Continuous and Discrete Tight Frames of Orthogonal Polynomials for a Radially Symmetric Weight

This paper considers tight frame decompositions of the Hilbert space ℘ _n of orthogonal polynomials of degree n for a radially symmetric weight on ℝ ^d , e.g., the multivariate Gegenbauer and Hermite polynomials. We explicitly construct a single zonal polynomial p∈℘ _n with the property that each f∈℘ _n can be reconstructed as a sum of its projections onto the orbit of p under SO(d) (symmetries of the weight), and hence of its projections onto the zonal polynomials p _ξ obtained from p by moving its pole to ξ∈S:={ξ∈ℝ ^d :|ξ|=1}. Furthermore, discrete versions of these integral decompositions also hold where SO(d) is replaced by a suitable finite subgroup, and S by a suitable finite subset. One consequence of our decomposition is a simple closed form for the reproducing kernel for ℘ _n .      

Capillary electrophoresis separation of a mixture of chitin and chitosan oligosaccharides derivatized using a modified fluorophore conjugation procedure

A capillary electrophoresis (CE) method was developed for the simultaneous analysis of small chitin and chitosan oligosaccharides. For detection purposes, the oligomers were derivatized with 8-aminopyrene-1,3,6-trisulfonic acid (APTS), a well known fluorophore for oligosaccharides analysis. The detection was performed by laser-induced fluorescence (LIF) with an argon ion laser having an excitation wavelength of 488 nm and with emission monitored at 520 nm. Derivatization parameters such as reaction time and conditions were examined. Separation conditions were also varied by testing a range of buffer pHs and concentrations. The best conditions were found using an 80 mM borate buffer at pH 8.4. This CE-LIF optimized method was used for the analysis of an enzymatically produced oligo-chitosan sample composed of a complex mixture and having an average degree of polymerization of 3.7 monomer units and 80% deacetylation. The oligo-chitosan sample was treated with a chitin deacetylase-like enzyme, the products were derivatized with APTS, and then analyzed without purification. The goal was to determine whether the deacetylase-like enzyme could increase the extent of deacetylation of the oligo-chitosan sample.     

Cloning and analysis of the spinosad biosynthetic gene cluster of Saccharopolyspora spinosa

BACKGROUND: Spinosad is a mixture of novel macrolide secondary metabolites produced by Saccharopolyspora spinosa. It is used in agriculture as a potent insect control agent with exceptional safety to non-target organisms. The cloning of the spinosyn biosynthetic gene cluster provides the starting materials for the molecular genetic manipulation of spinosad yields, and for the production of novel derivatives containing alterations in the polyketide core or in the attached sugars. RESULTS: We cloned the spinosad biosynthetic genes by molecular probing, complementation of blocked mutants, and cosmid walking, and sequenced an 80 kb region. We carried out gene disruptions of some of the genes and analyzed the mutants for product formation and for the bioconversion of intermediates in the spinosyn pathway. The spinosyn gene cluster contains five large open reading frames that encode a multifunctional, multi-subunit type I polyketide synthase (PKS). The PKS cluster is flanked on one side by genes involved in the biosynthesis of the amino sugar forosamine, in O-methylations of rhamnose, in sugar attachment to the polyketide, and in polyketide cross-bridging. Genes involved in the early common steps in the biosynthesis of forosamine and rhamnose, and genes dedicated to rhamnose biosynthesis, were not located in the 80 kb cluster. CONCLUSIONS: Most of the S. spinosa genes involved in spinosyn biosynthesis are found in one 74 kb cluster, though it does not contain all of the genes required for the essential deoxysugars. Characterization of the clustered genes suggests that the spinosyns are synthesized largely by mechanisms similar to those used to assemble complex macrolides in other actinomycetes. However, there are several unusual genes in the spinosyn cluster that could encode enzymes that generate the most striking structural feature of these compounds, a tetracyclic polyketide aglycone nucleus.     

Vibrational spectra and structure of cis- and trans-1,2- dimethoxyethylenes

The vapor, liquid and CCl₄ solution infrared spectra of cis- and trans-1,2-dimethoxyethylene were recorded in the region 250–4000 cm^?1. The laser-Raman spectra were obtained in the liquid state only. The vibrational spectra show that at least two rotational isomers exist for each molecule. Further, the spectra indicate that for both the cis- and trans molecules, one of the rotational isomers has at least one planar conformer. Some vibrational assignments are made for the observed infrared and Raman bands of the cis- and trans- 1,2-dimethoxyethylenes.     

独居石微晶玻璃中玻璃相含量的红外光谱定量测定

独居石微晶玻璃由偏磷酸盐玻璃和独居石两相组成。玻璃和独居石的红外吸收谱带彼此不相重叠,且1275和616cm~(-1)谱带的吸收强度随玻璃相的含量变化而变化。两谱带的对数吸光度比值与玻璃相含量(w％)的相关系数r=0.9975,其回归方程为y=48.356 25.93x。合成独居石的IR谱中952和616cm~(-1)谱带的吸光度比值也随不同的Ce_2O_3/La_2O_3比值规律变化。其r=0.9917,回归方程为y=0.2211exp(0.0221x)。高的相关性表明IR技术可在磷酸盐微晶玻璃物相定量分析中得到实际应用。     

Quantum cosmology and conformal invariance

According to Belinsky, Khalatnikov, and Lifshitz, gravity near a spacelike singularity reduces to a set of decoupled one-dimensional mechanical models at each point in space. We point out that these models fall into a class of conformal mechanical models first introduced by de Alfaro, Fubini, and Furlan (DFF). The deformation used by DFF to render the spectrum discrete corresponds to a negative cosmological constant. The wave function of the Universe is the zero-energy eigenmode of the Hamiltonian, or the spherical vector of the representation of the conformal group SO(1,2). A new class of conformal quantum mechanical models with enhanced ADE symmetry is constructed, based on the quantization of nilpotent coadjoint orbits.     

Ethanol production usingZymomonas mobilis in a cross-linked immobilized cell reactor

The bacteriumZymomonas mobilis may be utilized to produce ethanol from glucose in a cross-linked immobilized cell reactor. Reactor startup is much more rapid with cross-linkedZymomonas than with the yeastSaccharomyces cerevisiae. Volumetric ethanol productivities (based on liquid holdup) three times those obtained with cross-linked yeast, and comparable to those obtained withZymomonas immobilized by other methods, are possible.     

Engineered biosynthesis of novel spinosyns bearing altered deoxyhexose substituents

Novel spinosyns have been prepared by biotransformation, using a genetically engineered strain of Saccharopolyspora erythraea, in which the beta-D-forosamine moiety in glycosidic linkage to the hydroxy group at C17 is replaced by alpha-L-mycarose.     

Effects of tank tracking on range grasses

The Department of Defense (DoD) must constantly balance its military mission and its commitment to stewardship on large tracks of federal land. These military training lands are some of the most intensely used land in the United States, and training requires that vegetation, primarily grasses, be as resilient as possible. The objectives of this study were to evaluate (i) plant establishment and (ii) the effect of light to heavy tank traffic that ranged from zero to four passes on range grasses at the Yakima Training Center, Yakima, Washington. Characteristics measured include the number of 10-cm gaps without plant materials in seeded rows of the target (sown) species, the biomass of the target species, and the percentages of bluegrass colonization, bare ground, and cheatgrass encroachment in tracked and untracked areas. Both stand establishment and the ability to produce rhizomes are associated with the ability to recover after training. The wildryes did not establish well and subsequently had more 10-cm gaps and lower yields than the other introduced species tested. Among the natives, Snake River wheatgrass and western wheatgrass exhibited the most resilience across the different tracking intensities. The largest decline in percentage target species was observed between the two- and four-pass treatments. After five years, cheatgrass was not able to encroach on Snake River wheatgrass, Siberian wheatgrass, and bluebunch wheatgrass plots. Tracking generally reduced the stand of the target species and increased the amount of bare ground.