A review on some classes of algebraic systems

ABSTRACT

In this paper, we review some algebraic control system. Precisely, linear and bilinear systems on Euclidean spaces and invariant and linear systems on Lie groups. The fourth classes of systems have a common issue: to any class, there exists an associated subgroup. From this object, we survey the controllability property. Especially, from those coming from our contribution to the theory.     

Tracking influent inorganic suspended solids through wastewater treatment plants.

From an experimental and theoretical investigation of the continuity of influent inorganic suspended solids (ISS) along the links connecting the primary settling tank (PST), fully aerobic or N removal activated sludge (AS) and anaerobic and aerobic sludge digestion unit operations, it was found that the influent wastewater (fixed) ISS concentration is conserved through primary sludge anaerobic digestion, activated sludge and aerobic digestion unit operations. However, the measured ISS flux at different stages through a series of wastewater treatment plant (WWTP) unit operations is not equal to the influent ISS flux, because the ordinary heterotrophic organisms (OHO) biomass contributes to the ISS flux by differing amounts depending on the active fraction of the VSS solids at that stage.     

Word length and lexical activation: Longer is better.

Many models of spoken word recognition posit the existence of lexical and sublexical representations, with excitatory and inhibitory mechanisms used to affect the activation levels of such representations. Bottom-up evidence provides excitatory input, and inhibition from phonetically similar representations leads to lexical competition. In such a system, long words should produce stronger lexical activation than short words, for 2 reasons: Long words provide more bottom-up evidence than short words, and short words are subject to greater inhibition due to the existence of more similar words. Four experiments provide evidence for this view. In addition, reaction-time-based partitioning of the data shows that long words generate greater activation that is available both earlier and for a longer time than is the case for short words. As a result, lexical influences on phoneme identification are extremely robust for long words but are quite fragile and condition-dependent for short words. Models of word recognition must consider words of all lengths to capture the true dynamics of lexical activation. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Atomistic simulations of grain boundary migration in copper

While the motion of twist boundaries can be readily studied by atomistic simulations with molecular dynamics (MD) under the action of an elastic driving force, the approach fails for tilt boundaries. This is due to the interaction of the elastic stress with the grain boundary (GB) structure, which causes plastic strain by GB sliding. A novel concept, the orientation correlated driving force, is introduced to circumvent this problem. It is shown that this concept can be successfully applied to the study of the migration of tilt boundaries. The migration behavior of several twist and tilt GBs was investigated. The transition from low-to high-angle boundaries can be captured, and a structural transition of tilt boundaries was found at high temperatures, which also affected the migration behavior. The results compare well with experimental results of the motion high-angle boundaries, but for low-angle boundaries, the agreement is poor. This article is based on a presentation made in the “Hillert Symposium on Thermodynamics & Kinetics of Migrating Interfaces in Steels and Other Complex Alloys,” December 2–3, 2004, organized by The Royal Institute of Technology in Stockholm, Sweden.     

Reliable eye-diagram analysis of data links via device macromodels

This paper addresses the impact of device macromodels on the accuracy of signal integrity and performance predictions for critical digital interconnecting systems. It exploits nonlinear parametric models for both single-ended and differential devices, including the effects of power supply fluctuations and receiver bit detection. The analysis demonstrates that the use of well-designed macromodels dramatically speeds up the simulation as well it preserves timing accuracy even for long bit sequences.     

Design of a retention tank: comparison of stormwater quality models with various levels of complexity.

Stormwater quality simulation models are useful tools for the design and management of sewer systems. Modelling results are highly sensitive to experimental data used for calibration. This sensitivity is examined for three modelling approaches of various complexities (site mean concentration approach, event mean concentration approach and build-up, washoff and transport modelling approach) applied to a typical case study (design of a dry detention tank), accounting for the variability of calibration data and their effect on simulation results. Calibrated models with different calibration data sets were used to simulate 3 years of rainfall with different retention tank specific volumes. Annual pollutant load interception efficiencies were determined. Simulations results revealed (i) that there is no advantage in using the EMC model compared to the SMC model and (ii) that the BWT model resulted in higher design ratios than those given by the SMC/hydraulic approach. For both EMC and BWT models, using an increasing number n of events for calibration leads to narrower confidence intervals for the design ratios. It is crucial for design ratios to account for successive storm events in chronological order and to account for the maximum allowable flow to be transferred to the downstream WWTP.     

Catalytic epoxidation of olefins in the presence of a vanadyl porphyrin complex

It was found that vanadyl porphyrin complexes synthesized from petroleum metal porphyrin concentrates stimulated epoxidation during the olefin oxygenation process. The yields of obtained oxiranes turned out to be 38–75%, depending on the olefin structure. An epoxidation mechanism that suggests the formation of a protonated dioxygen adduct as an intermediate during oxygenation of olefins in the presence of vanadyl porphyrin complexes was proposed. An analogy is drawn between the epoxide formation reaction upon the catalytic oxygenation of olefins and the Prilezhaev reaction.     

Note on B-splines, wavelet scaling functions, and Gabor frames

Let g be a continuous, compactly supported function on such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g,a,b), with window g and time-shift and frequency-shift parameters a,b>0 has no lower frame bound larger than 0 if b=2,3,... and a>0. In particular, (g,a,b) is not a Gabor frame if g is a continuous, compactly supported wavelet scaling function and if b=2,3,... and a>0. We give an example for our result for the case that g=B/sub 1/, the triangle function supported by [-1,1], by showing pictures of the canonical dual corresponding to (g,a,b) where ab=1/4 and b crosses the lines N=2,3,.     

On the origin of strain hardening in glassy polymers

The influence of network density on the strain hardening behaviour of amorphous polymers is studied. The network density of polystyrene is altered by blending with poly(2,6-dimethyl-1,4-phenylene-oxide) and by cross-linking during polymerisation. The network density is derived from the rubber-plateau modulus determined by dynamic mechanical thermal analysis. Subsequently uniaxial compression tests are performed to obtain the intrinsic deformation behaviour and, in particular, the strain hardening modulus. At room temperature, the strain hardening modulus proves to be proportional to the network density, irrespective of the nature of the network, i.e. physical entanglements or chemical cross-links. With increasing temperature, the strain hardening modulus is observed to decrease. This decrease appears to be related to the influence of thermal mobility of the chains, determined by the distance to the glass-transition temperature (T−T_g).     

Experimental and modeling approaches of MR behaviors under large step strains

Rheological properties of MR fluids under large step strain shear are presented in this paper. The experiments were carried out using a rheometer with parallel-plate geometry. Under the large step strain shear, MR fluids behave as nonlinear viscoelastic properties, where the stress relaxation modulus, G(t, γ), shows a decreasing trend with step strain. The experimental results indicate that G(t, γ) obeys time-strain separability. Thus, a mathematical form based on finite exponential serials is proposed to predict MR behavior. In this model, G(t, γ) is represented as the product of a linear stress relaxation, G(t), and the damping function, h(γ), i.e. G(t, γ)=G(t) h(γ). G(t) is simply represented as a three-parameter exponential serial and h(γ) has a sigmoidal form with two parameters. The parameters are identified by adopting an efficient optimization method proposed by Stango et al. The comparison between the experimental results and the model-predicted values indicates that this mathematical model can accurately predict MR behavior.