Discrimination of the geometrical isomers of 2,3-, 2,5-, and 2,6-dimethylpiperazines based on 1 H?Nmr spectral data

¹ H-Nmr spectra of cis and trans isomers of 2,3-, 2,5-, and 2,6-dimethylpiperazines were taken at various temperatures. The spectra of geometrical isomers bearing the ae or ea dimethyl groups showed broadening at lower temperatures. It was clarified that the measurement of the spectra at lower temperatures is useful for the discrimination of the geometrical isomers of dimethylpiperazines.     

A new method for the synthesis of some 9-β-D-arabinofuranosylpurines by a combination of chemical and enzymatic reactions

An enzymatic transarabinosylation between 2-chlorohypoxanthine and 1-β-$\text{D}$-arabinofuranosyluracil gave 9-β-$\text{D}$-arabinofuranosyl-2-chlorohypoxanthine which was chemically converted to 9-β-$\text{D}$-arabinofuranosylguanine and its derivatives.     

There exists no self-dual [24,12,10] code over $${{\mathbb F}_5}$$

Self-dual codes over exist for all even lengths. The smallest length for which the largest minimum weight among self-dual codes has not been determined is 24, and the largest minimum weight is either 9 or 10. In this note, we show that there exists no self-dual [24, 12, 10] code over , using the classification of 24-dimensional odd unimodular lattices due to Borcherds.      

A Characterization of Designs Related to an Extremal Doubly-Even Self-Dual Code of Length 48

The uniqueness of a binary doubly-even self-dual [48, 24, 12] code is used to prove that a self-orthogonal 5-(48, 12, 8) design, as well as some of its derived and residual designs, including a quasi-symmetric 2-(45, 9, 8) design, are all unique up to isomorphism.Received November 5, 2003     

Non-level semi-standard graded Cohen–Macaulay domain with h-vector (h0,h1,h2)

Let $\mathbb{k}$ be an algebraically closed field of characteristic 0, and $A={?}_{i\in \mathbb{N}}{A}_i$ a Cohen–Macaulay graded domain with $A_0=\mathbb{k}$. If A is semi-standard graded (i.e., A is finitely generated as a $\mathbb{k}[A_1]$-module), it has the h-vector$(h_0,h_1,\dots ,h_s)$, which encodes the Hilbert function of A. From now on, assume that $s=2$. It is known that if A is standard graded (i.e., $A=\mathbb{k}[A_1]$), then A is level. We will show that, in the semi-standard case, if A is not level, then $h_1+1$ divides $h_2$. Conversely, for any positive integers h and n, there is a non-level A with the h-vector $(1,h,(h+1)n)$. Moreover, such examples can be constructed as Ehrhart rings (equivalently, normal toric rings).     

Spatial distribution and formation of nitrate radical NO<Stack><Subscript>3</Subscript><Superscript>2−</Superscript></Stack> in Antarctic calcitic evaporates

Nitrate radical NO₃²⁻ in calcitic evaporate was discovered in Antarctica. The distribution and formation of nitrate radical NO₃²⁻ in the calcite have been studied by pulse and continuous-wave electron spin resonance. In samples that had been annealed to destroy the NO₃²⁻, regeneration of the radical by γ-rays or UV light indicated that the radical was formed by UV light (with wavelengths less than 340 nm) from solar rays, not by environmental radiation. The nonuniform spatial distribution of the nitrate radical, which was deduced from high ratios of local spin density to total spin density, suggests that the nitrate impurity was introduced into the calcium carbonate after carbonate grain formation. Formation of the carbonate-containing nitrate requires the presence of high amounts of nitrate and a dry climate. Formation of the nitrate radical requires sample exposure to UV light. These conditions are satisfied in the environment of Antarctica.     

Hydrothermal formation of tobermorite studied by in situ X‐ray diffraction under autoclave condition

Hydrothermal formation of tobermorite from a pre‐cured cake has been investigated by transmission X‐ray diffraction (XRD) using high‐energy X‐rays from a synchrotron radiation source in combination with a newly designed autoclave cell. The autoclave cell has a large and thin beryllium window for wide‐angle X‐ray diffraction; nevertheless, it withstands a steam pressure of more than 1.2 MPa, which enables in situ XRD measurements in a temperature range of 373 to 463 K under a saturated steam pressure. Formation and/or decomposition of several components has been successfully observed during 7.5 h of reaction time. From the intensity changes of the intermediate materials, namely non‐crystalline C–S–H and hydroxylellestadite, two pathways for tobermorite formation have been confirmed. Thus, the newly developed autoclave cell can be used for the analyses of reaction mechanisms under specific atmospheres and temperatures.