On p -nilpotency and minimal subgroups of finite groups

We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ core(H). In this paper it is proved that a finite group G is p-nilpotent if G is S ₄-free and every minimal subgroup of P ∩ G ^N is c-supplemented in N _G(P), and when p = 2 P is quaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of G. As some applications of this result, some known results are generalized.     

DNA Computing of Bipartite Graphs for Maximum Matching

Let M be a matching in a graph G. It is defined that an M-augmenting path must obtain one element of M. In this paper, it is obtained that a matching M in a graph G is a maximum matching if and only if G contains no M-augmenting path and M is a maximal matching in G. It supplies a theoretical basis to DNA computing. A detailed discussion is given of DNA algorithms for the solutions of the maximal matching problem and maximum matching one in a bipartite graph.     

Homogeneous Fermi liquid with ‘artificial’ repulsive inverse square law interparticle potential energy

A good deal is known by now on the so-called jellium model of the homogeneous electron liquid. However, much of the quantitative progress at experimentally realizable densities has come from quantal computer simulation. Therefore, we here consider a homogeneous Fermion liquid with ‘artificial’ repulsive interaction λ/(r_ij )² between Fermions i and j at separation r_ij . We discuss first of all the way the static structure function S(q), essentially the Fourier transform of the pair correlation function, is changed because of non-zero λ from the ‘Fermi hole’ form due entirely to Pauli principle effects between parallel spin Fermions. Unlike jellium with e ²/r_ij repulsive interactions, S(q) is proportional to q at long wavelengths, whereas the plasmon in jellium annulls the q term and S(q) is quadratic in q as q tends to zero. However for λ/(r_ij )² interactions, the coefficient of q appearing in the Fermi hole structure factor, is renormalized by particle repulsions. Then some discussion is given of Fermion quasiparticle lifetimes τ as the Fermi surface is approached. Arguments are presented that τ^?1 is proportional to |E???E _F| as E tends to the Fermi energy. This is already interesting, in fact, in connection with the jellium model and therefore an approximate analytic form of τ is finally derived.     

Synthese et Comportement Polarographique Des Cis et Trans Azoxycyclohexanes

Abstract

In order to compare the polarographic behaviour of cis and trans aliphatic azoxy compounds, synthesis and polarographic study of cis and trans azoxycyclohexanes are performed. The cis form is a new compound obtained by photoisomerisation of the trans compound. In acid medium the polarographic reduction process is the same for both forms: hydrazocyclohexane is the final reduction product. In alkaline medium the trans azoxy compound is electroinactive and the cis azoxy compound is reducible and leads to a mixture of trans azocyclohexane and hydrazocyclohexane.     

Conformal Mixtures with Concentration-dependent Interactions; Application to Liquid Li—Mg

Abstract

The conformal model for binary liquids is extended to the case when the interaction energies are linear in the concentration, c. It is found that a suitably defined c-dependent ordering energy w is the single most important indication of the general character of the alloy, in particular of the behaviour of the excess free energy ΔF^XS and of the concentration fluctuation function S_cc . There are three cases:

• w is of fixed sign and varies by less than a factor of 2. Then ΔF^XS and S_cc —c(1 - c) both have opposite sign from w. The latter functions are largest (absolutely) in roughly the same region of c.

  w changes sign. Then ΔF^XS and S_cc —c(1 - c) are of opposite sign from w at each end of the diagram (much as one would expect on the basis of I).
  w is of fixed sign but varies by more than a factor of 2. Then ΔF^XS is of opposite sign from w and S_cc —c(1 - c) is mainly so. The latter function is, however, (marginally) of the same sign as w in a limited range of c at the end where w (and ΔF^XS ) is absolutely smallest. The alloy system Li-Mg appears to be of this type.

     

Discrepancy in the near-solute electric dipole moment calculated from the electric field

The electric dipole moment p ( r ) was computed as the integral of the permanent dipole moment of the solvent molecule μ( r ) weighted by the orientational probability distribution Ω( r ; O ) over all orientations, where O is the orientation of the solvent molecule at r . The relationship between Ω( r ; O ) and the potential of the mean torque was derived; p ( r ) is proportional to the electric field E ( r ) under the following assumptions: (1) the van der Waals (vdW) interaction is independent of the orientation of the solvent molecule at r ; (2) the solvent molecule and its electrical effect are modeled as a point dipole moment; (3) the solvent molecule at r is in a region far from the solute; and (4) μE( r ) ? k_BT, where k_B is Boltzmann's constant and T is absolute temperature. The errors caused by calculating near‐solute Ω( r ) and p ( r ) from E ( r ) are unclear. The results show that Ω( r ) is inconsistent with the value calculated from E ( r ) for water molecules in the first and second shells of solute with charge state Q = ±1 e, and a large variation in solvent molecular polarizability γ_mol(r), which appeared in the first valley of 4πr²E(r) for |Q| < 1 e. Nonetheless, p (r) is consistent with the values calculated from E (r) for |Q| ≤ 1 e. The implication is that the assumptions for calculating p ( r ) can be ignored in the calculation of the solvation free energy of biomolecules, as they pertain to protein folding and protein–protein/ligand interactions. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Some properties of the structure factor S(q) in two-dimensional classical liquids near freezing

We explore general properties of the main peak of the structure factor S(q) near the melting temperature T _melt in liquids confined in two dimensions, especially for the one component plasma model and for monatomic liquids interacting through inverse twelfth-power potentials. Those properties are the height of the peak, S(q _m), where q _m is the position of maximum in the peak, and the ratio between S(q _m) and q _m/Δq, where 2Δq is the width of the peak. The results obtained are then compared with those for similar systems in three dimensions. Other magnitude that we use to compare two-dimensional and three-dimensional simple liquids is r _m/Δr, where r _m is the position of the main peak in the pair distribution function g(r) and 2Δr is the width of that peak.     

The PI index of phenylenes

The Padmakar–Ivan (PI) index is a graph invariant defined as the summation of the sums of n _eu (e|G) and n _ev (e|G) over all the edges e = uv of a connected graph G, i.e., PI(G) = ∑ _e∈E(G)[n _eu (e|G) + n _ev (e|G)], where n _eu (e|G) is the number of edges of G lying closer to u than to v and n _ev (e|G) is the number of edges of G lying closer to v than to u. An efficient formula for calculating the PI index of phenylenes is given, and a simple relation is established between the PI index of a phenylene and of the corresponding hexagonal squeeze.     

Effects of mechanical and thermal stresses on electric degradation of polyolefins and related materials

Degradation under the simultaneous effects of mechanical stress and temperature in polyolefins (PE, PP), composites on their basis (PE+PP fibre, PP+PP fibre, PP+glass fibre) and radiation low-density polyethylene (X-LDPE) used in high-voltage cables obeys the thermofluctuation theory of Zhourkov (in certain σ and τ₀ intervals) based on the theory of Arrhenius is presented in the following form: τ_σ = τ₀ exp[(U₀ − γσ)/ RT] (1) where τ is durability. τ₀ is a constant (10⁻¹²-10⁻¹³s) equal to period of vibrations of atoms around equilibrium position, U₀ is the activation energy of the mechanical destruction process (at σ = 0), γ is a structure-sensitive parameter, T is absolute temperature and R is universal gas constant. Electric degradation under the effects of electric field and temperature in the materials mentioned above obeys the equation: τ_E = τ₀ exp[(W₀ − χE)/ RT] (2) Here, τ_E, W₀ and χ are analogous to τ_σ, U₀ and γ, respectively. It is assumed that the following equation is valid under the simultaneous effects of E, σ and T: τ_σ,E = τ₀ exp[(U₀ − (γσ + χE))/ RT]. (3) electric degradation     

Physical aging and dye diffusion in polysulfone below the glass transition temperature

The effect of physical aging on the tracer diffusion coefficient D of camphorquinone in polysulfone is investigated. It is shown that if the sample is sufficiently annealed and physical aging is nearly complete, the temperature dependence of D will reflect the primary α-relaxation process of the host polymer. In the temperature range between T_g (=185°C) and 165°C, D is found to be a function of time, and the time dependence of D is given by D = At^?μ, with μ approximately equal to unity. © 1994 John Wiley & Sons, Inc.     

The true diatomic potential as a perturbed Morse function

The problem of representing a diatomic (true) Rydberg-Klein-Rees potential U^t by an analytical function U^a is discussed. The perturbed Morse function is in the form U^a = U^M + ∑b_nyⁿ, where the Morse potential is U^M = Dy², y = 1 ?exp(?;a(r ? r_e)). The problem is reduced to determination of the coefficients b_n so U^a(r) = U^t(r). A standard least-squares method is used, where the number N of b_n is given and the average discrepancy ΔU = |(U^t ? U^a)/U^t| is observed over the useful range of r. N is varied until ΔU is stable. A numerical application to the carbon monoxide X¹∑ state is presented and compared to the results of Huffaker¹ using the same function with N = 9. The comparison shows that the accuracy obtained by Huffaker is reached in one model with N = 5 only and that the best ΔU is obtained for N = 7 with a gain in accuracy. Computation of the vibrational energy E_v and the rotational constant B_v, for both potentials, shows that the present method gives values of ΔE and ΔB that are smaller than those found by Huffaker. The dissociation energy obtained here is 2.3% from the experimental value, which is an improvement over Huffaker's results. Applications to other molecules and other states show similar results. © 1995 by John Wiley & Sons, Inc.     

Depolarization field effect on the ferroelectric behavior of polymers

The effect of the depolarization field in crystallites on the ferroelectric behavior of polymers is discussed on the assumption that the crystallite is a prolate ellipsoid with its major axis directed along the electric field. The theory relates the polarization P and the electric field E in the crystallite to the overall values P and E for the polymer. The determination of the P -E hysteresis of a crystallite from the P-E hysteresis is given with examples for poly(vinylidene fluoride) (PVDF) and vinylidene fluoride (VDF)–trifluoroethylene (TrFE) copolymer. The ratio R = J/(P_s ? P), with J the switching current density and P_s the saturation polarization of polymer, is proved to be free from the depolarization field effect and the plot of logR against logarithmic time is shown to have merit for characterization of switching behavior. Examples of the curves are given for PVDF and VDF-TrFE copolymers. The temporal change of local electric field in the unreversed domains in the crystallite in the course of polarization reversal is predicted by the theory and this change is proved to be a significant mechanism of switching acceleration.     

Plasma polymerization investigated by the substrate temperature dependence

Plasma polymerization of tetra fluoroethylene (TFE), perfluoro-2-butyl-tetrahydrofuran (PFBTHF), ethylene, and styrene were investigated in various combinations of monomer flow rates and discharge wattages for the substrate temperature range of ?50 to 80°C. The polymer deposition rates can be generally expressed by k₀ = Ae^?bt, where k₀ is the specific deposition rate given by k₀ = (deposition rate)/(mass flow rate of monomer), A is the preexponential factor representing the extrapolated value of k₀ at zero absolute temperature, and b is the temperature-dependence coefficient. It was found that the value of b is not dependent on the condensibility of monomer but depends largely on the group of monomer; that is, perfluorocarbons versus hydrocarbons. The values of A are dependent on domains of plasma polymerization. In the energy deficient region A is given by A = α(W/FM)ⁿ, where α is the proportionality constant, W is discharge wattage, FM is the mass flow rate, and n is close to unity. In the monomer deficient region A becomes a constant. The kinetic equation is discussed in view of the bicyclic rapid step-growth polymerization mechanisms.     

Modeling the Effects of Primary Radicals in Free‐Radical Polymerization

The effects of non‐ideal initiator decomposition, i.e., decomposition into two primary radicals of different reactivity toward the monomer, and of primary radical termination, on the kinetics of steady‐state free‐radical polymerization are considered. Analytical expressions for the exponent n in the power‐law dependence of polymerization rate on initiation rate are derived for these two situations. Theory predicts that n should be below the classical value of 1/2. In the case of non‐ideal initiator decomposition, n decreases with the size of the dimensionless parameter α ≡ (k_tz /k_dz) √r_ink_t, where k_tz is the termination rate coefficient for the reaction of a non‐propagating primary radical with a macroradical, k_dz is the first‐order decomposition rate coefficient of non‐propagating (passive) radicals, r_in is initiation rate, and k_t is the termination rate coefficient of two active radicals. In the case of primary radical termination, n decreases with the size of the dimensionless parameter β ≡ k_t,s r_in^1/2/k_p,s M r_t,l^1/2, where k_t,s is the termination rate coefficients for the reaction of a primary (“short”) radical with a macroradical, k_t,l is the termination rate coefficients of two large radicals, k_p,s is the propagation rate coefficient of primary radicals and M is monomer concentration. As k_t is deduced from coupled parameters such as k_t /k_p, the dependence of k_p on chain length is also briefly discussed. This dependence is particularly pronounced at small chain lengths. Moreover, effects of chain transfer to monomer on n are discussed.     

Photocontrol of Polar Aromatic Interactions by a Bis‐Hemithioindigo Based Helical Receptor

The first example of a bis‐hemithioindigo (bis‐HTI)‐based molecular receptor was realized. Its folding and selective binding affinity for aromatic guest molecules can be precisely controlled by visible light and heat. The thermodynamically stable state of the bis‐HTI is the s‐shaped planar Z,Z‐configuration. After irradiation with 420 nm light only the E,Z‐configuration is formed in a highly selective photoisomerization. The E,Z‐isomer adopts a helical conformation because of the implementation of repulsive steric interactions. The E,Z‐configured helix is able to recognize electron‐poor aromatic guests exclusively through polar aromatic interactions and also distinguishes between regioisomers. After heating, the Z,Z‐configuration is completely restored and the aromatic guest molecule is efficiently released.     

Scattering function for wormlike chains with finite thickness

The particle scattering function P(k) is approximately evaluated for the Kratky–Porod wormlike chain with a circular cross section to examine the effect of chain diameter d on the scattering curve of k²P(k) versus k, the magnitude of the scattering vector, for stiff chains and also the applicability of the cross‐section plot of ln[kP(k)] versus k² to them. In the evaluation, series expansions from the rod and coil limits up to the fifth‐order and third‐order deviations, respectively, are combined together. The major results or conclusions derived are as follows. First, the conventional equation, P(k) = P₀(k) exp(?k²d²/16), for straight cylinders overestimates k²P(k) at relatively large values of k, whereas its alternative, P(k) = P₀(k)[2J₁(kd/2)/(kd/2)]², is a good approximation to exact P(k) unless contour length L is shorter than 10d. Here, P₀(k) denotes the scattering function for the chain contour, and J₁(x) is the Bessel function of the first order. Second, as d is increased for a fixed value of L (relative to the Kuhn segment length), the k²P(k)–k curve lowers with a pronounced maximum, and the peak position shifts to a lower scattering angle. Third, if the chain is somewhat flexible, the cross‐section plot has an approximately linear region, with a slope fairly close to ?d²/16 expected from the aforementioned conventional equation. This plot for rods appreciably bends down, and thus the experimental observation of an approximately linear relation (over a wide k range) implies that, in contrast to the prevailing notion, the polymer examined is not completely rigid but instead is somewhat flexible. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1398–1407, 2004     

All-electron SCF LCAO MO calculations on various conformations of cis- and trans-stilbene

Ab initio SCF calculations of cis- and trans-stilbene at different conformations were performed using two program systems. Minimal energy is obtained for cis-stilbene when the phenyl rings are rotated by 52 ° out of the molecular plane. The deviation from planarity due to steric hindrance is smaller for the trans isomer yielding a rotational angle of 19 °. The trans isomer is calculated to be more stable by 5.7 kcal/mole than the cis isomer, confirming the experimental estimate according to which the energy of isomerization is about 3 kcal/mole. This is an improvement over semiempirical calculations which predict a lower energy for the trans configuration.     

Morphology development during isothermal crystallization. II. Isotactic and syndiotactic polypropylene blends

Morphology development during isothermal crystallization in equal molecular weight isotactic polypropylene (iPP), syndiotactic polypropylene (sPP), and iPP/sPP blends was studied with time‐resolved simultaneous small‐angle X‐ray scattering (SAXS) and wide‐angle X‐ray diffraction (WAXD) with synchrotron radiation. The sPP melting point is 15–20 °C below that of the iPP component, and sPP multiple melting is not affected by blending for 50–100 wt % sPP compositions. SAXS and WAXD (at 115 and 137.5 °C) show that sPP crystallizes more slowly than iPP. The sPP long spacing is larger than that of iPP at both crystallization temperatures, exhibits a broader distribution, and changes to a greater extent during crystallization. Differential scanning calorimetry (DSC) cooling and SAXS/WAXD measurements show iPP crystallizing first and nearly to completion before sPP in a 50:50 iPP/sPP blend. At 115 °C, iPP crystals nucleate sPP in a 50:50 blend and modify the sPP lamellar spacing. The nucleation does not overcome the large difference in the iPP and sPP rates at 137.5 °C. Before sPP crystallization in a 50:50 blend (115 °C), the iPP long spacing is not affected by molten sPP. The iPP long spacing is slightly expanded by molten sPP, and the WAXD induction time is delayed at 137.5 °C. The observed iPP long spacing in the presence of molten sPP is consistent with previously reported results for iPP/atactic polypropylene (aPP) blends of similar molecular weight. Quantitative differences between the two types of blends are consistent with previously reported thermodynamic rankings. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1876–1888, 2001     

Kinetics of Bulk Free‐Radical Polymerization of Butyl Methacrylate Isomers Studied by Reaction Calorimetry

The kinetics of bulk free‐radical polymerizations of n‐butyl methacrylate (n‐BMA), iso‐butyl methacrylate (i‐BMA), and tert‐butyl methacrylate (t‐BMA) are studied by differential scanning calorimetry and with the aid of a mathematical model previously reported by the authors. In all the cases, the rate of polymerization (R_p) evolution curve exhibits a minimum at low conversions and the characteristic maximum of the autoacceleration effect. It is found that the monomer conversion x_min at which the minimum is observed, follows the order n‐BMA > i‐BMA > t‐BMA and that for monomer conversions (x) smaller than x_min, the termination rate coefficient (k_t) shows a plateau. According to the model results it is obtained that for x > x_min, the termination reaction is chemically controlled whereas for x > x_min, it is diffusion‐controlled and that the x_min values are related to the value of the termination rate coefficient of the chemical step (k_t0) of every isomer, which is highly influenced by the steric hindrance of the alkyl substituent group.