DSpace Community:https://dspace.lboro.ac.uk/2134/802016-07-27T17:25:32Z2016-07-27T17:25:32ZAsymmetry in student achievement on multiple-choice and constructed-response items in reversible mathematics processesSangwin, Christopher J.Jones, Ianhttps://dspace.lboro.ac.uk/2134/221202016-07-26T15:12:36Z2016-01-01T00:00:00ZTitle: Asymmetry in student achievement on multiple-choice and constructed-response items in reversible mathematics processes
Authors: Sangwin, Christopher J.; Jones, Ian
Abstract: In this paper we report the results of an experiment designed to test
the hypothesis that when faced with a question involving the inverse direction
of a reversible mathematical process, students solve a multiple-choice version by
verifying the answers presented to them by the direct method, not by undertaking
the actual inverse calculation. Participants responded to an online test contain-
ing equivalent multiple-choice and constructed-response items in two reversible
algebraic techniques: factor/expand and solve/verify. The ndings supported this
hypothesis: Overall scores were higher in the multiple-choice condition compared
to the constructed-response condition, but this advantage was significantly greater
for items concerning the inverse direction of reversible processes compared to those
involving direct processes.
Description: This paper is embargoed until 12 months after publication.2016-01-01T00:00:00ZThe use of differential equations in optimizationZghier, Abbas K.https://dspace.lboro.ac.uk/2134/220892016-07-25T12:43:39Z1981-01-01T00:00:00ZTitle: The use of differential equations in optimization
Authors: Zghier, Abbas K.
Abstract: A new approach for unconstrained optimization of a function f(x)
has been investigated. The method is based on solving the differential
equation dx/dt = ± ∇f(x) which defines orthogonal trajectories in Rⁿ-space.
A number of numerical integration techniques have been used for solving
the above differential equation, the most powerful one which gives rise to
a very efficient optimization algorithm is the generalization of the
Trapezoidal rule. The interaction between the parameters which appear
as a result of using the numerical integration has been investigated.
In the above approach factorization of the positive definite matrix
(θG + λI), allowing some control over the diagonal elements of the matrix.
is presented.
A Liapunov function approach has been used in constructing a number
of different differential equations of the above form. It is well known
that if a Liapunov function which satisfies certain conditions can be
found for a given system of differential equations then the origin of
the system is stable. Pursuing this idea further we constructed a Liapunov
function and then the corresponding differential equation. Application
of this differential equation to the problem of finding a minimum of a
function f is shown to yield a vector that converges to a point where
∇f = 0.
The use of differential equations is also extended to the optimal
control problem. The technique is only applicable to unconstrained optimal
control problems. If a terminal condition and inequality constraints are
presented, the problem should be converted to unconstrained form, e.g. by
the use of penalty functions. The method tends to converge, even from a
poor approximation point to the minimum without using line searches.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.1981-01-01T00:00:00ZHigh performance gel permeation chromatography with silica microspheresYeadon, Grahamhttps://dspace.lboro.ac.uk/2134/220872016-07-25T11:48:07Z1981-01-01T00:00:00ZTitle: High performance gel permeation chromatography with silica microspheres
Authors: Yeadon, Graham
Abstract: An instrument for high performance gel permeation chromatography
(HPGPC) has been assembled with equipment designed for
high performance liquid chromatography separations. The pump was
a syringe-type giving uniform pulseless flow from 0.05 to 6.0 cm3
min-1 at pressures up to 3000 p.s.i.. Low dead-volume septum and
septumless injection heads have been used for single columns and
multiple column sets. Two ultraviolet detectors and a refractometer having low cell volumes were used to detect the low weights
of solute which were separated.
Narrow distribution silica gels of varying particle size and
porosity, as supplied by A.E.R.E. Harwell, have been packed into
columns. Efficiencies of permeating and non-permeating polystyrenes
determined with this HPGPC instrument gave an assessment
of chromatogram broadening due to mass transfer as a function of
eluent flow rate and polystyrene molecular weight. The results
show that fast separations can be obtained in several minutes and
that the most precise measurements of polydispersity are accomplished at very slow rates. A further assessment of chromatogram
broadening was made by deactivating the surface of the silica
particles with a hydrophilic bonded phase and examining the column
efficiency and polydispersity of proteins in aqueous buffer.
Results show that even after surface modification the composition
of the aqueous eluent used must be adjusted, e.g. by careful
selection of pH and ionic strength, to minimize interactions.
When interactions occur, they can be explained in terms of a
thermodynamic representation of a mixed mechanism. A comparison
of retention data for proteins, which do not participate in
interaction effects with the stationary phase, dextrans, which are
considered as "non-ionic" macromolecules, and polystyrenes suggest
that solute diameter is a reasonable universal size parameter for
the representation of macromolecules separating by a steric
exclusion mechanism operating close to equilibrium conditions.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.1981-01-01T00:00:00ZRing opening/cyclisation in oxiranyl carbinyl free radicalsZaidi, Naveed A.https://dspace.lboro.ac.uk/2134/220832016-07-25T10:09:11Z1991-01-01T00:00:00ZTitle: Ring opening/cyclisation in oxiranyl carbinyl free radicals
Authors: Zaidi, Naveed A.
Abstract: A study aimed to examine the electronic and possible stereoelectronic factors controlling the opening of
the epoxide C-O versus C-C bond in 4<. ,5-epoxy-5<' -cholestan-3-yl-radicals. formed by photolysis of
3B -acetoxy-4<' ,5-epoxy-5<' -cholestanes in HMPAlH20 and by BU3SnH reduction of 4<. ,5-epoxy-
3B -[jmidazol-l-yl(thiocarbonyJ)oxyl-5<' -cholestanes. These derived radicals gave cholest-3-en-5B -01
via the cholest-3-en-5<' -oxy-radicals and reversible cleavage of the C5- CIO bond. The 4<. ,5-epoxy-
5<' -cholestan-6-yl-radicals, formed by photolysis of 6a -acetoxy-4<' ,5-epoxy-5E. -cholestanes in
HMPA/H20, and by BU3SnH reduction of 4E. ,5-epoxy-6a -[jmidazol-l-yl(thiocarbonyJ)oxyl-5E. -
cholestanes gave the cholest-5-en-4E. -oxy-radicals, which were reduced to give the cholest-
5-en-4E. -ols.
In the study of bicycloI2.2.llheptane systems, the reduction with BU3SnH of eOO0-2-[jmidazol-l-yl(
thiocarbonyJ)oxyl-anti-3 '-phenylbicycloI2.2.1 Iheptan-3-spiro-2 '-oxiranes and the ant;-3 '-p-chlorophenyl
and 3'-methylene analogues failed to generate a radical at C-2 irrespective of the stereochemistry
(exo- or eOOo-) of the epoxides. Unexpected products were derived from the reduction of the thioester
group to methoxy and acetal groups; the epnxide groups remained unaltered. This novel reduction has
not been observed before.
The photolysis in HMPA/H20 of end0-2-acetoxy-anti-3 '-phenylbicycloI2.2.llheptan-3-spiro-
2' -oxiranes and the anti-3' -p-chlorophenyl and 3' -methylene analogues failed to generate a radical at
C-2 irrespective of the stereochemistry (exo- or endo-) of the epoxides; but instead gave cleavage of the
C-O bonds of the aryl epnxides which stereoselectively gave the eOO0-2-acetoxy-4f. -phenylbicyclo-
13.2.J1octan-3-ones. The methylene epoxides were obtained unchanged after photolysis, in low yield.
The reaction between BU3SnH and the ex0-2-bromo-anti-3 '-phenylbicycloI2.2.J1heptan-3-spiro-
2' -oxiranes and the anti-3' -p-chlorophenyl analogue (exo- and endo-epoxides) generated a radical at
C-2 and the products, norcamphor, benzyl alcohol and p-chlorobenzyl alcohol, were derived exclusively
from C-C bond cleavage.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.1991-01-01T00:00:00Z