The objective of the study was to investigate the air pollution of working place and the fence of aluminum plants. Four sites were selected for conducting the sampling of particulate matter¡]PM¡^to establish the fingerprints of PM in aluminum plants. Moreover, the receptor model was used to apportion the major contributing sources of particulate matter. The results of the study showed that PM concentrations in the working places were high, which might be emitted from manufacturing or mechanical operating process in the melting furnace, the continuous casting, and etc. The total suspended solid concentrations from non-combustion pollution source ¡]such as hot rolling , cold rolling, and plate industry¡^ were usually below 200 µg /m3. Moreover, the size distributions of PM in working places were usually bi-modal type. The particle sizes with the highest concentration in five and coarse fractions were 0.18~0.56 µm respectively. As for the combustion sources, the particle sizes with the highest concentration were 0.56~1.0 µm and 11.5~24.7 µm, respectively. The particle emitted from zinc casting source were mostly in the fine particle fraction¡]1.0~3.2 µm¡^. The fingerprint profiles of PM from the working places showed that the major metal content of the hot rolling were Al, Zn, K, Cr. Among then, Cr might be source of from the using of chromate acid. The most abundant water-soluble ions were sulfate ion and chlorine and chloride. The carbon content accounted for about 22% of the PM mass. The ratio of organic carbon to elemental carbon were 2.54 and 2.80. The major metal content of melting process was Al, the minor metals were Zn, k, Ca, Fe. The ratio of anion to cation¡]A/C¡^ was about 0.80. The most abundant ion sulfate, while the chloride, the fluoride, potassium, and the ammonium ions were minor ones. The carbon content accounted about 19.2% and 27.3% of PM mass respectively. The ratio of organic carbon to elemental carbon were 1.21 and 1.07. Moreover, the major metals were k, Ca, Fe. The major ion was chloride, while the nitrate calcium and potassium ions were minor ones. The A/C was 0.7. The carbon content accounted for 54.8% and 51.0% of PM2.5 and PM10, respectively. The ratio of organic carbon to elemental carbon was about 2.9. The results obtained from receptor modeling showed that the contribution percentage of fugitive PM from the aluminum plant (including hot rolling, melting furnace, and low-wave furnace) was between 5.9 and 13.2%, Another major source was traffic refracted pollution with a contribution percentage between 17.0% and 23.0%, Fur then more, in the surrounding PM, was between 11.2% and 20.7%, while the contribution from the steel plant and Moreover, the municipal incineration was 2.5~6.5% and 2.3~5.0%,respectively. The sea salt contributed 4.3~7.1% of PM mass. The unsolved percentage was 7.0~11.8%.

The objective of the first study was to determine which combination of bimodal (2-population) distribution models best fit non-feeding interval data to distinguish intervals within (1st population) and between (2nd population) meals in beef cattle fed a corn-based diet. Feeding behavior traits were measured in 119 heifers fed a corn-based diet using a GrowSafe system. Bimodal distribution models were fitted to the log10-transformed interval lengths between bunk visit (BV) events for each animal using Gaussian (G); Weibull (W); Log-Normal; Gamma and Gumbel statistical functions. Criterion (AIC) and likelihood probability estimates. Objectives of the second study were to quantify individual meal criterion and examine the associations between feeding behavior traits, performance, and feed efficiency traits in heifers fed a corn-based diet. Results from study one indicate that the G-W bimodal distribution model is a statistically better fitting and likely a more appropriate model to define meal criterion compared to the standard G-G model used in previous literature. Results from the second study suggest that the meal criterion for heifers fed a corn-based diet is 11.48 min when applying the G-W bimodal model to log-transformed interval lengths between BV events. Moderate phenotypic correlations between feed efficiency (residual feed intake- RFI) and several feeding behavior traits were found. Inclusion of these feeding behavior traits to the base model for RFI accounted for an additional 25% of the variation in DMI not explained by ADG or mid-test BW0.75. Significant (P < 0.05) differences in 11 observed feeding behavior traits between RFI classification groups were also found suggesting that differences in feeding behaviors may contribute to the variation in RFI due to differences in energetic costs related to feeding activities.

The strength of the ultrafine-grained materials is increased with grain refinement, but it will also reduce the ductility. In the previous study, there are higher strength and better ductility for the copper with bimodal distribution of grain size. In this study, Ni with lamellar structure is fabricated by electrodeposition in order to explore the mechanical properties of the materials with bimodal distribution of grain size, which is obtained by controlling the grain size. From the result of EBSD analysis, it shows that the area ratio of coarse grains and fine grains is from 0.3 to 3 by changing the plating parameters. The average grain size of fine grains is about 0.5 £gm, and the maximum average grain size of coarse grains is up to 6.0 £gm. From the result of tensile test, the materials with 35% of micro-grains embedded regularly inside a matrix of ultrafine grains have better strength and ductility. When the area ratio of micro-grains is up to 62.5%, there is no difference in mechanical properties between the general electrodeposited materials and ones with bimodal distribution of grain size. For pure Ni, the enhancement of ductility for bimodal distribution of grain size is only in post uniform elongation. Otherwise, it is found that the strength and ductility of the material with lamellar structure are increased through the heat treatmeant under the appropriate temperature.

<p>The notion that humans have specialized chemicals used for communication between conspecifics, so-called pheromones, has attracted much attention and discussion. This thesis demonstrates in four separate studies that a human endogenous steroidal compound that is abundant in male sweat, androstadienone, affects women in several ways that differ to that of common odors. Specifically, androstadienone was found in Study I to have unique psychophysical characteristics in that the sensitivity distribution of the odor is bimodal with a smaller subpopulation consisting of highly sensitive individuals. Trigeminal mediation of this bimodality was experimentally excluded. Moreover, Study II demonstrated that women’s cortical activation of androstadienone exposure was found to differ to that of common odorants in that androstadienone was processed faster than two perceptually similar control odors. It was further demonstrated that a non-detectable amount of androstadienone can reliably modulate both mood and physiology in women (Study III & IV); in particular mood referring to attention processes. Study IV showed that androstadienone-induced mood changes in heterosexual women were only evident when the experiment was administered by an experimenter of different sex. The combined results from these studies suggest that androstadienone serves as a human modulator pheromone that guides our behavior by inducing subtle changes in higher cognitive processes in relation to the ecological context at hand. A new definition of human pheromones is proposed and discussed in relation to the obtained results.</p>

The notion that humans have specialized chemicals used for communication between conspecifics, so-called pheromones, has attracted much attention and discussion. This thesis demonstrates in four separate studies that a human endogenous steroidal compound that is abundant in male sweat, androstadienone, affects women in several ways that differ to that of common odors. Specifically, androstadienone was found in Study I to have unique psychophysical characteristics in that the sensitivity distribution of the odor is bimodal with a smaller subpopulation consisting of highly sensitive individuals. Trigeminal mediation of this bimodality was experimentally excluded. Moreover, Study II demonstrated that women’s cortical activation of androstadienone exposure was found to differ to that of common odorants in that androstadienone was processed faster than two perceptually similar control odors. It was further demonstrated that a non-detectable amount of androstadienone can reliably modulate both mood and physiology in women (Study III &amp; IV); in particular mood referring to attention processes. Study IV showed that androstadienone-induced mood changes in heterosexual women were only evident when the experiment was administered by an experimenter of different sex. The combined results from these studies suggest that androstadienone serves as a human modulator pheromone that guides our behavior by inducing subtle changes in higher cognitive processes in relation to the ecological context at hand. A new definition of human pheromones is proposed and discussed in relation to the obtained results.

A atividade agrícola é uma das atividades mais importantes para o ser humano, pois é fonte de matéria prima, alimentação e energia. No entanto, os principais grandes riscos desta atividade são os de produção e de mercado. A maneira mais popular de gerenciamento destes riscos são os seguros agrícolas. O seguro de produtividade agrícola gerencia o risco de quebra de produção relacionado às adversidades climáticas. Por sua vez, o seguro de faturamento agrícola é uma maneira de gerenciar os riscos de produção e de mercado (preços) conjuntamente. Portanto, este trabalho tem por objetivo apresentar métodos alternativos para precificação dos riscos de produtividade e faturamento agrícola. Na modelagem da distribuição de produtividade utilizou-se distribuições paramétricas que capturam a simetria, a assimetria e a bimodalidade dos dados, características estas geralmente encontradas em produtividades brasileiras. Além disso, a metodologia de cópulas foi utilizada na análise multivariada entre produtividade e preço. Esta metodologia apresenta um ganho significante para estudos de problemas multivariados comparados à distribuição normal multivariada, pois pode-se levar em consideração estruturas de dependências linear, não linear e dependência somente nas caudas da distribuição multivariada. Além disso especifica qualquer tipo de distribuição para as distribuições marginais. Ademais, analisou-se a estrutura de dependência entre produtividade, preços futuros de contrato de soja negociados na Chicago Mercantil Exchange (CME) e a cotação do dólar. Esta análise tridimensional do problema do seguro de faturamento é inédita e foi utilizada pelo fato da soja produzida no Brasil ser exportada e os produtores utilizarem como referência internacional de preços a bolsa americana. Além disso, esta análise tridimensional via cópulas considera a variabilidade e a influência do dólar e o preço futuro da commoditie na modelagem do seguro. Todas as análises foram discutidas e comparadas com as taxas dos seguros aplicadas pelas seguradoras brasileiras. No caso do seguro de produtividade e faturamento (tridimensional), os resultados sugerem que as taxas cobradas pelas seguradoras estão superfaturadas quando comparadas com a metodologia apresentada. A superestimação da taxa dificulta a expressiva venda de seguros no Brasil, além de atrair agricultores com maiores riscos, fortalecendo o problema de seleção adversa. No caso do seguro de faturamento (bidimensional), em que não se leva em consideração a influência do câmbio (dólar) na modelagem, os resultados sugerem que as seguradoras subestimam as taxas do seguro de faturamento, o que pode levar a uma perda grande para a seguradora, pois esta pode estar considerando um risco muito menor do que deveria ser levado em consideração. Na realização das análises foi utilizado o software R. / The agricultural activity is one of the most important activities for humans, as it is a source of raw materials, food and energy. However, this activity presents two major risks: production and market. Agricultural insurance is the most efficient way of managing these risks. Insuring agricultural productivity allows to manage the risk of crop failure due to weather adversities. However, revenue insurance is a way to manage both the production and the market (prices) risks simultaneously. This study aims to present alternative pricing methods risks of agricultural productivity and billing. In modeling the distribution of yield, parametric distributions that capture symmetry, asymmetry and bimodality of the data were used, features usually found in yield in Brazil. In addition, the coupling methodology was used in multivariate analysis between yield and prices. This methodology offers an exceptional gain of multivariate problems compared to the Multivariate Normal distribution, as it takes into account structures of linear and non-linear dependencies and dependency only on the tails of multivariate distribution, in addition to specifying any distribution type for marginal distributions. In addition, we analyzed the dependence structure between yield soybean, future prices traded at the Chicago Mercantil Exchange(CME) and, exchange rate (USD/R$). The three-dimensional analysis of insurance billing via copulas considers variability and influence of dollar and price of commodities exported and traded at CME. All analyses were discussed and compared with insurance rates applied by insurance companies. All analysis are conducted using the R software.

A atividade agrícola é uma das atividades mais importantes para o ser humano, pois é fonte de matéria prima, alimentação e energia. No entanto, os principais grandes riscos desta atividade são os de produção e de mercado. A maneira mais popular de gerenciamento destes riscos são os seguros agrícolas. O seguro de produtividade agrícola gerencia o risco de quebra de produção relacionado às adversidades climáticas. Por sua vez, o seguro de faturamento agrícola é uma maneira de gerenciar os riscos de produção e de mercado (preços) conjuntamente. Portanto, este trabalho tem por objetivo apresentar métodos alternativos para precificação dos riscos de produtividade e faturamento agrícola. Na modelagem da distribuição de produtividade utilizou-se distribuições paramétricas que capturam a simetria, a assimetria e a bimodalidade dos dados, características estas geralmente encontradas em produtividades brasileiras. Além disso, a metodologia de cópulas foi utilizada na análise multivariada entre produtividade e preço. Esta metodologia apresenta um ganho significante para estudos de problemas multivariados comparados à distribuição normal multivariada, pois pode-se levar em consideração estruturas de dependências linear, não linear e dependência somente nas caudas da distribuição multivariada. Além disso especifica qualquer tipo de distribuição para as distribuições marginais. Ademais, analisou-se a estrutura de dependência entre produtividade, preços futuros de contrato de soja negociados na Chicago Mercantil Exchange (CME) e a cotação do dólar. Esta análise tridimensional do problema do seguro de faturamento é inédita e foi utilizada pelo fato da soja produzida no Brasil ser exportada e os produtores utilizarem como referência internacional de preços a bolsa americana. Além disso, esta análise tridimensional via cópulas considera a variabilidade e a influência do dólar e o preço futuro da commoditie na modelagem do seguro. Todas as análises foram discutidas e comparadas com as taxas dos seguros aplicadas pelas seguradoras brasileiras. No caso do seguro de produtividade e faturamento (tridimensional), os resultados sugerem que as taxas cobradas pelas seguradoras estão superfaturadas quando comparadas com a metodologia apresentada. A superestimação da taxa dificulta a expressiva venda de seguros no Brasil, além de atrair agricultores com maiores riscos, fortalecendo o problema de seleção adversa. No caso do seguro de faturamento (bidimensional), em que não se leva em consideração a influência do câmbio (dólar) na modelagem, os resultados sugerem que as seguradoras subestimam as taxas do seguro de faturamento, o que pode levar a uma perda grande para a seguradora, pois esta pode estar considerando um risco muito menor do que deveria ser levado em consideração. Na realização das análises foi utilizado o software R. / The agricultural activity is one of the most important activities for humans, as it is a source of raw materials, food and energy. However, this activity presents two major risks: production and market. Agricultural insurance is the most efficient way of managing these risks. Insuring agricultural productivity allows to manage the risk of crop failure due to weather adversities. However, revenue insurance is a way to manage both the production and the market (prices) risks simultaneously. This study aims to present alternative pricing methods risks of agricultural productivity and billing. In modeling the distribution of yield, parametric distributions that capture symmetry, asymmetry and bimodality of the data were used, features usually found in yield in Brazil. In addition, the coupling methodology was used in multivariate analysis between yield and prices. This methodology offers an exceptional gain of multivariate problems compared to the Multivariate Normal distribution, as it takes into account structures of linear and non-linear dependencies and dependency only on the tails of multivariate distribution, in addition to specifying any distribution type for marginal distributions. In addition, we analyzed the dependence structure between yield soybean, future prices traded at the Chicago Mercantil Exchange(CME) and, exchange rate (USD/R$). The three-dimensional analysis of insurance billing via copulas considers variability and influence of dollar and price of commodities exported and traded at CME. All analyses were discussed and compared with insurance rates applied by insurance companies. All analysis are conducted using the R software.

Les applications d’électronique de spin telles les mémoires à accès aléatoire (MRAM), les capteurs (e.g.les têtes de lecture des disques durs d’ordinateurs) et les éléments de logique magnétique utilisent les interactionsd’échange ferromagnétique/antiferromagnétique (F/AF) dans le but de définir une direction de référence pour lespin des électrons de conduction. Les MRAM à écriture assistée thermiquement (TA-MRAM) utilisent mêmedeux bicouches F/AF : une pour le stockage de l’information et l’autre comme référence. Ces dernièresapplications technologiques impliquent des étapes de nanofabrication des couches minces continues pour formerune matrice de cellules mémoires individuelles. La qualification industrielle du produit final impose de sérieusescontraintes sur la largeur des distributions des propriétés magnétiques - y compris d’échange F/AF - de cellulemémoire à cellule mémoire. Des phases verres de spin réparties de manière aléatoire sur la couche continue, àl’interface F/AF ou dans le coeur de l’AF pourraient contribuer de manière significative à ces distributionsd’échange F/AF dans les dispositifs, après nanofabrication ; comme supposé il y a de cela quelques années. Lebut de cette thèse est d’étudier factuellement le possible lien entre verre de spin répartis dans des couches mincesF/AF et dispersions de propriétés d’échange de cellule mémoire à cellule mémoire dans les dispositifs TAMRAMcorrespondants. Avant cela, l’origine de ces régions verre de spin a été étudiée et une attention plusparticulière a été portée au rôle joué par les diffusions de Mn. Ces dernières ont été directement observées,comprises et l’utilisation de barrières complexes pour les réduire et par là même pour diminuer la quantité dephases verre de spin a été mise en oeuvre avec succès. En guise d’alternative pour varier la quantité de verres despin, l’utilisation d’AFs composites a été également étudiée dans le cadre de cette thèse. Ce type d’AF permet dumême coup de varier la stabilité thermique des grains AF et de répondre à un autre problème identifié pour lesTA-MRAM qui consiste à trouver des matériaux AF avec des propriétés de rétention et d’écriture intermédiairespar rapport aux matériaux actuellement utilisés. Finalement, ces AFs composites ont été utilisés comme moyende varier la quantité de verres de spin dans des dispositifs TA-MRAM réels et de prouver le lien direct avec ladispersion de propriétés de cellule mémoire à cellule mémoire. / Spintronics applications such as magnetic random access memories (MRAM), sensors (e.g.. hard diskdrive read head) and logic devices use ferromagnetic/antiferromagnetic (F/AF) exchange bias (EB) interactionsto set the reference direction required for the spin of conduction electrons. Thermally-assisted (TA-) MRAMapplications even use two F/AF exchange biased bilayers: one for reference and one for storage. Suchtechnological applications involve patterning full sheet wafers into matrix of individual bit-cells. Industrialproducts qualification imposes stringent requirements on the distributions of the magnetic properties from cell tocell, including those related to EB. It was supposed few years ago that randomly spread spin-glass like phases atthe F/AF interface or within the bulk of the AF layer significantly contribute to the distributions of EB propertiesin devices after processing. This thesis aimed at factually studying the link between spin-glasses spread overF/AF thin films and bit-cell dispersions of EB in corresponding TA-MRAM. Prior to that the origin of the spinglasslike regions and more specifically the role of Mn-diffusion was consolidated. Mn-diffusion was directlyobserved, understood and the use of complex barriers to reduce such diffusion and consequently to minimize theamount of spin-glass was successfully studied. Mixing AFs as another way to tune the amount of spin-glass likephases was also evidenced in the framework of this thesis. All at once, this last solution also tuned the AF grainsthermal stability and this solved another issue related to TA-MRAM, i.e. finding AF-materials with intermediateretention and write properties compared to the AFs presently used. Finally, those mixed antiferromagnets werethe mean chosen to tune the amount of spin-glass like phases in real TA-MRAM devices and to factually provetheir link with bit-cell distributions of EB properties.

Les applications d’électronique de spin telles les mémoires à accès aléatoire (MRAM), les capteurs (e.g.les têtes de lecture des disques durs d’ordinateurs) et les éléments de logique magnétique utilisent les interactionsd’échange ferromagnétique/antiferromagnétique (F/AF) dans le but de définir une direction de référence pour lespin des électrons de conduction. Les MRAM à écriture assistée thermiquement (TA-MRAM) utilisent mêmedeux bicouches F/AF : une pour le stockage de l’information et l’autre comme référence. Ces dernièresapplications technologiques impliquent des étapes de nanofabrication des couches minces continues pour formerune matrice de cellules mémoires individuelles. La qualification industrielle du produit final impose de sérieusescontraintes sur la largeur des distributions des propriétés magnétiques - y compris d’échange F/AF - de cellulemémoire à cellule mémoire. Des phases verres de spin réparties de manière aléatoire sur la couche continue, àl’interface F/AF ou dans le coeur de l’AF pourraient contribuer de manière significative à ces distributionsd’échange F/AF dans les dispositifs, après nanofabrication ; comme supposé il y a de cela quelques années. Lebut de cette thèse est d’étudier factuellement le possible lien entre verre de spin répartis dans des couches mincesF/AF et dispersions de propriétés d’échange de cellule mémoire à cellule mémoire dans les dispositifs TAMRAMcorrespondants. Avant cela, l’origine de ces régions verre de spin a été étudiée et une attention plusparticulière a été portée au rôle joué par les diffusions de Mn. Ces dernières ont été directement observées,comprises et l’utilisation de barrières complexes pour les réduire et par là même pour diminuer la quantité dephases verre de spin a été mise en oeuvre avec succès. En guise d’alternative pour varier la quantité de verres despin, l’utilisation d’AFs composites a été également étudiée dans le cadre de cette thèse. Ce type d’AF permet dumême coup de varier la stabilité thermique des grains AF et de répondre à un autre problème identifié pour lesTA-MRAM qui consiste à trouver des matériaux AF avec des propriétés de rétention et d’écriture intermédiairespar rapport aux matériaux actuellement utilisés. Finalement, ces AFs composites ont été utilisés comme moyende varier la quantité de verres de spin dans des dispositifs TA-MRAM réels et de prouver le lien direct avec ladispersion de propriétés de cellule mémoire à cellule mémoire. / Spintronics applications such as magnetic random access memories (MRAM), sensors (e.g.. hard diskdrive read head) and logic devices use ferromagnetic/antiferromagnetic (F/AF) exchange bias (EB) interactionsto set the reference direction required for the spin of conduction electrons. Thermally-assisted (TA-) MRAMapplications even use two F/AF exchange biased bilayers: one for reference and one for storage. Suchtechnological applications involve patterning full sheet wafers into matrix of individual bit-cells. Industrialproducts qualification imposes stringent requirements on the distributions of the magnetic properties from cell tocell, including those related to EB. It was supposed few years ago that randomly spread spin-glass like phases atthe F/AF interface or within the bulk of the AF layer significantly contribute to the distributions of EB propertiesin devices after processing. This thesis aimed at factually studying the link between spin-glasses spread overF/AF thin films and bit-cell dispersions of EB in corresponding TA-MRAM. Prior to that the origin of the spinglasslike regions and more specifically the role of Mn-diffusion was consolidated. Mn-diffusion was directlyobserved, understood and the use of complex barriers to reduce such diffusion and consequently to minimize theamount of spin-glass was successfully studied. Mixing AFs as another way to tune the amount of spin-glass likephases was also evidenced in the framework of this thesis. All at once, this last solution also tuned the AF grainsthermal stability and this solved another issue related to TA-MRAM, i.e. finding AF-materials with intermediateretention and write properties compared to the AFs presently used. Finally, those mixed antiferromagnets werethe mean chosen to tune the amount of spin-glass like phases in real TA-MRAM devices and to factually provetheir link with bit-cell distributions of EB properties.

Nous présentons dans ce mémoire un nouvel algorithme de type Metropolis-Hastings dans lequel la distribution instrumentale a été conçue pour l'estimation de distributions cibles bimodales. En fait, cet algorithme peut être vu comme une modification de l'algorithme Metropolis de type marche aléatoire habituel auquel on ajoute quelques incréments de grande envergure à des moments aléatoires à travers la simulation. Le but de ces grands incréments est de quitter le mode de la distribution cible où l'on se trouve et de trouver l'autre mode. Par la suite, nous présentons puis démontrons un résultat de convergence faible qui nous assure que, lorsque la dimension de la distribution cible croît vers l'infini, la chaîne de Markov engendrée par l'algorithme converge vers un certain processus stochastique qui est continu presque partout. L'idée est similaire à ce qui a été fait par Roberts et al. (1997), mais la technique utilisée pour la démonstration des résultats est basée sur ce qui a été fait par Bédard (2006). Nous proposons enfin une stratégie pour trouver la paramétrisation optimale de notre nouvel algorithme afin de maximiser la vitesse d'exploration locale des modes d'une distribution cible donnée tout en estimant bien la pondération relative de chaque mode. Tel que dans l'approche traditionnellement utilisée pour ce genre d'analyse, notre stratégie passe par l'optimisation de la vitesse d'exploration du processus limite. Finalement, nous présentons des exemples numériques d'implémentation de l'algorithme sur certaines distributions cibles, dont une ne respecte pas les conditions du résultat théorique présenté. / In this thesis, we present a new Metropolis-Hastings algorithm whose proposal distribution has been designed to successfully estimate bimodal target distributions. This sampler may be seen as a variant of the usual random walk Metropolis sampler in which we propose large candidate steps at random times. The goal of these large candidate steps is to leave the actual mode of the target distribution in order to find the second one. We then state and prove a weak convergence result stipulating that if we let the dimension of the target distribution increase to infinity, the Markov chain yielded by the algorithm converges to a certain stochastic process that is almost everywhere continuous. The theoretical result is in the flavour of Roberts et al. (1997), while the method of proof is similar to that found in Bédard (2006). We propose a strategy for optimally parameterizing our new sampler. This strategy aims at optimizing local exploration of the target modes, while correctly estimating the relative weight of each mode. As is traditionally done in the statistical literature, our approach consists of optimizing the limiting process rather than the finite-dimensional Markov chain. Finally, we illustrate our method via numerical examples on some target distributions, one of which violates the regularity conditions of the theoretical result.