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A series of stereoregular polymers including atactic, syndiotactic and isotactic poly 4(N, N-diphenyl)styrene (PNNDPS) and poly 4(N, N-ethylphenyl)styrene (PNNEPS) were synthesized to exam the tacticity effect on the photoluminescence (PL) behavior. Also, different degrees of the regularity as well as the chemical modification of the fluorophor were explored in the stereoregular polymers. Because of the increase of the steric hindrance among the bulky triphenylamine pendants in the polymer chains, a red shift of the PL emission with an accompanying increase in the emissive intensity was found in contrast to the weakened emission of triphenylamine monomers. In solution state, the PL spectra of these stereoregular polymers reveal multiple PL emissive bands including monomeric and aggregation emissions as evidenced by the time-resolved lifetime measurement. Because of the huge triphenylamine pendants, the triphenylamine pendants attached on the iPNNDPS17 (mmmmmm~50%) might encounter higher steric hindrance than that in the sPNNDPS23 (rrrrrr~59%) due to the stereoregularity evidenced by simulation. Accordingly, the iPNNDPS17 (mmmmmm~50%) exhibits more emissive intensity than the sPNNDPS23 (rrrrrr~59%) due to the effective blockage of the intramolecular rotation of the phenyl blade i.e., the restriction of intramolecular rotation (RIR). Accordingly, the RIR-active PNNDPS is highly sensitive to the temperature variations. The chemical modification of the fluorophor was carried out to examine the effect of the chemical structure. By comparison, the sPNNDPS2 (rrrrrr~70%) with high regularity exhibits much higher emissive intensity than the sPNNDPS23 (rrrrrr~59%) with low regularity due to the less solubility. However, more intense PL emission can be found in the sPNNEPS17 than aPNNEPS8 due to the ethyl substitution of the fluorophor. In aggregation solution, with the increase of the poor water contents, the PL emission decreases significantly in the sPNNDPS23 (rrrrrr~59%) and sPNNDPS2 (rrrrrr~70%) due to the formation of H-aggregate in which extra energetic loss is conducted. By contrast, the PL spectra display that the emissive intensity decreases first as fw=0.1~0.5 and then intensifies later as fw=0.6~0.9. This might be resulted from the competition between the £k-£k interaction and RIR effect. Interestingly, the PL emissive intensity drops down significantly in the sPNNEPS, whereas the PL emissive intensity is almost unchanged in the aPNNEPS8 with the increase of the poor water contents. We suggest that because the aPNNEPS8 might contain both syndiotactic and isotactic configurations, the isotactic configurations having the ethyl group pointing out of the plane may prevent the formation of the £k-stacking between the fluorophors. The PL behavior in thin film is also explored for these stereoregular polymers. After slow cooling from melt, the crystalline sPNNDPS2 (rrrrrr~70%) thin film exhibits very strong emission in comparison with the thin film after quenching from melt, indicating the crystallization-induced emission enhancement. Although the iPNNDPS17 (mmmmmm~50%) is noncrystallizable as evidenced by differential scanning calorimetry (DSC) and polarized light microscope (PLM), the PL emissive intensity of the iPNNDPS17 (mmmmmm~50%) thin film is significantly stronger after slow cooling from melt than that after quenching from melt. We suggest that this might be attributed to the free volume effect varied with the thermal history associated with the steric hindrance. Notably, this enhanced PL emission in the iPNNDPS17 (mmmmmm~50%) thin film is extremely larger than that in the sPNNDPS23 (rrrrrr~59%) and aPNNDPS8, indicating the stereoregularity effect associated with the RIR effect. By contrast, this free volume effect is not significant in the PNNEPS thin film due to the flexible ethyl substitutions. As a result, the stereoregular polymers with different tacticities and regularities indeed exhibit distinct PL behavior in solution and thin film.

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We study the optimal regularity and nondegeneracy of a free boundary problem related to the fractional Laplacian through the extension technique of Caffarelli and Silvestre. Specifically, we show that minimizers of the energy [mathematical equation] where [mathematical equations] with 0 < [gamma] < 1, with free behavior on the set {y=0}, are Holder continuous with exponent [Beta] = 2[sigma]/2-[gamma]. These minimizers exhibit a free boundary: along {y = 0}, they divide into a zero set {u = 0} and a positivity set where {u > 0}; we call the interface between these sets the free boundary. The regularity is optimal, due to the non-degeneracy property of the minimizers: in any ball of radius r centered at the free boundary, the minimizer grows (in the supremum sense) like r[Beta]. This work is related to, but addresses a different problem from, recent work of Caffarelli, Roquejoffre, and Sire. / text

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / O objetivo deste trabalho à estudar o comportamento da regularidade de Castelnuovo- Mumford em arranjos de subespaÃos lineares no espaÃo projetivo, para isto, nos norteamos pelo artigo de tÃtulo "Uma limitaÃÃo sharp para a regularidade de Castelnuovo-Mumford de arranjos de subespaÃos" dos autores Harm Derksen e Jessica Sidman. Em um primeiro momento, daremos algumas noÃÃes preliminares e apresentaremos resultados auxiliares. Num segundo momento, definiremos os principais objetos deste trabalho, demonstraremos os resultados principais e daremos um exemplo que mostra que a limitaÃÃo encontrada à a melhor possÃvel. / The objetive of this work is study the behavior of the Castelnuovo-Mumford regularity in arrangements of linear subspaces in projetive spaces, for this, we use Jessica Sidman and Harm Derksen article of title "A sharp bound for the Castelnuovo-Mumford regularity of subspace arrengements". At first, we give some preliminary notions and present auxiliary results. In a second moment, we define the main objects of this work proof the main results and give a example which show that the bound is sharp.

Submitted by Luiz Felipe Barbosa (luiz.fbabreu2@ufpe.br) on 2015-03-10T19:41:00Z No. of bitstreams: 2 DISSERTAÇÃO Vinicius Cezar Monteiro de Lira.pdf: 4006584 bytes, checksum: 5d1301329fabe34879780b3b17bb1e8a (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) / Approved for entry into archive by Daniella Sodre (daniella.sodre@ufpe.br) on 2015-03-10T19:43:51Z (GMT) No. of bitstreams: 2 DISSERTAÇÃO Vinicius Cezar Monteiro de Lira.pdf: 4006584 bytes, checksum: 5d1301329fabe34879780b3b17bb1e8a (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) / Made available in DSpace on 2015-03-10T19:43:51Z (GMT). No. of bitstreams: 2 DISSERTAÇÃO Vinicius Cezar Monteiro de Lira.pdf: 4006584 bytes, checksum: 5d1301329fabe34879780b3b17bb1e8a (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Previous issue date: 2014-08-28 / The analysis of human movements has been the subject of several studies since the 70s. In recent years, the exponential growth of location aware devices must allow the study of the behavior of the individuals’ mobility from their trajectories collected. However, a significant part of the available literature is focused on the development of techniques for analyzing trajectories of people from a purely geometric point of view, while a smaller part, but increasingly group is looking at the semantic aspects of mobility. This work presents a contribution to the latest trend, and is concerned with the definition of semantic regularity profiles and the applicability of these concepts to the practice of carpooling. We propose a semantic regularity profile based on the entropy of the spatial and temporal frequency of visits to certain categories of places. We analyze the user’s behavior with respect to regularity and irregularity, identifying users who are more or less loyal to certain locations, in contrast to the irregularity of visiting different places. In a different point of view, an analysis over the place perspective was also performed. A web tool was developed to show on map, for each place of a given category, the computed information about the loyal behavior of their visitors. From the study about regularity, we have evidences that some human activities are not strictly associated to a unique POI (Point of Interest) and neither to a specific schedule of the day. Bringing to the carpooling context, in some situations it is worth for a person to change his destination or the time to perform an activity if there is a possibility of ride for him due all the benefits involved with the carpooling practice. This dissertation also presents a novel matching method for carpooling that is oriented to the passenger’s intended activity, aiming to boost the possibilities of rides. Three algorithms for carpool matching are proposed, which manipulates differently the spatial and temporal dimensions. Using a real data set of trajectories, we conducted experiments and our results showed that the proposed matching algorithms improved the traditional carpooling approach in +46.84% when the spatial dimension was considered, in +50.89% when the temporal dimension was prioritized and in +82.30% when both dimensions were tackled.

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This paper is a view into the conception of regularity in mathematics. Possible approaches to the concept of regularity in mathematics are dicussed. There is a presentation of the characteristics and relations of regular geometric figures. The conception of regularity on the part of students is explored based on the analysis of the math textbooks. This analysis of textbooks in terms of regularity is also part of the work. The aim is to identify the types of objects which pupils are able to perceive as relationed by regularity of these objects and whether they rather use other criteria when selecting objects that do not belong to the group. Mostly the frequency and manner of expression of selection on the basis of regularity was monitored when analyzing acquired data, as well as the other most common selection criteria and the relations between the criteria used. Keywords: regularity, conception of regularity, geometry, questionnaire

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Cette thèse est dédiée a l''etude de certaines propriétés des équations d' évolutions non-autonomes $u'(t)+A(t)u(t)=f(t), u(0)=x.$ Il s'agit précisément de la propriété de la régularité maximale $L^p$: étant donnée $fin L^{p}(0,tau;H)$, montrer l'existence et unicité de la solution $u in W^{1,p}(0,tau;H)$. Ce problème a 'et'e intensivement étudie dans le cas autonome, i.e., $A(t)=A$ pour tout $t$. Dans le cas non-autonome, le problème a été considéré par J.L.Lions en 1960. Nous montrons divers résultats qui étendent tout ce qui est connu sur ce problème. On suppose ici que la famille des opérateurs $(mathcal{A}(t))_{tin [0,tau]}$ est associée à des formes quasi-coercives, non autonomes $(fra(t))_{t in [0,tau]}.$ Nous considérons également le problème de régularité maximale pour les d'ordre 2 (équations des ondes). Plusieurs exemples et applications sont considérés. / This Thesis is devoted to certain properties of non-autonomous evolution equations $u'(t)+A(t)u(t)=f(t), u(0)=x.$ More precisely, we are interested in the maximal $L^p$-regularity: given $fin L^{p}(0,tau;H),$ prove existence and uniqueness of the solution $u in W^{1,p}(0,tau;H)$. This problem was intensively studied in the autonomous cas, i.e., $A(t)=A$ for all $t.$ In the non-autonomous cas, the problem was considered by J.L.Lions in 1960. We prove serval results which extend all previously known ones on this problem. Here we assume that the familly of the operators $(mathcal{A}(t))_{tin [0,tau]}$ is associated with quasi-coercive, non-autonomous forms $(fra(t))_{t in [0,tau]}.$ We also consider the problem of maximal regularity for second order equations (the wave equation). Serval examples and applications are given in this Thesis.