316,798 research outputs found
Understanding the World Wool Market: Trade, Productivity and Grower Incomes. Part 2: The Toolbox
This is Chapter 2 of my PhD thesis Understanding the World Wool Market: Trade, Productivity and Grower Incomes, UWA, 2006. In this chapter we present the tools used to construct the theoretical structure of the model presented in Chapter 3. The theory of the model is highly nonlinear but is specified in linearised form. In deriving the linearised form of the nonlinear functions, we make explicit the optimising behaviour that underlies the tools and their properties. We use the notational convention of expressing the levels form of a variable in capital letters and the percentage-change equivalent in lower case letters. We also discuss how the tools can be combined by assuming separability between functions.In this chapter we present the tools used to construct the theoretical structure of the model presented in Chapter 3. The theory of the model is highly nonlinear but is specified in linearised form. In deriving the linearised form of the nonlinear functions, we make explicit the optimising behaviour that underlies the tools and their properties. We use the notational convention of expressing the levels form of a variable in capital letters and the percentage-change equivalent in lower case letters. We also discuss how the tools can be combined by assuming separability between functions.
A Note on Cyclic Codes from APN Functions
Cyclic codes, as linear block error-correcting codes in coding theory, play a
vital role and have wide applications. Ding in \cite{D} constructed a number of
classes of cyclic codes from almost perfect nonlinear (APN) functions and
planar functions over finite fields and presented ten open problems on cyclic
codes from highly nonlinear functions. In this paper, we consider two open
problems involving the inverse APN functions and the Dobbertin
APN function . From the calculation of
linear spans and the minimal polynomials of two sequences generated by these
two classes of APN functions, the dimensions of the corresponding cyclic codes
are determined and lower bounds on the minimum weight of these cyclic codes are
presented. Actually, we present a framework for the minimal polynomial and
linear span of the sequence defined by ,
where is a primitive element in . These techniques can also be
applied into other open problems in \cite{D}
The ultrarelativistic Reissner-Nordstrom field in the Colombeau algebra
The electromagnetic field of the ultrarelativistic Reissner-Nordstrom
solution shows the physically highly unsatisfactory property of a vanishing
field tensor but a nonzero, i.e., delta-like, energy density. The aim of this
work is to analyze this situation from a mathematical point of view, using the
framework of Colombeau's theory of nonlinear generalized functions. It is shown
that the physically unsatisfactory situation is mathematically perfectly
defined and that one cannot aviod such situations when dealing with
distributional valued field tensors.Comment: final version, minor grammatical change
Testing for Smooth Transition Nonlinearity in Adjustments of Cointegrating Systems
This paper studies testing for the presence of smooth transition nonlinearity in adjustment parameters of the vector error correction model. We specify the generalized model with multiple cointegrating vectors and different transition functions across equations. Given that the nonlinear model is highly complex, this paper proposes an optimal LM test based only on estimation of the linear model. The null asymptotic distribution is derived using empirical process theory and since the transition parameters of the model cannot be identified under the null hypothesis bootstrap procedures are used to approximate the limit. Monte Carlo simulations indicate a good performance of the test.Nonlinearity ; Cointegration ; Empirical process theory ; Bootstrap
Using the Zeldovich dynamics to test expansion schemes
We apply various expansion schemes that may be used to study gravitational
clustering to the simple case of the Zeldovich dynamics. Using the well-known
exact solution of the Zeldovich dynamics we can compare the predictions of
these various perturbative methods with the exact nonlinear result and study
their convergence properties. We find that most systematic expansions fail to
recover the decay of the response function in the highly nonlinear regime.
``Linear methods'' lead to increasingly fast growth in the nonlinear regime for
higher orders, except for Pade approximants that give a bounded response at any
order. ``Nonlinear methods'' manage to obtain some damping at one-loop order
but they fail at higher orders. Although it recovers the exact Gaussian
damping, a resummation in the high-k limit is not justified very well as the
generation of nonlinear power does not originate from a finite range of
wavenumbers (hence there is no simple separation of scales). No method is able
to recover the relaxation of the matter power spectrum on highly nonlinear
scales. It is possible to impose a Gaussian cutoff in a somewhat ad-hoc fashion
to reproduce the behavior of the exact two-point functions for two different
times. However, this cutoff is not directly related to the clustering of matter
and disappears in exact equal-time statistics such as the matter power
spectrum. On a quantitative level, the usual perturbation theory, and the
nonlinear scheme to which one adds an ansatz for the response function with
such a Gaussian cutoff, are the two most efficient methods. These results
should hold for the gravitational dynamics as well (this has been checked at
one-loop order), since the structure of the equations of motion is identical
for both dynamics.Comment: 29 pages, published in A&
Linear Codes from Some 2-Designs
A classical method of constructing a linear code over \gf(q) with a
-design is to use the incidence matrix of the -design as a generator
matrix over \gf(q) of the code. This approach has been extensively
investigated in the literature. In this paper, a different method of
constructing linear codes using specific classes of -designs is studied, and
linear codes with a few weights are obtained from almost difference sets,
difference sets, and a type of -designs associated to semibent functions.
Two families of the codes obtained in this paper are optimal. The linear codes
presented in this paper have applications in secret sharing and authentication
schemes, in addition to their applications in consumer electronics,
communication and data storage systems. A coding-theory approach to the
characterisation of highly nonlinear Boolean functions is presented
Two-Dimensional Fluctuating Vesicles in Linear Shear Flow
The stochastic motion of a two-dimensional vesicle in linear shear flow is
studied at finite temperature. In the limit of small deformations from a
circle, Langevin-type equations of motion are derived, which are highly
nonlinear due to the constraint of constant perimeter length. These equations
are solved in the low temperature limit and using a mean field approach, in
which the length constraint is satisfied only on average. The constraint
imposes non-trivial correlations between the lowest deformation modes at low
temperature. We also simulate a vesicle in a hydrodynamic solvent by using the
multi-particle collision dynamics technique, both in the quasi-circular regime
and for larger deformations, and compare the stationary deformation correlation
functions and the time autocorrelation functions with theoretical predictions.
Good agreement between theory and simulations is obtained.Comment: 13 pages, 7 figure
- …