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.

The Complete Works of John Milton: Volume III: The Shorter Poems (816pp.)

Volume III of the new eleven-volume edition of Milton's Complete Works provides a definitive scholarly edition of all of Milton's shorter poems in English, Latin, Italian, and Greek, as well as his Mask, taken from both published and manuscript sources. It includes his 1645 Poems complete with all prefatory materials, thus illuminating the ways in which author, publisher, and print shop shaped this volume. It then presents all the new poems added in the 1673 edition (with the new Table of Contents), as well as the poems omitted from both editions. A careful collation of textual variants among these sources as well as the 1637 anonymous publication of Milton's Mask is provided. The Bridgewater manuscript of Milton's Mask (probably close to the acting version) and his working copy from the Trinity Manuscript, with its many alterations and additions, are transcribed in their entirety, so that the various versions may be compared and studied. 

A special feature of this edition is a new translation of Milton's many Latin and Greek poems that is both accurate and attentive to their literary qualities. This is augmented by a detailed and comprehensive commentary that highlights classical, vernacular, and neo-Latin parallels. A poetic translation of Milton's six Italian sonnets and Canzone is also supplied. In addition, the Appendices contain all the versions of Milton's shorter poems in all the contemporary manuscript and printed sources, so they may be examined in relation to their specific contexts. The transcription of all the versions of Milton's poems in the Trinity Manuscript allows in several cases, notably 'Lycidas' and 'At a Solemn Music,' for examination of the evolution of these poems as Milton weighed choiced of diction and sound qualities, enabling further understanding of his poetic practices. 

Barbara Lewalski is responsible for text, textual apparatus, and commentary pertaining to the vernacular poems in all sections of this edition including the appendices, and manuscript transcriptions (with the exception of A Maske), as well as the Occasions, Vernacular Poems,and Textual Introductions. Estelle Haan is responsible for text, textual apparatus, and commentary for the Poemata in all sections of this edition,and for the Poemata Introduction. She has also provided all translations from Latin, Italian, and Greek in the Testimonia, Poemata, and associated commentary, and transcriptions of the BL Damon, the Bodleian AdJoannem Rousium, and A Maske from the Trinity and Bridgewater manuscripts. Andrew McNeillie has provided poetic translations for Milton’s Italian sonnets, and Jason Rosenblatt has provided some Hebrew text and commentary pertaining to Milton’s Psalm translations.John Cunningham has transcribed Henry Lawes’ music for Milton’s masque, with commentary (Appendix E). Biblical references are taken from the King James (Authorized) Version.

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.