Monomial ideals with tiny squares and Freiman ideals

Czechoslovak Mathematical Journal - We provide a construction of monomial ideals in R = K[x, y] such that μ(I2) < μ(I), where μ denotes the least number of generators. This...     

Electron paramagnetic resonance studies of GdMnO3 single crystal and thin film deposited onto a LaAlO3 substrate

Electronic paramagnetic resonance (EPR) spectra of a GdMnO₃ single crystal and GdMnO₃/LaAlO₃ thin film have been measured at X- and Q-band frequencies in the temperature range from 4.2 to 300 K. It is found that the EPR spectrum of a GdMnO₃ single crystal consists of only one broad exchange-narrowed line. Unusual magnetism is observed at the interface between the GdMnO₃ thin film and LaAlO₃ substrate, where it is possible to see the fine structure of the EPR spectrum for a Gd³⁺ ion. The parameters characterizing the fine structure related to the Gd³⁺ ion in the GdMnO₃ film deposited onto the LaAlO₃ substrate are determined.     

Synthesis of a new 1,2,3,4,5‐pentasubstituted cyclohexanol and determining its stereochemistry by NMR spectroscopy and quantum‐chemical calculations

The presence of substituents in cyclohexane can influence to the ratio of conformers; for some cases, the boat form is preferable. The new six‐membered cyclohexanol derivative 2 has been obtained by the synthesis of (E)‐1‐(bromophenyl)‐3‐phenylpropen‐2‐one ( 1 ). The NMR and quantum‐chemical conformational analysis for the 2 have carried out, and its possible mechanism of formation was given. Copyright © 2015 John Wiley & Sons, Ltd.     

Thiadiazole fused indolo[2,3-a]carbazoles as new building blocks for optoelectronic applications

New indolo[2,3-a][1,2,5]thiadiazolo[3,4-c]carbazoles including functional groups (halide or hydroxyl groups) on the meta positions relative to the nitrogen atoms which are known to be the most conjugated, have been synthesized following two synthetic routes. The characterizations of their optical and electrochemical properties evidence their potential as new building blocks for optoelectronic materials.     

A low-frequency high-speed correlator

Summary After a brief explanation of the basic ideas of correlation, the paper describes a cheap and portable low-frequency high-speed correlator designed to overcome some of the practical difficulties which make conventional correlators very slow and tedious to operate.The correlation functions of ergodic signals such as are encountered in rheology, seismology, electrophysiology, etc., can be conveniently plotted. The correlator can also be used as a spectrum analyser. The signals of bandwidth 0–1 kHz to be analysed are recorded on two standard commercial tape recorders by means of a novel pulse-frequency modulation technique. The outputs of the tape recorders are demodulated, a continuously variable delay is introduced between them and they are then fed to aHall effect multiplier. The product is integrated to give a continuous and non-sequential correlation function which is recorded on anX-Y plotter.

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Zusammenfassung Nach einer kurzen Erläuterung der Grundbegriffe der Korrelation folgt die Beschreibung eines billigen, tragbaren, niederfrequenten Hochgeschwindigkeitskorrelators. Dieses Gerät wurde entwickelt, um einige praktische Schwierigkeiten zu überwinden, die konventionelle Korrelatoren in ihrer Arbeitsweise sehr langsam und damit zeitraubend machen.Die Korrelationsfunktionen des Ergodiesignals, wie man es in der Rheologie, Seismologie, der Elektrophysiologie usw. findet, können ohne weiteres bestimmt werden. Der Korrelator läßt sich auch als Spektrumanalysator verwenden. Die Signale von der Bandbreite 0–1 kHz, die analysiert werden sollen, werden von zwei normalen kommerziellen Tonbandgeräten in einer neuen Impulsfrequenzmodulationstechnik aufgenommen. Die Ausgangsleistungen der Tonbandgeräte werden demoduliert. Eine kontinuierlich veränderliche Verzögerung wird dazwischengeschaltet. Sie werden dann einemHall-Effekt-Multiplier zugeführt. Das Produkt ist so integriert, daß eine kontinuierliche, von Sequenzen freie Korrelationsfunktion entsteht, die von einemX-Y-Schreiber aufgezeichnet wird.

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Paper presented at the Conference on Experimental Rheology, University of Bradford, April 17–19, 1968.     

Large Eddy Simulation of a Propagating Turbulent Premixed Flame

A large eddy simulation of a turbulent premixed flame propagatingthrough a chamber containing a square obstruction is presented anddiscussed. The governing equations for compressible, reacting flowsare Favre filtered and turbulence closure is achieved using thedynamic Smagorinsky subgrid model. A simple flame surface densitymodel based on the flamelet concept is employed for the subgrid scalereaction rate. The simulation gives very good agreement with experimentalresults for the speed and the shape of the flame as it propagates throughthe chamber. The peak pressures, however, are underpredicted by20–30%. Reasons for this are discussed and it is concluded that amore sophisticated combustion model is required for complex flowssuch as this one, if a more accurate prediction of the pressureis to be achieved.     

An improved approach for random parametric response of dynamic systems with non-linear inertia

A non-Gaussian closure scheme is developed for determining the stationary response of dynamic systems including non-linear inertia and stochastic coefficients. Numerical solutions are obtained and examined for their validity based on the preservation of moments properties. The method predicts the jump phenomenon, for all response statistics at an excitation level very close to the threshold level of the condition of almost sure stability. In view of the increased degree of non-linearity, resulting from the non-Gaussian closure scheme, the mean square of the response displacement is found to be less than those values predicted by other methods such as the Gaussian closure or the first order stochastic averaging.     

Relationship between multibody dynamics computation and nonlinear vibration theory

This paper presents the ground-work of implementing the multibody dynamics codes to analyzing nonlinear coupled oscillators. The recent developments of the multibody dynamics have resulted in several computer codes that can handle large systems of differential and algebraic equations (DAE). However, these codes cannot be used in their current format without appropriate modifications. According to multibody dynamics theory, the differential equations of motion are linear in the acceleration, and the constraints are appended into the equations of motion through Lagrange's multipliers. This formulation should be able to predict the nonlinear phenomena established by the nonlinear vibration theory. This can be achieved only if the constraint algebraic equations are modified to include all the system kinematic nonlinearities. This modification is accomplished by considering secondary nonlinear displacements which are ignored in all current codes. The resulting set of DAE are solved by the Gear stiff integrator. The study also introduced the concept of constrained flexibility and uses an instantaneous energy checking function to improve integration accuracy in the numerical scheme. The general energy balance is a single scalar equation containing all the energy component contributions. The DAE solution is then compared with the solution predicted by the nonlinear vibration theory. It also establishes new foundation for the use of multibody dynamics codes in nonlinear vibration problems. It is found that the simulation CPU time is much longer than the simulation of the original equations of the system.