A dynamic soil chamber system coupled with a tunable diode laser for online measurements of δ13C, δ18O,and efflux rate of soil‐respired CO2

High frequency observations of the stable isotopic composition of CO₂ effluxes from soil have been sparse due in part to measurement challenges. We have developed an open‐system method that utilizes a flow‐through chamber coupled to a tunable diode laser (TDL) to quantify the rate of soil CO₂ efflux and its δ¹³C and δ¹⁸O values (δ¹³C_R and δ¹⁸O_R, respectively). We tested the method first in the laboratory using an artificial soil test column and then in a semi‐arid woodland. We found that the CO₂ efflux rates of 1.2 to 7.3 µmol m^?2 s^?1 measured by the chamber‐TDL system were similar to measurements made using the chamber and an infrared gas analyzer (IRGA) (R² = 0.99) and compared well with efflux rates generated from the soil test column (R² = 0.94). Measured δ¹³C and δ¹⁸O values of CO₂ efflux using the chamber‐TDL system at 2 min intervals were not significantly different from source air values across all efflux rates after accounting for diffusive enrichment. Field measurements during drought demonstrated a strong dependency of CO₂ efflux and isotopic composition on soil water content. Addition of water to the soil beneath the chamber resulted in average changes of +6.9 µmol m^?2 s^?1, ?5.0‰, and ?55.0‰ for soil CO₂ efflux, δ¹³C_R and δ¹⁸O_R, respectively. All three variables initiated responses within 2 min of water addition, with peak responses observed within 10 min for isotopes and 20 min for efflux. The observed δ¹⁸O_R was more enriched than predicted from temperature‐dependent H₂O‐CO₂ equilibration theory, similar to other recent observations of δ¹⁸O_R from dry soils (Wingate L, Seibt U, Maseyk K, Ogee J, Almeida P, Yakir D, Pereira JS, Mencuccini M. Global Change Biol. 2008; 14: 2178). The soil chamber coupled with the TDL was found to be an effective method for capturing soil CO₂ efflux and its stable isotope composition at high temporal frequency. Published in 2010 by John Wiley & Sons, Ltd.     

Directed supramolecular assembly of Cu(II)-based "paddlewheels" into infinite 1-D chains using structurally bifunctional ligands

The construction of Cu(II)-containing supramolecular chains is achieved by combining suitable anionic ligands (for controlling the coordination geometry and for creating a neutral building block) with four new bifunctional ligands containing a metal-coordinating pyridyl site and a self-complementary hydrogen-bonding moiety. Seven crystal structures are presented and in each case, the copper(II) complex displays a "paddlewheel" arrangement, with four carboxylate ligands occupying the equatorial sites, leaving room for the bifunctional ligand to coordinate in the axial positions. The supramolecular chemistry, which organizes the coordination-complexes into the desired infinite 1-D chains, is driven by a combination of N-H...N and N-H...O hydrogen-bonds in five of the seven structures.     

Hydrogen-bonded networks formed by substituted 2,6-diarylpyrazines

The X-ray crystal structure of 2,6-bis(4-hydroxyphenyl)pyrazine and 2,6-bis(4carboxyphenyl)pyrazine are reported. The structure of the 2,6-bis(4-carboxyphenyl) pyrazine dimethylsulfoxide complex (C₁₈H₁₂N₂O₄)(C₂H₆OS) is triclinic, P-1, with a = 7.9933(8), b = 10.7165(10), c = 12.1337(12) Å, = 66.385(2), = 84.070(2), = 77.219(2). The structure comprises stacked two-dimensional sheets of the hydrogen bonded complex. The two-dimensional sheets comprise hydrogen-bonded ribbons of the (carboxyphenyl)pyrazine that are connected by bridging hydrogen bonds to the dimethylsulfoxide. The structure of 2,6-bis(4-hydroxyphenyl)pyrazine, C₁₆H₁₂N₂O₂, is monoclinic, P2₁/c, with a = 10.6107(13) Å, b = 14.6743(18) Å, c = 8.3772(10) Å and = 104.982(2). The structure reveals that two-dimensional hydrogen-bonded sheets are formed with pyrazine–phenol and phenol–phenol hydrogen bonds.     

Photosensitive organosilicon polymers for microlithographic application

Two new families of photosensitive organo-silicon polymers are described. One is based on the Si-Si σ-bond photochemistry and another is based on the combinations of new alkaline-soluble organosilicon polymers with diazoquinone photosensitizers. Both of these photoactive materials not only give positive photoresist formulations but can act as oxygen reactive ion etch masks in the double-layer resist scheme to finally offer steep submicrometer organic patterns with high aspect ratio.     

Finite Frame Varieties: Nonsingular Points, Tangent Spaces, and Explicit Local Parameterizations

The (μ,S)-frames are frames with lengths in [μ ₁⋅⋅⋅μ _N ] and with frame operator S, or the F=[f₁?f_N] ? M_d×N(\mathbbE)F=[f_{1}\cdots f_{N}]\in M_{d\times N}(\mathbb{E}) with column lengths listed by μ and which satisfy FF ^∗=S. In this paper, we characterize the nonsingular points of real and complex finite (μ,S)-frame varieties by determining where generalized tori and distorted Stiefel manifolds intersect transversally in Hilbert-Schmidt spheres. This provides us with a characterization of the tangent space for each nonsingular point of the (μ,S)-frame varieties, and we leverage this characterization to demonstrate the existence of structured, locally well defined analytic coordinate patches. We conclude by deriving explicit expressions for these coordinates.     

Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups

The partition algebra \(\mathsf {P}_k(n)\) and the symmetric group \(\mathsf {S}_n\) are in Schur–Weyl duality on the k-fold tensor power \(\mathsf {M}_n^{\otimes k}\) of the permutation module \(\mathsf {M}_n\) of \(\mathsf {S}_n\), so there is a surjection \(\mathsf {P}_k(n) \rightarrow \mathsf {Z}_k(n) := \mathsf {End}_{\mathsf {S}_n}(\mathsf {M}_n^{\otimes k})\), which is an isomorphism when \(n \ge 2k\). We prove a dimension formula for the irreducible modules of the centralizer algebra \(\mathsf {Z}_k(n)\) in terms of Stirling numbers of the second kind. Via Schur–Weyl duality, these dimensions equal the multiplicities of the irreducible \(\mathsf {S}_n\)-modules in \(\mathsf {M}_n^{\otimes k}\). Our dimension expressions hold for any \(n \ge 1\) and \(k\ge 0\). Our methods are based on an analog of Frobenius reciprocity that we show holds for the centralizer algebras of arbitrary finite groups and their subgroups acting on a finite-dimensional module. This enables us to generalize the above result to various analogs of the partition algebra including the centralizer algebra for the alternating group acting on \(\mathsf {M}_n^{\otimes k}\) and the quasi-partition algebra corresponding to tensor powers of the reflection representation of \(\mathsf {S}_n\).     

Quantum integer-valued polynomials

We define a q-deformation of the classical ring of integer-valued polynomials which we call the ring of quantum integer-valued polynomials. We show that this ring has a remarkable combinatorial structure and enjoys many positivity properties: For instance, the structure constants for this ring with respect to its basis of q-binomial coefficient polynomials belong to \(\mathbb {N}[q]\). We then classify all maps from this ring into a field, extending a known classification in the classical case where \(q=1\).     

Constructing all self-adjoint matrices with prescribed spectrum and diagonal

The Schur–Horn Theorem states that there exists a self-adjoint matrix with a given spectrum and diagonal if and only if the spectrum majorizes the diagonal. Though the original proof of this result was nonconstructive, several constructive proofs have subsequently been found. Most of these constructive proofs rely on Givens rotations, and none have been shown to be able to produce every example of such a matrix. We introduce a new construction method that is able to do so. This method is based on recent advances in finite frame theory which show how to construct frames whose frame operator has a given prescribed spectrum and whose vectors have given prescribed lengths. This frame construction requires one to find a sequence of eigensteps, that is, a sequence of interlacing spectra that satisfy certain trace considerations. In this paper, we show how to explicitly construct every such sequence of eigensteps. Here, the key idea is to visualize eigenstep construction as iteratively building a staircase. This visualization leads to an algorithm, dubbed Top Kill, which produces a valid sequence of eigensteps whenever it is possible to do so. We then build on Top Kill to explicitly parametrize the set of all valid eigensteps. This yields an explicit method for constructing all self-adjoint matrices with a given spectrum and diagonal, and moreover all frames whose frame operator has a given spectrum and whose elements have given lengths.