Graphs of relations and Hilbert series

We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by $n$ generators and $\frac {n(n-1)}{2}$ relations for $n \leq 7$. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated to each color are pairwise 2-isomorphic.

Acoustic, volumetric, compressibility and refractivity properties and Flory’s reduction parameters of some homologous series of alkyl alkanoates from 298.15 to 333.15 K

The speeds of sound u in, densities ? and refractive indices nD of some homologous series, such as n-alkyl ethanoates, n-alkyl propionates, methyl alkanoates, ethyl alkanoates, dialkyl malonates, and alkyl haloalkanoates, were measured in the temperature range from 298.15 to 333.15 K. Molar volume V, isentropic and isothermal compressibilities ?S and ?T, molar refraction Rm, Eykman’s constant Cm, molecular radius r, Rao’s molar function R, thermal expansion coefficient a, thermal pressure coefficient ?, and Flory’s characteristic parameters image, P*, V*, and T* have been calculated from the measured experimental data. Applicability of Rao theory and Flory–Patterson–Pandey (FPP) theory have been examined and discussed for these alkanoates.

Acoustic, volumetric, compressibility and refractivity properties and reduction parameters for the ERAS and Flory models of some homologous series of amines from 298.15 to 328.15 K

The speeds of sound u, densities ? and refractive indices nD of homologous series of mono-, di-, and tri-alkylamines were measured in the temperature range from 298.15 to 328.15 K. Isentropic and isothermal compressibilities ?S and ?T, molar refraction Rm, Eykman’s constant Cm, Rao’s molar sound function R, thermal expansion coefficient a, thermal pressure coefficient ?, and reduction parameters P*, V*, and T* in frameworks of the ERAS model for associated amines and Flory model for tertiary amines have been calculated from the measured experimental data. Applicability of the Rao theory and the ERAS and Flory models have been examined and discussed for the alkyl amines.

Idealised operation of zero-voltage-switching series-L/parallel-tuned Class-E power amplifier

An analysis of a modified series-L/parallel-tuned Class-E power amplifier is presented, which includes the effects that a shunt capacitance placed across the switching device will have on Class-E behaviour. In the original series L/parallel-tuned topology in which the output transistor capacitance is not inherently included in the circuit, zero-current switching (ZCS) and zero-current derivative switching (ZCDS) conditions should be applied to obtain optimum Class-E operation. On the other hand, when the output transistor capacitance is incorporated in the circuit, i.e. in the modified series-L/parallel-tuned topology, the ZCS and ZCDS would not give optimum operation and therefore zero-voltage-switching (ZVS) and zero-voltage-derivative switching (ZVDS) conditions should be applied instead. In the modified series-L/parallel-tuned Class-E configuration, the output-device inductance and the output-device output capacitance, both of which can significantly affect the amplifier's performance at microwave frequencies, furnish part, if not all, of the series inductance L and the shunt capacitance COUT, respectively. Further, when compared with the classic shunt-C/series-tuned topology, the proposed Class-E configuration offers some advantages in terms of 44% higher maximum operating frequency (fMAX) and 4% higher power-output capability (PMAX). As in the classic topology, the fMAX of the proposed amplifier circuit is reached when the output-device output capacitance furnishes all of the capacitance COUT, for a given combination of frequency, output power and DC supply voltage. It is also shown that numerical simulations agree well with theoretical predictions.

Even order harmonic Series-L/Parallel-Tuned Class-E frequency multiplier

In this brief, we propose a new Class-E frequency multiplier based on the recently introduced Series-L/Parallel-Tuned Class-E amplifier. The proposed circuit produces even-order output harmonics. Unlike previously reported solutions the proposed circuit can operate under 50% duty ratio which minimizes the conduction losses. The circuit also offers the possibility for increased maximum operating frequency, reduced peak switch voltage, higher load resistance and inherent bond wire absorption; all potentially useful in monolithic microwave integrated circuit implementations. In addition, the circuit topology suggested large transistors with high output capacitances can be deployed. Theoretical design equations are given and the predictions made using these are shown to agree with harmonic balance circuit simulation results.

Transmission line matching effects on the performance of shunt-C/series-tuned and series-L/parallel-tuned Class-E amplifiers

The impact that the transmission-line load-network has on the performance of the recently introduced series-L/parallel-tuned Class-E amplifier and the classic shunt-C/series-tuned configuration when compared to optimally derived lumped load networks is discussed. In addition an improved load topology which facilitates harmonic suppression of up to 5 order as required for maximum Class-E efficiency as well as load resistance transformation and a design procedure involving the use of Kuroda's identity and Richard's transformation enable a distributed synthesis process which dispenses with the need for iterative tuning as previously required in order to achieve optimum Class-E operation. © 2005 IEEE.

Oxidation of N,N,N ',N '-tetraalkyl-para-phenylenediamines in a series of room temperature ionic liquids incorporating the bis(trifluoromethylsulfonyl)imide anion

The five room temperature ionic liquids: 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([CnMIM][N(Tf)(2)], n = 2, 4, 8, 10) and n-hexyltriethylammonium bis(trifluoromethylsulfonyl)imide ([N-6222][N(Tf)(2)]) were investigated as solvents in which to study the electrochemical oxidation of N,N,N',N'-tetramethyl-para-phenylenediamine (TMPD) and N,N,N',N'-tetrabutyl-paraphenylenediamine (TBPD), using 20 mul micro-samples under vacuum conditions. The effect of dissolved atmospheric gases on the accessible electrochemical window was probed and determined to be less significant than seen previously for ionic liquids containing alternative anions. Chronoamperometric transients recorded at a microdisk electrode were analysed via a process of non-linear curve fitting to yield values for the diffusion coefficients of the electroactive species without requiring a knowledge of their initial concentration. Comparison of experimental and simulated cyclic voltammetry was then employed to corroborate these results and allow diffusion coefficients for the electrogenerated species to be estimated. The diffusion coefficients obtained for the neutral compounds in the five ionic liquids via this analysis were, in units of 10(-11) m(2) s(-1), 2.62, 1.87, 1.12, 1.13 and 0.70 for TMPD. and 1.23, 0.80, 0.40, 0.52 and 0.24 for TBPD (listed using the same order for the ionic liquids as stated above). The most significant consequence of changing the cationic component of the ionic liquid was found to be its effect on the solvent viscosity; the diffusion coefficient of each species was found to be approximately inversely proportional to viscosity across the series of ionic liquids, in accordance with Walden's rule. (C) 2003 Elsevier B.V. All rights reserved.

Electroreduction of oxygen in a series of room temperature ionic liquids composed of group 15-centered cations and anions

The electrochemical reduction of oxygen is reported in four room temperature ionic liquids (RTILs) based on quaternary alkyl -onium cations and heavily fluorinated anions in which the central atom is either nitrogen or phosphorus. Data were collected using cyclic voltammetry and potential step chronoamperometry at gold, platinum, and glassy carbon disk electrodes of micrometer dimension under water-free conditions at a controlled temperature. Analysis via fitting, to appropriate theoretical equations was then carried out to obtain kinetic and thermodynamic information pertaining to the electrochemical processes observed. In the quaternary ammonium electrolytes, reduction of oxygen was found to occur reversibly to give stable superoxide, in an analogous manner to that seen in conventional aprotic solvents such as dimethyl sufoxide and acetonitrile. The most significant difference is in the relative rate of diffusion; the diffusion coefficients of oxygen in the RTILs are an order of magnitude lower than in common organic solvents, and for superoxide these values are reduced by a further factor of 10. In the quaternary phosphonium ionic liquids, however, more complex voltammetry is observed, akin to that expected for the reduction of oxygen in acidified organic media. This is shown to be consistent with the occurrence of a proton abstraction reaction between the electrogenerated superoxide and quaternary alkyl phosphonium cations following the initial electron transfer.