977 resultados para Non-complete extended p-sums (NEPS)
Resumo:
Abstract
Continuous variable is one of the major data types collected by the survey organizations. It can be incomplete such that the data collectors need to fill in the missingness. Or, it can contain sensitive information which needs protection from re-identification. One of the approaches to protect continuous microdata is to sum them up according to different cells of features. In this thesis, I represents novel methods of multiple imputation (MI) that can be applied to impute missing values and synthesize confidential values for continuous and magnitude data.
The first method is for limiting the disclosure risk of the continuous microdata whose marginal sums are fixed. The motivation for developing such a method comes from the magnitude tables of non-negative integer values in economic surveys. I present approaches based on a mixture of Poisson distributions to describe the multivariate distribution so that the marginals of the synthetic data are guaranteed to sum to the original totals. At the same time, I present methods for assessing disclosure risks in releasing such synthetic magnitude microdata. The illustration on a survey of manufacturing establishments shows that the disclosure risks are low while the information loss is acceptable.
The second method is for releasing synthetic continuous micro data by a nonstandard MI method. Traditionally, MI fits a model on the confidential values and then generates multiple synthetic datasets from this model. Its disclosure risk tends to be high, especially when the original data contain extreme values. I present a nonstandard MI approach conditioned on the protective intervals. Its basic idea is to estimate the model parameters from these intervals rather than the confidential values. The encouraging results of simple simulation studies suggest the potential of this new approach in limiting the posterior disclosure risk.
The third method is for imputing missing values in continuous and categorical variables. It is extended from a hierarchically coupled mixture model with local dependence. However, the new method separates the variables into non-focused (e.g., almost-fully-observed) and focused (e.g., missing-a-lot) ones. The sub-model structure of focused variables is more complex than that of non-focused ones. At the same time, their cluster indicators are linked together by tensor factorization and the focused continuous variables depend locally on non-focused values. The model properties suggest that moving the strongly associated non-focused variables to the side of focused ones can help to improve estimation accuracy, which is examined by several simulation studies. And this method is applied to data from the American Community Survey.
Resumo:
Several landforms found in the fold-and-thrust belt area of Central Precordillera, Pre-Andes of Argentina, which were often associated with tectonic efforts, are in fact related to non-tectonic processes or gravitational superficial structures. These second-order structures, interpreted as gravitational collapse structures, have developed in the western flank of sierras de La Dehesa and Talacasto. These include rock-slides, rock falls, wrinkle folds, slip sheets and flaps, among others; which together constitute a monoclinal fold dipping between 30º and 60º to the west. Gravity collapse structures are parallel to the regional strike of the Sierra de la Dehesa and are placed in Ordovician limestones and dolomites. Their sloping towards the west, the presence of bed planes, fractures and joints; and the lithology (limestone interbedded with incompetent argillaceous banks) would have favored their occurrence. Movement of the detached structures has been controlled by lithology characteristics, as well as by bedding and joints. Detachment and initial transport of gravity collapse structures and rockslides in the western flank of the Sierra de la Dehesa were tightly controlled by three structural elements: 1) sliding surfaces developed on parallel bedded strata when dipping >30° in the slope direction; 2) Joint’s sets constitute lateral and transverse traction cracks which release extensional stresses and 3) Discontinuities fragmenting sliding surfaces. Some other factors that could be characterized as local (lithology, structure and topography) and as regional (high seismic activity and possibly wetter conditions during the postglacial period) were determining in favoring the steady loss of the western mountain side in the easternmost foothills of Central Precordillera.
Non-thermal Plasma Exposure Rapidly Attenuates Bacterial AHL-Dependent Quorum Sensing and Virulence.
Resumo:
The antimicrobial activity of atmospheric pressure non-thermal plasma has been exhaustively characterised, however elucidation of the interactions between biomolecules produced and utilised by bacteria and short plasma exposures are required for optimisation and clinical translation of cold plasma technology. This study characterizes the effects of non-thermal plasma exposure on acyl homoserine lactone (AHL)-dependent quorum sensing (QS). Plasma exposure of AHLs reduced the ability of such molecules to elicit a QS response in bacterial reporter strains in a dose-dependent manner. Short exposures (30-60 s) produce of a series of secondary compounds capable of eliciting a QS response, followed by the complete loss of AHL-dependent signalling following longer exposures. UPLC-MS analysis confirmed the time-dependent degradation of AHL molecules and their conversion into a series of by-products. FT-IR analysis of plasma-exposed AHLs highlighted the appearance of an OH group. In vivo assessment of the exposure of AHLs to plasma was examined using a standard in vivo model. Lettuce leaves injected with the rhlI/lasI mutant PAO-MW1 alongside plasma treated N-butyryl-homoserine lactone and n-(3-oxo-dodecanoyl)-homoserine lactone, exhibited marked attenuation of virulence. This study highlights the capacity of atmospheric pressure non-thermal plasma to modify and degrade AHL autoinducers thereby attenuating QS-dependent virulence in P. aeruginosa.
Resumo:
This paper describes a substantial effort to build a real-time interactive multimodal dialogue system with a focus on emotional and non-verbal interaction capabilities. The work is motivated by the aim to provide technology with competences in perceiving and producing the emotional and non-verbal behaviours required to sustain a conversational dialogue. We present the Sensitive Artificial Listener (SAL) scenario as a setting which seems particularly suited for the study of emotional and non-verbal behaviour, since it requires only very limited verbal understanding on the part of the machine. This scenario allows us to concentrate on non-verbal capabilities without having to address at the same time the challenges of spoken language understanding, task modeling etc. We first summarise three prototype versions of the SAL scenario, in which the behaviour of the Sensitive Artificial Listener characters was determined by a human operator. These prototypes served the purpose of verifying the effectiveness of the SAL scenario and allowed us to collect data required for building system components for analysing and synthesising the respective behaviours. We then describe the fully autonomous integrated real-time system we created, which combines incremental analysis of user behaviour, dialogue management, and synthesis of speaker and listener behaviour of a SAL character displayed as a virtual agent. We discuss principles that should underlie the evaluation of SAL-type systems. Since the system is designed for modularity and reuse, and since it is publicly available, the SAL system has potential as a joint research tool in the affective computing research community.
Resumo:
A non-Markovian process is one that retains `memory' of its past. A systematic understanding of these processes is necessary to fully describe and harness a vast range of complex phenomena; however, no such general characterisation currently exists. This long-standing problem has hindered advances in understanding physical, chemical and biological processes, where often dubious theoretical assumptions are made to render a dynamical description tractable. Moreover, the methods currently available to treat non-Markovian quantum dynamics are plagued with unphysical results, like non-positive dynamics. Here we develop an operational framework to characterise arbitrary non-Markovian quantum processes. We demonstrate the universality of our framework and how the characterisation can be rendered efficient, before formulating a necessary and sufficient condition for quantum Markov processes. Finally, we stress how our framework enables the actual systematic analysis of non-Markovian processes, the understanding of their typicality, and the development of new master equations for the effective description of memory-bearing open-system evolution.
Resumo:
Current treatment strategies for the treatment of brain tumor have been hindered primarily by the presence of highly lipophilic insurmountable blood-brain barrier (BBB). The purpose of current research was to investigate the efficiency of engineered biocompatible polymeric nanoparticles (NPs) as drug delivery vehicle to bypass the BBB and enhance biopharmaceutical attributes of anti-metabolite methotrexate (MTX) encapsulated NPs. The NPs were prepared by solvent diffusion method using cationic bovine serum albumin (CBA), and characterized for physicochemical parameters such as particle size, polydispersity index, and zeta-potential; while the surface modification was confirmed by FTIR, and NMR spectroscopy. Developed NPs exhibited zestful relocation of FITC tagged NPs across BBB in albino rats. Further, hemolytic studies confirmed them to be non-toxic and biocompatible as compared to free MTX. In vitro cytotoxicity assay of our engineered NPs on HNGC1 tumor cells proved superior uptake in tumor cells; and elicited potent cytotoxic effect as compared to plain NPs and free MTX solution. The outcomes of the study evidently indicate the prospective of CBA conjugated poly (D,L-lactide-co-glycolide) (PLGA) NPs loaded with MTX in brain cancer bomber with amplified capability to circumvent BBB.
Resumo:
MORAES, Maísa Suares Teixeira; ROLIM, Lariane Thays Albuquerque; ENDERS, Bertha Cruz; FARIAS, Glaucea Maciel de; DAVIM, Rejane Marie Barbosa. Applicability of non-pharmacological strategies for pain relief in parturient: integrative review. Revista de Enfermagem UFPE on line, v.4, n.especial, p.131-136, May/June 2010. Disponivel em:< http://www.ufpe.br/revistaenfermagem/index.php/revista/>.
Resumo:
Selon la théorie de l’auto-détermination, l’autonomie est un besoin universel de base qui, lorsque soutenu, permet aux individus de mieux fonctionner et de vivre plus de bien-être psychologique (p. ex., Deci & Ryan, 2008). Le style parental des parents qui soutiennent l’autonomie de leur enfant est caractérisé par le soutien du fonctionnement autodéterminé de ce dernier. Sa définition traditionnelle inclut des pratiques telles qu’offrir des explications et des choix lors des requêtes, communiquer de l’empathie, et encourager les prises d’initiatives tout en minimisant l’utilisation d’un langage contrôlant (p. ex., Soenens et al., 2007). Les bénéfices d’un style parental qui soutient l’autonomie d’un enfant ont été bien documentés (p. ex., Grolnick, Deci, & Ryan, 1997), toutefois, peu d’études ont été effectuées auprès des bambins. Or, cette thèse visait à enrichir la littérature sur le « parentage » en explorant les pratiques soutenantes qui sont utilisées par des parents de bambins dans un contexte de socialisation (étude 1), ainsi qu’en examinant les facteurs qui peuvent brimer leur mise en pratique (étude 2). La première étude a examiné un grand nombre de pratiques de socialisation que les parents qui favorisent davantage le soutien à l’autonomie (SA) pourraient utiliser plus fréquemment lorsqu’ils font des demandes à leurs bambins. Cette étude nous a permis d’explorer comment les parents manifestent leur SA et si le SA dans ce type de contexte est associé à un plus grand niveau d’internalisation des règles. Des parents (N = 182) de bambins (M âge = 27.08 mois) ont donc été invités à rapporter la fréquence avec laquelle ils utilisent 26 pratiques potentiellement soutenantes lorsqu’ils demandent à leurs bambins de compléter des tâches importantes mais non intéressantes et de rapporter à quel point ils valorisent le SA. Huit pratiques ont été identifiées comme étant soutenantes: quatre façons de communiquer de l’empathie, donner des explications courtes, expliquer pourquoi la tâche est importante, décrire le problème de façon informative et neutre, et mettre en pratique le comportement désiré soi-même. De plus, l’ensemble des huit pratiques corrélait positivement avec le niveau d’internalisation des bambins, suggérant aussi que celles-ci représentent bien le concept du SA. Des études futures pourraient tenter de répliquer ces résultats dans des contextes potentiellement plus chargés ou ébranlants (p. ex., réagir face à des méfaits, avec des enfants souffrant de retard de développement). La deuxième étude a poursuivi l’exploration du concept du SA parental en examinant les facteurs qui influencent la fréquence d’utilisation des stratégies soutenantes dans des contextes de socialisation. Puisque la littérature suggère que le stress parental et le tempérament difficile des bambins (c.-à-d., plus haut niveau d’affectivité négative, plus faible niveau de contrôle volontaire/autorégulation, plus faible niveau de surgency) comme étant des facteurs de risque potentiels, nous avons exploré de quelle façon ces variables étaient associées à la fréquence d’utilisation des stratégies soutenantes. Les buts de l’étude étaient: (1) d’examiner comment le tempérament des bambins et le stress parental influençaient le SA parental, et (2) de vérifier si le stress parental médiait la relation possible entre le tempérament des bambins et le SA parental. Le même échantillon de parents a été utilisé. Les parents ont été invités à répondre à des questions portant sur le tempérament de leur enfant ainsi que sur leur niveau de stress. Les résultats ont démontré qu’un plus grand niveau d’affectivité négative était associé à un plus grand niveau de stress parental, qui à son tour prédisait moins de SA parental. De plus, le stress parental médiait la relation positive entre l’autorégulation du bambin et le SA parental. Des recherches futures pourraient évaluer des interventions ayant pour but d’aider les parents à préserver leur attitude soutenante durant des contextes de socialisation plus difficiles malgré certaines caractéristiques tempéramentales exigeantes des bambins, en plus du stress qu’ils pourraient vivre au quotidien.
Resumo:
MORAES, Maísa Suares Teixeira; ROLIM, Lariane Thays Albuquerque; ENDERS, Bertha Cruz; FARIAS, Glaucea Maciel de; DAVIM, Rejane Marie Barbosa. Applicability of non-pharmacological strategies for pain relief in parturient: integrative review. Revista de Enfermagem UFPE on line, v.4, n.especial, p.131-136, May/June 2010. Disponivel em:< http://www.ufpe.br/revistaenfermagem/index.php/revista/>.
Resumo:
This paper addresses the construction and structuring of a technological niche – i.e. a protected space where promising but still underperforming technologies are stabilized and articulated with societal needs – and discusses the processes that influence niche development and may enable niche breakout. In theoretical terms the paper is grounded on the multi-level approach to sustainability transitions, and particularly on the niche literature. But it also attempts to address the limitations of this literature in what concerns the spatial dimension of niche development. It is argued that technological niches can transcend the narrow territorial boundaries to which they are often confined, and encompass communities and actions that span several spatial levels, without losing some territorial embeddedness. It is further proposed that these features shape the niche trajectory and, therefore, need to be explicitly considered by the niche theoretical framework. To address this problem the paper builds on and extends the socio-cognitive perspective to technology development, introducing a further dimension – space – which broadens the concept of technological niche and permits to better capture the complexity of niche behaviour. This extended framework is applied to the case of an emerging renewable energy technology – wave energy - which exhibits a particularly slow and non-linear development trajectory. The empirical analysis starts by examining how an “overall niche space” in wave energy was spatially constructed over time. Then it investigates in greater detail the niche development processes that took place in Portugal, a country that was among the pioneers in the field, and whose actors have been, from very early stages, engaged in the activities conducted at various spatial levels. Through this combined analysis, the paper seeks to understand whether and how niche development is shaped by processes taking place at different spatial levels. More specifically it investigates the interplay between territorial and relational elements in niche development, and how these different dynamics influence the performance of the niche processes and impact on the overall niche trajectory. The results confirm the niche multi-spatial dynamics, showing that it is shaped by the interplay between a niche relational space constructed by actors’ actions and interactions on/across levels, and the territorial effects introduced by these actors’ embeddedness in particular geographical and institutional settings. They contribute to a more precise understanding of the processes that can accelerate or slow down the trajectory of a technological niche. In addition, the results shed some light into the niche activities conducted in/originating from a specific territorial setting - Portugal - offering some insights into the behaviour of key actors and its implications for the positioning of the country in the emerging field, which can be relevant for the formulation of strategies and policies for this area.
Resumo:
Non-finite clauses are sentential constituents with a verbal head that lacks a morphological specification for tense and agreement. In this paper I contend that these clauses are defective not only morphologically but also syntactically, in the sense that they all lack some of the functional categories that make up a full sentence. In particular I argue that to-infinitive clauses, gerund(ive) clauses and participial clauses differ among themselves, and with respect to other subordinate clauses, in the degree of structural defectiveness they display, which goes from the almost complete functional structure of the infinitive to the maximal degree of syntactic truncation of participial clauses (analyzed here as verbal small clauses). I also show the significant parallelism that exists in this respect between English and Spanish non-finite clauses, pointing to the implication this may have for a cross-linguistic approach to the cartography of syntactic structures.
Resumo:
Conventional Si complementary-metal-oxide-semiconductor (CMOS) scaling is fast approaching its limits. The extension of the logic device roadmap for future enhancements in transistor performance requires non-Si materials and new device architectures. III-V materials, due to their superior electron transport properties, are well poised to replace Si as the channel material beyond the 10nm technology node to mitigate the performance loss of Si transistors from further reductions in supply voltage to minimise power dissipation in logic circuits. However several key challenges, including a high quality dielectric/III-V gate stack, a low-resistance source/drain (S/D) technology, heterointegration onto a Si platform and a viable III-V p-metal-oxide-semiconductor field-effect-transistor (MOSFET), need to be addressed before III-Vs can be employed in CMOS. This Thesis specifically addressed the development and demonstration of planar III-V p-MOSFETs, to complement the n-MOSFET, thereby enabling an all III-V CMOS technology to be realised. This work explored the application of InGaAs and InGaSb material systems as the channel, in conjunction with Al2O3/metal gate stacks, for p-MOSFET development based on the buried-channel flatband device architecture. The body of work undertaken comprised material development, process module development and integration into a robust fabrication flow for the demonstration of p-channel devices. The parameter space in the design of the device layer structure, based around the III-V channel/barrier material options of Inx≥0.53Ga1-xAs/In0.52Al0.48As and Inx≥0.1Ga1-xSb/AlSb, was systematically examined to improve hole channel transport. A mobility of 433 cm2/Vs, the highest room temperature hole mobility of any InGaAs quantum-well channel reported to date, was obtained for the In0.85Ga0.15As (2.1% strain) structure. S/D ohmic contacts were developed based on thermally annealed Au/Zn/Au metallisation and validated using transmission line model test structures. The effects of metallisation thickness, diffusion barriers and de-oxidation conditions were examined. Contacts to InGaSb-channel structures were found to be sensitive to de-oxidation conditions. A fabrication process, based on a lithographically-aligned double ohmic patterning approach, was realised for deep submicron gate-to-source/drain gap (Lside) scaling to minimise the access resistance, thereby mitigating the effects of parasitic S/D series resistance on transistor performance. The developed process yielded gaps as small as 20nm. For high-k integration on GaSb, ex-situ ammonium sulphide ((NH4)2S) treatments, in the range 1%-22%, for 10min at 295K were systematically explored for improving the electrical properties of the Al2O3/GaSb interface. Electrical and physical characterisation indicated the 1% treatment to be most effective with interface trap densities in the range of 4 - 10×1012cm-2eV-1 in the lower half of the bandgap. An extended study, comprising additional immersion times at each sulphide concentration, was further undertaken to determine the surface roughness and the etching nature of the treatments on GaSb. A number of p-MOSFETs based on III-V-channels with the most promising hole transport and integration of the developed process modules were successfully demonstrated in this work. Although the non-inverted InGaAs-channel devices showed good current modulation and switch-off characteristics, several aspects of performance were non-ideal; depletion-mode operation, modest drive current (Id,sat=1.14mA/mm), double peaked transconductance (gm=1.06mS/mm), high subthreshold swing (SS=301mV/dec) and high on-resistance (Ron=845kΩ.μm). Despite demonstrating substantial improvement in the on-state metrics of Id,sat (11×), gm (5.5×) and Ron (5.6×), inverted devices did not switch-off. Scaling gate-to-source/drain gap (Lside) from 1μm down to 70nm improved Id,sat (72.4mA/mm) by a factor of 3.6 and gm (25.8mS/mm) by a factor of 4.1 in inverted InGaAs-channel devices. Well-controlled current modulation and good saturation behaviour was observed for InGaSb-channel devices. In the on-state In0.3Ga0.7Sb-channel (Id,sat=49.4mA/mm, gm=12.3mS/mm, Ron=31.7kΩ.μm) and In0.4Ga0.6Sb-channel (Id,sat=38mA/mm, gm=11.9mS/mm, Ron=73.5kΩ.μm) devices outperformed the InGaAs-channel devices. However the devices could not be switched off. These findings indicate that III-V p-MOSFETs based on InGaSb as opposed to InGaAs channels are more suited as the p-channel option for post-Si CMOS.
Resumo:
In this paper, we present a formalism designed to model tidal interaction with a viscoelastic body made of Maxwell material. Our approach remains regular for any spin rate and orientation, and for any orbital configuration including high eccentricities and close encounters. The method is to integrate simultaneously the rotation and the position of the planet as well as its deformation. We provide the equations of motion both in the body frame and in the inertial frame. With this study, we generalize preexisting models to the spatial case and to arbitrary multipole orders using a formalism taken from quantum theory. We also provide the vectorial expression of the secular tidal torque expanded in Fourier series. Applying this model to close-in exoplanets, we observe that if the relaxation time is longer than the revolution period, the phase space of the system is characterized by the presence of several spin-orbit resonances, even in the circular case. As the system evolves, the planet spin can visit different spin-orbit configurations. The obliquity is decreasing along most of these resonances, but we observe a case where the planet tilt is instead growing. These conclusions derived from the secular torque are successfully tested with numerical integrations of the instantaneous equations of motion on HD 80606 b. Our formalism is also well adapted to close-in super-Earths in multiplanet systems which are known to have non-zero mutual inclinations.
Resumo:
Selon la théorie de l’auto-détermination, l’autonomie est un besoin universel de base qui, lorsque soutenu, permet aux individus de mieux fonctionner et de vivre plus de bien-être psychologique (p. ex., Deci & Ryan, 2008). Le style parental des parents qui soutiennent l’autonomie de leur enfant est caractérisé par le soutien du fonctionnement autodéterminé de ce dernier. Sa définition traditionnelle inclut des pratiques telles qu’offrir des explications et des choix lors des requêtes, communiquer de l’empathie, et encourager les prises d’initiatives tout en minimisant l’utilisation d’un langage contrôlant (p. ex., Soenens et al., 2007). Les bénéfices d’un style parental qui soutient l’autonomie d’un enfant ont été bien documentés (p. ex., Grolnick, Deci, & Ryan, 1997), toutefois, peu d’études ont été effectuées auprès des bambins. Or, cette thèse visait à enrichir la littérature sur le « parentage » en explorant les pratiques soutenantes qui sont utilisées par des parents de bambins dans un contexte de socialisation (étude 1), ainsi qu’en examinant les facteurs qui peuvent brimer leur mise en pratique (étude 2). La première étude a examiné un grand nombre de pratiques de socialisation que les parents qui favorisent davantage le soutien à l’autonomie (SA) pourraient utiliser plus fréquemment lorsqu’ils font des demandes à leurs bambins. Cette étude nous a permis d’explorer comment les parents manifestent leur SA et si le SA dans ce type de contexte est associé à un plus grand niveau d’internalisation des règles. Des parents (N = 182) de bambins (M âge = 27.08 mois) ont donc été invités à rapporter la fréquence avec laquelle ils utilisent 26 pratiques potentiellement soutenantes lorsqu’ils demandent à leurs bambins de compléter des tâches importantes mais non intéressantes et de rapporter à quel point ils valorisent le SA. Huit pratiques ont été identifiées comme étant soutenantes: quatre façons de communiquer de l’empathie, donner des explications courtes, expliquer pourquoi la tâche est importante, décrire le problème de façon informative et neutre, et mettre en pratique le comportement désiré soi-même. De plus, l’ensemble des huit pratiques corrélait positivement avec le niveau d’internalisation des bambins, suggérant aussi que celles-ci représentent bien le concept du SA. Des études futures pourraient tenter de répliquer ces résultats dans des contextes potentiellement plus chargés ou ébranlants (p. ex., réagir face à des méfaits, avec des enfants souffrant de retard de développement). La deuxième étude a poursuivi l’exploration du concept du SA parental en examinant les facteurs qui influencent la fréquence d’utilisation des stratégies soutenantes dans des contextes de socialisation. Puisque la littérature suggère que le stress parental et le tempérament difficile des bambins (c.-à-d., plus haut niveau d’affectivité négative, plus faible niveau de contrôle volontaire/autorégulation, plus faible niveau de surgency) comme étant des facteurs de risque potentiels, nous avons exploré de quelle façon ces variables étaient associées à la fréquence d’utilisation des stratégies soutenantes. Les buts de l’étude étaient: (1) d’examiner comment le tempérament des bambins et le stress parental influençaient le SA parental, et (2) de vérifier si le stress parental médiait la relation possible entre le tempérament des bambins et le SA parental. Le même échantillon de parents a été utilisé. Les parents ont été invités à répondre à des questions portant sur le tempérament de leur enfant ainsi que sur leur niveau de stress. Les résultats ont démontré qu’un plus grand niveau d’affectivité négative était associé à un plus grand niveau de stress parental, qui à son tour prédisait moins de SA parental. De plus, le stress parental médiait la relation positive entre l’autorégulation du bambin et le SA parental. Des recherches futures pourraient évaluer des interventions ayant pour but d’aider les parents à préserver leur attitude soutenante durant des contextes de socialisation plus difficiles malgré certaines caractéristiques tempéramentales exigeantes des bambins, en plus du stress qu’ils pourraient vivre au quotidien.
Resumo:
We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.