Two methods for the calculation of the degree of an approximate greatest common divisor of two inexact polynomials

The calculation of the degree d of an approximate greatest common divisor of two inexact polynomials f(y) and g(y) reduces to the determination of the rank loss of a resultant matrix, the entries of which are functions of the coefficients of f(y) and g(y). This paper considers this issue by describing two methods to calculate d, such that knowledge of the noise level imposed on the coefficients of f(y) and g(y) is not assumed. One method uses the residual of a linear algebraic equation whose coefficient matrix and right hand side vector are derived from the Sylvester resultant matrix S(f,g), and the other method uses the first principal angle between a line and a hyperplane, the equations of which are calculated from S(f,g). Computational results on inexact polynomials whose exact forms have multiple roots of high degree are shown and very good results are obtained. These results are compared with the rank loss of S(f,g) for the calculation of d, and it is shown that this method yields incorrect results for these examples.     

Evaluation of an adaptive and intelligent educational hypermedia for enhanced individual learning of mathematics: A qualitative study

The purpose of this study is to design a personalized adaptive and intelligent web based tutoring system based on learning style and expert system named UZWEBMAT and to evaluate its effects on 10th grade students’ learning of the unit of probability. In the study, initially, learning objects were prepared in three different ways in relation to three sub-learning areas of Visual–Auditory–Kinesthetic (VAK) learning style for each subject of the probability unit. These were appropriate for secondary school mathematics curricula. Then, they were transferred into the digital environment. Each student’s dominant learning style determines the content to which s/he will be directed since s/he is directed to the content that is appropriate for his/her learning style. The course to be followed by the students within UZWEBMAT and their browsing around the pages are decided by expert system integrated into the system. This expert system sets the situations in which s/he will get solution supports and the course s/he will follow in accordance with the performance of the student. Hereby, each student may follow a different course, and the solution supports s/he will get may also differ highlighting the individual learning. The sample of the study consists of 81 10th grade students and 3 mathematics teachers from two high schools in Trabzon, Turkey. Qualitative data were obtained both from the teachers and students participating in the study in order to answer the research questions about the implementation and evaluation of UZWEBMAT for mathematics teaching in a high school classroom. Obtained data were analyzed using qualitative data analysis methods. According to the results of the present study, positive opinions of students and teachers such as taking into account the individual learning differences and deriving mathematical relations and formulas through exploration became prominent. In addition, there were also other positive opinions of students and teachers such as providing permanent learning and introducing learning responsibility to the students. In this sense, it was concluded that UZWEBMAT is a beneficial instrument for both students and teachers.     

On Logical Foundations of Multilevel Secure Databases

It is envisaged that the application of the multilevel security (MLS) scheme will enhance flexibility and effectiveness of authorization policies in shared enterprise databases and will replace cumbersome authorization enforcement practices through complicated view definitions on a per user basis. However, the critical problem with the current model is that the belief at a higher security level is cluttered with irrelevant or inconsistent data as no mechanism for attenuation is supported. Critics also argue that it is imperative for MLS database users to theorize about the belief of others, perhaps at different security levels, an apparatus that is currently missing and the absence of which is seriously felt.The impetus for our current research is the need to provide an adequate framework for belief reasoning in MLS databases. In this paper, we show that these concepts can be captured in a F-logic style declarative query language, called MultiLog, for MLS deductive databases for which a proof theoretic, model theoretic and fixpoint semantics exist. This development is significant from a database perspective as it now enables us to compute the semantics of MultiLog databases in a bottom-up fashion. We also define a bottom-up procedure to compute unique models of stratified MultiLog databases. Finally, we establish the equivalence of MultiLog's three logical characterizations—model theory, fixpoint theory and proof theory.     

Destructive and non-destructive evaluation of concrete for optimum sand to aggregate volume ratio

Aggregates are the biggest contributor to concrete volume and are a crucial parameter in dictating its mechanical properties. As such, a detailed experimental investigation was carried out to evaluate the effect of sand-to-aggregate volume ratio (s/a) on the mechanical properties of concrete utilizing both destructive and non-destructive testing (employing UPV (ultrasonic pulse velocity) measurements). For investigation, standard cylindrical concrete samples were made with different s/a (0.36, 0.40, 0.44, 0.48, 0.52, and 0.56), cement content (340 and 450 kg/m³), water-to-cement ratio (0.45 and 0.50), and maximum aggregate size (12 and 19 mm). The effect of these design parameters on the 7, 14, and 28 d compressive strength, tensile strength, elastic modulus, and UPV of concrete were assessed. The careful analysis demonstrates that aggregate proportions and size need to be optimized for formulating mix designs; optimum ratios of s/a were found to be 0.40 and 0.44 for the maximum aggregate size of 12 and 19 mm, respectively, irrespective of the W/C (water-to-cement) and cement content.     

Modeling of Dispersive Materials Using Dispersion Models for FDTD Application

A nonlinear optimization algorithm based on the Nelder Mead method is used to characterize the frequency dependent permittivity of 15 materials based on Lorentz, modified Lorentz, Drude and Lorentz-Drude models. The optimized model parameters are used to calculate the complex relative permittivity of each material and compare it with experimental data. In each case, a very good match is found between the optimized and experimental data over a long wavelength range. Comparative study of the models used for each material is performed based on accuracy, wavelength range of applicability and computational efficiency. The parameters presented can be used for computer simulation of electromagnetic wave phenomena involving these materials.     

Mixed convective heat transfer enhancement in a ventilated cavity by flow modulation via rotating plate

The present study numerically explores the mixed convection phenomena in a differentially heated ventilated square cavity with active flow modulation via a rotating plate. Forced convection flow in the cavity is attained by maintaining external fluid flow through an opening at the bottom of the left cavity wall while leaving it through another opening at the right cavity wall. A counter-clockwise rotating plate at the center of the cavity acts as an active flow modulator. Moving mesh approach is used for the rotation of the plate and the numerical solution is achieved using arbitrary Lagrangian-Eulerian finite element formulation with a quadrilateral discretization scheme. Transient parametric simulations have been performed for various frequency of the rotating plate for a fixed Reynolds number (Re) of 100 based on maximum inlet flow velocity while the Richardson number (Ri) is maintained at unity. Heat transfer performance has been evaluated in terms of spatially averaged Nusselt number and time-averaged Nusselt number along the heated wall. Power spectrum analysis in the frequency domain obtained from the fast Fourier transform analysis indicates that thermal frequency and plate frequency start to deviate from each other at higher values of velocity ratio (>4).     

A comparative study of SiAlON ceramics

Two different varieties of Si₃N₄ powders were used to prepare SiAlON ceramics. 100% β-Si₃N₄ was used from refractory grade powders (B1) and another purer 98% α-Si₃N₄ (50A) powder was used to prepare the SiAlON samples. Since SiC + SiAlON composites reportedly perform better, batches were prepared with 15% SiC addition to the refractory powders (B1) and 17.5% SiC was added to the other SiAlON composition (50A). The samples were gas pressure sintered at 1840 °C and at 22 bar with 1 h dwelling time. Thereby, we could achieve 97–98% theoretical density. The hardness was recorded 14–17 GPa while fracture toughness varied from 4.3 to 5 MPa m^1/2. Fretting experiments showed initial running-in period of 300 cycles for all the tribo-couples. After which, the steady state coefficient of frictions (COF) were achieved. Steel ball of 10 mm diameter, fretting against 50A composition, showed 0.6 average steady state COF while the same composition while fretting against alumina ball of the same diameter, showed 0.57 average steady state COF. Results have been compared with SiAlON composition derived from refractory powder (B1) and found that the 50A composition performs better under identical test conditions. Moreover, cytocompatibility study also suggests that the investigated 50A composition can be used as substrate to support cell adhesion and proliferation of L929 mouse fibroblast cell lines whereas B1 composition derived from refractory powders are toxic in nature.     

Formal probabilistic analysis of a surgical robot control algorithm with different virtual fixtures

Surgical robots are increasingly being used in operation theaters involving normal or laparoscopic surgeries. The working of these surgical robots is highly dependent on their control algorithms, which require very rigorous analysis to ensure their correct functionality due to the safety-critical nature of surgeries. Traditionally, safety of control algorithms is ensured by simulations, but they provide incomplete and approximate analysis results due to their inherent sampling-based nature. We propose to use probabilistic model checking, which is a formal verification method, for quantitative analysis, to verify the control algorithms of surgical robots in this paper. As an illustrative example, the paper provides a formal analysis of a virtual fixture control algorithm, implemented in a neuro-surgical robot, using the PRISM model checker. In particular, we provide a formal discrete-time Markov chain-based model of the given control algorithm and its environment. This formal model is then analyzed for multiple virtual fixtures, like cubic, hexagonal and irregular shapes. This verification allowed us to discover new insights about the considered algorithm that allow us to design safer control algorithms.