A convenient method of anion exchange in quaternary salts

A convenient and efficient method for the preparation of anion exchanged quaternary salts has been developed. The method involves treatment of quaternary halides with methanolic solutions of suitable protic acids. The process is effective for aromatic and aliphatic quaternary halides with no loss of alkyl group integrity in the quaternary salt.     

Synthesis and solid state structure of fluorous probe molecules for fluorous separation applications

A series of colored hydrocarbon and fluorocarbon tagged 1-fluoro-4-alkylamino-anthraquinones and 1,4-bis-alkylamino-anthraquinone probe molecules were synthesized from a (fluorinated) alkyl amine and 1,4-difluoroanthraquinone to aid in the development of fluorous separation applications. The anthraquinones displayed stacking of the anthraquinone tricycle and interdigitation of the (fluorinated) alkyl chains in the solid state. Furthermore, intramolecular N-H?O hydrogen bonds forced the hydrocarbon and fluorocarbon tags into a conformation pointing away from the anthraquinone tricycle, with the angle of the tricycle plane normal and the main (fluorinated) alkyl vector ranging from 1° to 39°. Separation of the probe molecules on fluorous silica gel showed that the degree of fluorination of the probe molecules plays only a minor role with most eluents (e.g., hexane/ethyl acetate and methyl nonafluorobutyl ethers/ethyl acetate). However, toluene as eluent caused a pronounced separation by degree of fluorination for fluorocarbon, but not hydrocarbon tagged probe molecules on both silica gel and fluorous silica gel. These studies suggest that hydrocarbon and fluorocarbon tagged anthraquinones are useful probe molecules for the development of laboratory scale fluorous separation applications.     

Four positive formulae for type A quiver polynomials

We give four positive formulae for the (equioriented type A) quiver polynomials of Buch and Fulton [BF99 ]. All four formulae are combinatorial, in the sense that they are expressed in terms of combinatorial objects of certain types: Zelevinsky permutations, lacing diagrams, Young tableaux, and pipe dreams (also known as rc-graphs). Three of our formulae are multiplicity-free and geometric, meaning that their summands have coefficient 1 and correspond bijectively to components of a torus-invariant scheme. The remaining (presently non-geometric) formula is a variant of the conjecture of Buch and Fulton in terms of factor sequences of Young tableaux [BF99 ]; our proof of it proceeds by way of a new characterization of the tableaux counted by quiver constants. All four formulae come naturally in “doubled” versions, two for double quiver polynomials, and the other two for their stable limits, the double quiver functions, where setting half the variables equal to the other half specializes to the ordinary case. Our method begins by identifying quiver polynomials as multidegrees [BB82 , Jos84 , BB85 , Ros89 ] via equivariant Chow groups [EG98 ]. Then we make use of Zelevinsky’s map from quiver loci to open subvarieties of Schubert varieties in partial flag manifolds [Zel85 ]. Interpreted in equivariant cohomology, this lets us write double quiver polynomials as ratios of double Schubert polynomials [LS82 ] associated to Zelevinsky permutations; this is our first formula. In the process, we provide a simple argument that Zelevinsky maps are scheme-theoretic isomorphisms (originally proved in [LM98 ]). Writing double Schubert polynomials in terms of pipe dreams [FK96 ] then provides another geometric formula for double quiver polynomials, via [KM05 ]. The combinatorics of pipe dreams for Zelevinsky permutations implies an expression for limits of double quiver polynomials in terms of products of Stanley symmetric functions [Sta84 ]. A degeneration of quiver loci (orbit closures of GL on quiver representations) to unions of products of matrix Schubert varieties [Ful92 , KM05 ] identifies the summands in our Stanley function formula combinatorially, as lacing diagrams that we construct based on the strands of Abeasis and Del Fra in the representation theory of quivers [AD80 ]. Finally, we apply the combinatorial theory of key polynomials to pass from our lacing diagram formula to a double Schur function formula in terms of peelable tableaux [RS95a , RS98 ], and from there to our formula of Buch–Fulton type.     

旋转回归分析在提高作物产量中的应用

本文根据旋转回归正交试验,深入研究探讨了不同肥量、密度条件下对小麦产量的影响。创建了小麦产量与种植密度、施肥量之间的回归模型。通过检验,肯定了模型的可靠性和应用的有效性。为农业生产起到了很好的指导作用。     

矩形法兰孔孔口模态辐射阻抗的计算与分析*

针对半空间矩形法兰孔孔口模态辐射阻抗计算困难的问题,提出一种模态辐射阻抗的计算方法。该方法通过坐标变换将四重积分转换为二重积分并消除奇异积分,且将这一系列过程通过MATLAB内置函数直接实现,显著降低了模态辐射阻抗计算的复杂程度。通过对比与分析,验证了该方法的正确性,得到了自模态辐射阻抗随模态阶次增加峰值逐渐往高频移动且呈减小趋势、互模态辐射阻抗相比于自模态辐射阻抗小到可以忽略不计的性质。     

The honeycomb model of tensor products II: Puzzles determine facets of the Littlewood-Richardson cone

The set of possible spectra of zero-sum triples of Hermitian matrices forms a polyhedral cone, whose facets have been already studied by Knutson and Tao, Helmke and Rosenthal, Totaro, and Belkale in terms of Schubert calculus on Grassmannians. We give a complete determination of these facets; there is one for each triple of Grassmannian Schubert cycles intersecting in a unique point. In particular, the list of inequalities determined by Belkale to be sufficient is in fact minimal.

We introduce puzzles, which are new combinatorial gadgets to compute Grassmannian Schubert calculus, and seem to have much interest in their own right. As the proofs herein indicate, the Hermitian sum problem is very naturally studied using puzzles directly, and their connection to Schubert calculus is quite incidental to our approach. In particular, we get new, puzzle-theoretic, proofs of the results of Horn, Klyachko, Helmke and Rosenthal, Totaro, and Belkale.

Along the way we give a characterization of ``rigid' puzzles, which we use to prove a conjecture of W. Fulton: ``if for a triple of dominant weights of the irreducible representation appears exactly once in , then for all , appears exactly once in .'

     

H-transfer rates in ion-neutral complexes versus those in intact aliphatic ions

The relative rates of H-transfer between partners in ion-neutral complexes were compared with those in intramolecular rearrangements using results of first differential photoionization mass spectrometry measurements. Complex-mediated H-transfers are inferred to have rates of the same order as those for intramolecular hydrogen rearrangements, suggesting a similar range of motion of the reactive sites in both types of reactions. It is also concluded that at their fastest H-transfers take place between the partners in ion-neutral complexes within at most the time of several rotations of the partners in the complexes. Copyright 1999 John Wiley & Sons, Ltd.     

A study of deuteron quadrupole moment effects in sub-coulomb scattering of tensor polarized deuterons

Measurements of the tensor analyzing power T₂₀ are presented for deuteron elastic scattering from ²⁰⁸Pb at energies below the Coulomb barrier. It is found that, for energies below about 7 MeV, T₂₀ arises primarily from the interaction of the deuteron quadrupole moment with the nuclear electric field gradient. Contributions to T₂₀ from nuclear interactions with the target are shown to be very small for E_d ? 5 MeV. Measurements of T₂₀ at E_d = 4 MeV, accurate to ± 8 × 10^?5, are presented. After correcting for deuteron stretching and a number of additional small effects, the data are used to make a new determination of the quadrupole moment. The result, Q = 0.282 ± 0.019 fm², is in good agreement with the conventional value deduced from molecular hyperfine structure data.     

IR spectrum of CH3CN-BF3 in solid neon: matrix effects on the structure of a Lewis acid-base complex

We have observed several IR bands of CH3CN-BF3 in neon and nitrogen matrices. For the 11B isotopomer in neon matrices, we observed the BF3 symmetric deformation band (nu7) as a doublet at 600 and 603 cm(-1), the BF3 symmetric stretching band (nu6) as a doublet at 833 and 838 cm(-1), the BF3 asymmetric stretching mode (nu13) at 1281 cm(-1) (partially obscured), and the C-N stretching mode (nu2) as a doublet at 2352 and 2356 cm(-1). The nitrogen matrix data are largely consistent with those reported recently, though we do propose a refinement of one band assignment. Comparisons of the frequencies of a few key, structurally sensitive vibrational modes either observed in various condensed-phase environments or calculated for two minimum-energy gas-phase structures indicate that inert matrix media significantly alter the structural properties of CH3CN-BF3. Specifically, the B-N dative bond compresses relative to the gas phase and other concomitant changes occur as well. Furthermore, the frequency shifts depict structural changes that occur across the various matrix hosts in a manner that largely parallels the degree of stabilization offered by these inert media.     

Revalidation of the isobaric multiplet mass equation

We have determined the energy of the J(pi) = 1/2(+), T = 3/2 resonance in 32S(p,p) to be E(p) = 3374.7+/-0.8 keV. This disagrees with the previously accepted value of E(p) = 3370+/-1 keV by Abbondanno et al. [Nuovo Cimento 70A, 391 (1970)] and solves a problem raised by recent observations of unexpected deviations from the isobaric multiplet mass equation. This resonance is also important in calibrating the beta-delayed proton spectra from 33Ar and 32Ar, and our findings may modify previous conclusions.