Analysing student programs in the PHP intelligent tutoring system

Programming is a subject that many beginning students find difficult. The PHP Intelligent Tutoring System (PHP ITS) has been designed with the aim of making it easier for novices to learn the PHP language in order to develop dynamic web pages. Programming requires practice. This makes it necessary to include practical exercises in any ITS that supports students learning to program. The PHP ITS works by providing exercises for students to solve and then providing feedback based on their solutions. The major challenge here is to be able to identify many semantically equivalent solutions to a single exercise. The PHP ITS achieves this by using theories of Artificial Intelligence (AI) including first-order predicate logic and classical and hierarchical planning to model the subject matter taught by the system. This paper highlights the approach taken by the PHP ITS to analyse students’ programs that include a number of program constructs that are used by beginners of web development. The PHP ITS was built using this model and evaluated in a unit at the Queensland University of Technology. The results showed that it was capable of correctly analysing over 96 % of the solutions to exercises supplied by students.

New insights from IODP Expedition 340 offshore Montserrat: First drilling of large volcanic island landslides

Montserrat now provides one of the most complete datasets for understanding the character and tempo of hazardous events at volcanic islands. Much of the erupted material ends up offshore, and this offshore record may be easier to date due to intervening hemiplegic sediments between event beds. The offshore dataset includes the first scientific drilling of volcanic island landslides during IODP Expedition 340, together with an unusually comprehensive set of shallow sediment cores and 2-D and 3-D seismic surveys. Most recently in 2013, Remotely Operated Vehicle (ROV) dives mapped and sampled the surface of the main landslide deposits. This contribution aims to provide an overview of key insights from ongoing work on IODP Expedition 340 Sites offshore Montserrat.Key objectives are to understand the composition (and hence source), emplacement mechanism (and hence tsunami generation) of major landslides, together with their frequency and timing relative to volcanic eruption cycles. The most recent major collapse event is Deposit 1, which involved ~1.8 km cubed of material and produced a blocky deposit at ~12-14ka. Deposit 1 appears to have involved not only the volcanic edifice, but also a substantial component of a fringing bioclastic shelf, and material locally incorporated from the underlying seafloor. This information allows us to test how first-order landslide morphology (e.g. blocky or elongate lobes) is related to first-order landslide composition. Preliminary analysis suggests that Deposit 1 occurred shortly before a second major landslide on the SW of the island (Deposit 5). It may have initiated English's Crater, but was not associated with a major change in magma composition. An associated turbidite-stack suggests it was emplaced in multiple stages, separated by at least a few hours and thus reducing the tsunami magnitude. The ROV dives show that mega-blocks in detail comprise smaller-scale breccias, which can travel significant distances without complete disintegration. Landslide Deposit 2 was emplaced at ~130ka, and is more voluminous (~8.4km cubed). It had a much more profound influence on the magmatic system, as it was linked to a major explosive mafic eruption and formation of a new volcanic centre (South Soufriere Hills) on the island. Site U1395 confirms a hypothesis based on the site survey seismic data that Deposit 2 includes a substantial component of pre-existing seafloor sediment. However, surprisingly, this pre-existing seafloor sediment in the lower part of Deposit 2 at Site U1395 is completely undeformed and flat lying, suggesting that Site U1395 penetrated a flat lying block. Work to date material from the upper part of U1396, U1395 and U1394 will also be summarised. This work is establishing a chronostratigraphy of major events over the last 1 Ma, with particularly detailed constraints during the last ~250ka. This is helping us to understand whether major landslides are related to cycles of volcanic eruptions.

Numerical analysis of a new space-time variable fractional order advection-dispersion equation

Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space–time variable fractional order advection–dispersion equation on a finite domain. The equation is obtained from the standard advection–dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Maximal regularity for second order non-autonomous Cauchy problems

We consider some non-autonomous second order Cauchy problems of the form u + B(t)(u) over dot + A(t)u = f (t is an element of [0, T]), u(0) = (u) over dot(0) = 0. We assume that the first order problem (u) over dot + B(t)u = f (t is an element of [0, T]), u(0) = 0, has L-p-maximal regularity. Then we establish L-p-maximal regularity of the second order problem in situations when the domains of B(t(1)) and A(t(2)) always coincide, or when A(t) = kappa B(t).

Compressible second-order boundary layers for three-dimensional stagnation point flows with mass transfer

All the second-order boundary-layer effects have been studied for the steady laminar compressible 3-dimensional stagnation-point flows with variable properties and mass transfer for both saddle and nodal point regions. The governing equations have been solved numerically using an implicit finite-difference scheme. Results for the heat transfer and skin friction have been obtained for several values of the mass-transfer rate, wall temperature, and also for several values of parameters characterizing the nature of stagnation point and variable gas properties. The second-order effects on the heat transfer and skin friction at the wall are found to be significant and at large injection rates, they dominate over the results of the first-order boundary layer, but the effect of large suction is just the opposite. In general, the second-order effects are more pronounced in the saddle-point region than in the nodal-point region. The overall heat-transfer rate for the 3-dimensional flows is found to be more than that of the 2-dimensional flows.

Truth, Proof and Gödelian Arguments : A Defence of Tarskian Truth in Mathematics

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion.

Unsteady laminar incompressible second-order boundary-layer flow at a three-dimensional stagnation point

The unsteadely laminar incompressible second-order boundary-layer flow at the stagnation point of a three-dimensional body has been studied for both nodal and saddle point regions. The effects of mass transfer and Prandtl number have been taken into account. The equations governing the flow have been solved numerically using an implicit finite-difference scheme. It has been found that the parameter characterizing the unsteadiness in the velocity of the free stream, the nature of the stagnation point, the mass transfer and Prandtl number strongly affect the second-order skin friction and heat transfer. The overall skin friction becomes less due to second-order effects but the heat transfer has the opposite behaviour. For large injection, the second-order skin-friction and heat-transfer results prevail over the first-order boundary layer results whereas for the case of large suction the behaviour is just the opposite.

Unsteady compressible second-order boundary layers at the stagnation point of two-dimensional and axisymmetric bodies

The unsteady laminar compressible boundary-layer flow over two-dimensional and axisymmetric bodies at the stagnation point with mass transfer has been studied for all second-order boundary layer effects when the basic potential flow admits selfsimilarity. The solutions for the governing equations are obtained by using an implicit finite-difference scheme. Computations have been carried out for different values of the parameters characterizing the unsteadiness in the free stream velocity, wall temperature, mass transfer rate and variable gas properties. The results are found to be strongly affected by the unsteadiness in the free stream velocity. For large injection rates the second-orderboundary layer effects may prevail over the first-order boundary layer, but reverse is true for suction. The wall temperature and the variation of the density-viscosity product across the boundary layer appreciably change the skin-friction and heat-transfer rates due to second-order boundary-layer effects.

Unsteady laminar compressible stagnation-point boundary-layer flow over a three-dimensional body: Higher order effects

The unsteady laminar compressible three-dimensional stagnation-point boundary-layer flow with variable properties has been studied when the velocity of the incident stream, mass transfer and wall temperature vary arbitrarily with time. The second-order unsteady boundary-layer equations for all the effects have been derived by using the method of matched asymptotic expansions. Both nodal and saddle point flows as well as cold and hot wall cases have been considered. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. Computations have been carried out for an accelerating stream, a decelerating stream and a fluctuating stream. The results indicate that the unsteady free stream velocity distributions, the nature of the stagnation point, the mass transfer, the wall temperature and the variation of the density-viscosity product across the boundary significantly affect the skin friction and heat transfer. The variation of the wall temperature with time strongly affects the heat transfer whereas its effect is comparatively less on skin friction. Suction increases the skin friction and heat transfer but injection does the opposite. The skin friction in the x direction due to the combined effects of first- and second-order boundary layers is less than the skin-friction in the x direction due to the first-order boundary layers for all the parameters. The overall skin friction in the z direction and heat transfer are more or less than the first-order boundary layers depending upon the values of the various parameters.

Compressible 2nd-order boundary-layers for 3-dimensional stagnation point flows with mass-transfer

All the second-order boundary-layer effects have been studied for the steady laminar compressible 3-dimensional stagnation-point flows with variable properties and mass transfer for both saddle and nodal point regions. The governing equations have been solved numerically using an implicit finite-difference scheme. Results for the heat transfer and skin friction have been obtained for several values of the mass-transfer rate, wall temperature, and also for several values of parameters characterizing the nature of stagnation point and variable gas properties. The second-order effects on the heat transfer and skin friction at the wall are found to be significant and at large injection rates, they dominate over the results of the first-order boundary layer, but the effect of large suction is just the opposite. In general, the second-order effects are more pronounced in the saddle-point region than in the nodal-point region. The overall heat-transfer rate for the 3-dimensional flows is found to be more than that of the 2-dimensional flows.

Study of third-order non-linear systems- Variation of parameters approach

In this paper, the transient response of a third-order non-linear system is obtained by first reducing the given third-order equation to three first-order equations by applying the method of variation of parameters. On the assumption that the variations of amplitude and phase are small, the functions are expanded in ultraspherical polynomials. The expansion is restricted to the constant term. The resulting equations are solved to obtain the response of the given third-order system. A numerical example is considered to illustrate the method. The results show that the agreement between the approximate and digital solution is good thus vindicating the approximation.

Automata and logics over finitely varying functions

We extend some of the classical connections between automata and logic due to Büchi (1960) [5] and McNaughton and Papert (1971) [12] to languages of finitely varying functions or “signals”. In particular, we introduce a natural class of automata for generating finitely varying functions called View the MathML source’s, and show that it coincides in terms of language definability with a natural monadic second-order logic interpreted over finitely varying functions Rabinovich (2002) [15]. We also identify a “counter-free” subclass of View the MathML source’s which characterise the first-order definable languages of finitely varying functions. Our proofs mainly factor through the classical results for word languages. These results have applications in automata characterisations for continuously interpreted real-time logics like Metric Temporal Logic (MTL) Chevalier et al. (2006, 2007) [6] and [7].

Robust fixed order lateral H-2 controller for micro air vehicle

This paper presents a robust fixed order H-2 controller design using Strengthened discrete optimal projection equations, which approximate the first order necessary optimality condition. The novelty of this work is the application of the robust H-2 controller to a micro aerial vehicle named Sarika2 developed in house. The controller is designed in discrete domain for the lateral dynamics of Sarika2 in the presence of low frequency atmospheric turbulence (gust) and high frequency sensor noise. The design specification includes simultaneous stabilization, disturbance rejection and noise attenuation over the entire flight envelope of the vehicle. The resulting controller performance is comprehensively analyzed by means of simulation.

Second-order boundary-layer effects for the unsteady laminar incompressible three-dimensional stagnation-point flow

All the second-order boundary-layer effects on the unsteady laminar incompressible flow at the stagnation-point of a three-dimensional body for both nodal and saddle point regions have been studied. It has been assumed that the free-stream velocity, wall temperature and mass transfer vary arbitrarily with time. The effect of the Prandtl number has been taken into account. The partial differential equations governing the flow have been derived for the first time and then solved numerically unsteady free-stream velocity distributions, the nature of the using an implicit finite-difference scheme. It is found that the stagnation point and the mass transfer strongly affect the skin friction and heat transfer whereas the effects of the Prandtl number and the variation of the wall temperature with time are only on the heat transfer. The skin friction due to the combined effects of first- and second-order boundary layers is less than the skin friction due to, the first-order boundary layers whereas the heat transfer has the opposite behaviour. Suction increases the skin friction and heat transfer but injection does the opposite

Impact of energy quantisation in single electron transistor island on hybrid complementary metal oxide semiconductor-single electron transistor integrated circuits

For the first time, the impact of energy quantisation in single electron transistor (SET) island on the performance of hybrid complementary metal oxide semiconductor (CMOS)-SET transistor circuits has been studied. It has been shown through simple analytical models that energy quantisation primarily increases the Coulomb Blockade area and Coulomb Blockade oscillation periodicity of the SET device and thus influences the performance of hybrid CMOS-SET circuits. A novel computer aided design (CAD) framework has been developed for hybrid CMOS-SET co-simulation, which uses Monte Carlo (MC) simulator for SET devices along with conventional SPICE for metal oxide semiconductor devices. Using this co-simulation framework, the effects of energy quantisation have been studied for some hybrid circuits, namely, SETMOS, multiband voltage filter and multiple valued logic circuits. Although energy quantisation immensely deteriorates the performance of the hybrid circuits, it has been shown that the performance degradation because of energy quantisation can be compensated by properly tuning the bias current of the current-biased SET devices within the hybrid CMOS-SET circuits. Although this study is primarily done by exhaustive MC simulation, effort has also been put to develop first-order compact model for SET that includes energy quantisation effects. Finally, it has been demonstrated that one can predict the SET behaviour under energy quantisation with reasonable accuracy by slightly modifying the existing SET compact models that are valid for metallic devices having continuous energy states.