The spread of unicyclic graphs with given size of maximum matchings

The spread s(G) of a graph G is defined as s(G) = max _i,j |λ _i − λ _j |, where the maximum is taken over all pairs of eigenvalues of G. Let U(n,k) denote the set of all unicyclic graphs on n vertices with a maximum matching of cardinality k, and U ^*(n,k) the set of triangle-free graphs in U(n,k). In this paper, we determine the graphs with the largest and second largest spectral radius in U ^*(n,k), and the graph with the largest spread in U(n,k).      

The kinetics of the decarboxylation of n-butylmalonic acid in alkanols and amines

Rate constants and activation parameters are reported for the decarboxylation of n-butylmalonic acid in four normal alkanols (hexanol? 1, octanol? 1, decanol? 1, and dodecanol? 1) and in five amines (aniline, N-methylaniline, N-ethylaniline, N-n-propylaniline, and N-n-butylaniline). Both ΔH? and ΔS? of the reaction in both homologous series decrease regularly with increasing length of the hydrocarbon chain of solvent. If we compare data for the reaction in alkanol–amine pairs containing the same total number of carbon atoms in the molecule, we find that the ΔH? values are identical, but that the value of ΔS? is 0.8 eu/mole higher for the reaction in the amines as compared with the alcohol. The rate constant, at all temperatures, is 1.5 times as large in the amine as it is in the corresponding alcohol. Empirical equations are deduced relating the parameters ΔH? ΔS? ΔG? and k of the reaction to the parameters n and T, where n is the total number of carbon atoms in the solvent molecule and T is the absolute temperature. The results reported herein are compared with previously reported data for malonic acid.     

The dependence of cyclopolymerizability of acrylic and methacrylic anhydrides on various conditions: New interpretation of temperature dependency of cyclization constant in radical cyclopolymerization of nonconjugated dienes

The cyclization constant K_c in the radical cyclopolymerization of acrylic and methacrylic anhydrides was evaluated in detail under various conditions. No linear relationship between in K_c and 1/T was observed; cyclization was acceleratively enhanced at elevated temperatures. The K_c values also increased with decreased monomer concentration and increased solvent polarity. These increasing dependencies of K_c are ascribed to the increased significance of depropagation, demonstrating a new interpretation of the temperature dependence of the cyclization constant in the radical cyclopolymerization of nonconjugated dienes.     

Grafting onto wool. V. Kinetics of graft copolymerization of methyl methacrylate in the viscous media of wool fibers

The graft copolymerization of methyl methacrylate in S-carboxymethylated wool fibers was investigated in the aqueous LiBr-K₂S₂O₈ system. The rate of grafting, the degree of polymerization of graft polymer, and the number of grafting sites were determined on varying the thiol content at a constant concentration of monomer. Kinetic considerations lead to the following expression in agreement with the experimental results: Z/DP = {(k_td + k_tc)/k_p²[M]²} R_p, where Z is the number of DNP endgroups of polymer; DP is the average degree of polymerization; k_p, k_td, and k_tc are the rate constants of propagation, termination by disproportionation, and termination by recombination, respectively; [M] is the concentration of monomer in fibers, and R_p is the overall rate of grafting. For wool fibers in media sufficiently high viscosity, the rate constants k_td and k_tc of diffusion-controlled termination are approximately equal and not affected by the change in cross-link density, provided that the thiol and disulfide interchange occurs. The possibility of occurrence of mechanical bond scission through a radical mechanism is involved in systems with extremely small amounts of thiol groups.     

Spectral Study of the Reaction of Functionally Substituted Enehydrazides with Proton Donors

Reactions of new enehydrazides, N',N'-dimethyl-N-vinylpropenohydrazide and N',N'-dimethyl-N-vinylbenzohydrazide with chloroform, phenol, and hydrogen chloride in carbon tetrachloride were studied by IR spectroscopy. In the first two cases, molecular complexes are formed between the hydrazide and proton donor. The reaction of N',N'-dimethyl-N-vinylpropenohydrazide with HCl results in formation of dihydropyrazole derivative which exists as a tautomeric mixture of the major lactam and minor lactim forms. N',N'-dimethyl-N-vinylbenzohydrazide reacts with hydrogen chloride to give protonated form in which proton is localized on the amino nitrogen atom. The structure of the initial compounds and the products was analyzed in terms of AM1 quantum-chemical calculations.     

Pulsed NMR observation of ultradrawn polypropylene

Proton spin-spin relaxation times have been measured as a function of temperature for ultradrawn polypropylene with draw ratios λ up to 24. The three relaxation times T_2a (the longest), T_2i (intermediate), and T_2c (the shortest), observed for all the samples, have been ascribed to the relaxations of the amorphous, constrained amorphous, and crystalline components, respectively. T_2i and T_2a, which reflect the changes in structure and mobility in the noncrystalline regions, decrease with increasing λ; T_2i becomes saturated at λ > 9, whereas T_2a shows a substantial decrease up to λ = 24. The continued decrease in T_2a indicates that the constraint on the amorphous segments keeps increasing up to the highest λ. The associated mass fractions F_a, F_i, and F_c also change with λ. At λ < 9, the increasc in F_i with increasing λ is accompanied by a decrease in F_a, with F_c remaining unchanged. At higher λ, however, F_a is almost constant, and stepwise rises in F_c at about λ = 12 and 24 are accompanied by corresponding drops in F_i. It seems that, in this high draw ratio range, some of the taut molecules are fully extended and are in sufficiently good lateral register to transform into crystalline bridges. This conjecture is supported by the similarity in the λ dependence of F_c and the mass-fraction crystallinity obtained from the heat of fusion.     

Biodegradation of Polyhydroxyalkanoate Films in Natural Environments

Summary: Biodegradation of film specimens from polyhydroxyalkanoates (PHAs) of two types – poly-3-hydroxybutyrate (PHB) and poly-3-hydroxybutyrate-co-3-hydroxyvalerate (PHBV) – was analysed in different environments: tropical sea waters of the South China Sea (Nha Trang, Vietnam) and soils in the environs of Hanoi (Vietnam), Nha Trang (Vietnam) and Krasnoyarsk (Siberia, Russia). In seawater, the mass loss of the specimens of both types was almost equal. However, in tropical soils, PHB degraded quicker than PHBV. In the Siberian soil, the degradation rate of the PHBV was generally higher than that of PHBV. Analysis of molecular mass of PHA specimens showed its decreasing during biodegradation. In the tropical sea conditions, PHA degrading microorganisms were represented by bacteria of Enterobacter, Bacillus and Gracilibacillus genera. Among PHA degrading bacteria, Burkholderia, Alcaligenes, Bacillus, Mycobacterium and Streptomyces genera were identified in Vietnamese soils, and Variovorax, Stenotrophomonas, Acinetobacter, Pseudomonas, Bacillus and Xanthomonas genera in Siberian soils. Micromycetes of Gongronella, Paecilomyces, Penicillium and Trichoderma genera exhibited PHA degrading activity in Vietnamese soils, and Paecilomyces, Penicillium, Acremonium, Verticillium and Zygosporium genera – in Siberian soils.     

Preparation of maleopimar adducts of polyfluoroalkyl esters of tall colophony

Maleopimar adducts of tall colophony esters with alcohols-telomers 1H,1H,5H-perfluoropentane-1-ol, 1H,1H,7H-perfluoroheptane-1-ol, and 1H,1H,9H-perfluorononane-1-ol were synthesized in conditions of Diels-Alder reaction.     

Estimation of the lattice heat capacity of rare-earth compounds

On the basis of the experimental data reported in literature, the contributions of cation mass (m) and molar volume (V) to lattice heat capacity (C) were analyzed. The volumetric-mass formula, C_x=(l —f)·C₁+f·C₂+C_m·(m_x — m_x′), was presented for estimating the heat capacities of rare-earth compounds. In the formula C₁ and C₂ represent the lattice heat capacities of two reference substances respectively, f = V_x—V₁/V₂—V₁ and C_m represents the lattice heat capacity variation with the variation 1 g of cation mass. The equation relating the C_m with temperatures was derived as follows: C_m = 0.084 e ?0.0074T ?0.27 e ?0.045T, and m_x and m_x′ (= (1 - f) m₁₊f m₂) represent the practical and “assumed” cation masses of the substance in question respectively.     

Graphical representation of the state of orientation of polymer systems

The orientation distribution function for noncrystalline structural units in polymer systems cannot be determined completely from any experimental source; only the second and/or fourth moments of the distribution function, i.e., the second and/or fourth orders of the generalized orientation factors F_lm^j, can be evaluated. It is there-fore necessary to estimate the distribution function from F_2m^j and F_4m^j. In this paper, a graphical representation of the state of orientation is first discussed in terms of plots of F₄₀^j against F₂₀^j for several types of distribution functions for uniaxial orientation. These are three types of extreme concentration of the distribution at particular polar angles θ₀ given by θ₀ = 0, 0<θ₀<π/2, and θ₀ = π/2; five types of rather realistic distributions having single maxima at θ_j = 0, θ₀, π/2 and double maxima at θ_j = 0, π/2, and a single minimum at θ_j = θ₀; and four types of more realistic distributions including Kratky's floating rod model in an affine matrix. Second, estimation of the distribution function for uniaxial orientation from F₄₀^j and F₂₀^j is discussed quantitatively in terms of the mean-square error by three approximation methods: (a) expansion of the distribution function in finite series of spherical harmonics through the fourth order, (b) approximation of the distribution function as a composite of two components, random orientation and a particular orientation distribution given by N_a (cos²θ_j)^a, N_a being a constant, and (c) approximation of the distribution function by N_a (cos²θ_j)^a alone. It is concluded that when the orientation distribution is sharp, estimation by the second method of approximation gives a smaller error than the first.     

Molecular Recognition of Pyranosides by a Family of Trimeric, 1,1′-Binaphthalene-Derived Cyclophane Receptors

The synthesis and carbohydrate-recognition properties of a new family of optically active cyclophane receptors, 1 – 3 , in which three 1,1′-binaphthalene-2,2′-diol spacers are interconnected by three buta-1,3-diynediyl linkers, are described. The macrocycles all contain highly preorganized cavities lined with six convergent OH groups for H-bonding and complementary in size and shape to monosaccharides. Compounds 1 – 3 differ by the functionality attached to the major groove of the 1,1′-binaphthalene-2,2′-diol spacers. The major grooves of the spacers in 2 are unsubstituted, whereas those in 1 bear benzyloxy (BnO) groups in the 7,7′-positions and those in 3 2-phenylethyl groups in the 6,6′-positions. The preparation of the more planar, D₃-symmetrical receptors (R,R,R)- 1 (Schemes 1 and 2), (S,S,S)- 1 (Scheme 4), (S,S,S)- 2 (Scheme 5), and (S,S,S)- 3 (Scheme 8) involved as key step the Glaser-Hay cyclotrimerization of the corresponding OH-protected 3,3′-diethynyl-1,1′-binaphthalene-2,2′-diol precursors, which yielded tetrameric and pentameric macrocycles in addition to the desired trimeric compounds. The synthesis of the less planar, C₂-symmetrical receptors (R,R,S)- 2 (Scheme 6) and (S,S,R)- 3 (Scheme 9) proceeded via two Glaser-Hay coupling steps. First, two monomeric precursors of identical configuration were oxidatively coupled to give a dimeric intermediate which was then subjected to macrocyclization with a third monomeric 1,1′-binaphthalene precursor of opposite configuration. The 3,3′-dialkynylation of the OH-protected 1,1′-binaphthalene-2,2′-diol precursors for the macrocyclizations was either performed by Stille (Scheme 1) or by Sonogashira (Schemes 4, 5, and 8) cross-coupling reactions. The flat D₃-symmetrical receptors (R,R,R)- 1 and (S,S,S)- 1 formed 1 : 1 cavity inclusion complexes with octyl 1-O-pyranosides in CDCl₃ (300 K) with moderate stability (ΔG⁰ ca. −3 kcal mol⁻¹) as well as moderate diastereo- (Δ(ΔG⁰) up to 0.7 kcal mol⁻¹) and enantioselectivity (Δ(ΔG⁰)=0.4 kcal mol⁻¹) (Table 1). Stoichiometric 1 : 1 complexation by (S,S,S)- 2 and (S,S,S)- 3 could not be investigated by ¹H-NMR binding titrations, due to very strong signal broadening. This broadening of the ¹H-NMR resonances is presumably indicative of higher-order associations, in which the planar macrocycles sandwich the carbohydrate guests. The less planar C₂-symmetrical receptor (S,S,R)- 3 formed stable 1 : 1 complexes with binding free enthalpies of up to ΔG⁰=−5.0 kcal mol⁻¹ (Table 2). With diastereoselectivities up to Δ(ΔG⁰)=1.3 kcal mol⁻¹ and enantioselectivities of Δ(ΔG⁰)=0.9 kcal mol⁻¹, (S,S,R)- 3 is among the most selective artificial carbohydrate receptors known.     

Effect of surfactant adsorption time on the observation of Newton black film in foam film

Observation of Newton black film (NBF) in foam film is possible only with a certain probability W which depends on the concentration C of surfactant in the solution and on the time t_a during which adsorption of surfactant at the solution/air interface has taken place. In the paper, the W(C,t_a) dependence is derived and used to analyze the effect of t_a on the critical surfactant concentration C_c below which NBF in foam film practically cannot be observed. An expression for the C_c(t_a) function is obtained which reveals that C_c decreases substantially with increasing t_a. This expression is found to describe well experimental C_c(t_a) data for foam films obtained from aqueous solution of the therapeutic surfactant INFASURF.     

The stability of silver iodide sols in the presence of polyacrylic acids of various molecular weights

Summary The effect of a series of polyacrylic acids, ranging in molecular weight from 1.67×10⁴ to 2.36×10⁶, on the stability of positively charged silver iodide particles has been examined. Flocculation of the sol occurred at a well defined concentration of polyacrylic acid,c _f , and a further increase in concentration of the polyelectrolyte caused restabilization of the sol. Over the range examinedc _f appeared to be related to the viscosity average molecular weight of the acid,M _v , by an equation of the form,c _f =a ·M _v ^{– b} wherea andb are constants.     

An orthorhombic polymorph of a cyclization product of perindopril

Low‐temperature X‐ray diffraction experiments were employed to investigate the crystal structures of an orthorhombic polymorph of the intramolecular cyclization product of perindopril, a popular angiotensive‐converting enzyme (ACE) inhibitor, namely ethyl (2S)‐2‐[(3S,5aS,9aS,10aS)‐3‐methyl‐1,4‐dioxo‐5a,6,7,8,9,9a,10,10a‐octahydro‐3H‐pyrazino[1,2‐a]indol‐2‐yl]pentanoate, C₁₉H₃₀N₂O₄, (Io), and its tetragonal equivalent, (It), which was previously reported at ambient temperature [Bojarska et al. (2013). J. Chil. Chem. Soc. 58 , 1415–1417]. Polymorph (Io) crystallizes in the orthorhombic space group P2₁2₁2₁ with two molecules in the asymmetric unit, while tetragonal form (It) crystallizes in the space group P4₁2₁2 with one molecule in the asymmetric unit. The geometric parameters of (Io) are very similar to those of (It). The six‐membered rings in both polymorphs adopt a slightly deformed chair conformation and the piperazinedione rings are in a boat conformation. However, the proline rings adopt an envelope conformation in (Io), while in (It) the ring exists in a slightly deformed half‐chair conformation. The most significant difference between the two structures is the orientation of the ethyl pentanoate chain. Molecules associate in pairs in a head‐to‐tail manner forming infinite columns. In (Io), molecules are related by a twofold screw axis forming identical columns, while in (It), molecules in successive neighbouring columns are related by alternating twofold screw axes and fourfold screw axes. In both cases, the crystal packing is stabilized by weak intermolecular C—H...O interactions only.     

Low-tempereture photolysis of diazoketones: the conformational isomerism of benzoylphenylmethylene and the IR spectrum of anthronylidene

Low-temperature photolysis of benzoylphenyldiazomethane, 1, and diazoanthrone, 2, in the polycrystal phase resulted in the high-intensity ESR spectra of benxoylphenymethylene 1a and anthronylidene 2a, respectively. Photolyses of argon matrix-isolated 1 and 2, coupled with IR spectroscopy, have now been carried out. Photolysis of 1 yielded the IR spectrum of diphenylketene as the only IR-observable product and indicated the presence in the matrix of the two s-E, s-Z, isomers of 1. On the other hand, photolysis of 2 yielded the IR spectrum of carbene 2a as the only observable product.     

Construction of characteristic polynomial of reciprocal graphs from the number of pendant vertices

A method for construction of the characteristic polynomial (CP) coefficients of the three classes of reciprocal graphs, viz., L_n + n(p), C_n + n(p), and K_1,n?1 + n(p), has been developed that requires only the value of n. The working formulas have been expressed in matrix product form, computer programs for which can easily be developed. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Isomorphism in electron-pair densities of atoms

The spherically averaged electron-pair intracule (relative motion) h(u) and extracule (center-of-mass motion) d(R) densities are a couple of densities which characterize the motion of electron pairs in atomic systems. We study a generalized electron-pair density (q; a, b) that represents the probability density function for the magnitude of two-electron vector a r _j +b r _k of any pair of electrons j and k to be q, where a and b are nonzero real numbers. In particular, h(u)=g(u;1, −1) and d(R) = . It is shown that the scaling property of the Dirac delta function and the inversion symmetry of orbitals in atoms due to the central force field generate several isomorphic relations in the electron-pair density (q; a, b) with respect to the two parameters a and b. The approximate isomorphism d(R)≅8h(2R) known in the literature between the intracule and extracule densities is a special case of the present results. Received: 24 May 2000 / Accepted: 18 July 2000 / Published online: 27 September 2000     

Carbon-13 NMR spectra of all-trans-N-retinylidene-n-butylamine as an analogue of the Schiff's base linkage-compound in visual pigment

Carbon-13 NMR spectra have been obtained for all-trans-N-retinylidene-n-butylamine as an analogue of the Schiff's base linkage compound in visual pigment. The chemical shift changes on going from all-trans-retinal₁ to all-trans-N-retinylidene-n-butylamine are observed. These changes indicate the collapse of the bond alternation in conjugated polyene carbons, whereas N-protonation in all-trans-N-retinylidene-n-butylamine does not affect the bond alternation.     

Stereoisomeric fragment ions arising from decomposition of enol cation radicals of different internal energy content

The least-squares analysis of collisional activation mass spectra provides evidence that 1,1-dihydroxy-3-methylbutene cation radical (a) and 1-hydroxy-1-methoxy-3-methylbutene cation radical (c) (generated in a McLafferty-type rearrangement from 2-isopropyl-3-methylbutanoic acid and its methyl ester) give rise to product ions b and d, the stereochemistry of which at the double bond is determined by the lifetime (internal energy) of a and c, respectively. Decompositions of a and c in the ion source yield predominantly the less stable cis-configurated stereoisomers of b and d, whereas dissociation of a and c at longer lifetimes (lower internal energy) results in the formation of the thermochemically more stable trans isomers of b and d. A qualitative MNDO analysis is provided which takes into account the special features of stereoelectronic control of radical chemistry in the cleavage of a carbon? carbon bond.     

Effect of temperature of liquid sulphur on kinetics of transformation of chains in its amorphous modification

The rate of transformation of the chains in amorphous sulphur was examined by calorimetry at 298 K. The amorphous samples were remelted at the temperatureT _f in the range from 458 to 573 K. Increase ofT _f decreased the transformation rate. The results satisfy the equationX=1-exp[-(kt)^z] (X=transformation degree,t=time, andk andz=constants). A one-stage transformation was observed for samples remelted atT _f473 K. ForT _f 523 K, transformation in two stages was observed.The effects ofT _f on the kinetics of nucleation and the growth of the nuclei are discussed.