Direct Identification of the Carbon Skeleton of Organic Compounds using Double Quantum Coherence 13C-NMR Spectroscopy. The INADEQUATE Pulse Sequence

NMR spectroscopy plays an important part in the determination of the structures of organic compounds. The parameters of importance here are the chemical shifts of the ¹H and ¹³C nuclei and the spin-spin interactions both between ¹H nuclei and between ¹H and ¹³C nuclei. Couplings between ¹³C nuclei were almost completely neglected until a few years ago, since they were extremely difficult to observe because of the low natural abundance of ¹³C. However, it is these couplings which afford information directly on the carbon-carbon connectivities in the molecule. It is now possible to use a special NMR pulse sequence to make these couplings more readily visible: the result of using this sequence is a ¹³C-NMR spectrum from which the carbon skeleton concerned can be directly read off. Two-dimensional spectra in particular are very easy to evaluate. The pulse sequence involved, which bears the somewhat puzzling name INADEQUATE, produces double-quantum coherences from which the NMR signals of the coupled carbon nuclei can be obtained. In this article the principle of double-quantum coherence is described and a number of examples for the application of the INADEQUATE pulse sequences to problems in synthetic organic chemistry, biosynthesis and natural products chemistry are presented; in addition, the possibility of applying the INADEQUATE method to other nuclei is considered.     

RATE OF INTRA-MOLECULAR CONTACT FORMATION IN SHORT TWO-DIMENSIONAL COMPACT POLYMERS CHAINS

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.     

Multivariate analysis of non-homogeneous peaks in liquid chromatography

Summary The effects of concentration, separation and spectral similarity as factors influencing the accuracy of iterative target testing factor analysis (ITT-FA) are investigated for three component systems by the application of analysis of variance (ANOVAR). ANOVAR is applied over a range of peak separations to map the changing effects of the three factors with increasing overlap. Two error responses were measured and analysed, (a) Relative cluster error (RCE) a measure of the error over all peaks in a cluster and (b) Relative peak error (RPE) the error of an individual peak. Multicomponent analysis (MCA) a method requiringa priori spectral information, is used as a referee method for ITT-FA.     

Rare numbers

Suppose thatX ₁,X ₂,... is a sequence of iid random variables taking values inZ ⁺. Consider the random sequenceA(X)(X ₁,X ₂,...). LetY _n be the number of integers which appear exactly once in the firstn terms ofA(X). We investigate the limit behavior ofn ^–(1–) Y _n for [0, 1].     

Synthesis of large generation poly(propyl ether imine) (PETIM) dendrimers

Large generation poly(propyl ether imine) (PETIM) dendrimers are synthesized in iterative synthetic cycles of two reductions and two Michael addition reactions. Dendrimers up to sixth generation, containing up to 128 peripheral functionalities, are synthesized. Growth of the PETIM dendrimers, possessing a tertiary amine as the branch juncture and an ether as the linker component, is assessed systematically by routine spectroscopic methods. The peripheries of these dendrimers possess either alcohols, amines, carboxylic acids, esters, or nitriles, thereby opening up possibilities for varied studies involving PETIM dendrimers.     

关于两两NQD列的若干极限性质

本文讨论了两两ＮＱＤ列的Ｍａｒｃｉｎｋｉｅｗｉｃｚ型弱大数律及Ｊａｍｉｓｏｎ型加权和的强稳定性，指出了两两ＮＱＤ列与独立列的一个本质性区别，从而提出了解决两两ＮＱＤ旬几乎处处收敛和完全收敛的一种方式。     

Inequalities for linear combinations of monomials in p-Newton sequences

The partial order on monomials that corresponds to domination when evaluated at positive Newton sequences is fully understood. Here we take up the corresponding partial order on linear combinations of monomials. In part using analysis based upon the cone structure of the exponents in p-Newton sequences, an array of conditions is given for this new partial order. It appears that a characterization in general will be difficult. Within the case in which all coefficients are 1, the situation in which, for general sequence length, there are two monomials, each of length two and nonnegative integer exponents, the partial order is fully characterized. The characterization is combinatorial, in terms of indices in the monomials, and, already here there is much more than term-wise domination.     

Automatic β-expansions of formal Laurent series over finite fields

We consider β-expansions of formal Laurent series over finite fields. If the base β is a Pisot or Salem series, we prove that the β-expansion of a Laurent series α is automatic if and only if α is algebraic.     

Gauss–Seidel Estimation of Generalized Linear Mixed Models With Application to Poisson Modeling of Spatially Varying Disease Rates

Generalized linear mixed models (GLMMs) are often fit by computational procedures such as penalized quasi-likelihood (PQL). Special cases of GLMMs are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints make it difficult to apply these iterative procedures to datasets having a very large number of records.

We propose a computationally efficient strategy based on the Gauss–Seidel algorithm that iteratively fits submodels of the GLMM to collapsed versions of the data. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status, and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. For Poisson and binomial regression models, the Gauss–Seidel approach is found to substantially outperform existing methods in terms of maximum analyzable sample size. Remarkably, for both models, the average time per iteration and the total time until convergence of the Gauss–Seidel procedure are less than 0.3% of the corresponding times for the IWLS algorithm. Platform-independent pseudo-code for fitting GLMS, as well as the source code used to generate and analyze the datasets in the simulation studies, are available online as supplemental materials.