Th. 3e cycle--Math. pures--Toulouse 3, 1977. N°: 2001.

Le foncteur D_cris de Fontaine nous permet d'obtenir des isocristaux à partir des représentations cristallines. Pour un groupe reductif G, on s'intéresse à étudier la réduction des réseaux dans une représentation cristalline avec G-structure V, vers les cristaux avec G-structure contenus dans D_cris(V). En utilisant la théorie des modules de Kisin, on donne une description de cette réduction en termes du groupe G, dans le cas où la représentation est (G-)ordinaire. Pour cela, il faut d'abord généraliser la construction de la filtration de Harder-Narasimhan des groupes p-divisibles, donnée par Fargues, aux modules de Kisin. / Fontaine’s D_cris functor allows us to associate an isocrystal to any crystalline representation. For a reductive group G, we study the reduction of lattices inside a germ of crystalline representations with G-structure V, to lattices (which are crystals) with G-structure inside D_cris(V). Using Kisin modules theory, we give a description of this reduction in terms of G, in the case when the representation V is (G-)ordinary. In order to do that, first we need to generalize Fargues’ construction of the Harder-Narasimhan filtration for p-divisible groups to Kisin modules.

Vienas svarbiausių šiuolaikinės diferencialinės geometrijos skyrių yra glodžių G- struktūrų teorija, kuriai pradžią davė klasikinės Rymano erdvės struktūros nagrinėjimas. G- struktūra glodžioje daugdaroje yra gaunama paėmus jos reperių sluoksniuotės redukciją , atitinkantį neišsigimusių matricų grupės pogrupį G. G-struktūros egzistuoja ne bet kurioje daugdaroje. Šiame darbe yra nagrinėjama tik baigtinio tipo G- struktūrų vidinės sietys. Yra įrodoma, kad kiekvieną baigtinio tipo G- struktūrą atitinka baigtinio tipo diferencialinė lygtis ant daugdaros . G- struktūrų geometrija nagrinėjama netradiciniu būdu nagrinėjant jų infinitezimalių simetrijų diferencialines lygtis. Šiuo metodu yra išnagrinėtos G- struktūrų afininės sietys, taip pat ir normalinės sietys. Paskutiniosios G- struktūrų geometrijoje nebuvo iki šiol tyrinėtos. / The most important part of differential geometry in our days is the theory of smooth G- structures, which started with the analyses of clasical construction of Riemannian space. G-structure in smooth manifold is acquired, when we take reduction of its frame bundle corresponding to subgroup G of non-degeneracy matrix group . It‘s important to note, that G- structures do not exist in every manifold. In this paper are considering intrisic connections only of finite type of G- structures. It is proved, that every finite type of G- structure corresponds to finite type of differential equation on the manifold . The Geometry of G- structures is investigated not traditionally while analyzing differential equations of infetisimal simmetrics of G- structures. There are analysed affine connections of G- structures, also and normal connections. The former haven‘t been investigated in geometry of G- structures.

Scientific external representations (ERs), such as diagrams, images, pictures, graphs and animations are considered to be powerful teaching and learning tools, because they assist learners in constructing mental models of phenomena, which allows for the comprehension and integration of scientific concepts. Sometimes, however, students experience difficulties with the interpretation of ERs, which· has a negative effect on their learning of science, . . including biochemistry. Unfortunately, many educators are not aware of such student difficulties and make the wrong assumption that what they, as experts, consider to be an educationally sound ER will necessarily promote sound. learning and understanding among novices. On the contrary, research has shown that learners who engage in the molecular biosciences can experience considerable problems interpreting, visualising, reasoning and learning with ERs of biochemical structures and processes, which are both abstract and often represented by confusing computer-generated symbols and man-made markings. The aim of this study was three-fold. Firstly, to identify and classify students' conceptual and reasoning difficulties with a selection of textbook ERs representing· IgG structure and function. Secondly, to use these difficulties to identify sources of the difficulties and, therefore, factors influencing students' ability to interpret the ERs. Thirdly, to develop a model of these factors and investigate the practical applications of the model, including guidelines fOf improving ER design and the teaching and learning with ERs. The study was conducted at the University of KwaZulu-Natal, South Africa and involved a total of 166 second and third-year biochemistry students. The research aims were addressed using a p,ostpositivistic approach consisting of inductive and qualitative research methods. Data was collected from students by means of written probes, audio- and video-taped clinical interviews, and student-generated diagrams. Analysis of the data revealed three general categories of student difficulties, with the interpretation of three textbook ERs depicting antibody structure and interaction with antigen, termed the process-type (P), the. structural-type (S) and DNA-related (D) difficulties. Included in the three general categories of difficulty were seventeen sub-categories that were each classified on the four-level research framework of Grayson et al. (2001) according to v how much information we had about the nature ofeach difficulty and, therefore, whether they required further research. The incidences of the classified difficulties ranged from 3 to 70%, across the student populations and across all three ERs. Based on the evidence of the difficulties, potential sources of the classified difficulties were isolated. Consideration of the nature of the sources of the exposed difficulties indicated that at least three factors play a major role in students' ability to interpret ERs in biochemistry. The three factors are: students' ability to reason with an ER and with their own conceptual knowledge (R), students' understanding (or lack thereof) of the concepts of relevance to the ER (C), and the mode in which the desired phenomenon is represented by the ER (M). A novel three-phase single interview technique (3P-SIT) was designed to explicitly investigate the nature of the above three factors. Application of3P-SIT to a range of abstract to realistic ERs of antibody structure and interaction with antigen revealed that the. instrument was extremely useful for generating data corresponding to the three factors.. In addition; analysis of the 3P-SIT data showed evidence for the influence ofone factor on another during students' ER interpretation, leading to the identification of a further four interactive factors, namely the reasoning-mode (R-M), reasoning conceptual (R-C), conceptual-mode (C-M) and conceptual-reasoning-mode (C-R-M) factors. The Justi and Gilbert (2002) modelling process was employed to develop a model of the seven identified factors. Empirical data generated using 3P-SIT allowed the formulation and validation of operational definitions for the seven factors and the expression of the model as a Venn diagram, Consideration ofthe implications of the model, yielded at least seven practical applications of the model, including its use for: establishing whether sound or unsound interpretation, learning and visualisation of an ER has occurred; identifying the nature and source of any difficulties; determining which of the factors of the model are positively or negatively influencing interpretation; establishing what approaches to ER design and teaching and learning with ERs will optimise the interpretation and learning process; and, generally framing and guiding researchers', educators' and authors' thinking about the nature of students' difficulties with the interpretation of both static and animated ERs in any scientific context. In addition, the study demonstrated how each factor of the expressed model can be used to inform the design of strategies for remediating or preventing students' difficulties with the interpretation of scientific ERs, a target for future research. / Thesis (Ph.D.)-University of KwaZulu-Natal, Pietermaritzburg, 2005.