Ring Modulator Research Articles

Variable Symmetry in Salmonella typhimurium Flagellar Motors

Electron cryomicroscopy of rotor complexes of the Salmonella typhimurium flagellar motor, overproduced in a nonmotile Escherichia coli host, has revealed a variation in subunit symmetry of the cytoplasmic ring (C ring) module. C rings with subunit symmetries ranging from 31 to 38 were found. They formed a Gaussian distribution around a mean between 34 and 35, a similar number to that determined for native C rings. C-ring diameter scaled with the number of subunits, indicating that the elliptical-shaped subunits maintained constant intersubunit spacing. Taken together with evidence that the M ring does not correspondingly increase in size, this finding indicates that rotor assembly does not require strict stoichiometric interactions between the M- and C-ring subunits. Implications for motor function are discussed.

Polymer micro-ring filters and modulators

Micro-ring wavelength filters and resonant modulators using polymer materials at 1300 nm and 1550 nm are analyzed, designed, and demonstrated. The rings are integrated with vertically coupled input and output waveguides. The devices are fabricated using optical lithography. Filters with a finesse of 141 and free spectral range of 5 nm at 1300 nm and finesse of 117 with a free spectral range (FSR) of 8 nm at 1550 nm are demonstrated. Ring resonators with a Q as high as 1.3 /spl times/ 10/sup 5/ at 1300 nm are demonstrated. The filters can be temperature tuned at the rate of 14 GHz//spl deg/C. Resonant ring modulators, which use an electrooptic polymer, are demonstrated. The resonance wavelength voltage tunes at the rate of 0.82 GHz/V. The modulators have a bandwidth larger than 2 GHz. Using the resonant modulator, and open eye diagram at 1 Gb/s is demonstrated.

Canonical Modules of Semigroup Rings and a Conjecture of Reiner

We prove that the homotopy types of two naturally defined simplicial complexes are related in the following way: one is homotopy equivalent to a multiple suspension of the canonical Alexander dual of the other. These simplicial complexes arise in free resolutions of semigroup rings and modules. The relation between their homotopy types was conjectured by Reiner, and was suggested by a homological consequence of a result due independently to Danilov and Stanley on canonical modules of normal semigroup rings. Our proof is purely topological, and gives an alternative proof of their result. We also prove a generalization of a result of Hochster saying that these rings are Cohen—Macaulay, and indicate a new proof of Ehrhart’s reciprocity law for rational polytopes.

HIGH ORDER KÄHLER MODULES OF NONCOMMUTATIVE RING EXTENSIONS

We construct the high order Kähler modules of noncommutative ring extensions B/A and show their fundamental properties. Our Kähler modules represent not only high order left derivations for one-sided modules but also high order central derivations for bimodules, which are usual derivations. This new viewpoint enables us to prove new results which were not known even though B is an algebra over a commutative ring A. Our results are the decomposition of Kähler modules by an idempotent element, exact sequences of Kähler modules, the Kähler modules of factor rings, and the relation to separable extensions. In particular, our exact sequences of high order Kähler modules were not known even though B is commutative.

Conference Matrices and Unimodular Lattices

Conference matrices are used to define complex structures on real vector spaces. Certain lattices in these spaces become modules for rings of quadratic integers. Multiplication of these lattices by nonprincipal ideals yields simple constructions of further lattices including the Leech lattice.

S-modules and symmetric spectra

We study a symmetric monoidal adjoint functor pair between the category of S-modules and the category of symmetric spectra. The functors induce equivalences between the respective homotopy categories of spectra, module spectra and ring spectra. Then at approximately the same time, two categories of spectra with nice smash products were discov- ered. Elmendorf, Kriz, Mandell and May constructed the category of S-modules (EKMM), and Je Smith introduced symmetric spectra (HSS). Both categories are Quillen model categories and have associated notions of ring and module spectra. However these two categories arise in completely dierent ways. And even though the homotopy categories are equivalent, it is not a priori clear if both frameworks give rise to the same homotopy theory of rings and modules. Both categories have their merits, described in detail in the introductions of (EKMM) and (HSS), and it is desirable to be able to translate results obtained in one category into conclusions valid in the other. The present paper describes an easy mechanism which facilitates such comparisons. Below we dene a lax symmetric monoidal functor :MS ! Sp from the category of S-modules to the category of symmetric spectra. The functor preserves homotopy groups and has a strong symmetric monoidal left adjoint. We show that the two functors induce inverse equivalences of the homotopy categories of spectra, ring spectra, commutative ring spectra and module spectra: Main Theorem. The functor from the category MS of S-modules to the category Sp of symmetric spectra passes to a symmetric monoidal equivalence of homotopy categories

On the structure of closed ideals

Let R be a Noetherian ring for which we seek to map a path to its integral closure. The ring will be specified in some manner, say by generators and relations over a field or over Z. The multiplier approach consists in the following. For each ideal I containing regular elements, the ring of endomorphisms of I, HomROI;IU ,c an be identified as an integral extension of R in its total ring of fractions. We say that I is closed if Ra HomROI;IU. Despite the arithmetical definition, this notion will be better expressed by homological means. Examples of closed ideals are principal ideals, or more generally invertible ideals, canonical modules of rings satisfying Serre’s condition S2 ,a nd ideals of grade at least two. The condition holds universally for all nonzero ideals of R precisely when R is integrally closed. It is in connection with this last fact that our interest in non-closed ideals lies: Finding the integral closure R of R amounts to identifying sufficiently many non-closed ideals I such that Ra [ HomROI;IU:

Finiteness properties of local cohomology modules for regular local rings of mixed characteristic: the unramified case

In this note we partially extend results on the finite-ness properties of local cohomology modules from the case of a regular local ring containing a field to the unramified case of a regular local ring of mixed characteristic.

Influence of species and abiotic factors on extreme tree ring modulation:

The influence of biotic (tree species) and abiotic factors (regional climate, altitude and stand aspect) on extreme tree-ring widths is dendroecologically investigated. Negative pointer years are observed when abrupt radial growth reductions (exceeding 40%) occurred synchronously in a given tree population. Pointer year intensity is expected to follow several theoretical models when trees are sampled along ecological gradients in various site conditions. Hypotheses are made about expected patterns of pointer year spatial distribution. They are compared with observed results obtained with Norway spruce [Picea abies (L.) Karst.] and silver fir (Abies alba Mill.) sampled in two French Alpine valleys (Tarentaise and Maurienne) with different regional climates, on two aspects and three altitude levels. Results reveal that extreme years follow expected patterns well. Thus, clear site modulations are observed in 1956 and 1986 (only trees located in Maurienne reacted). Moreover, species differences are observed, with typical cases of single species sensitivity (for spruce, occurring in 1962 and 1992). Abiotic factors such as altitude and aspect also involve clear pointer year patterns, such as narrow rings in 1976 due to summer drought that occurred especially at lower altitudes. However, some observed extreme years sometimes appear to be a combination of two (or three) of these one-factor theoretical models (e.g. 1921 with both lower altitude level and only observed in Tarentaise; 1948 involving both higher altitude and northern slopes). These results demonstrate the consistency of various tree-ring and climate relationships along ecological gradients.

Adiabatic modulation of a superconducting quantum interference device (SQUID) ring by an electromagnetic field

In this paper we consider the modulation of a SQUID ring (a Josephson weak link enclosed by a thick superconducting ring) by an external electromagnetic (em) field for the case where the ring remains adiabatically in its ground state. We demonstrate that very good agreement can be found between experimental modulation data and the results predicted theoretically by solving the time-dependent Schrödinger equation for the ring-em-field system. We also show that the non-linear dynamical coupling between the ring and an external resonant circuit can influence the exact form of the modulation. Again we find consistent agreement between experiment and theory.

On the recurrent property of canonical modules of rees rings

On the recurrent property of canonical modules of rees rings

A new representation of elements of finite fields GF(2/sup m/) yielding small complexity arithmetic circuits

Let F/sub 2/ denote the binary field and F/sub 2m/, an algebraic extension of degree m>1 over F/sub 2/. Traditionally, elements of F/sub 2m/ are either represented as powers of a primitive element of F/sub 2m/ together with 0, or by an expansion in a basis of the vector space F/sub 2m/ over F/sub 2/. We propose a new representation based on an isomorphism from F/sub 2m/ into the residue polynomial ring module X/sup n/+1. The new representation simultaneously satisfies the properties of various traditional representations, which leads, in some cases, to architectures of parallel-in-parallel-out arithmetic circuits (adder, multiplier, exponentiator/inverter, squarer, divider) with average to small complexity. We show that the implementation of all the arithmetic circuits designed for the new representation on an integrated circuit sometimes has smaller complexity than the implementation of all the arithmetic circuits designed for other representations. In addition, we derive a serial multiplier for the field F/sub 2m/ which comprises the least number of gates of all the serial multipliers known to the author, when m+1 is a prime such that 2 is primitive in the field Z/sub m+1/.

Exterior Powers of Modules for Group Rings of Polycyclic Groups

One of the principal impulses for this paper was the consideration of the question, first raised in 1973 by G. Baumslag [2], of whether every finitely generated Abelian by polycyclic group can be embedded in a finitely presented Abelian by polycyclic group. That this cannot be done follows at once from THEOREM A. Every finitely presented Abelian by polycyclic group has a metanilpotent normal subgroup of finite index.

Musical tone electronic synthesizer and method

A tone generator (501) for a musical synthesizer has digital waveform generators (602,603) arranged such that a proportion of an output from a waveform generator (602) is supplied to a phase modulating input of a next waveform generator (603), wherein a proportion of the output from the last waveform generator in a chain (603) of serially connected waveform generators is supplied to a phase modulating input of the first waveform generator (602) in said chain, thereby providing a degree of recursion. Outputs from a plurality of waveform generators are supplied to a ring modulator (604) for generating harmonic sums and differences of frequencies produced by said recursion. A variable precision waveform lookup table (803) may be used to select a particular harmonic characteristic of tone and a frequency doubler (1001) may be included in the feedback loop to enable tones containing predominantly odd harmonics to be generated.

Spectral Mutation in Soundhack

Soundhack is a widely used program available for the Apple Macintosh computer that performs a variety of sound file manipulations. The functions of the program, authored by one of us (Tom Erbe), include sound-file type conversion, spectral dynamic processing, a varispeed/sample rate converter, sound file convolution, ring modulation, a phase vocoder, a binaural filter, and an amplitude analysisand-gain-change module. In Soundhack versions 0.8 and above, the authors have implemented a system of spectral mutation functions that allow for a number of different trans-

Rings of Homogeneous Functions Determined by Artinian Ring Modules

Given an R-module V, the centralizer near-ring M R ( V) is the collection of all functions ƒ: V → V such that ƒ( vr) = ƒ( v) r, for all v ∈ V, r ∈ R with the operations of point-wise addition and composition of functions, In this paper necessary and/or sufficient conditions are found for M R ( V) to be a ring when R is a commutative local ring with nilpotent radical.

On the finiteness and uniqueness of certain 2-tame N-groups

Unlike ring modules certain faithful N-groups are unique. The main theorem is that if N is a 2-tame ring-free near-ring where N/J(N) has DCCR, then all faithful 2-tame N-groups are finite and N-isomorphic. The finiteness of such an N-group follows easily from the fact it has a composition series. It is then shown that the length of a composition series depends only on N. This fact is used at key points in the proof. The situations where the N-group has or has not a minimal submodule require different analysis. The first case makes use of other interesting results and the second makes strong use of the inductive assumption.

Resolutions by gorenstein injective andprojective modules and modules of finite injective dimension overgorenstein rings

Resolutions by gorenstein injective andprojective modules and modules of finite injective dimension overgorenstein rings

Near-Rings Associated with Matched Pairs on Ring Modules

Near-Rings Associated with Matched Pairs on Ring Modules

A RELATIONSHIP BETWEEN RING RADICALS AND MODULE RADICALS

Abstract A bridging criterion between the category of rings and the category of A-modules is given. This is obtained via a functional relationship between Hoehnke radicals of rings and radicals of A-mod.