})$-c-Wilf equivalent. For example, we will show that if $\alpha$ and $\beta$ are minimally overlapping permutations in $S_j$ which start with 1 and end with the same element and $\mathrm{des}(\alpha) = \mathrm{des}(\beta)$ and $\mathrm{inv}(\alpha) = \mathrm{inv}(\beta)$, then $\alpha$ and $\beta$ are $(\mathrm{des},\mathrm{inv})$-c-Wilf equivalent.Comment: arXiv admin note: text overlap with arXiv:1510.0431

WHIZARD 2.2 for Linear Colliders

We review the current status of the WHIZARD event generator. We discuss, in particular, recent improvements and features that are relevant for simulating the physics program at a future Linear Collider.Comment: Talk presented at the International Workshop on Future Linear Colliders (LCWS13), Tokyo, Japan, 11-15 November 201

Renormalized Electron Mass in Nonrelativistic QED

Within the framework of nonrelativistic QED, we prove that, for small values of the coupling constant, the energy function, E_|P|, of a dressed electron is twice differentiable in the momentum P in a neighborhood of P = 0. Furthermore, (E_|P|)" is bounded from below by a constant larger than zero. Our results are proven with the help of iterative analytic perturbation theory

Uniqueness of the ground state in the Feshbach renormalization analysis

In the operator theoretic renormalization analysis introduced by Bach, Froehlich, and Sigal we prove uniqueness of the ground state.Comment: 10 page

Hyperfine splitting in non-relativistic QED: uniqueness of the dressed hydrogen atom ground state

We consider a free hydrogen atom composed of a spin-1/2 nucleus and a spin-1/2 electron in the standard model of non-relativistic QED. We study the Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum. For small enough values of the fine-structure constant, we prove that the ground state is unique. This result reflects the hyperfine structure of the hydrogen atom ground state.Comment: 22 pages, 3 figure

Reconsidering the role of carbonate ion concentration in calcification by marine organisms

Marine organisms precipitate 0.5–2.0 Gt of carbon as calcium carbonate (CaCO3) every year with a profound impact on global biogeochemical element cycles. Biotic calcification relies on calcium ions (Ca2+) and generally on bicarbonate ions (HCO3−) as CaCO3 substrates and can be inhibited by high proton (H+) concentrations. The seawater concentration of carbonate ions (CO32−) and the CO32−-dependent CaCO3 saturation state (ΩCaCO3) seem to be irrelevant in this production process. Nevertheless, calcification rates and the success of calcifying organisms in the oceans often correlate surprisingly well with these two carbonate system parameters. This study addresses this dilemma through rearrangement of carbonate system equations which revealed an important proportionality between [CO32−] or ΩCaCO3 and the ratio of [HCO3−] to [H+]. Due to this proportionality, calcification rates will always correlate equally well with [HCO3−]/[H+] as with [CO32−] or ΩCaCO3 when temperature, salinity, and pressure are constant. Hence, [CO32−] and ΩCaCO3 may simply be very good proxies for the control by [HCO3−]/[H+] where [HCO3−] would be the inorganic carbon substrate and [H+] would function as calcification inhibitor. If the "substrate-inhibitor ratio" (i.e. [HCO3−]/[H+]) rather than [CO32−] or ΩCaCO3 controls CaCO3 formation then some of the most common paradigms in ocean acidification research need to be reviewed. For example, the absence of a latitudinal gradient in [HCO3−]/[H+] in contrast to [CO32−] and ΩCaCO3 could modify the common assumption that high latitudes are affected most severely by ocean acidification