Modes of information processing were examined for 91 subjects aged between 5 years 7 months and 6 years 3 months, using A.R. Luria's model of brain function as the theoretical basis of the study. A factor analysis of the results of six psychometric tests administered to all subjects indicated the presence of two distinct factors. These were hypothesised to represent the separate contributions of simultaneous and successive synthesis. Further separate factor analyses, of the six psychometric tests and tests of M-Space (derived from the work of R. Case) and tests of standard school assessment tasks (that were also administered to the subjects), were performed. The results indicated that although both modes of synthesis are available to children of this age, simultaneous synthesis is not a potent factor in school learning. A further exploratory study was carried out using the same 91 subjects. Subjects were given a series of verbal subtraction problems requiring understanding of mathematical relationships, and randomly assigned to two presentation groups. One group received pictorial information in addition to the verbal presentation. The other group received concrete materials. A multiple regression analysis was performed on the whole group using factor scores for simultaneous and successive syntheses (derived from the factor analysis of the six psychometric tests) as independent variables and criterion test scores for the verbal subtraction problems as the dependent variable. The analysis indicated that although neither aptitude for successive synthesis nor aptitude for simultaneous synthesis had predictive value for this kind of probelm solving, simultaneous synthesis was possibly the predominant mode of information processing. Further multiple regression analyses performed on each of the presentation groups indicated an interaction between successive synthesis and the modes of presentation of information. Due to the small numbers of subjects in each presentation group this result was inconclusive.

We study variants of P-frames and associated rings, which can be viewed as natural generalizations of the classical variants of P-spaces and associated rings. To be more precise, we de ne quasi m-rings to be those rings in which every prime d-ideal is either maximal or minimal. For a completely regular frame L, if the ring RL of real-valued continuous functions of L is a quasi m-ring, we say L is a quasi cozero complemented frame. These frames are less restricted than the cozero complemented frames. Using these frames we study some properties of what are called quasi m-spaces, and observe that the property of being a quasi m-space is inherited by cozero subspaces, dense z- embedded subspaces, and regular-closed subspaces among normal quasi m-space. M. Henriksen, J. Mart nez and R. G. Woods have de ned a Tychono space X to be a quasi P-space in case every prime z-ideal of C(X) is either minimal or maximal. We call a point I of L a quasi P-point if every prime z-ideal of RL contained in the maximal ideal associated with I is either maximal or minimal. If all points of L are quasi P-points, we say L is a quasi P-frame. This is a conservative de nition in the sense that X is a quasi P-space if and only if the frame OX is a quasi P-frame. We characterize these frames in terms of cozero elements, and, among cozero complemented frames, give a su cient condition for a frame to be a quasi P-frame. A Tychono space X is called a weak almost P-space if for every two zero-sets E and F of X with IntE IntF, there is a nowhere dense zero-set H of X such that E F [H. We present the pointfree version of weakly almost P-spaces. We de ne weakly regular rings by a condition characterizing the rings C(X) for weak almost P-spaces X. We show that a reduced f-ring is weakly regular if and only if every prime z-ideal in it which contains only zero-divisors is a d-ideal. We characterize the frames L for which the ring RL of real-valued continuous functions on L is weakly regular. We introduce the notions of boundary frames and boundary rings, and use them to give another ring-theoretic characterization of boundary spaces. We show that X is a boundary space if and only if C(X) is a boundary ring. A Tychono space whose Stone- Cech compacti cation is a nite union of closed subspaces each of which is an F-space is said to be nitely an F-space. Among normal spaces, S. Larson gave a characterization of these spaces in terms of properties of function rings C(X). By extending this notion to frames, we show that the normality restriction can actually be dropped, even in spaces, and thus we sharpen Larson's result. / Mathematics / D. Phil. (Mathematics)

In this thesis we present an extensive characterization of weak* sequentially precompact subsets of the dual of a sequentially order complete M-space with an order unit. This central part of the thesis generalizes results due to H.H. Schaefer and X.D. Zhang showing that small weak* compact subsets of the dual of a space of bounded measurable real-valued functions (continuous real-valued functions on a compact quasi-Stonian space) are weakly compact. Moreover, while the proofs of Schaefer and Zhang use measure theoretical arguments, the arguments presented here are purely elementary and are based on the well-known result, that the space l1 has the Schur property. Finally some applications are given. For example, we investigate compact or sequentially precompact subsets, which consist of order-weakly compact operators, in the space of continuous linear operators defined on a sequentially order complete Riesz space with values in a Banach space provided with the strong operator topology: as an immediate consequence of the results, we can easily deduce extended versions of the Vitali-Hahn-Saks theorem for vector measures. For this we need a generalization of the Yosida-Hewitt decomposition theorem, which is proved here with other techniques like the factorization of an order-weakly compact operator through a Banach lattice with order continuous norm.