Effective lambda-models vs recursively enumerable lambda-theories

A longstanding open problem is whether there exists a non syntactical model of the untyped lambda-calculus whose theory is exactly the least lambda-theory (l-beta). In this paper we investigate the more general question of whether the equational/order theory of a model of the (untyped) lambda-calculus can be recursively enumerable (r.e. for brevity). We introduce a notion of effective model of lambda-calculus calculus, which covers in particular all the models individually introduced in the literature. We prove that the order theory of an effective model is never r.e.; from this it follows that its equational theory cannot be l-beta or l-beta-eta. We then show that no effective model living in the stable or strongly stable semantics has an r.e. equational theory. Concerning Scott's semantics, we investigate the class of graph models and prove that no order theory of a graph model can be r.e., and that there exists an effective graph model whose equational/order theory is minimum among all theories of graph models. Finally, we show that the class of graph models enjoys a kind of downwards Lowenheim-Skolem theorem.Comment: 34

Analytical and experimental study of investment casting with laser stereolithography models

This dissertation presents an analytical and experimental investigation of ceramic shell cracking during the burnout process in investment casting with internally webbed laser stereolithography (SLA) patterns. Included in the consideration are the cracking temperature of the ceramic shell, the web link buckling temperature, and the glass transition temperature of the epoxy resin. The hypothesis is that shell cracking will occur when the cracking temperature is lower than the glass transition temperature and the web buckling temperature. An analytical and experimental study has been conducted, with the cross-sectional area, the span length of the web structure, and the shell thickness being the variables. It is found that the ceramic shell cracking and the internal web structure buckling are related to the cross-sectional area, the span length of the web structure, and the shell thickness. A finite element analysis (FEA) model is developed to simulate the burnout process in investment casting with an SLA webbed pattern. The numerical results show that the shell cracking in investment casting can be prevented by the buckling of epoxy webbed pattern in early stages of the burnout process. A strain gauge based experimental study validates the trend of the computational prediction from FEA of the burnout process in investment casting with SLA webbed epoxy patterns. The thermal insulation property of materials, additional expansion of adhesive and wax, and difficulty in temperature measurement contribute to the discrepancy of results. The FEA model is used to evaluate a new design of internal web structure for better yield of investment casting with SLA epoxy patterns. A hexagonal web structure has been analyzed in comparison with triangular and square web structures. The void ratio is increased to 0.89 for the hexagonal web structure from 0.79 for the triangular web structure and 0.83 for the square web structure. The induced stress on the ceramic shell is reduced by 32% and 22% compared with the triangular structure and square structure, respectively. In addition, the drainage of uncured liquid resin within the webbed SLA pattern is more efficient because of the larger interior angle and cross-sectional area of the hexagonal web geometry

Implementation of Integrated Learning Models in Improving Elementary School Student’s Learning Outcomes

Periset ini dibingkai pada poin besar program pelaksanaan bentuk kegiatan belajar mengajar terstruktur yang difokuskan agar sanggup menaikkan keberhasilan peserta ajar di Sekolah Dasar. Tujuan pada riset ini merupakan untuk mengenali penerapan model pembelajaran terpadu dalam meningkatkan hasil belajar siswa SD. Metode penelitian ini menggunakan literture review dengan menggunakan search engine Google Scholar ditemukan 78 artikel dengan hasil akhir dari data ekstraksi 9 artikel. Pembelajaran terpadu di Sekolah Dasar memiliki sepuluh model pembelajaran terpadu yang dapat digunakan yaitu: terpisah, terhubung, tersarang, terurut, terbagi, terjaring, terikat, terpadu, terbenam dan jaringan. Keberhasilan kegiatan belajar mengajar terstruktur terlihat dari bermaknanya kegiatan belajar mengajar. Kegiatan belajar mengajar yang berarti membuahkan peserta didik yang aktif pada metode berlatih membimbing yang menyenangkan, alhasil terjalin komunikasi 2 arah guru serta sisw

Relational Graph Models at Work

We study the relational graph models that constitute a natural subclass of relational models of lambda-calculus. We prove that among the lambda-theories induced by such models there exists a minimal one, and that the corresponding relational graph model is very natural and easy to construct. We then study relational graph models that are fully abstract, in the sense that they capture some observational equivalence between lambda-terms. We focus on the two main observational equivalences in the lambda-calculus, the theory H+ generated by taking as observables the beta-normal forms, and H* generated by considering as observables the head normal forms. On the one hand we introduce a notion of lambda-K\"onig model and prove that a relational graph model is fully abstract for H+ if and only if it is extensional and lambda-K\"onig. On the other hand we show that the dual notion of hyperimmune model, together with extensionality, captures the full abstraction for H*

Non-linear analysis of two-layer beams with interlayer slip and uplift

A new mathematical model for the non-linear analysis of two-layer planar beams considering flexible connections is introduced and an effective, strain-based finite element numerical solution method derived. The model and the solution method account for the exact geometrically non-linear behaviour in each separate layer. Material is assumed homogeneous but can be different in each layer. The shear strains are neglected. The laws of contact in both tangent and normal directions are taken non-linear. Numerical examples verify the proposed approach. The comparisons with numerical and experimental results from literature are made and the effects of uplift on ductility and stress distribution in beams are systematically explored. The theoretical model, combined with the present numerical formulation, has been found to result in realistic behaviour, while the numerical method proves to be accurate, reliable and computationally effective. (C) 2011 Elsevier Ltd. All rights reserved

Lambda theories of effective lambda models

A longstanding open problem is whether there exists a non-syntactical model of untyped lambda-calculus whose theory is exactly the least equational lambda-theory (=Lb). In this paper we make use of the Visser topology for investigating the more general question of whether the equational (resp. order) theory of a non syntactical model M, say Eq(M) (resp. Ord(M)) can be recursively enumerable (= r.e. below). We conjecture that no such model exists and prove the conjecture for several large classes of models. In particular we introduce a notion of effective lambda-model and show that for all effective models M, Eq(M) is different from Lb, and Ord(M) is not r.e. If moreover M belongs to the stable or strongly stable semantics, then Eq(M) is not r.e. Concerning Scott's continuous semantics we explore the class of (all) graph models, show that it satisfies Lowenheim Skolem theorem, that there exists a minimum order/equational graph theory, and that both are the order/equ theories of an effective graph model. We deduce that no graph model can have an r.e. order theory, and also show that for some large subclasses, the same is true for Eq(M).Comment: 15 pages, accepted CSL'0

From Features via Frames to Spaces: Modeling Scientific Conceptual Change Without Incommensurability or Aprioricity

The (dynamic) frame model, originating in artificial intelligence and cognitive psychology, has recently been applied to change-phenomena traditionally studied within history and philosophy of science. Its application purpose is to account for episodes of conceptual dynamics in the empirical sciences (allegedly) suggestive of incommensurability as evidenced by “ruptures” in the symbolic forms of historically successive empirical theories with similar classes of applications. This article reviews the frame model and traces its development from the feature list model. Drawing on extant literature, examples of frame-reconstructed taxonomic change are presented. This occurs for purposes of comparison with an alternative tool, conceptual spaces. The main claim is that conceptual spaces save the merits of the frame model and provide a powerful model for conceptual change in scientific knowledge, since distinctions arising in measurement theory are native to the model. It is suggested how incommensurability as incomparability of theoretical frameworks might be avoided (thus coming on par with a key-result of applying frames). Moreover, as non(inter-)translatability of worldviews, it need not to be treated as a genuine problem of conceptual representation. The status of laws vis à vis their dimensional bases as well as diachronic similarity measures are (inconclusively) discussed