Cadmium nitrate coordination polymers with substituted pyridazino[4,5‐d]pyridazines

catena‐Poly[[aquabis(nitrato‐κ²O,O′)cadmium(II)]‐μ‐1,2,3,6,7,8‐hexa­hydro­cinnolino[5,4,3‐cde]cinnoline‐κN¹:κN⁶], [Cd(NO₃)₂(C₁₂H₁₂N₄)(H₂O)]_n, (I), and catena‐poly[[[bis(nitrato‐κ²O,O′)cadmium(II)]‐μ‐2,2,7,7‐tetra­methyl‐1,2,3,6,7,8‐hexahydro­cinnolino[5,4,3‐cde]cinnoline‐κN¹:κN⁶] chloro­form solvate], {[Cd(NO₃)₂(C₁₂H₁₂N₄)]·CHCl₃}_n, (II), are the first structurally examined cadmium–pyridazine coordination compounds. They possess one‐dimensional polymeric structures supported by the bidentate bridging function of the cinnolino[5,4,3‐cde]cinnoline ligands, which lie about inversion centres. The Cd atoms are seven‐coordinated in (I) and six‐coordinated in (II), involving two bidentate nitrate groups [Cd—O = 2.229 (2)–2.657 (2) Å], two N atoms of the cinnoline ligands [Cd—N = 2.252 (2)–2.425 (2) Å], and, additionally, a water O atom in (I) [Cd—O = 2.284 (2) Å]. In (I), the coordinated organic and aqua ligands form an intra­molecular O—H⋯N hydrogen bond [O⋯N = 2.730 (3) Å].     

Er5Ni3Al3Ge4: a quaternary variant of the NbCoB type

Single crystals of penta­erbium trinickel trialuminium tetra­germanium were synthesized from the elements by arc‐melting. The novel compound crystallizes in the space group Pmmn, e⁶b²a, with all nine crystallographically unique atoms in special positions of site symmetries m.. and mm2. This compound represents a new ordered variant of the NbCoB type. Its two‐layer structure is described as an inter­growth of the Er₃NiAl₃Ge₂ (Y₃NiAl₃Ge₂ type) and ErNiGe (TiNiSi type) structures. The coordination polyhedra are distorted penta­gonal prisms around Er atoms, tetra­gonal prisms around Al and Ni atoms, and trigonal prisms around Ge and Ni atoms, capped with eight, four and three extra vertices, respectively.     

Diffusion of thermonuclear alpha particles under the influence of intense LH waves

Recently, a new mechanism was proposed by Fisch and Rax which should lead to amplification of lower hybrid (LH) waves at the expense of alpha particles energy, improving thus the LH current drive efficiency. The present contribution investigates the possibility of achieving the conditions on which this mechanism — based on the spatial diffusion of fusion alpha particles — could become operative. The analysis performed shows that in reactor grade tokamaks, the penetration of LH waves into the plasma column is very poor due to the intense electron Landau damping and the complicated geometry of the equilibrium magnetic fields. Consequently, at acceptable LHW input power levels, the waves do not reach the regions where fusion alpha particle power could reasonably compensate the losses of LHW energy due to the damping by electrons. The model of Fisch and Rax is based on special features of the induced diffusion of alpha particles in the energy-configuration space. Using suitable Hamiltonian formalism, the LHW induced radial diffusion of alpha particles and the energy transport between LHW and alpha particles in the frame of generalized quasilinear lines of diffusion constraint is also investigated. A rather strong change ofk of LHW along the ray trace can contribute to the change of energy transport between LHW and alpha particles as well.The authors are indebted to Dr. R. Klíma for valuable discussions.     

Temperley-Lieb pfaffinants and Schur Q-positivity conjectures

We study pfaffian analogues of immanants, which we call pfaffinants. Our main object is the TL-pfaffinants which are analogues of Rhoades and Skandera's TL-immanants. We show that TL-pfaffinants are positive when applied to planar networks and explain how to decompose products of complementary pfaffians in terms of TL-pfaffinants. We conjecture in addition that TL-pfaffinants have positivity properties related to Schur Q-functions.     

Hydrate frameworks involving the pyridazino[4,5‐d]pyridazine unit as a multiple hydrogen‐bond acceptor

1,4,5,8‐Tetramethylpyridazino[4,5‐d]pyridazine trihydrate, C₁₀H₁₂N₄·3H₂O, (I), and 1,2,3,6,7,8‐hexahydrocinnolino[5,4,3‐cde]cinnoline tetrahydrate, C₁₂H₁₂N₄·4H₂O, (II), exhibit exceptional functionality of the condensed N₄‐heteroaromatic frame as a symmetric acceptor of four hydrogen bonds [N...O = 2.843 (2)–2.8716 (10) Å]. Thus, all the N atoms of the electron‐deficient and highly π‐acidic polynitrogen heterocycles function as lone‐pair donors. In (I), all the molecular components lie on or across special positions; the site symmetry is 2/m for the organic and m2m and m for the two water molecules. In (II), the organic polycycle lies across a crystallographic inversion center. Both structures involve a hydrogen‐bonded centrosymmetric water–pyridazine dimer as the basic supramolecular unit, which is integrated into two‐dimensional [in (I)] and three‐dimensional [in (II)] hydrate frameworks by hydrogen bonding with the additional water molecules [O...O = 2.744 (2)–2.8827 (19) Å]. The hydrate connectivity exists in the form of an (H₂O)₃ trimer in (I) and as a one‐dimensional zigzag (H₂O)_n chain in (II).     

A sample-path approach to optimal position liquidation

We consider the problem of optimal position liquidation where the expected cash flow stream due to transactions is maximized in the presence of temporary or permanent market impact. A stochastic programming approach is used to construct trading strategies that differentiate decisions with respect to the observed market conditions, and can accommodate various types of trading constraints. As a scenario model, we use a collection of sample paths representing possible future realizations of state variable processes (price, trading volume etc.), and employ a heuristical technique of sample-path grouping, which can be viewed as a generalization of the standard nonanticipativity constraints.     

Self-assembly sodalite-like framework

The dense packing of shape complementary N-donor molecules dominates the self-assembly of coordination polymers possessing sodalite-like topology and supports nanosize molecular cages.     

Total positivity for loop groups II: Chevalley generators

This is the second in a series of papers developing a theory of total positivity for loop groups. In this paper, we study infinite products of Chevalley generators. We show that the combinatorics of infinite reduced words underlies the theory, and develop the formalism of infinite sequences of braid moves, called a braid limit. We relate this to a partial order, called the limit weak order, on infinite reduced words. The limit semigroup generated by Chevalley generators has a transfinite structure. We prove a form of unique factorization for its elements, in effect reducing their study to infinite products which have the order structure of ?. For the latter infinite products, we show that one always has a factorization which matches an infinite Coxeter element. One of the technical tools we employ is a totally positive exchange lemma which appears to be of independent interest. This result states that the exchange lemma (in the context of Coxeter groups) is compatible with total positivity in the form of certain inequalities.     

Collisionally assisted spectroscopy of water from 27,000 to 34,000 cm(-1)

We report here an experimental approach that enables measurement of weak transitions to a wide range of rovibrational levels of water in the energy region 27,000-34,200 cm(-1). We have previously demonstrated the use of laser double-resonance overtone excitation to access highly excited vibrational levels from single rovibrational states. Although this approach simplifies the assignment of the spectra, it strongly reduces the number of observed transitions and hence our ability to test theoretical predictions. Here, we increase significantly the number of observed transitions by allowing rotational relaxation of H2O at intermediate levels of the double-resonance excitation scheme to the levels of the same nuclear spin (ortho or para). Our recently developed semiempirical potential energy surface PES12 enables assignment of the resulting complex spectra and reproduction of the measured transitions with accuracy better than 1 cm(-1).