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.     

Drying of persimmons (Diospyros kaki L.) and the following changes in the studied bioactive compounds and the total radical scavenging activities

Fresh persimmons were subjected to two different processes: sun-drying during 1 month and dehydration at 60 °C during 12 h. To assess the effect of this process on nutritional and health-related properties of persimmons dietary fibers, minerals, trace elements, polyphenols and the total radical scavenging activities (TRSAs) were determined before and after processing. It was found that the contents of dietary fibers, minerals and trace elements in fresh and dried persimmons fruits were comparable. Total polyphenols in fresh persimmons was higher than in dried fruits (1.3 vs. 0.9 and 0.8 mg/100 g FW, respectively) and percentage of inhibition was higher than in dried fruits (70% vs. 59% and 55% and 58% vs. 53% and 46% for 1,1-diphenyl-2-picrylhydrazyl (DPPH) and 2,2′-azino-bis (3-ethylbenzthiazoline-6-sulfonic acid) [ABTS] radicals, respectively (P>0.05 in all cases). In conclusion: (1) the differences in the contents of dietary fibers, minerals and trace elements in fresh and dried persimmons are not significant; (2) the contents of polyphenols and the level of the TRSA are higher in fresh persimmons than in dried fruits; however, both variables are also high in dried persimmons; (3) when fresh fruits are not available, proper dried persimmons could be used as a valuable substitute.     

Abrasive wear in filled elastomers

The abrasive wear of rubbers is strongly affected by the filler particles dispersed in the elastomer matrix. The fillers are incorporated usually for the purposes of mechanical reinforcement and improving the conductivity of the neat resins. It is found that the wear rates of the filled silicone rubbers increase slowly with filler concentration until a critical volume fraction,v _c, is reached, at which point they increase very rapidly with increasing filler concentration. This behaviour appeared to be universal in all the filled silicones we studied, regardless of the type of filler and silicone rubber used. However the magnitude of the critical filler fraction,v _c, can be changed significantly with the filler shape, resin cross-linking density and filler surface treatments. No reasonable relationship could be found between this wear behaviour and the mechanical properties measured in a macroscopic manner. Experimental evidence suggests that the incipient cracks that lead to wear losses may start within the thin layers of highly stressed material, the damage zones, surrounding the rigid particles. A simple model taking into account the stress concentration induced by the rigid fillers shows excellent correlation between the wear rate and the damage zones volume. With this new model, the observed wear behaviours can be explained satisfactorily.     

Adoption of open source software in software-intensive organizations – A systematic literature review

ContextOpen source software (OSS) is changing the way organizations develop, acquire, use, and commercialize software.ObjectiveThis paper seeks to identify how organizations adopt OSS, classify the literature according to these ways of adopting OSS, and with a focus on software development evaluate the research on adoption of OSS in organizations.MethodBased on the systematic literature review method we reviewed publications from 24 journals and seven conference and workshop proceedings, published between 1998 and 2008. From a population of 24,289 papers, we identified 112 papers that provide empirical evidence on how organizations actually adopt OSS.ResultsWe show that adopting OSS involves more than simply using OSS products. We moreover provide a classification framework consisting of six distinctly different ways in which organizations adopt OSS. This framework is used to illustrate some of the opportunities and challenges organizations meet when approaching OSS, to show that OSS can be adopted successfully in different ways, and to organize and review existing research. We find that existing research on OSS adoption does not sufficiently describe the context of the organizations studied, and it fails to benefit fully from related research fields. While existing research covers a large number of topics, it contains very few closely related studies. To aid this situation, we offer directions for future research.ConclusionThe implications of our findings are twofold. On the one hand, practitioners should embrace the many opportunities OSS offers, but consciously evaluate the consequences of adopting it in their own context. They may use our framework and the success stories provided by the literature in their own evaluations. On the other hand, researchers should align their work, and perform more empirical research on topics that are important to organizations. Our framework may be used to position this research and to describe the context of the organization they are studying.     

A novel model for arc territory design: promoting Eulerian districts

The problem of district design for the implementation of arc routing activities is addressed. The aim is to partition a road network into a given number of sectors to facilitate the organization of the operations to be implemented within the region. This problem arises in numerous applications such as postal delivery, meter readings, winter gritting, road maintenance, and municipal solid waste collection. An integer linear programming model is proposed where a novel set of node parity constraints to favor Eulerian districts is introduced. Series of instances were solved to assess the impact of these parity constraints on the objective function and deadhead distance. Networks with up to 401 nodes and 764 edges were successfully solved. The model is useful at a tactical level as it can be used to promote workload balance, compactness, deadhead distance reduction and parity in districts.     

Isochronous sets of invariant control systems

Let G be a connected Lie group with Lie algebra g and Σ=(G,D) a controllable invariant control system. A subset A⊂G is said to be isochronous if there exists a uniform time T_A>0 such that any two arbitrary elements in A can be connected by a positive orbit of Σ at exact time T_A. In this paper, we search for classes of Lie groups G such that any Σ has the following property: there exists an increasing sequence of open neighborhoods (V_n)_n≥0 of the identity in G such that the group can be decomposed in isochronous rings W_n=V_n+1−V_n. We characterize this property in algebraic terms and we show that three classes of Lie groups satisfy this property: completely solvable simply connected Lie groups, semisimple Lie groups and reductive Lie groups.     

Theoretical Analysis of Polynuclear Zinc Complexes Isolobally Related to Hydrocarbons

Based on the isolobal analogy of ZnCp (Cp = η⁵-C₅H₅) and ZnR (R = alkyl or aryl group) fragments with hydrogen atom and fragment [Zn(CO)₂] with a CH₂ carbene, the following complexes [(ZnCp)₂{µ-Zn(CO)₂}], 1, [(ZnPh)₂{µ-Zn(CO)₂}], 2, [(ZnPh){µ-Zn(CO)₂}(ZnCp)], 3, [(ZnCp)₂{µ-Zn₂(CO)₄}], 4, [(ZnPh)₂{µ-Zn₂(CO)₄}], 5, [(ZnPh){µ-Zn(CO)₂}₂(ZnCp)], 6, [Zn₃(CO)₆], 7 and [Zn₅(CO)₁₀], 8, were built. These polynuclear zinc compounds are isolobally related to simple hydrocarbons (methane, ethane, cyclopropane and cyclopentane). They have been studied by density functional theory (DFT) and quantum theory of atoms in molecules (QTAIM) to compare the nature and topology of the Zn–Zn bond with previous studies. There are bond critical points (BCPs) between each pair of adjacent Zn centers in complexes 1–8 with Zn–Zn distances within the range 2.37–2.50 Å. The nature of the Zn–Zn bond in these complexes can be described as polar rather than pure covalent bonds. Although in a subtle way, the presence of different ligands and zinc oxidation states introduces asymmetry and polarity in the Zn–Zn bond. In addition, the Zn–Zn bond is delocalized in nature in complex 7 whereas it can be described as a localized bond for the remaining zinc complexes here studied.     

Perfect discrete Morse functions on 2-complexes

This paper is focused on the study of perfect discrete Morse functions on a 2-simplicial complex. These are those discrete Morse functions such that the number of critical i-simplices coincides with the ith Betti number of the complex. In particular, we establish conditions under which a 2-complex admits a perfect discrete Morse function and conversely, we get topological properties necessary for a 2-complex admitting such kind of functions. This approach is more general than the known results in the literature (Lewiner et al., 2003), since our study is not restricted to surfaces. These results can be considered as a first step in the study of perfect discrete Morse functions on 3-manifolds.