Towards a microchannel‐based X‐ray detector with two‐dimensional spatial and time resolution and high dynamic range

X‐ray detectors that combine two‐dimensional spatial resolution with a high time resolution are needed in numerous applications of synchrotron radiation. Most detectors with this combination of capabilities are based on semiconductor technology and are therefore limited in size. Furthermore, the time resolution is often realised through rapid time‐gating of the acquisition, followed by a slower readout. Here, a detector technology is realised based on relatively inexpensive microchannel plates that uses GHz waveform sampling for a millimeter‐scale spatial resolution and better than 100 ps time resolution. The technology is capable of continuous streaming of time‐ and location‐tagged events at rates greater than 10⁷ events per cm². Time‐gating can be used for improved dynamic range.     

Symmetric Powers of Galois Modules on Dedekind Schemes

We prove a certain Riemann–Roch-type formula for symmetric powers of Galois modules on Dedekind schemes which, in the number field or function field case, specializes to a formula of Burns and Chinburg for Cassou–Noguès–Taylor operations.     

Unbalanced optimal transport: Dynamic and Kantorovich formulations

This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative formulations: (i) a dynamic formulation defining the distance as a geodesic distance over the space of measures (ii) a static “Kantorovich” formulation where the distance is the minimum of an optimization problem over pairs of couplings describing the transfer (transport, creation and destruction) of mass between two measures. Both formulations are convex optimization problems, and the ability to switch from one to the other depending on the targeted application is a crucial property of our models. Of particular interest is the Wasserstein–Fisher–Rao metric recently introduced independently by [7], [15]. Defined initially through a dynamic formulation, it belongs to this class of metrics and hence automatically benefits from a static Kantorovich formulation.     

Horospherical transform on real symmetric varieties: Kernel and cokernel

In this paper, we define a horospherical transform for a semisimple symmetric space Y. A natural double fibration is used to assign a more geometrical space Ξ of horospheres to Y. The horospherical transform relates certain integrable analytic functions on Y to analytic functions on Ξ by fiber integration. We determine the kernel of the horospherical transform and establish that the transform is injective on functions belonging to the most continuous spectrum of Y.     

Construction of relative difference sets and Hadamard groups

‘There exist normal \((2m,2,2m,m)\) relative difference sets and thus Hadamard groups of order \(4m\) for all \(m\) of the form $$\begin{aligned} m= x2^{a+t+u+w+\delta -\epsilon +1}6^b 9^c 10^d 22^e 26^f \prod _{i=1}^s p_i^{4a_i} \prod _{i=1}^t q_i^2 \prod _{i=1}^u \left( (r_i+1)/2)r_i^{v_i}\right) \prod _{i=1}^w s_i \end{aligned}$$ under the following conditions: \(a,b,c,d,e,f,s,t,u,w\) are nonnegative integers, \(a_1,\ldots ,a_r\) and \(v_1,\ldots ,v_u\) are positive integers, \(p_1,\ldots ,p_s\) are odd primes, \(q_1,\ldots ,q_t\) and \(r_1,\ldots ,r_u\) are prime powers with \(q_i\equiv 1\ (\mathrm{mod}\ 4)\) and \(r_i\equiv 1\ (\mathrm{mod}\ 4)\) for all \(i, s_1,\ldots ,s_w\) are integers with \(1\le s_i \le 33\) or \(s_i\in \{39,43\}\) for all \(i, x\) is a positive integer such that \(2x-1\) or \(4x-1\) is a prime power. Moreover, \(\delta =1\) if \(x>1\) and \(c+s>0, \delta =0\) otherwise, \(\epsilon =1\) if \(x=1, c+s=0\) , and \(t+u+w>0, \epsilon =0\) otherwise. We also obtain some necessary conditions for the existence of \((2m,2,2m,m)\) relative difference sets in partial semidirect products of \(\mathbb{Z }_4\) with abelian groups, and provide a table cases for which \(m\le 100\) and the existence of such relative difference sets is open.     

Identifying sources and processes controlling the sulphur cycle in the Canyon Creek watershed, Alberta, Canada

Sources and processes affecting the sulphur cycle in the Canyon Creek watershed in Alberta (Canada) were investigated. The catchment is important for water supply and recreational activities and is also a source of oil and natural gas. Water was collected from 10 locations along an 8?km stretch of Canyon Creek including three so-called sulphur pools, followed by the chemical and isotopic analyses on water and its major dissolved species. The δ(2)H and δ(18)O values of the water plotted near the regional meteoric water line, indicating a meteoric origin of the water and no contribution from deeper formation waters. Calcium, magnesium and bicarbonate were the dominant ions in the upstream portion of the watershed, whereas sulphate was the dominant anion in the water from the three sulphur pools. The isotopic composition of sulphate (δ(34)S and δ(18)O) revealed three major sulphate sources with distinct isotopic compositions throughout the catchment: (1) a combination of sulphate from soils and sulphide oxidation in the bedrock in the upper reaches of Canyon Creek; (2) sulphide oxidation in pyrite-rich shales in the lower reaches of Canyon Creek and (3) dissolution of Devonian anhydrite constituting the major sulphate source for the three sulphur pools in the central portion of the watershed. The presence of H(2)S in the sulphur pools with δ(34)S values ～30?‰ lower than those of sulphate further indicated the occurrence of bacterial (dissimilatory) sulphate reduction. This case study reveals that δ(34)S values of surface water systems can vary by more than 20?‰ over short geographic distances and that isotope analyses are an effective tool to identify sources and processes that govern the sulphur cycle in watersheds.     

Rhodium‐Catalyzed Asymmetric Intramolecular Hydroamination of Allenes

The rhodium‐catalyzed asymmetric intramolecular hydroamination of sulfonyl amides with terminal allenes is reported. It provides selective access to 5‐ and 6‐membered N‐heterocycles, scaffolds found in a large range of different bioactive compounds. Moreover, gram scale reactions, as well as the application of suitable product transformations to natural products and key intermediates thereof are demonstrated.     

Synthesis of α-fluoro-α,β-unsaturated esters monitored by 1D and 2D benchtop NMR spectroscopy

For optimization and control of pharmaceutically and industrially important reactions, chemical information is required in real time. Instrument size, handling, and operation costs are important criteria to be considered when choosing a suitable analytical method apart from sensitivity and resolution. This present study explores the use of a robust and compact nuclear magnetic resonance (NMR) spectrometer to monitor the stereo-selective formation of α-fluoro-α,β-unsaturated esters from α-fluoro-β-keto esters via deprotonation and deacylation in real time. These compounds are precursors of various pharmaceutically active substances. The real-time study revealed the deprotonation and deacylation steps of the reaction. The reaction was studied at temperatures ranging from 293 to 333 K by interleaved one-dimensional ¹H and ¹⁹F and two-dimensional ¹H–¹H COSY experiments. The kinetic rate constants were evaluated using a pseudo first-order kinetic model. The activation energies for the deprotonation and deacylation steps were determined to 28 ± 2 and 63.5 ± 8 kJ/mol, respectively. This showed that the deprotonation step is fast compared with the deacylation step and that the deacylation step determines the rate of the overall reaction. The reaction was repeated three times at 293 K to monitor the repeatability and stability of the system. The compact NMR spectrometer provided detailed information on the mechanism and kinetics of the reaction, which is essential for optimizing the synthetic routes for stepwise syntheses of pharmaceutically active substances.     

{(MesGa)3[GaP(H)Mes](PMes)4}, Ein phosphorsubstituiertes Ga?P-Heterocuban

{(MesGa)₃[GaP(H)Mes](PMes)₄}, a Phosphorus-substituted Ga? P-Heterocubane A mixture of MesGaCl₂/GaCl₃ (ratio 3:1) reacts with 5 equivalents of MesPLi₂ in THF at ?78°C to the title compound {(MesGa)₃[GaP(H)Mes](PMes)₄} ( 1 ) by use of the “dilution principle”. 1 can be obtained in 30% yield. Recrystallization of 1 from DME and toluene, respectively, gives 1 · 0.5 DME and 1 · toluene. 1 was characterized by NMR-, IR-, and MS-techniques. According to the X-ray structure determination of 1 · toluene, 1 has a heterocubane structure, one corner of which is substituted with an P(H)Mes group.     

The Uracil C(5) Position as a Metal Binding Site: Solution and X-ray Crystal Structure Studies of Pt(II) and Hg(II) Compounds

1,3-Dimethyluracil (1,3-DimeU) reacts with trans-[(CH(3)NH(2))(2)Pt(H(2)O)(2)](+) to give trans-[(CH(3)NH(2))(2)Pt(1,3-DimeU-C5)(H(2)O)]X (X = NO(3)(-), 1a, ClO(4)(-), 1b) and subsequently with NaCl to give trans-(CH(3)NH(2))(2)Pt(1,3-DimeU-C5)Cl (2) or with NH(3) to yield trans-[(CH(3)NH(2))(2)Pt(1,3-DimeU-C5)(NH(3))]ClO(4) (3). In a similar way, (dien)Pt(II) forms [dienPt(1,3-DimeU-C5)](+) (4). Reactions leading to formation of 1 and 4 are slow, taking days. In contrast, Hg(CH(3)COO)(2) reacts fast with 1,3-DimeU to give (1,3-DimeU-C5)Hg(CH(3)COO) (5). Both 1-methyluracil (1-MeUH) and uridine (urdH) react with (dien)Pt(II) initially at N(3) and subsequently with either (dien)Pt(II) or Hg(CH(3)COO)(2) also at C(5) to give the diplatinated species 7 and 9 or the mixed PtHg complex 8. C(5) binding of either Pt(II) or Hg(II) is evident from coupling of uracil-H(6) with either (195)Pt or (199)Hg nuclei and (3)J values of 47-74 Hz (for Pt compounds) and 185-197 Hz (for Hg compounds). J values of Pt compounds are influenced both by the ligands trans to the uracil C(5) position and by the number of metal entities bound to a uracil ring. Both 2 and 5 were X-ray structurally characterized. 2: monoclinic system, space group P2(1)/c, a = 15.736(6) ?, b = 11.481(6) ?, c = 25.655 (10) ?, beta = 145.55(3) degrees, V = 2621.9(28) ?(3), Z = 4. 5: monoclinic system, space group P2(1)/c, a = 4.905(2) ?, b = 18.451(6) ?, c = 11.801(5) ?, beta = 94.47(3) degrees, V = 1064.77(72) ?(3), Z = 4.