Diamond hydrocarbons revisited: partitioned formula tables of diamondoids

Isomeric diamondoids with the same number $n$ of adamantane units (or cells), which share the same molecular formula $\text{ C}_\mathrm{Q}(\text{ CH})_\mathrm{T}(\text{ CH}_{2})_\mathrm{S}$ , can be divided into valence isomers by partitioning the number $C $ of their carbon atoms according to whether they are Quaternary, Tertiary, or Secondary: $C =Q +T +S$ . Each [ $n$ ]diamondoid has a dualist (or inner dual) with $n$ vertices (situated at centers of adamantane units), and edges connecting vertices of adjacent adamantane units sharing a chair-shaped hexagon of carbon atoms. Such a dualist is characterized by a quadruplet of indices (denoted as p, s, t, q for primary, secondary, tertiary, or quaternary) specifying again the connectivity of each vertex by assimilating it with a virtual carbon atom. The diamond lattice is self-dual. Dualists help in classifying diamondoids as catamantanes with acyclic dualists, perimantanes with dualists having chair-shaped six-membered rings, or coronamantanes with dualists having only higher-membered rings. In turn, catamantanes can be either regular when they have formulas $\text{ C}_{4n+6}\text{ H}_{4n+12}$ , or irregular when the numbers of carbon and hydrogen atoms are lower than the above values for the given numbers $n$ of adamantane units. Regular catamantanes can have branched or non-branched dualists and they are isomeric when having the same $n$ . Partitioned formulas reflect the branching patterns, encoded in their dualists. Partition formulas and codes are presented for all possible diamondoids with up to 7 adamantane units. A remarkable symmetry is observed for the table of partition periodic table of regular catamantanes with up to 7 adamantane units. Isomeric irregular catamantanes with six or more adamantane units may be valence-isomeric (or homomeric, sharing both the molecular and the partitioned formulas), or heteromeric when they have different partitioned formulas.     

Note on the asymptotic isomer count of large fullerenes

The leading term in the large- $N$ asymptotics of the isomer count of fullerenes with $N$ carbon atoms is extracted from the published enumerations for $N\le 400$ with the help of methods of series analysis. The uncovered simple $N^9$ scaling is distinct from isomer counts of most classes of chemical structures that conform to mixed exponential/power-law asymptotics. The second leading asymptotic term is found to be proportional to $N^{25/3}$ . A conjecture concerning isomer counts of the IPR fullerenes is also formulated.     

A method for the determination of d-kynurenine in biological tissues

d-Kynurenine (d-KYN), a metabolite of d-tryptophan, can serve as the bioprecursor of kynurenic acid (KYNA) and 3-hydroxykynurenine, two neuroactive compounds that are believed to play a role in the pathophysiology of several neurological and psychiatric diseases. In order to investigate the possible presence of d-KYN in biological tissues, we developed a novel assay based on the conversion of d-KYN to KYNA by purified d-amino acid oxidase (d-AAO). Samples were incubated with d-AAO under optimal conditions for measuring d-AAO activity (100 mM borate buffer, pH 9.0), and newly produced KYNA was detected by high-performance liquid chromatography (HPLC) with fluorimetric detection. The detection limit for d-KYN was 300 fmol, and linearity of the assay was ascertained up to 300 pmol. No assay interference was noted when other d-amino acids, including d-serine and d-aspartate, were present in the incubation mixture at 50-fold higher concentrations than d-KYN. Using this new method, d-KYN was readily detected in the brain, liver, and plasma of mice treated systemically with d-KYN (300 mg/kg). In these experiments, enantioselectivity was confirmed by determining total kynurenine levels in the same samples using a conventional HPLC assay. Availability of a sensitive, specific, and simple method for d-KYN measurement will be instrumental for evaluating whether d-KYN should be considered for a role in physiology and pathology.     

Asymptotics (p\rightarrow \infty ) of L_p-norms of hypergeometric orthogonal polynomials

The determination of the weighted $L_p$ norms of the real orthogonal polynomials of hypergeometric type $\left\{ y_n(x)\right\} $ is not only a very important problem per se in the theory of special functions, but also because of their recent entropic characterization and applications in quantum chemistry, quantum physics and information theory. Indeed, they essentially describe the $p$ th-order Rényi and Tsallis entropies of the numerous quantum systems whose wavefunctions are controlled by these polynomials. Moreover, for different values of $p$ , up to a constant factor, these norms characterize various fundamental and experimentally accessible quantities of many-electron systems. As well, the $L_p$ norms have been used to develop and interpret all energy components in the density-functional theory of the ground-state of atoms and molecules. The asymptotics of these quantities when $n \rightarrow \infty $ and $p>0$ have been recently calculated for Hermite polynomials, although not yet for Laguerre and Jacobi polynomials. Here, we determine the asymptotics ( $p\rightarrow \infty $ , $n$ fixed) of the weighted $L_p$ norms for general orthogonal polynomials in terms of the weight function and the coefficients of the second-order hypergeometric differential equation that they satisfy, and we apply it to the three classical families of real orthogonal polynomials. Moreover we analyse and discuss the monotonicity of this asymptotics, and we carry out a detailed numerical study of it.     

Short- and long-range behavior of the inner and outer densities

We report the short- and long-range behavior of the inner $ \rho_<(r) $ and outer $ \rho_>(r) $ densities, which result from a rigorous partitioning of the spherically averaged one-electron density $ \rho(r) $ in many-electron atoms. It is found that for a small r, $ \rho_<(r) $ has one-electron nature but $ \rho_>(r) $ has two-electron nature. For a large r, however, the opposite is true.     

Rate constants for the etching of gallium arsenide by atomic chlorine

Known chlorine atom concentrations were prepared in a discharge flow system and used to etch the (100) face of a gallium arsenide single crystal. The etch rate was monitored by mass spectrometry, laser interferometry, and surface proftlometry. In the temperature range from 90 to 160°C the reaction can be described by the rate law $$Etch rate = kP_{Cl} $$ where $$k = 9 \times 10^{(6 \pm 0.5)} \mu m min^{ - 1} Torr^{ - 1} e^{ - 9 \pm 1)kcal/RT} $$      

Electron-pair shell density approximation applied to inner and outer densities of atoms

The shell density approximation to the electron-pair radial density of atoms is applied to the inner $D_< (r)$ and outer $D_> (r)$ densities, which are two components of the single-electron density $D(r)$ . The inner and outer densities are found to be expressed by product sums of shell densities and shell distributions or their complements. The expressions clarify physical meaning of the two densities and give examples for constructing two-electron properties from single-electron properties. Examination of the 53 atoms He through Xe shows that the quantum similarity indices between the original and approximate densities, bounded by 0 (complete dissimilarity) and 1 (complete similarity), are never smaller than 0.99998 and 0.99987 for the inner and outer densities, respectively. The local nature of the shell density and the monotonically increasing property of the shell distribution are used to derive simple shellwise lower and upper bounds to $D_< (r)$ and $D_> (r)$ in terms of $D(r)$ and the numbers of shell electrons. Numerical tests of the bounds demonstrate their utility.     

Clar and Fries numbers for benzenoids

A Kekulé structure of a benzenoid or a fullerene $\Gamma $ Γ is a set of edges $K$ K such that each vertex of $\Gamma $ Γ is incident with exactly one edge in $K$ K . The set of faces in $\Gamma $ Γ that have exactly three edges in $K$ K are called the benzene faces of $K$ K . The Fries number of $\Gamma $ Γ is the maximum number of benzene faces over all possible Kekulé structures for $\Gamma $ Γ . The Clar number is the maximum number of independent benzene faces over all possible Kekulé structures for $\Gamma $ Γ . It is often assumed, but never proved, that some set of independent benzene faces giving the Clar number is a subset of a set of benzene faces giving the Fries number. In Hartung (The Clar structure of fullerenes, Ph.D. Dissertation. Syracuse University, 2012) it is shown that this assumption is false for a large class of fullerenes. In this paper, we prove that this assumption is valid for a large a class of benzenoids.     

d- and l-amino acids in Antarctic lakes: assessment of a very sensitive HPLC-MS method

Amino acids represent a fraction of organic matter in marine and freshwater ecosystems, and a source of carbon, nitrogen and energy. l-Amino acids are the most common enantiomers in nature because these chiral forms are used during the biosynthesis of proteins and peptide. To the contrary, the occurrence of d-amino acids is usually linked to the presence of bacteria. We investigated the distribution of l- and d-amino acids in the lacustrine environment of Terra Nova Bay, Antarctica, in order to define their natural composition in this area and to individuate a possible relationship with primary production. A simultaneous chromatographic separation of 40 l- and d-amino acids was performed using a chiral stationary phase based on teicoplainin aglycone (chirobiotic tag). The chromatographic separation was coupled to two different mass spectrometers—an LTQ-Orbitrap XL (Thermo Fisher Scientific) and an API 4000 (ABSciex)—in order to investigate their quantitative performance. High-performance liquid chromatography coupled with mass spectrometry methods were evaluated through the estimation of their linear ranges, repeatability, accuracy and detection and quantification limits. The high-resolution mass spectrometer LTQ-Orbitrap XL presented detection limits between 0.4 and 7 μg?l ^?1, while the triple quadrupole mass spectrometer API 4000 achieved the best detection limits reported in the literature for the quantification of amino acids (between 4 and 200 ng?l ^?1). The most sensitive method, HPLC-API 4000, was applied to lake water samples. Figure

?     

Specific energy distribution within cytoplasm and nucleoplasm of a typical mammalian cell due to various beta radionuclides

The use of beta radionuclides for treatment in radiotherapies leads for a need of better understanding of interactions and local energy depositions of beta particles within tissue and tissue equivalent media. The aim of this work is to determine microdosimetric quantities for various radionuclides. Specific energy, z, and its distribution, $ f(z) $ , mean specific energy, $ \bar{z} $ , and its standard deviations, $ \sigma \left( {\bar{z}_{f} } \right) $ , were evaluated for typical single cell where nucleus is the cellular region of interest. Three possible positions of radionuclides were taken into account—cellular membrane, cytoplasm and nucleoplasm. Taking these regions as the source of radiation, microdosimetric quantities were calculated for beta emitting radionuclides: ¹⁹¹Os, ¹⁹⁹Au, ¹⁷⁷Lu, ⁶⁷Cu, ⁷⁷As, ¹³¹I, ¹⁸⁶Re, ³²P, ¹⁸⁸Re and ⁹⁰Y. It was found that low range beta emitters have the largest efficiency and can deliver radiation doses up to 1 mGy per decay. Determination of the specific energy and its distribution for radionuclides is a useful start in order to determine beta emitters for a particular radionuclide therapy.     

Transport of Water by Group 1 and 2 Ions with t-Butyl Alcohol as Reference Substance: Comparison with Raffinose and Dioxan

Measurement of the transport of water with respect to the second solvent component in a binary aqueous mixture gives the Washburn number, $ w_{\text{W}} = (n_{\text{W}} )_{ + } t_{ + } - (n_{\text{W}} )_{ - } t_{ - } $ , in a transport number determination, where the ions move in opposite directions, and give the Erdey–Grúz number, $ \Upsigma n_{\text{W}} = (n_{\text{W}} )_{ + } + (n_{\text{W}} )_{ - } $ , in a diffusion experiment, where the ions move in the same direction. Here n _W and t are the number of water molecules and transport number, respectively, of the anion or cation. Combination of the results of these two experiments allows unambiguous determination of values for the solvent transport numbers, $ n_{\text{W}} $ , of the individual ions. While the values of $ n_{\text{W}} $ depend on the cosolvent, at high dilutions of the second component the highest value of $ n_{\text{W}} $ found, $ N_{\text{W}} $ , should approach the number of water molecules transported by the ion in pure water, $ N_{\text{W}}^{0} $ . New data for alkali-metal, alkaline-earth metal, hydrogen and halide ions in dilute mixtures of t-butyl alcohol with water are presented. Values of $ N_{\text{W}} $ rounded to whole numbers thus found are: 12 (Li⁺), 10 (Na⁺), 6 (K⁺), 5 (Rb⁺), 5 (Cs⁺), 1 (H⁺), 13 (Ca²⁺), 16 (Sr²⁺) and 15 (Ba²⁺). Factors influencing preferential solvation are briefly discussed. Detailed recalculations of $ n_{\text{W}} $ in the raffinose–water system from literature data also allows resolution of a problem with the Onsager Relations.     

Thermodynamic Analysis of Homologous α-Amino Acids in Aqueous Potassium Fluoride Solutions at Different Temperatures

Partial molal volumes ( $V_{\phi} ^{0}$ ) and partial molal compressibilities ( $K_{\phi} ^{0}$ ) for glycine, L-alanine, L-valine and L-leucine in aqueous potassium fluoride solutions (0.1 to 0.5?mol?kg^?1) have been measured at T=(303.15,308.15,313.15 and 318.15) K from precise density and ultrasonic speed measurements. Using these data, Hepler coefficients ( $\partial^{2}V_{\phi} ^{0}/\partial T^{2}$ ), transfer volumes ( $\Delta V_{\phi} ^{0}$ ), transfer compressibilities ( $\Delta K_{\phi} ^{0}$ ) and hydration number (n _H) have been calculated. Pair and triplet interaction coefficients have been obtained from the transfer parameters. The values of $V_{\phi} ^{0}$ and $K_{\phi} ^{0}$ vary linearly with increasing number of carbon atoms in the alkyl chain of the amino acids. The contributions of charged end groups ( $\mathrm{NH}_{3}^{+}$ , COO^?), CH₂ group and other alkyl chains of the amino acids have also been estimated. The results are discussed in terms of the solute?Ccosolute interactions and the dehydration effect of potassium fluoride on the amino acids.     

Kekuléan benzenoids

A Kekulé structure for a benzenoid or a fullerene $\Gamma $ is a set of edges $K$ such that each vertex of $\Gamma $ is incident with exactly one edge in $K$ , i.e. a perfect matching. All fullerenes admit a Kekulé structure; however, this is not true for benzenoids. In this paper, we develop methods for deciding whether or not a given benzenoid admits a Kekulé structure by constructing Kekulé structures that have a high density of benzene rings. The benzene rings of the Kekulé structure $K$ are the faces in $\Gamma $ that have exactly three edges in $K$ . The Fries number of $\Gamma $ is the maximum number of benzene rings over all possible Kekulé structures for $\Gamma $ and the set of benzene rings giving the Fries number is called a Fries set. The Clar number is the maximum number of independent benzene rings over all possible Kekulé structures for $\Gamma $ and the set of benzene rings giving the Clar number is called a Clar set. Our method of constructing Kekulé structures for benzenoids generally gives good estimates for the Clar and Fries numbers, often the exact values.     

Compound-specific isotope analysis of benzotriazole and its derivatives

Compound-specific isotope analysis (CSIA) is an important tool for the identification of contaminant sources and transformation pathways, but it is rarely applied to emerging aquatic micropollutants owing to a series of instrumental challenges. Using four different benzotriazole corrosion inhibitors and its derivatives as examples, we obtained evidence that formation of organometallic complexes of benzotriazoles with parts of the instrumentation impedes isotope analysis. Therefore, we propose two strategies for accurate $\delta^{13}$ C and $\delta^{15}$ N measurements of polar organic micropollutants by gas chromatography isotope ratio mass spectrometry (GC/IRMS). Our first approach avoids metallic components and uses a Ni/Pt reactor for benzotriazole combustion while the second is based on the coupling of online methylation to the established GC/IRMS setup. Method detection limits for on-column injection of benzotriazole, as well as its 1-CH $_{3}$ -, 4-CH $_{3}$ -, and 5-CH $_{3}$ -substituted species were 0.1–0.3 mM and 0.1–1.0 mM for δ¹³C and δ¹⁵N analysis respectively, corresponding to injected masses of 0.7–1.8 nmol C and 0.4–3.0 nmol N, respectively. The Ni/Pt reactor showed good precision and was very long-lived ( $>$ 1000 successful measurements). Coupling isotopic analysis to offline solid-phase extraction enabled benzotriazole-CSIA in tap water, wastewater treatment effluent, activated sludge, and in commercial dishwashing products. A comparison of $\delta ^{13}$ C and $\delta ^{15}$ N values from different benzotriazoles and benzotriazole derivatives, both from commercial standards and in dishwashing detergents, reveals the potential application of the proposed method for source apportionment.     

Sensitive chemiluminescence method for the determination of glutathione, l-cysteine and 6-mercaptopurine

Glutathione (GSH), l-cysteine (l-Cys) and 6-mercaptopurine (6-MP) inhibit the CL reaction of luminol–H₂O₂ catalyzed by gold colloids. In order to explore this, GSH, l-Cys and 6-MP were injected into the chemiluminescence system of luminol and H₂O₂ catalyzed by gold colloids. The results showed that gold colloids interact with GSH, l-Cys and 6-MP and decrease the CL emission. Based on this phenomenon, a simple, sensitive and convenient flow injection CL method was developed for the determination of GSH, l-Cys and 6-MP. This method provides a novel, and effective CL assay for GSH, l-Cys and 6-MP that has been applied to the determination of GSH in human serum.     

Double stable isotope ultra performance liquid chromatographic-tandem mass spectrometric quantification of tissue content and activity of phenylethanolamine N-methyltransferase, the crucial enzyme responsible for synthesis of epinephrine

Here, we describe a novel method utilizing double stable isotope ultra performance liquid chromatography-tandem mass spectrometry to measure tissue contents and activity of phenylethanolamine N-methyltransferase (PNMT), the enzyme responsible for synthesis of the stress hormone, epinephrine. The method is based on measurement of deuterium-labeled epinephrine produced from the reaction of norepinephrine with deuterium-labeled S-adenosyl-l-methionine as the methyl donor. In addition to enzyme activity, the method allows for determination of tissue contents of PNMT using human recombinant enzyme for calibration. The calibration curve for epinephrine was linear over the range of 0.1 to 5,000 pM, with 0.5 pM epinephrine representing the lower limit of quantification. The calibration curve relating PNMT to production of deuterium-labeled epinephrine was also linear from 0.01 to 100 ng PNMT. Intra- and inter-assay coefficients of variation were respectively 12.8 % (n?=?10) and 10.9 to 13.6 % (n?=?10). We established utility of the method by showing induction of the enzyme by dexamethasone in mouse pheochromocytoma cells and strong relationships to PNMT gene expression and tissue epinephrine levels in human pheochromocytomas. Development of this assay provides new possibilities for investigations focusing on regulation of PNMT, the crucial final enzyme responsible for synthesis of epinephrine, the primary fight-or-flight stress hormone.

Laserspray and Matrix-Assisted Ionization Inlet Coupled to High-Field FT-ICR Mass Spectrometry for Peptide and Protein Analysis

We present the first coupling of laser spray ionization inlet (LSII) and matrix assisted ionization inlet (MAII) to high-field Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) for generation of electrospray-like ions to take advantage of increased sensitivity, mass range, and mass resolving power afforded by multiple charging. We apply the technique to top-down protein analysis and characterization of metalloproteins. We also present a novel method for generation of multiply-charged copper–peptide complexes with varying degrees of copper adduction by LSII. We show an application of the generated copper–peptide complexes for protein charge state and molecular weight determination, particularly useful for an instrument such as a linear ion trap mass analyzer.      

Synthesis and characterization of new N-phenylmaleimide thioglycosides

Thioglycosides derivatives of N-phenylmaleimide have been prepared by the reaction of derivatives of 1-thio-d-glucopyranose, d-galactopyranose, d-lactose, and d-maltose with 3,4-dichloro-N-phenylmaleimide. The reaction of 3,4-dichloro-N-phenyl maleimide with sugar thiols (protected or unprotected) took place by displacement of both chlorine atoms by sulfide nucleophile giving the corresponding bis-thioglycoside products.     

Rendements de fission cumulatifs du252Cf

The cumulative yields of 28 isotopes have been measured in the spontaneous fission of²⁵²Cf. Measurements were made by Ge(Li) gamma-spectrometry. An average number of neutrons per fission \(\bar V:3.71\) was derived from the mass distribution. Using Terrell's method, and with the mass distribution before neutron emission, measured in an other laboratory and with our results, the mass-dependent variation of \(\bar V\) was also deduced.     

On k-resonance of grid graphs on the plane,torus and cylinder

Grid graphs on the plane, torus and cylinder are finite 2-connected bipartite graphs embedded on the plane, torus and cylinder, respectively, whose every interior face is bounded by a quadrangle. Let \(k\) be a positive integer, a grid graph is \(k\) -resonant if the deletion of any \(i \le k\) vertex-disjoint quadrangles from \(G\) results in a graph either having a perfect matching or being empty. If \(G\) is \(k\) -resonant for any integer \(k \ge 1\) , then it is called maximally resonant. In this study, we provide a complete characterization for the \(k\) -resonance of grid graphs \(P_m\times P_n\) on plane, \(C_m\times C_n\) on torus and \(P_m\times C_n\) on cylinder.