Subgroups of a Direct Product of Groups that Satisfy the Strong Frattini Argument

We give criteria to characterize subgroups of a direct product of finite solvable groups that satisfy the strong Frattini argument.     

Walker's Cancellation Theorem

Walker's cancellation theorem says that, if B ⊕ Z is isomorphic to C ⊕ Z in the category of abelian groups, then B is isomorphic to C. We construct an example in a diagram category of abelian groups where the theorem fails. As a consequence, the original theorem does not have a constructive proof even if B and C are subgroups of the free abelian group on two generators. Both of these results contrast with a group whose endomorphism ring has stable range one, which allows a constructive proof of cancellation and also a proof in any diagram category.     

Topological relations between separating circles

The family of separating circles of two finite sets in the plane consists of all the circles that enclose the first set but exclude the second set. We prove some theoretical results on distances between families of circles, and properties about enclosure and intersection. Most of these results state that a property that involves one or more infinite families of circles can be verified by examining a finite subcollection of circles. As a result enclosure and intersection can be decided, and distances can be computed with simple geometric algorithms. Furthermore, the circles of the finite subcollections correspond to the vertices of a polytope in the parameter space of separating circles. A polytope of separating circle parameters is well-known computational geometry, but we prove some new properties and we introduce the concept of an elementary circular separation as a concise way to define such a polytope.     

Stability in the first approximation of some volterra difference equations

volterra difference equations arise in the modeling of some real phenomena. In this paper stability problem of some volterra difference equations is investigated.Stability conditions are formulated in terms of the characteristics of equations.     

Normal Sections and Direct Product Decompositions

Abstract

In any finitely complete category, there is an internal notion of normal monomorphism. We give elementary conditions guaranteeing that a normal section s: Y → X of an arrow f: X → Y produces a direct product decomposition of the form X ? Y × W. We then show how these conditions gradually vanish in various algebraic contexts, such as Maltsev, protomodular and additive categories.     

On the effect of FineView,mean energy and anti-scatter grid on the DQE of a mammography system

The GE Senographe DS digital mammography system includes a preprocessing algorithm called FineView designed to improve spatial resolution. The effect of FineView on modulation transfer function MTF, normalized noise power spectrum NNPS, and detective quantum efficiency DQE has been measured by some authors under different experimental conditions and their results do not always agree. We have evaluated the effect of FineView on these functions under rigorous standard conditions, following the 2007 IEC guidelines for DQE measurement in digital mammography detectors. We have also investigated the impact on DQE of the use of different beam spectra and the presence of the anti-scatter grid. Measurements were made with Mo/Mo, 28 kV operating voltage, and 2 mm Al at tube exit. MTF was obtained with the edge method, detector air-kerma DAK levels ranged from 60 to 272 μGy, and the grid was set in or out, depending on the measurement. DQE values showed a dependence on DAK but were not significantly affected by FineView. The effect of the grid on DQE was of the order of 2% average difference and considered nonsignificant, while no effect of beam quality on DQE was observed at 200 μGy, and 6% average difference was observed between 18.5 and 19.4 keV mean energies at 60 μGy, also considered nonsignificant.     

Multi-environment probability density function method for modelling turbulent combustion using realistic chemical kinetics

A computational fluid dynamics (CFD) tool for performing turbulent combustion simulations that require finite-rate chemistry is developed and tested by modelling a series of bluff-body stabilized flames that exhibit different levels of finite-rate chemistry effects ranging from near equilibrium to near global extinction. The new modelling tool is based on the multi-environment probability density function (MEPDF) methodology and combines the following: the direct quadrature method of moments (DQMOM); the interaction-by-exchange-with-the-mean (IEM) mixing model; and realistic combustion chemistry. Using DQMOM, the MEPDF model can be derived from the transport PDF equation by depicting the joint composition PDF as a weighted summation of a finite number of multi-dimensional Dirac delta functions in the composition space. The MEPDF method with multiple reactive scalars retains the unique property of the joint PDF method of treating chemical reactions exactly. However, unlike the joint PDF methods that typically must resort to particle-based Monte-Carlo solution schemes, the MEPDF equations (i.e. the transport equations of the weighted delta-peaks) can be solved by traditional Eulerian grid-based techniques. In the current study, a pseudo time-splitting scheme is adopted to solve the MEPDF equations; the reaction source terms are computed with a highly efficient and accurate in-situ adaptive tabulation (ISAT) algorithm. A 19-species reduced mechanism based on quasi-steady state assumptions is used in the simulations of the bluff-body flames. The modelling results are compared with the experimental data, including mixing, temperature, major species and important minor species such as CO and NO. Compared with simulations using a Monte-Carlo joint PDF method, the new approach shows comparable accuracy.     

EPR-NMR Signal Enhancement with a Small Computer

A Digital Equipment Corporation PDP 8/S Computer is interfaced with an EPR Spectrameter to achieve signal enhancement.

A computer-based system for spectrum accumulation and noise averaging of EPR or NMR signals has been designed and implemented. The computer-based system was chosen over other perhaps more conventional systems because of its greater flexibility in the processing of spectra, especially after the accumulation is complete.(1)     

The Process of Particle Formation in the Flame Synthesis of Tin Oxide Nanoparticles

Tin oxide nanoparticles with sizes in the range 5-30 nm are generated within a low pressure flame reactor setup in the gas phase. We study the effect of preparation parameters such as precursor concentration, flame to substrate distance, and post-deposition annealing procedures on the morphology and crystal structure of the particles utilizing transmission electron microscopy and X-ray diffraction in order to characterize the particle formation process. The structural investigations indicate that monoxide particles form from SnO monomers within the flame. These primary particles need to be further oxidized and thermally annealed to transform into single phase rutile type SnO 2 nanoparticles.