Miracle-dz/UniFAR-FTUs huggingface dataset:
From lessons to lectures: NCEA mathematics results and first-year mathematics performance

Given the recent radical overhaul of secondary school qualifications in New Zealand, similar in style to those in the UK, there has been a distinct change in the tertiary entrant profile. In order to gain insight into this new situation that university institutions are faced with, we investigate some of the ways in which these recent changes have impacted upon tertiary level mathematics in New Zealand. To this end, we analyse the relationship between the final secondary school qualifications in Mathematics with calculus of incoming students and their results in the core first-year mathematics papers at Canterbury since 2005, when students entered the University of Canterbury with these new reformed school qualifications for the first time. These findings are used to investigate the suitability of this new qualification as a preparation for tertiary mathematics and to revise and update entrance recommendations for students wishing to succeed in their first-year mathematics study.
Estimation of a Time-Truncated Exponential Parameter Used in Life Testing

Abstract This article proves the asymptotic unbiasedness and consistency when the sample size of the maximum likelihood estimate of the mean θ of an exponential distribution in a time-truncated experiment is random. Convergence of to with μ and σ2 independent of x is established. Asymptotic normality is the same under both the conditional and the unconditional distribution, but our procedure and normalizing constants differ from those in Bartholomew (1963).
Quantitative estimates of the slab and 2-D power in solar wind turbulence using multispacecraft data

[1] A quantitative estimate of the field-aligned anisotropy of magnetohydrodynamic inertial range turbulence is obtained by comparing multispacecraft data with a fully three-dimensional turbulent magnetic field numerical model. The simulated turbulence is a superposition of slab fluctuations parallel to the mean field and 2-D fluctuations perpendicular to it. This model is fitted to spatial autocorrelation functions, computed from measurements made by the four Cluster spacecraft in the solar wind, by varying the slab-2-D fraction. The mean power in the 2-D fluctuations, 81 ± 3%, is consistent with solar wind fluctuations being anisotropic with energy mainly in wave vectors perpendicular to the large-scale mean magnetic field. Eight intervals of multipoint magnetic field data are analyzed, and a large degree of variation in the anisotropy estimates about the mean is observed. The origin of this variability is unclear. However, variations in the anisotropy estimates are correlated between different field components.
A deductive approach to the solution of the problem of optimal pairs trading from the viewpoint of stochastic control with time‐dependent parameters

In a fairly recent paper (2008 American Control Conference, June 11‐13, 1035‐1039), the problem of dealing with trading in optimal pairs was treated from the viewpoint of stochastic control. The analysis of the subsequent nonlinear evolution partial differential equation was based upon a succession of Ansätze, which can lead to a solution of the terminal‐value problem. Through an application of the Lie Theory of Continuous Groups to this equation, we show that the Ansätze are based upon the underlying symmetries of the equation (their (14)). We solve the problem in a more general context by allowing the parameters to be explicitly time dependent. The extension means thatmore realistic problems are amenable to the samemode of solution. Copyright © 2014 JohnWiley & Sons, Ltd.
Numerical continuation methods for nonlinear equations and bifurcation problems

and so we can follow x(t) by applying methods traditionally used for the solution of ordinary differential equations. In Chapter 2 we consider general single-step methods and, in particular, Runge-Kutta methods, for following x(t) . We also give conditions on the methods to attain rapid convergence to x* and, as a result, for a particular choice of H{x, t) we are able to derive methods which have improved rates of convergence to x* . We apply similar arguments in Chapter 3 to the class of linear multistep methods and again generate methods which follow x{t) accurately and then give rapid final convergence to x* .
Analysis of the saturable absorber transmission equation

The distortion of an intense light pulse by a saturable absorber is analysed on the basis of the dynamic transmission equation. The conclusions are in accord with an earlier numerical analysis for a particular pulse function, but are here proved for arbitrary pulse shape. Bounds are derived for maximum transmittance and energy loss, and the existence of stable periodic solutions is demonstrated. The region in which saturable absorption theory is valid is discussed and compared with that for self-induced transparency. The two phenomena are examples of completely incoherent and completely coherent absorption, respectively.
Level of Measurement

The distinctions between nominal, ordinal, interval, and ratio measurement were popularized by S. S. Stevens. Unfortunately, positions taken by Stevens have often been disseminated without criticism. One problem is the common assumption that "ordinal" statistics are the best statistics to use for presumed noninterval continuous social variables, when, in fact, they use addition, subtraction, and division, which make the measurements interval by definition. Additionally, the relationship of the normal distribution to interval measurement is commonly misunderstood, the latter existing by definition if a normal distribution exists. Concern with levels of measurements may mislead persons into attending to issues other than maximizing (utility, given) the particular limits of the state of the measurement art in the social sciences.
Nonsingular Integral Equation for Stability of a Bunched Beam

The linearized Vlasov equation for longitudinal motion of a bunched beam leads to a singular integral equation, the singularity being associated with the tune spectrum of the single-particle motion. A discretization for numerical solution of the equation in this form is not well justified. A simple change of the unknown function gives an equation that can more readily be approximated by a matrix equation. In contrast to the usual approach (Oide-Yokoya) the equation for eigen-frequencies does not have a continuum of solutions corresponding to single-particle frequencies, but only a few solutions corresponding to coherent modes.
Real-time disruption management in a two-stage production and inventory system

This paper presents a general disruption management approach for a two-stage production and inventory control system. A penalty cost for deviations of the new plan from the original plan is incorporated and the concept of a disruption recovery time window is introduced. We define two classes of problems: one with fixed setup epochs and another with flexible setup epochs. With linear or quadratic penalty functions for production/ordering quantity change and fixed setup epochs, the best recovery plan is obtained by solving a quadratic mathematical programming problem. With convex penalty functions for quantity changes and flexible setup epochs, it is shown that the second stage orders have identical order quantities within each production cycle. Therefore, in a lot-for-lot system, the ordering and production quantities for both stages are the same. As a special case, we consider disruption recovery problems with short time windows spanning one or two production cycles. We also discuss solution procedures for both major and minor disruption problems and give an extension for the case of multiple retailers. Throughout the paper managerial insights are presented that indicate how a company should respond to various types of disruptions during its operations.
The Importance of Structure Coefficients in Regression Research

Multiple regression analysis is frequently and increasingly being employed in both experimental and non-experimental research. However, when data include predictor variables that are correlated, either unavoidably or due to conscious design choices, some regression results can become difficult to interpret. The paper presents an actual study to provide a heuristic demonstration that structure coefficients may be helpful in these cases.
A flexible grid embedding technique with application to the Euler equations

An automated grid embedding procedure for solution of flows about complex geometries is described. The physical domain is subdivided into regions that can accommodate easily generated grids. The grids are organized in a hierarchical structure, and communication among grids is accomplished by interpolation of the flow variables at mesh boundaries. Algorithms for locating embedded boundaries, special treatment of the embedded grids, and the data structures required for manipulating the solution data are described. The method is demonstrated by solution of the Euler equations for transonic flow about a supercritical airfoil and a flapped airfoil.
Cross sections for J, m/sub J/. -->. J', m/sub J/' transitions within the 4 /sup 2/P states of potassium induced by collisions with He, Ne, and Kr

We have used selective excitation and monitoring of individual (J,m/sub J/) Zeeman sublevels of the 4 /sup 2/P/sub 1/2/ and 4 /sup 2/P/sub 3/2/ states of K at 22 kG and 131 kG to measure (J,m/sub J/.-->.J', m/sub J/') transition cross sections for K colliding with He, Ne, and Kr at 380 K. The results, translated into irreducible tensor cross sections for depolarization are, in units of 10/sup -16/ cm/sup 2/: /sup 2/P/sub 3/2/; . lambda. /sup 1//sub 3/2/(He) = 97 +- 13; . lambda. /sup 2//sub 3/2/(He) = 130 +- 17; . lambda. /sup 3//sub 3/2/(He) = 99 +- 23 . lambda. /sup 1//sub 3/2/(Ne) = 103 +- 10; . lambda. /sup 2//sub 3/2/(Ne) = 146 +- 14; . lambda. /sup 3//sub 3/2/ (Ne) = 111 +- 14 . lambda. /sup 1//sub 3/2/(Kr) = 270 +- 24; . lambda. /sup 2//sub 3/2/(Kr) = 341 +- 29; . lambda. /sup 3//sub 3/2/(Kr) = 276 +- 30 /sup 2/P/sub 1/2/; . lambda. /sup 1//sub 1/2/(He) = 45 +- 5 . lambda. /sup 1//sub 1/2/(Ne) = 56 +- 6 . lambda. /sup 1//sub 1/2/(Kr) = 81 +- 6. The measured total cross sections for intramultiplet transitions, sigma/sup 0//sub 1/2/(/sup 2/P/sub 1/2/.-->./sup 2/P/sub 3/2/) and sigma/sup 0//sub 3/2/ (/sup 2/P/sub 3/2/.-->. /sup 2/P/sub 1/2/), are, in units of 10/sup -16/ cm/sup 2/: sigma/sup 0//sub 1/2/(He) = 36.5more » +- 9.5; sigma/sup 0//sub 3/2/(He) = 18.7 +- 7 sigma/sup 0//sub 3/2/(Ne) = 5.9 +- 2.6 sigma/sup 0//sub 3/2/(Kr) = 25 +- 7« less
L1448 IRS 2: A HIRES-identified Class 0 Protostar

We present far-infrared and submillimeter images and millimeter-continuum photometry for L1448 IRS 2, a low-luminosity (5.2 L☉), embedded young stellar object discovered by IRAS. New far-infrared maps were produced from the archival IRAS data via high-resolution (HIRES) processing, the name given to the implementation of the maximum correlation method for image construction from the IRAS data streams. The HIRES-processed images of L1448 IRS 2 presented here have effective resolutions of ~35″ × 28″, ~35″ × 37″, and ~45″ × 40″ at 25, 60, and 100 μm, respectively, which represent an order of magnitude improvement over previously available far-infrared maps. L1448 IRS 2 was mapped at 450 and 850 μm, and we acquired continuum photometry at 1.3 mm. With these new data, we plot the most complete spectral energy distribution for L1448 IRS 2 to date. We also present sensitive 12CO J=1→0 emission-line maps of a 47′ × 7′ area of the L1448 dark cloud, centered on L1448 IRS 2, obtained with the on-the-fly imaging capability of the NRAO 12 m telescope. As a direct consequence of this mapping, we have discovered a parsec-scale molecular outflow associated with L1448 IRS 2. The combined continuum and molecular line data confirm the classification of L1448 IRS 2 as a new member of the rare, short-lived (a few × 104 yr), Class 0 phase of protostellar evolution. The use of HIRES imaging of IRAS data as a promising tool for identifying protostellar candidates is demonstrated by the example of L1448 IRS 2.
Collisional He ? He*(n) chemi-ionization and dielectronic He ? He+ ? e and He2+ ? e recombination: Differential and total reaction rate coefficients

From the semi-classical theory, the differential and total rate coefficients of collisional He – He*(n) chemi-ionization and dielectronic He – He+ – e and He2+ – e recombination, are determined in this paper. With the help of the calculated differential rate coefficient, the emitted/absorbed electron energy distributions were considered. The calculations were carried out in the case of non-equilibrium helium plasma with atomic temperature Ta and electronic temperature Te, within the ranges 500 K ≤ Ta ≤ 10 000 K and 2000 K ≤ Te ≤ 40 000 K, with the principal quantum number 3 ≤ n ≤ 10. We have determined here, as well, the conditions under which the considered processes are important for the kinetics of weakly ionized helium plasma.
Iterative Sequences for Asymptotically Quasi-nonexpansive Mappings

Let E be a real Banach space and T a self-mapping in E. T is called . asymptotically quasi-nonexpansive if there exists u 0, , lim n n n Ž . Ž . u 0, such that T x p 1 u x p , x E, p F T n n Ž Ž . F T denotes the set of fixed points . n n Ž . T is called asymptotically nonexpansive if T x T y 1 u x n y , x, y E. T is called quasi-nonexpansive if Tx p x p , x Ž . E, p F T . T is called nonexpansive if Tx Ty x y , x, y E. Ž . From the above definitions, it follows that if F T is nonempty, a nonexpansive mapping must be quasi-nonexpansive, and an asymptotically nonexpansive mapping must be asymptotically quasi-nonexpansive. But the converse does not hold. Petryshyn and Williamson 1 , in 1973, proved a sufficient and necessary condition for Mann iterative sequences to converge to fixed points for quasi-nonexpansive mappings. In 1997, Ghosh and Debnath 2 extended the results of 1 and gave the sufficient and necessary condition for Ishikawa iterative sequences to converge to fixed points for quasi-nonexpansive mappings. Using these, they have also obtained some sufficient conditions for Ishikawa iterative sequences converge to fixed points for nonexpansive mappings. In this manuscript, we will extend the above results to asymptotically quasi-nonexpansive mappings and will prove some sufficiency and necessary conditions for Ishikawa iterative sequences of asymptotically quasi-nonexpansive mappings to converge to fixed points; i.e., we will prove the following theorems.
Inverse problems in ion channel modelling

This paper reviews several inverse problems related to biological ion channels and polymer nanopores. Different problems arise at different scales and thus lead to different inversion tasks, which can be modelled as parameter identification in systems of partial differential equations, ordinary differential equations, or as the solution of integral equations. Due to the high potential for future developments, we will not only discuss the previous results and approaches, but in particular highlight a variety of open issues and unsolved inverse problems, as well as biological questions that could be modeled as inverse problems and might lead to interesting future developments.
Dynamic Stability of a Sandwich Beam with Magnetorheological Core #

Abstract This study investigated the dynamic stability of a simply supported sandwich beam with a magnetorheological core under an axial harmonic and parametric load. The complex modulus of the magnetorheological material is a function of the applied magnetic field. The governing equation of motion is theoretically derived using the Mead and Markus sandwich beam model, and also by applying Galerkin's method to simplify the governing equation of motion into a complex Mathieu equation with the coefficient function of the external magnetic field. The natural frequency and structural loss factor of the sandwich beam function of the applied magnetic field are conveniently computed from these coefficients. The influence of the magnetic field strength on the natural frequency and loss factor is also studied. Moreover, the boundaries of dynamic stability are analytically determined by applying the complex incremental harmonic balance (CIHB) method. Finally, the effects of the magnetic field strength, core thickness ratio, beam width, beam length, and static load parameter factor on the instability regions are also investigated. #Communicated by I. Elishakoff.
Large-area traveling-wave LT-GaAs photomixers for LO application

A new type of geometry for terahertz traveling-wave photomixers, vertically pumped free-space by two detuned continuous-wave diode lasers, is proposed and experimentally verified for devices based on low-temperature-grown GaAs (LT-GaAs). It combines the advantages of conventional interdigitated small area structures and traveling-wave devices. An output power of 1 μW at the mixing frequency of 1 THz was measured as a first result, which meets power requirements for superconducting heterodyne mixer devices.
Nonlinear Filtering and Control of a Switching Diffusion with Small Observation Noise

This paper is concerned with nonlinear filtering and control of a switching diffusion coupled by an unknown Markov chain. Two statistical estimation methods are used to track the unknown Markov chain. Computable approximate filters are obtained based on these methods. The filters are then used to construct controls for the partially observed system. These controls are shown to be asymptotically optimal as the observation noise tends to zero. Finally an example is considered and numerical experiments are reported.
A preliminary evaluation of robustness to noise using the compositional hierarchical model for music information retrieval

This paper presents a preliminary evaluation of a compositional hierarchical model for music information retrieval in terms of its robustness to noise. The model has been previously introduced and evaluated for automated chord estimation and multiple fundamental estimation tasks. The model claims to provide mechanisms aiding the model to perform well on noisy data. We evaluated the model’s robustness to noise by performing a set of tests by adding the white and pink noise to the audio data and reevaluating the model for the automated chord estimation (ACE) task. The paper describes the experiment and shows the model’s ability of producing relevant features in suboptimal conditions, resulting in a graceful degradation of the classification accuracy for the ACE task.
Continuous avalanche mixing of granular solids in a rotating drum

We consider the avalanche mixing of a monodisperse collection of granular solids in a slowly rotating drum. This process has been studied for the case where the drum rotates slowly enough that each avalanche ceases completely before a new one begins (Metcalfe G., Shinbrot T., McCarthy J. J. and Ottino J. M., Nature, 374 (1995) 39). We developa mathematical model for the mixing both in this discrete avalanche case and in the more useful case where the drum is rotated quickly enough to induce a continuous avalanche in the material but slowly enough to avoid significant inertial effects. When applied to the discrete case, our model yields results which are consistent with those obtained experimentally by Metcalfe et al.
Picture processing analysis of the optical structure of NGC 5128 /Centaurus A/

The spatial luminosity and color structure of the peculiar elliptical radio galaxy NGC 5128 are studied using photoelectrically calibrated photometry from plates taken with the CTIO 4-m telescope under conditions of excellent seeing (approx.1 arcsec). Using picture processing systems at KPNO and at the NASA Johnson Space Center, 10/sup 6/-pixel maps were constructed of the UBV surface brightness and of the color indices: U-B, B-V, and Q= (U-B)-0.72(B-V) over a 15.5 x 15.5-arcmin region centered on the nucleus of NGC 5128. The color maps reveal the existence of a young stellar population situated in a disk within the elliptical component of NGC 5128 that was previously masked by the absorption ''lane'' across the galaxy. The projection of the disk in the plane of the sky, as defined by OB stars and HII regions, is an ellipse with the major axis in PA=122/sup 0/ +- 4/sup 0/. If circular, the inclination of the plane of the disk in the sky is i=72/sup 0/ +- 3/sup 0/. At an assumed distance of 6 Mpc for NGC 5128, the diameter of the disk is approx.13 kpc. Vigorous star formation is occurring, mostly in elongated structures throughout the disk, with the greatest activity alongmore » most of its outer perimeter, where apparently the largest amounts of dust are present. The ages of blue associations in the disk vary from approx.2 x 10/sup 6/ to approx.4 x 10/sup 7/ yr, with most in the range (1--3) x 10/sup 7/ yr. The luminosity distribution of the elliptical component of NGC 5128 follows de Vaucouleurs's law over the range 20< or approx. =sigma/sub B/< or approx. =25 mag arcsec/sup -2/ in a manner that is similar to normal E2 galaxies. Optical emission above that expected from the elliptical population was marginally detected in the inner northeast and southwest radio lobes. The maximim B surface brightness of this emission was sigma/sub B/=25.1 mag arcsec/sup -2/ in the strongest regions of the northeast radio lobe. This emission may be an optical counterpart of synchrotron emission in the radio lobes. « less
A burst of energetic O+ ions during an upstream particle event

During an extended energetic particle event upstream of the earth's bow shock on September 5, 1984, a brief burst of energetic O/sup +/ ions have been observed using the time-of-flight spectrometer SULEICA on the AMPTE/IRM spacecraft. The event occurred during very active geomagnetic conditions. The onset of the O/sup +/ event coincides with a brief electron burst. O/sup +/ is predominantly streaming into the sunward direction, while the H/sup +/ and He/sup 2 +/ ions exhibit a net flow toward the bow shock with a second order anisotropy perpendicular to the interplanetary magnetic field (which was almost radial throughout the whole event). The energy spectrum of O/sup +/ is significantly harder than those of H/sup +/, He/sup 2 +/ and CNO (Q>2). The observations of two particle populations, different in temporal evolution, anisotropies and energy spectra, are discussed in terms of bow shock accelerated ions over the entire time period accompanied by a brief injection of magnetospheric particles.