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).      

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     

Synthesis of Optically Active P‐Chiral and Optically Inactive Oligophosphines

A series of optically active P‐chiral oligophosphines (S,R,R,S)‐ 2 , (S,R,S,S,R,S)‐ 3 , (S,R,S,R,R,S,R,S)‐ 4 , and (S,R,S,R,S,R,R,S,R,S,R,S)‐ 5 with four, six, eight, and 12 chiral phosphorus atoms, respectively, were successfully synthesized by a step‐by‐step oxidative‐coupling reaction from (S,S)‐ 1 . The corresponding optically inactive oligophosphines 1′ – 5′ were also prepared. Their properties were characterized by DSC, XRD, and optical‐rotation analyses. While optically active bisphosphine (S,S)‐ 1 and tetraphosphine (S,R,R,S)‐ 2 behaved as small molecules, octaphosphine (S,R,S,R,R,S,R,S)‐ 4 and dodecaphosphine (S,R,S,R,S,R,R,S,R,S,R,S)‐ 5 exhibited the features of a polymer. Furthermore, DSC and XRD analyses showed that hexaphosphine (S,R,S,S,R,S)‐ 3 is an intermediate between a small molecule and a polymer. Comparison of optically active oligophosphines 1 – 5 with the corresponding optically inactive oligophosphines 1′ – 5′ revealed that the optically active phosphines have higher crystallinity than the optically inactive counterparts. It is considered that the properties of oligophosphines depend on the enantiomeric purity as well as the oligomer chain length.     

Enumeration of the isomers of phenylenes

Summary The [h]phenylene C_6h H_2h+4 isomers are enumerated up toh=12. The numbers are compared with old and new data for C _n H₅ isomers of benzenoids, fluoranthenoids and biphenylenoids.

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Anzahl möglicher Isomerer von Phenylenen

Zusammenfassung Die Anzahl der [h]Phenylen-Isomeren C_6h H_2h+4 wurde bish=12 ausgewertet. Die Zahlen wurden mit alten und neuen Daten für C _n H _s -Isomere von Benzenoiden, Fluoranthenoiden und Biphenyloiden verglichen.

     

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.     

Chromatographic Evaluation of the Lipophilic Properties of Selected Pesticides

Monolinuron, chlortoluron, diuron, isoproturon, linuron, diflubenzuron, dimefuron, teflubenzuron, and lufenuron have been chromatographed on an RP-HPLC column and on RP-HPTLC plates with methanol–water in different volume proportions as mobile phases. The retention values log k, and R_M were extrapolated to zero methanol content. Chromatographic lipophilicities (log k_w, R_Mw, _o(HPLC), and _{o (TLC)}) were compared with measured (log P_exp) partition coefficients and with values (A log Ps, IA log P, C log P, log P_Kowin, and x log P) calculated by use of five different software products. The most significant correlations were found between the chromatographic lipophilicities and C log P values. Satisfactory linear correlation was also obtained between lipophilicity (log k_w, R_Mw) and the valence Gutman index (M).     

Concentrations of Active Species in the Flowing Afterglow of a Nitrogen Microwave Plasma

Measurements of nitrogen atom density, by means of NO chemical titration, along with an evaluation of the densities of some excited species N ₂ (B, v=11), N ₂ (B, v=2), N ₂ (C, v=0), and N ₂ ⁺ (B,v=0), by means of a spectroscopic study of some bands of dinitrogen, are achieved along the flowing afterglow of a dinitrogen microwave plasma (2450 MHz) for several pressures. The concentrations obtained are in the following range: [N]10 ⁺¹⁵ , [N ₂ (B, 2)]10 ⁺⁹ –10 ⁺¹⁰ , [N ₂ (B, 11)]10 ⁺⁸ –10 ⁺⁹ , [N ₂ (C, 0)]10 ⁺⁶ –10 ⁺⁷ , [N ₂ ⁺ (B,0)]10 ⁺⁶ -10 ⁺⁸ (cm^-3). From a kinetic study of the formation and decay of excited and charged species, an estimation of N ₂ (A, v), N ₂ (X, v, and N ₂ ⁺ (X) densities can be derived: [N ₂ (A, v)]10 ⁺¹² , [N ₂ (X, v6)]10 ⁺¹⁵ –10 ⁺¹⁶ , [N ₂ (X, v12)]10 ⁺¹⁴ –10 ⁺¹⁵ , [N ₂ ⁺ (X)]10 ⁺¹⁰ (cm ^-3 ).     

Synthesis of cationic indenyl- and fluorenyl-arene complexes of ruthenium

Interaction of [Ru(-C ₆ H ₆ )Cl ₂ ] ₂ with indenyl- or fluorenyllithium in THF gives, together with cationic benzene complexes [Ru( ⁵ -C ₉ H ₇ )(-C ₆ H ₆ )]⁺ and [Ru( ⁵ -C ₁₃ H ₉ )(-C ₆ H ₆ )]⁺, the neutral cyclohexadienyl derivatives Ru( ⁵ -C ₉ H ₆ -C ₉ H ₇ ) and Ru( ⁵ -C ₁₃ H ₉ )( ⁵ -C ₆ H ₆ -C ₁₃ H ₉ ), respectively. Interaction of the cyclohexadienyl complexes with Al ₂ O ₃ , Ph ₃ C⁺, and CF ₃ CO ₂ H has been studied. Reaction of Ru( ⁵ -C ₁₃ H ₉ )( ⁵ -C ₆ H ₇ ) with CF ₃ CO ₂ H in the presence of an arene yields cationic cyclohexadienylarene complexes: [Ru( ⁵ -C ₁₃ H ₉ )( ⁶ -arene)]⁺ (arene=C ₆ H ₆ or 1,3,5-Me ₃ C ₆ H ₃ ).A. N. Nesmeyanov Institute of Organoelemental Compounds, Russian Academy of Sciences, 117813 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 3, pp. 699–706, March, 1992.     

N-Glucosides of Aminobenzoic Acids and Aminophenols

N-o-, -m-, and -p-carboxyphenyl-D-glucosylamines and N-o-, -m-, and -p-hydroxyphenyl-D-glucosylamines were synthesized by reaction of D-glucose with o-, m-, and p-aminobenzoic acids and o-, m-, and p-aminophenols. It was demonstrated that both - and -anomers were formed by N-glycosylation of o-, m-, and p-aminobenzoic acids; only -anomers, by N-glycosylation of o-, m-, and p-aminophenols.     

Structures and energies of seleno derivatives of biuret.Ab Initio comparative studies of diselenobiuret, selenobiuret, and selenothiobiuret

Ab initio studies (LCAO-MO method) on conformers of three seleno derivatives of the biuret molecules diselenobiuret [I], selenobiuret [II], and selenothiobiuret [III] were carried out at the Hartree-Fock (HF) and MP2 levels. The molecular geometries of these species were fully optimized at the HF level and characterized by analysis of the harmonic vibrational frequencies using a split-valence triple-zeta basis set augmented by a set ofd polarization functions on heavy atoms andp polarization functions on hydrogen atoms [TZP(d, p)]. The total energies of the HF-optimized structures were calculated at the MP2 (frozen core) level using a larger TZP (2df, 2pd) basis set. The potential energy searches revealed a total of 11 minimum-energy conformers (assigned astrans-trans, trans-cis, cis-trans, andcis-cis) and seven transition-state species for the title molecules. The two predicted conformers for diselenobiuret (Ia=trans-trans andIc=cis-cis) are characterized byC ₂ and the third byC _s symmetry. For selenothiobiuret two forms (IIIa=trans-trans andIIId=cis-cis) possessC ₁ and two (IIIb=trans-cis andIIIc=cis-trans) possessC _s symmetries, respectively. For selenobiuret, four formsIIa=trans-trans (C₁),IIb=trans-cis (C _s),IIc=cis-trans (C ₁), andIId=cis-cis (C₁), were obtained as a result of gradient optimization. Comparison of the relative energies for the considered species indicated that thecis-trans forms are the most stable conformations for all three systems at both the HF and MP2 levels of theory.     

呋喃西林水溶液在光和热作用下的稳定性

The influence of both light and heat on the stability of nitrofurazone aqueous solution was studied. Results show that in either heating experiments or the exposure to light at high temperatures, the degradation rate obeyed zero-order kinetics. The total rate constant ktotal caused by both light and heat can be divided into two parts: ktotal =kdark klight, where kdark and klight are the degradation rate constants caused by heat and light, respectively. The klight can be expressed as klight=Alight*exp(-Ea,light/RT)*E, where E is the illuminance of light, and Alight and Ea,light both are experimental constants. The values of these kinetic parameters were determined based on the experiments in the dark and upon exposure to three different light sources. Results show that the values of Alight and Ea, light varied with the light source. To save time, labor, and drugs, exponential heating experiments were employed and compared with the isothermal experiments. Results indicated that kinetic parameters obtained by exponential heating experiments are comparable to those obtained by isothermal experiments either in the dark or upon exposure to light.     

Stereoselective and Enantioselective Syntheses of the Four Stereoisomers of Muscol from (3RS)‐Muscone

Two trans stereoisomers of 3‐methylcyclopentadecanol (=muscol), (1R,3R)‐ 2 and (1S,3S)‐ 2 , were efficiently synthesized from (3RS)‐3‐methylcyclopentadecanone (=muscone; (3RS)‐ 1 ) by a highly stereoselective reduction (Scheme). L‐Selectride^® (=lithium tri(sec‐butyl)borohydride) was used, followed by the enantiomer resolution by lipase QLG (Alcaligenes sp.). The cis stereoisomers of muscol, (1S,3R)‐ 2 and (1R,3S)‐ 2 , were obtained by the Mitsunobu inversion of (1R,3R)‐ 2 and (1S,3S)‐ 2 , respectively (Scheme). The absolute configuration of (1R,3R)‐ 2 was determined by X‐ray crystal‐structure analysis of its 3‐nitrophthalic acid monoester, 2‐[(1R,3R)‐3‐methylcyclopentadecyl hydrogen benzene‐1,2‐dicarboxylate ((1R,3R)‐ 3b ), and by oxidation of (1R,3R)‐ 2 to (3R)‐muscone.     

Relationships on the effect of water on glass transition temperature and young's modulus of nylon 6

The glass transition temperature T_g of nylon 6 decreases monotonically toward a finite value T_gl upon increase of the moisture content. The mechanism of this decrease entails the reversible replacement of intercaternary hydrogen bonds in the accessible regions of the polyamide. The limiting glass transition temperature T_gl is approached when the moisture content approaches W_l, which corresponds to the amount of water required for complete interaction with all accessible amide groups. Denoting with T_g0 the glass transition temperature of the dry polymer, the effect of water on T_g is represented by the equation, T_g = (ΔT_g)₀ exp{?[ln(ΔT_g)₀]W/_τW_l} + T_gl, where (ΔT_g)₀ = T_g0 ?T_gl, and τ = W(T_gl+1)/W_l. This equation appears to be generally applicable to hydrophilic polymers, since correspondingly calculated data are also in very good agreement with experimental data for polymers such as nylon 66, poly(vinyl alcohol), and polyN-vinylpyrrolidone. The effect of water of Young's modulus E of nylon 6 is represented by an analogous relationship, and the quantity In[(E?E_l)/(T_g?T_gl)] is a linear function of the moisture content.     

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.     

Influence of heating rate on kinetic quantities of solid phase thermal decomposition

Thermogravimetric analyses of thermal decomposition (pyrolysis, thermal dissociation and combustion) of 9 different samples were carried out in dynamic conditions at different heating rates. The kinetic parameters (E, A and k_m) of thermal decomposition were determined and interrelations between the parameters and heating rate q were analyzed. There were also relations between Arrhenius and Eyring equations analyzed for thermal decomposition of solid phase. It was concluded that Eyring theory is an element, which interconnects used thermokinetic equations containing Arrhenius law and suggests considering kinetic quantities in way relative to 3 kinetic constants (E, A and k_m). Analysis of quantities other than km (i.e. E, A, Δ⁺H, Δ⁺S) in relation to heating rate is an incomplete method and does not lead to unambiguous conclusions. It was ascertained that in ideal case, assuming constant values of kinetic parameters (E and A) towards heating rate and satisfying both Kissinger equations, reaction rate constant k_m should take on values intermediate between constants (k_m)₁ and (k_m)₂ determined from these equations. Whereas behavior of parameters E and A towards q were not subjected to any rule, then plotting relation k_m vs. q in the background of (k_m)₁ and (k_m)₂ made possible classification of differences between thermal decomposition processes taking place in oxidizing and oxygen-free atmosphere.     

Thermochemical studies for determination of the molar enthalpy of formation of aniline derivatives

The standard (p ^o=0.1 MPa) molar enthalpies of combustion atT=298.15 K were measured by static bomb combustion calorimetry for liquidN,N-diethylaniline,N,N-dimethyl-m-toluidine,N,N-dimethyl-p-toluidine, andN-ethyl-m-toluidine. Vaporization enthalpies forN,N-dimethyl-m-toluidine andN-ethyl-m-toluidine were determined by correlation gas chromatography. Derived standard molar values of _f H _m ^o (g) at 298.15 K forN,N-diethylaniline (62.1±7.6);N,N-dimethyl-m-toluidine (72.6±7.3),N,N-dimentyl-p-toluidine (68.9±7.4),N-ethyl-m-toluidine (30.5±3.8 kJ· mol^–1) were obtained.     

Viscoelasticity and birefringence of polyisoprene

The complex Young's modulus, E^*(ω), and the complex strain-optical coefficient, O^*(ω), which is the ratio of the birefringence to the strain, were measured for polyisoprene (PIP) over a frequency range of 1 ～ 130 Hz and a temperature range of 22 ～ ?100°C. The imaginary part of O^*, O″, was positive at low frequencies and negative at high frequencies. The real part, O′, was always positive and showed a maximum. The complicated behavior of O^* could be understood by the assumption that E^* = E_R^* + E_G^* and O^* = C_RE_R^* + C_GE_G^*, where E_R^* and E_G^* were complex quantities and C_R and C_G were constants. The C_R value, equal to the ordinary stress-optical coefficient measured in the rubbery plateau zone, was 2.0 × 10^?9 Pa^?1. The C_G value, defined as the ratio O″/E″ in the glassy zone, was ?1.1 × 10^?11 Pa^?1. The E_G^*, which was the major component of E^* in the glassy zone, showed almost the same frequency dependence as that of polystyrene and polycarbonate. The E_R^*, which was dominant in the rubbery zone, was described well by the bead-spring theory. The temperature dependence of the E_G^* was stronger than that of the E_R^*. This difference caused the breakdown of the thermorheological simplicity for E^* and O^* around the glass-to-rubber transition zone. © 1995 John Wiley & Sons, Inc.     

Synthesis of Phenyl- and Benzyl-Substituted Pyrrolidines and of a Piperidine by Intramolecular C-Alkylation. Synthons for tricyclic skeletons

The construction of new or novelly functionalized annulated and bridged tricylic compounds by two consecutive C,C-bond formations (a and b in la , Scheme 1) is described. In a first step, chloroalkyl-substituted aminonitriles yielded pyrrolidines 8 , 15a , 15b , 23 , 25 and piperidine 18 by carbanionic ring closure (Schemes 5, 6, 7 and 8). Subsequent Friedel-Crafts cyclization transformed the β-aminonitriles 8 , 15a , 15b , and 18 either directly or via their carboxylic acid derivatives to the indeno [1, 2-c]pyrrole, 2, 5-methano-3-benzazocine, benz [f]isoindoline and 1, 4-ethano-2-benzazapine skeletons 11 , 16a , 16b and 21 , respectively (Schemes 5, 6 and 7). By classical ring expansion reactions the pyrrolo [3, 4-c]isoquinoline and benzopyrano-[3, 4-c]pyrrole skeletons 28 resp. 31 were obtained from 11 (Scheme 9).     

Kinetics of the gas-phase thermal elimination of N-alkyl-pyrazoles

The kinetic study of the gas-phase thermal elimination reactions of N-ethyl-3,5 dimethyl-pyrazole (I), N-ethyl-pyrazole (II), N-sec-butyl-pyrazole (III), and N-tert-butyl-pyrazole (IV) using a flow system is reported. After obtaining activation parameters for I we carried out competitive reactions with II, III and IV using I as internal standard to obtain their E_a. The values of Δ(ΔH) calculated for II, III and IV agree with the little differences in E_a experimentally found.