High-resolution in-beam particle-gamma coincidence spectroscopy

A short summary of the present status of prompt particle decays in the mass region is presented. It includes recent results from a GAMMASPHERE experiment, which aimed at the combined high-resolution spectroscopy of light charged particles and -rays to allow for more detailed studies of known decays and the identification of new cases of discrete prompt proton and -particle emission from highly and superdeformed states.Received: 10 October 2002, Published online: 17 February 2004PACS: 23.50. + z Decay by proton emission - 23.60. + e decay - 27.40. + z - 27.50. + e      

The Generalized Cross Entropy Method, with Applications to Probability Density Estimation

Nonparametric density estimation aims to determine the sparsest model that explains a given set of empirical data and which uses as few assumptions as possible. Many of the currently existing methods do not provide a sparse solution to the problem and rely on asymptotic approximations. In this paper we describe a framework for density estimation which uses information-theoretic measures of model complexity with the aim of constructing a sparse density estimator that does not rely on large sample approximations. The effectiveness of the approach is demonstrated through an application to some well-known density estimation test cases.     

The materials science X‐ray beamline BL8 at the DELTA storage ring

The hard X‐ray beamline BL8 at the superconducting asymmetric wiggler at the 1.5 GeV Dortmund Electron Accelerator DELTA is described. This beamline is dedicated to X‐ray studies in the spectral range from ～1 keV to ～25 keV photon energy. The monochromator as well as the other optical components of the beamline are optimized accordingly. The endstation comprises a six‐axis diffractometer that is capable of carrying heavy loads related to non‐ambient sample environments such as, for example, ultrahigh‐vacuum systems, high‐pressure cells or liquid‐helium cryostats. X‐ray absorption spectra from several reference compounds illustrate the performance. Besides transmission measurements, fluorescence detection for dilute sample systems as well as surface‐sensitive reflection‐mode experiments have been performed. The results show that high‐quality EXAFS data can be obtained in the quick‐scanning EXAFS mode within a few seconds of acquisition time, enabling time‐resolved in situ experiments using standard beamline equipment that is permanently available. The performance of the new beamline, especially in terms of the photon flux and energy resolution, is competitive with other insertion‐device beamlines worldwide, and several sophisticated experiments including surface‐sensitive EXAFS experiments are feasible.     

Uniqueness of integrable solutions to {\nabla \zeta=G \zeta, \zeta|_\Gamma = 0} for integrable tensor coefficients G and applications to elasticity

Let ${\Omega \subset \mathbb{R}^{N}}$ be a Lipschitz domain and Γ be a relatively open and non-empty subset of its boundary ${\partial\Omega}$ . We show that the solution to the linear first-order system $$\nabla \zeta = G\zeta, \, \, \zeta|_\Gamma = 0 \quad \quad \quad (1)$$ is unique if ${G \in \textsf{L}^{1}(\Omega; \mathbb{R}^{(N \times N) \times N})}$ and ${\zeta \in \textsf{W}^{1,1}(\Omega; \mathbb{R}^{N})}$ . As a consequence, we prove $$||| \cdot ||| : \textsf{C}_{o}^{\infty}(\Omega, \Gamma; \mathbb{R}^{3}) \rightarrow [0, \infty), \, \, u \mapsto \parallel {\rm sym}(\nabla uP^{-1})\parallel_{\textsf{L}^{2}(\Omega)}$$ to be a norm for ${P \in \textsf{L}^{\infty}(\Omega; \mathbb{R}^{3 \times 3})}$ with Curl ${P \in \textsf{L}^{p}(\Omega; \mathbb{R}^{3 \times 3})}$ , Curl ${P^{-1} \in \textsf{L}^{q}(\Omega; \mathbb{R}^{3 \times 3})}$ for some p, q > 1 with 1/p + 1/q = 1 as well as det ${P \geq c^+ > 0}$ . We also give a new and different proof for the so-called ‘infinitesimal rigid displacement lemma’ in curvilinear coordinates: Let ${\Phi \in \textsf{H}^{1}(\Omega; \mathbb{R}^{3})}$ satisfy sym ${(\nabla\Phi^\top\nabla\Psi) = 0}$ for some ${\Psi \in \textsf{W}^{1,\infty}(\Omega; \mathbb{R}^{3}) \cap \textsf{H}^{2}(\Omega; \mathbb{R}^{3})}$ with det ${\nabla\Psi \geq c^+ > 0}$ . Then, there exist a constant translation vector ${a \in \mathbb{R}^{3}}$ and a constant skew-symmetric matrix ${A \in \mathfrak{so}(3)}$ , such that ${\Phi = A\Psi + a}$ .     

Compact formulations of the Steiner Traveling Salesman Problem and related problems

The Steiner Traveling Salesman Problem (STSP) is a variant of the TSP that is particularly suitable when routing on real-life road networks. The standard integer programming formulations of both the TSP and STSP have an exponential number of constraints. On the other hand, several compact formulations of the TSP, i.e., formulations of polynomial size, are known. In this paper, we adapt some of them to the STSP, and compare them both theoretically and computationally. It turns out that, just by putting the best of the formulations into the CPLEX branch-and-bound solver, one can solve instances with over 200 nodes. We also briefly discuss the adaptation of our formulations to some related problems.     

Resonance splitting in gyrotropic ring resonators

We present the theoretical concept of an optical isolator based on resonance splitting in a silicon ring resonator covered with a magneto-optical polymer cladding. For this task, a perturbation method is derived for the modes in the cylindrical coordinate system. A polymer magneto-optical cladding causing a 0.01 amplitude of the off-diagonal element of the dielectric tensor is assumed. It is shown that the derived resonance splitting of the clockwise and counterclockwise modes increases for smaller ring radii. For the ring with a radius of approximately 1.5μm, a 29GHz splitting is demonstrated. An integrated optical isolator with a 10μm geometrical footprint is proposed based on a critically coupled ring resonator.     

Unique continuation for first-order systems with integrable coefficients and applications to elasticity and plasticity

Let $\Omega ?{\mathbb{R}}^N$ be a Lipschitz domain and Γ be a relatively open and non-empty subset of its boundary ?Ω. We show that the solution to the linear first-order system:(1)$\mathrm{?}\zeta =G\zeta ,\zeta {|}_{\Gamma }=0,$ vanishes if $G\in {\mathsf{L}}^1(\Omega ;{\mathbb{R}}^{(N\times N)\times N})$ and $\zeta \in {\mathsf{W}}^{1,1}(\Omega ;{\mathbb{R}}^N)$. In particular, square-integrable solutions ζ of (1) with $G\in {\mathsf{L}}^1\cap {\mathsf{L}}^2(\Omega ;{\mathbb{R}}^{(N\times N)\times N})$ vanish. As a consequence, we prove that:$???:{\mathsf{C}}_{°}^{\infty }(\Omega ,\Gamma ;{\mathbb{R}}^3)\to [0,\infty ),u?6\mathrm{sym}\left(\mathrm{?}u{P}^{?1}\right)6_{{\mathsf{L}}^2(\Omega )}$ is a norm if $P\in {\mathsf{L}}^{\infty }(\Omega ;{\mathbb{R}}^{3\times 3})$ with $\mathrm{Curl}P\in {\mathsf{L}}^p(\Omega ;{\mathbb{R}}^{3\times 3})$, $\mathrm{Curl}{P}^{?1}\in {\mathsf{L}}^q(\Omega ;{\mathbb{R}}^{3\times 3})$ for some $p,q>1$ with $1/p+1/q=1$ as well as $\det P?c^{+}>0$. We also give a new and different proof for the so-called ‘infinitesimal rigid displacement lemma’ in curvilinear coordinates: Let $\Phi \in {\mathsf{H}}^1(\Omega ;{\mathbb{R}}^3)$, $\Omega ?{\mathbb{R}}^3$, satisfy $\mathrm{sym}(\mathrm{?}{\Phi }^{?}\mathrm{?}\Psi )=0$ for some $\Psi \in {\mathsf{W}}^{1,\infty }(\Omega ;{\mathbb{R}}^3)\cap {\mathsf{H}}^2(\Omega ;{\mathbb{R}}^3)$ with $\det \mathrm{?}\Psi ?c^{+}>0$. Then there exists a constant translation vector $a\in {\mathbb{R}}^3$ and a constant skew-symmetric matrix $A\in \mathfrak{so}(3)$, such that $\Phi =A\Psi +a$.     

Syntheses and Crystal Structures of Potassium–Lanthanoid(III) Complexes with the 1,2‐Benzenedisulfonate Ligand

The complexes [K(H₂O)₂LnL₂] (Ln = La or Nd; L = 1,2‐benzenedisulfonate) and [K(H₂O)Yb(H₂O)₄L₂] were initially isolated fortuitously from attempts to prepare the corresponding Ln₂L₃ complexes from Ln₂O₃ and H₂L in water. Indeed the bulk products from these reactions have the composition Ln₂L₃. Subsequently, deliberate syntheses by reacting equimolar amounts of Ln₂L₃ with K₂L in water gave the complexes in good yield. X‐ray crystal structures of [K(H₂O)₂LnL₂] (Ln = La or Nd) showed the complexes to be isostructural with a two dimensional polymeric network structure in which LnL₂ units are linked into chains crosslinked by potassium ions. Each Ln is nine coordinate with solely sulfonate oxygen donor atoms. Between adjacent lanthanoid ions there are three different types of sulfonate bridges and two examples of each. Most noteworthy is highly unsymmetrical bridging through μ‐η²‐sulfonate oxygen atoms. Consequently, one Ln–O bond is ca. 0.5 Å longer than the other eight. Potassium is nine‐coordinate with seven sulfonate oxygen atoms and two aqua ligands, and surprisingly <K–O(sulfonate)> is much longer than <K–O(H₂O)>. Pairs of potassium ions are linked by two μ‐η²‐sulfonate oxygen atoms, which are unsymmetrically bridging. The structure of [K(H₂O)Yb(H₂O)₄L₂] comprises discrete tetranuclear units containing two independent ytterbium ions, each coordinated by four water molecules and two chelating (via seven membered rings) disulfonate ligands, and two potassium ions, each coordinated by six sulfonate oxygen atoms and a water molecule. For each potassium, four of the coordinated sulfonate oxygen atoms are from sulfonate ligands bonded to one ytterbium atom and two from sulfonate ligands attached to the other ytterbium atom. In contrast to the Nd and La complexes, <K–O(sulfonate)> is shorter than <K–O(H₂O)>.     

Optical Control of Acetylcholinesterase with a Tacrine Switch

Photochromic ligands have been used to control a variety of biological functions, especially in neural systems. Recently, much effort has been invested in the photocontrol of ion channels and G‐protein coupled receptors found in the synapse. Herein, we describe the expansion of our photopharmacological approach toward the remote control of an enzyme. Building on hallmark studies dating from the late 1960s, we evaluated photochromic inhibitors of one of the most important enzymes in synaptic transmission, acetylcholinesterase (AChE). Using structure‐based design, we synthesized several azobenzene analogues of the well‐known AChE inhibitor tacrine (THA) and determined their effects on enzymatic activity. One of our compounds, AzoTHA, is a reversible photochromic blocker of AChE in vitro and ex vivo with high affinity and fast kinetics. As such, AzoTHA can be used to control synaptic transmission on the neuromuscular endplate based on the light‐dependent clearance of a neurotransmitter.