On maximal resonance of polyomino graphs

A polyomino graph is a finite plane 2-connected bipartite graph every interior face of which is bounded by a regular square of side length one. Let k be a positive integer, a polyomino graph G is k-resonant if the deletion of any i ≤ k vertex-disjoint squares from G results in a graph either having perfect matchings or being empty. If graph G is k-resonant for any integer k ≥ 1, then it is called maximally resonant. All maximally resonant polyomino graphs are characterized in this work. As a result, the least integer k such that a k-resonant polyomino graph is maximally resonant is determined.     

The compensation effect revisited

It is generally accepted that the compensation effect arises when a linear relation between InA andE is detected for a simple reaction taking place over different catalysts or for different reactions over one catalyst. For a perfect linear relation between InA andE representation of the reaction rate constant in an Arrhenius plot results in a series of straight lines which intersect in a single point. The importance is stressed of defining unambiguously what is meant by the compensation effect, and it is shown how the scatter in the values of InA is translated into Arrhenius plots.     

Stochastic theory of direct simulation Monte Carlo method

A treatment of direct simulation Monte Carlo method as a Markov process with a master equation is given and the corresponding master equation is derived. A hierarchy of equations for the reduced probability distributions is derived from the master equation. An equation similar to the Boltzmann equation for single particle probability distribution is derived using assumption of molecular chaos. It is shown that starting from an uncorrelated state, the system remains uncorrelated always in the limit N→∞, where N is the number of particles. Simple applications of the formalism to direct simulation money games are given as examples to the formalism. The formalism is applied to the direct simulation of homogenous gases. It is shown that appropriately normalized single particle probability distribution satisfies the Boltzmann equation for simple gases and Wang Chang–Uhlenbeck equation for a mixture of molecular gases. As a consequence of this development we derive Birds no time counter algorithm. We extend the analysis to the inhomogeneous gases and define a new direct simulation algorithm for this case. We show that single particle probability distribution satisfies the Boltzmann equation in our algorithm in the limit N→∞, V _k →0, Δt→0 where V _k is the volume of kth cell. We also show that our algorithm and Bird’s algorithm approach each other in the limit N _k →∞ where N _k is the number of particles in the volume V _k .     

Packing in honeycomb networks

Molecules arranging themselves into predictable patterns on silicon chips could lead to microprocessors with much smaller circuit elements. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. An H-packing of a graph G is a set of vertex disjoint subgraphs of G, each of which is isomorphic to a fixed graph H. If H is the complete graph K ₂, the maximum H-packing problem becomes the familiar maximum matching problem. In this paper we give algorithms to find a perfect packing of HC(n) with P ₆ and K _1,3 when n is even and thus determines their packing numbers. Further we also study the packing of HC(n) with 1, 3-dimethyl cyclohexane.     

Optical potential calculations for molecular collisions

The Feshbach optical formalism is applied to elastic, nonreactive atom-diatom scattering on a single potential energy surface. The optical potential depends on GQ, the resolvent of E-QHQ, where Q projects onto open as well as closed channels. A method for generating GQ is developed which goes beyond the free-space approximation by partitioning the radial part of the intermolecular separation into a set of intervals, on each of which the projected interaction QVQ is represented by a constant diagonal form. The resulting GQ is used in calculations on a model collinear system. The calculations are carried out with various approximations on the full nonlocal optical potential equation for Pψ Emphasis is placed on two of these, one of which is characterized by a local homogeneous equation for Pψ, and the other by a local inhomogeneous equation for Pψ.     

A master equation theory of excitonic annihilation phenomena for finite latices of low dimensionality

A master equation is written for the equation of motion for the vector p(t), in which the nth component corresponds to the probability of observing n excitons on a lattice with L sites. The dependence of the properties of p(t) on the magnitude of L, the intensity of excitation, the lattice dimensionality, and the magnitude of the biexcitonic annihilation rate is discussed. The dependence of the biexcitonic annihilation rate on the exciton density is discussed in the context of a simple simulation of exciton annihilation. The applicability of these ideas to excitonic annihilation in polymers is discussed.     

The drag of the row of parallel chains of spherical particles in the Stokes flow

The drag of thin-layered porous deposit consisting of dendrites of identical spherical particles with respect to the flow of viscous incompressible liquid is calculated. The deposit is approximated by a model system, a row of parallel chains of particles oriented perpendicular to a flow direction. The expression is derived for the dimensionless drag force acting on the unit chain length as a function of the ratio of a particle radius to a half-distance between chain axes, a/h. It is shown that, at a/h < 0.5, the hydrodynamic equivalent of the chains is the smooth cylinder whose radius is 1.16 times smaller than the particle radius that agrees with the experiment. It is also shown that, at a/h = 1, the drag force of a particle contacting with four adjacent particles in the layer with square packing is equal to F = 44F _St, where F _St is the Stokes drag force of a spherical particle. The pressure drop in this single layer is by 3.5% higher than in the layer of spherical particles with cubic packing. At a/h = 2/√3, drag force F of the particle contacting with six particles in a single layer with hexagonal packing is equal to 340F _St.     

La methode polarovoltrique : Principes généraux et bases de la méthode

The various steps in the development of the polarovoltric method and its utilisation in an automatic titration apparatus employing 2 polarized platinum electrodes are described. The method is based on the use of 2 types of polarization relationships applied to different chemical systems. These relationships are of the type I = f(V) and V = f(U), where V is the potential measured at the electrodes and U the potential applied to the electrodes across a resistance R, and are obtained directly from 2 indicating electrodes without the need for a reference electrode.The advantage of these relationships over the classic I= f(E) curves, where E is the potential of the indicating electrode with respect to a reference electrode, is to facilitate the prediction of the titration curves as a function of the resistance R and the applied voltage U. The use of these relationships has shown that a fixed applied voltage U of 3 V and a fixed series resistance R of 0.5 megohm are the most suitable for a differential polarovoltmeter for semi-automatic titrations.A symbolic notation is described which indicates the origin of the observed variations in potential. This notation permits a simple interpretation of polarovoltric curves and the rational use of unsymmetrical electrode arrangements.     

Electroporation: A unified,quantitative theory of reversible electrical breakdown and mechanical rupture in artificial planar bilayer membranes

We present a quantitative theory of electroporation of artificial planar lipid bilayer membranes. Assuming that aqueous pores are involved in electroporation, we describe the pore population of the membrane by the density function n (r, t), where n (r, t) dr is the number of pores with radius between r and r + dr at time t. We further assume that there is a minimum pore size r_min, that pores of radius r_min are created and destroyed by thermal fluctuations, and that the pore creation rate is proportional to exp(aΔφ_m²/kT, where a is a constant, Δφ_m is the membrane voltage, k is Boltzmann's constant, and T is the absolute temperature. We use a simple formula for the conductance of a pore as a function of radius, the expression for the pore energy previously derived by Pastushenko and Chizmadzhev, and a simple model of the external circuit. We solve the equations numerically and compare the solutions to the results of charge pulse experiments.In a charge-pulse experiment a membrane suffers one of four possible fates: (1) a slight increase in electrical conductance, (2) mechanical rupture, (3) incomplete reversible electrical breakdown, resulting in incomplete discharge of the membrane, or (4) reversible electrical breakdown (REB), resulting in complete discharge of the membrane. In agreement with experiment, this theory describes these four fates and predicts that the fate in any particular experiment is determined by the properties of the membrane and the duration and amplitude of the charging pulse.     

Vibrational spectra and vibrational states of simple gas-phase hydrogen-bonded dimers

The article aims to outline the growth of evidence and ideas about infrared band broadening for simple, gaseous, moderately strong, hydrogen bonded dimers B…HA, to draw attention to areas in need of further development and to collect together experimental information available at the present time about vibrational states associated with such dimers. The band associated with the modified HA stretching mode, ν_s, is observed for several dimers not only to be broad, but to have sub-band structure, which is satisfactorily interpreted as arising from combination bands of ν_s with the low frequency stretch-mode ν_σ, giving a progression ν_s ± nν_σ as a result of strong anharmonic coupling. For weaker dimers with lower values of ν_σ the sub-band structure is less evident, and may appear only as shoulders, while for still weaker dimers, the sub-bands may be merged into a featureless broad band. A major factor contributing to the breadth of the individual sub-bands in the band structure is the presence of hot-bands, especially a long series based on successive excited states of the low-frequency bending mode ν_β. A link is indicated with the interpretation of band-broadening for moderately strong hydrogen-bonded complexes in the liquid state. The anharmonic coupling of ν_s and ν_σ is again a central feature but there is a new factor, namely the coupling of ν_σ through a fluctuating potential with the surroundings, which has the result that the ν_s mode rapidly loses phase coherence resulting in a broad structureless band.     

Short diastereoselective synthesis of cis- and trans-hexahydropyrido[2,1-a]isoindole derivatives

A new and highly stereoselective access to 4,10b-trans or 4,10b-cis hexahydropyrido[2,1-a]isoindole derivatives is reported, both requiring an intramolecular Mannich-type reaction as key step. The cis diastereoisomer is obtained in three steps from a 2-alkyl benzaldehyde through the stereoselective formation of a 2,6-cis-disubstituted piperidine, while the trans stereomer is efficiently obtained, in a single step, if a 2-formyl benzoic acid is involved in the Mannich cyclization process.     

Two-photon ionization of an inner shell electron of the Cl atom

We have calculated, using second order perturbation theory, the two photon ionization cross section of a K-shell electron of chlorine forE=1.6 keV incident photons. Two classes of intermediate states must be considered, those in which a 1s electron moves to an emptyp-orbital, and those in which an electron from an occupiedp-orbital moves into the continuum. The first class of intermediate states is followed by the ejection of ap-electron into the continuum. The second class of intermediate states is followed by the transfer of a 1s electron into an emptyp-state. The largest contribution comes from 3p →d-continuum followed by 1s → 3p transition. Our result is σ⁽²⁾/I=2.06×10⁴¹ cm⁴/W where σ⁽²⁾ is the two photon ionization cross-section andI is the light intensity.     

Interpretation of static and dynamic responses of a dissolved oxygen electrode in viscous broths

The response of an amperometric oxygen electrode is studied theoretically and experimentally for the case of significant liquid film resistance at the outer side of the membrane. The behaviour of the probe in a gas stream is predicted by using a transfer function which involves an electrode model including oxygen diffusion within the electrode. The effects of the liquid film which exists at the membrane surface when dissolved oxygen concentrations are measured, are taken into account by modifying the transfer function. The new expression obtained is used to model the step response of the probe in a 2-1 stirred tank fermentor filled with water or xanthane solutions at different concentrations. First, the results are used to correct automatically the steady-state voltage readings of the probe. Secondly, the probe transfer function is used to evaluate k₁a by dynamic measurements: the response to a step change in the gas concentration is transformed via the fast Fourier transform algorithm and k₁a is identified in the Fourier domain by a Gauss-Newton algorithm. Data acquisition, Fourier transform and k₁a identification are implemented on-line on a HP-87 computer. This method of obtaining k₁a values appears to be a generalized moment method. It is shown that it is necessary to consider the liquid film dynamics around the probe in the actual fermenting conditions to evaluate k₁a successfully.     

Fragmentation of protonated amides through intermediate ion-neutral complexes: Neighboring group participation

It has been shown that neighboring group participation plays an important role in the fragmentation of protonated amides; the attachment of an adjacent functional group capable of accepting a proton provides alternative pathways of low energy for the formation of the inevitable N-protonated species in the fragmentation of the amide bond. Under methane chemical ionization (CI) conditions, protonated aniline (m/z 94) is only 1. 6% of the base peak MH⁺ ion for acetanilide; the abundance of the m/z 94 ion is increased to 15% for acetoacetanilide and protonated o-methoxyaniline reaches a relative intensity of 49% for N-acetyl-o-methoxyaniline. A more striking difference in ease of the formation of protonated anilines is found for acetanilides bearing a nitro group at different positions. Protonated nitroaniline (m/z 139) is the base peak in the methane CI spectrum of N-acetyl-o-nitroaniline; the m/z 139 ion drops to only 0.7% for the para isomer, and this ion is increased to 31.5% in the spectrum of N-acetoaceto-p-nitroaniline. By employing low energy collision-induced dissociation, it has been found that the fragmentation of protonated amides proceeds by way of ion-neutral complexes. In the case of acetanilide, for example, the cleavage of the amide bond gives rise to an acetylium ion and neutral aniline, which are bound together as a complex. An α-hydrogen of the acetylium ion, which is activated by the positive charge, is captured by aniline due to its higher proton affinity as compared with ketene. For those compounds having mobile protons other than the amidic hydrogen, it is indicated that such proton has the priority to be transferred in the reaction. Thus, the proton on the free carboxyl group of N-phenyl succinic and maleic monoamides is transferred in the fragmentation, leading to anhydrides as the neutral species in the formation of protonated aniline.     

Cascades of energy among the vibrational levels of diatomic molecules trapped in a rare gas matrix: With application to 12C16O(ν) in Ar

Energy stored in vibrational level ν = 1 of several individual dipolar diatomic molecules AB which are trapped in a rare gas matrix M is automatically accumulated in a higher level ν > 1 of a single molecule AB. This remarkable cascade of energy upwards competes with a cascade of energy downwards. the radiative decay. The interplay of both cascades, first observed by Dubost and Charneau, is explained a simple model. The model incorporates three processes into a master equation for the relative populations P_ν(t) of levels ν: (a) migration of single quanta by resonance energy transfer, AB(1) + AB(0) ? AB(0) + AB(1); (b) phonon assisted excitation of upper levels, AB(1) + AB(ν) → AB(0) + AB(ν+1); and (c) radiative decay, AB(ν) → AB(ν-1). The model assumes that there is only one isotopic species AB which has a small but nonzero vibrational anharmonicity, that the temperature is low, T → 0 K, the concentration ratio ?_M/?_AB is large and that, initially, at time t = 0, a small fraction p₁ of molecules AB is excited to level ν = 1. The master equation has only two parameters, the radiative lifetime t_rad and k  2/[?_AB?₁k(1,1 → 0,2)t_rad], where k(1,1 → 0,2) is the reference rate constant of process (b). The master equation is solved in closed form for the Pν(t). For t_rad = 14 ms and k = 0.2, very satisfactory qualitative agreement is found for the theoretical P_ν(t) and the experimental time evolution of the relative population of vibrational levels of ¹²C¹⁶O in an argon matrix, for ?_M/?_AB = 2000 at T = 9 K. In agreement with experimental results it is concluded that the risetime of the fluorescence signals decreases whereas population inversion increases for decreasing values of ?_M/?AB. At long times, t > t_rad, any population inversion should disappear.     

Synthesis of enantiomeric pure lithium and potassium benzamidinate complexes

A new synthesis leading to the chiral amidines (S,S)- and (R,R)-N,N-bis-(1-phenylethyl)benzamidine ((S)- and (R)-HPEBA) in good yields is presented. Further reaction of (S)-HPEBA with n-BuLi gave the chiral lithium salt (S)-LiPEBA. Treatment of KH with (S)-HPEBA in boiling THF afforded the corresponding potassium salt (S)-KPEBA. In contrast by performing the reaction in boiling toluene a fast racemization was observed. In the solid state racemic KPEBA formed a dimer, in which all four nitrogen atoms are in a plane. To each potassium atom a toluene molecule is η⁶-coordinated.     

Different experimental results for the influence of immersion angle on the resonant frequency of a quartz crystal microbalance in a liquid phase: with a comment

This paper presents different experimental results of the influence of an immersion angle (θ, the angle between the surface of a quartz crystal resonator and the horizon) on the resonant frequency of a quartz crystal microbalance (QCM) sensor exposed one side of its sensing surfaces to liquid. The experimental results show that the immersion angle is an added factor that may influence the frequency of the QCM sensor. This type of influence is caused by variation of the reflection conditions of the longitudinal wave between the QCM sensor and the walls of the detection cell. The frequency shifts, measured by varying θ, are related to the QCM sensor used. When a QCM sensor with a weak longitudinal wave is used, its resonant frequency is nearly independent of θ. But, if a QCM sensor with a strong longitudinal wave is employed, the immersion angle is a potential error source for the measurements performed on the QCM sensor. When the reflection conditions of the longitudinal wave are reduced, the influence of θ on the resonant frequency of the QCM sensor is negligible. The slope of the plot of frequency shifts (ΔF) versus (ρη)^1/2, the square root of the product of solution density (ρ) and viscosity (η), may be influenced by θ in a single experiment for the QCM sensor with a strong longitudinal wave in low viscous liquids, which can however, be effectively weakened by using the averaged values of reduplicated experiments. In solutions with a large (ρη)^1/2 region (0-55 wt% sucrose solution as an example, with ρ value from 1.00 to 1.26 g cm⁻³ and η value from 0.01 to 0.22 g cm⁻¹ s⁻¹, respectively), the slope of the plot of ΔF versus (ρη)^1/2 is independent of θ even for the QCM sensor with a strong longitudinal wave in a single experiment. The influence of θ on the resonant frequency of the QCM sensor should be taken into consideration in its applications in liquid phase.     

Fractal nature and thermal analysis of powders

F(a) functions (wherea is the rate of conversion), frequently referred to when considering non-isothermal heterogeneous processes, are reconsidered from a fractal viewpoint. This is achieved on the basis of previous studies on the fundamental properties of powders, which show that any powder obtained by mechanical size reduction yields a fractal particle-size distributionP(X,t), whereX is a scaled particle size, with a material-dependent powern asP(X,t)∝X _n , and that the obtained powder has a specific surface area,S, expressed with the fractal particle sizex asS∝x ^D-3 with the fractal dimensionD. This can be interpreted to show that a powder obtained by mechanical grinding has a uniqueD for a specified particle-size range, and, in fact, TA results dependent on thisD were obtained. We also show that a mechanical size reduction process produces fractal surfaces. The phenomenologically known laws which relate input energy and the powder product are theoretically derived by assuming that the energy is consumed in producing fractal surfaces. The well-known reaction functions which relate the conversion rate with the physical and geometrical factors governing a reaction process are reconsidered from a fractal viewpoint. The validity of conventionalF(a) expressions based on integer dimensions are questioned.