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Displaying Results 226 - 250 of 808 on page 10 of 33
Marked
Mark
Simultaneous Diophantine approximation on the circle and Hausdorff dimension
(2001)
Dickinson, H.; Dodson, M. M.
Simultaneous Diophantine approximation on the circle and Hausdorff dimension
(2001)
Dickinson, H.; Dodson, M. M.
Abstract:
The functional relations between the coordinates of points on a manifold make the study of Diophantine approximation on manifolds much harder than the classical theory in which the variables are independent. Nevertheless there has been considerable progress in the metric theory of Diophantine approximation on smooth manifolds. To describe this, some notation and terminology are needed.
http://eprints.nuim.ie/1532/
Marked
Mark
Perturbations of vector fields on tori: resonant normal forms and Diophantine phenomena
(2002)
Dickinson, Detta; Gramchev, Todor; Yoshino, Masafumi
Perturbations of vector fields on tori: resonant normal forms and Diophantine phenomena
(2002)
Dickinson, Detta; Gramchev, Todor; Yoshino, Masafumi
Abstract:
This paper concerns perturbations of smooth vector fields on Tn (constant if n ≥ 3) with zeroth-order C∞ and Gevrey Gσ, σ ≥ 1, pseudodifferential operators. Simultaneous resonance is introduced and simultaneous resonant normal forms are exhibited (via conjugation with an elliptic pseudodifferential operator) under optimal simultaneous Diophantine conditions outside the resonances. In the C∞ category the results are complete, while in the Gevrey category the effect of the loss of the Gevrey regularity of the conjugating operators due to Diophantine conditions is encountered. The normal forms are used to study global hypoellipticity in C∞ and Gevrey Gσ. Finally, the exceptional sets associated with the simultaneous Diophantine conditions are studied. A generalized Hausdorff dimension is used to give precise estimates of the ‘size’ of different exceptional sets, including some inhomogeneous examples.
http://eprints.nuim.ie/1518/
Marked
Mark
Logarithmic asymptotics for a single-server processing distinguishable sources
(2008)
Duffy, Ken R.; Malone, David
Logarithmic asymptotics for a single-server processing distinguishable sources
(2008)
Duffy, Ken R.; Malone, David
Abstract:
We consider a single-server first-in-first-out queue fed by a finite number of distinct sources of jobs. For a large class of short-range dependent and light-tailed distributed job processes, using functional large deviation techniques we prove a large deviation principle and logarithmic asymptotics for the joint waiting time and queue lengths distribution.We identify the paths that are most likely to lead to the rare events of large waiting times and long queue lengths. A number of examples are presented to illustrate salient features of the results.
http://eprints.nuim.ie/1513/
Marked
Mark
L2(R) solutions of dilation equations and Fourier-like transforms
(2002)
Malone, David
L2(R) solutions of dilation equations and Fourier-like transforms
(2002)
Malone, David
Abstract:
We state a novel construction of theFourier transform on L2(R) based on translation and dilation properties which makes use of the multiresolution analysis structure commonly used in the design of wavelets. We examine the conditions imposed by variants of these translation and dilation properties. This allows other characterizations of the Fourier transform to be given, and operators which have similar properties are classified. This is achieved by examining the solution space of various dilation equations, in particular we show that the L2(R) solutions of f (x) = f (2x) + f (2x − 1) are in direct correspondence with L2(±[1, 2)).
http://eprints.nuim.ie/1512/
Marked
Mark
An unusual construction of the Fourier transform
(1999)
Malone, David
An unusual construction of the Fourier transform
(1999)
Malone, David
Abstract:
This article presents an unusual construction of the Fourier transform using its translation and dilation properties.
http://eprints.nuim.ie/1511/
Marked
Mark
Switching Stability of Automotive Roll Dynamics Subject to Interval Uncertainty
(2008)
Solmaz, Selim; Shorten, Robert; Mason, Oliver
Switching Stability of Automotive Roll Dynamics Subject to Interval Uncertainty
(2008)
Solmaz, Selim; Shorten, Robert; Mason, Oliver
Abstract:
In this paper we apply some recent results on the stability of switched systems with interval uncertainty for analyzing the roll stability of automotive vehicles subject to bounded parametric uncertainties and switching. The application is motivated by the fact that the roll dynamics of an automotive vehicle is affected in a significant and a nonlinear fashion due to possible sudden switches in the vehicle’s center of gravity (CG) height, as well as the uncertainty in the suspension parameters. Utilizing a recent stability result, it is possible to model such parametric variations as bounded interval uncertainties for this problem, and obtain easily verifiable conditions for analyzing the stability of the resulting switched/uncertain system.
http://eprints.nuim.ie/1264/
Marked
Mark
Cartan Invariants and Central Ideals of Group Algebras
(2006)
Murray, John; Breuer, Thomas; Hethelyi, Laszlo; Horvath, Erzsebet; Kulshammer, Burkhard
Cartan Invariants and Central Ideals of Group Algebras
(2006)
Murray, John; Breuer, Thomas; Hethelyi, Laszlo; Horvath, Erzsebet; Kulshammer, Burkhard
Abstract:
Abstract. In this paper we investigate general properties of Cartan invariants of a finite group G in characteristic 2. One of our results shows that the Cartan matrix of G in characteristic 2 contains an odd diagonal entry if and only if G contains a real element of 2-defect zero. We also apply these results to 2-blocks of symmetric groups and to blocks with normal or abelian defect groups. The second part of the paper deals with annihilators of certain ideals in centers of group algebras and blocks.
http://eprints.nuim.ie/971/
Marked
Mark
Projective modules and involutions
(2006)
Murray, John
Projective modules and involutions
(2006)
Murray, John
Abstract:
Let $G$ be a finite group, and let $\Omega:=\{t\in G\mid t^2=1\}$. Then $\Omega$ is a $G$-set under conjugation. Let $k$ be an algebraically closed field of characteristic $2$. It is shown that each projective indecomposable summand of the $G$-permutation module $k\Omega$ is irreducible and self-dual, whence it belongs to a real $2$-block of defect zero. This, together with the fact that each irreducible $kG$-module that belongs to a real $2$-block of defect zero occurs with multiplicity $1$ as a direct summand of $k\Omega$, establishes a bijection between the projective components of $k\Omega$ and the real $2$-blocks of $G$ of defect zero.
http://eprints.nuim.ie/246/
Marked
Mark
A Fuzzy Three Sphere and Fuzzy Tori
(2003)
Dolan, Dr Brian P; O'Connor, Prof Denjoe
A Fuzzy Three Sphere and Fuzzy Tori
(2003)
Dolan, Dr Brian P; O'Connor, Prof Denjoe
Abstract:
A fuzzy circle and a fuzzy 3-sphere are constructed as subspaces of fuzzy complex projective spaces, of complex dimension one and three, by modifying the Laplacians on the latter so as to give unwanted states large eigenvalues. This leaves only states corresponding to fuzzy spheres in the low energy spectrum (this allows the commutative algebra of functions on the continuous sphere to be approximated to any required degree of accuracy). The construction of a fuzzy circle opens the way to fuzzy tori of any dimension, thus circumventing the problem of power law corrections in possible numerical simulations on these spaces.
http://eprints.nuim.ie/254/
Marked
Mark
Minimal Surfaces from Monopoles
(2002)
Small, Anthony
Minimal Surfaces from Monopoles
(2002)
Small, Anthony
Abstract:
The geometry of minimal surfaces generated by charge 2 Bogomolny monopoles on 3-dimensional Euclidean space is described in terms of the moduli parameter k. We find that the distribution of Gaussian curvature on the surface reflects the monopole structure. This elucidated by the behaviour of the Gauss maps of the minimal surfaces.
http://eprints.nuim.ie/716/
Marked
Mark
Conical limit sets and continued fractions
(2007)
Short, Dr. Ian; Crane, Dr. Edward
Conical limit sets and continued fractions
(2007)
Short, Dr. Ian; Crane, Dr. Edward
Abstract:
Inspired by questions of convergence in continued fraction theory, Erdos, Piranian and Thron studied the possible sets of divergence for arbitrary sequences of Moebius maps acting on the Riemann sphere, S^2. By identifying S^2 with the boundary of three-dimensional hyperbolic space, H^3, we show that these sets of divergence are precisely the sets that arise as conical limit sets of subsets of H^3. Using hyperbolic geometry, we give simple geometric proofs of the theorems of Erdos, Piranian and Thron that generalise to arbitrary dimensions. New results are also obtained about the class of conical limit sets, for example, that it is closed under locally quasisymmetric homeomorphisms. Applications are given to continued fractions.
http://eprints.nuim.ie/721/
Marked
Mark
William Rowan Hamilton (1805-1865): Ireland's greatest mathematician
(2000)
O'Cairbre, Fiacre
William Rowan Hamilton (1805-1865): Ireland's greatest mathematician
(2000)
O'Cairbre, Fiacre
Abstract:
This paper looks at the life and works of Ireland's greatest mathematician, William Rowan Hamilton (1805-1865)
http://eprints.nuim.ie/769/
Marked
Mark
On the Kalman-Yakubovich-Popov lemma and common Lyapunov solutions for matrices with regular inertia
(2007)
Mason, Oliver; Shorten, Robert; Solmaz, Selim
On the Kalman-Yakubovich-Popov lemma and common Lyapunov solutions for matrices with regular inertia
(2007)
Mason, Oliver; Shorten, Robert; Solmaz, Selim
Abstract:
In this paper we extend the classical Lefschetz version of the Kalman-Yacubovich-Popov (KYP) lemma to the case of matrices with general regular inertia. We then use this result to derive an easily verifiable spectral condition for a pair of matrices with the same regular inertia to have a common Lyapunov solution (CLS), extending a recent result on CLS existence for pairs of Hurwitz matrices.
http://eprints.nuim.ie/885/
Marked
Mark
A global attractivity result for a class of switching discrete-time systems
(2007)
Solmaz, Selim; Shorten, Robert; O'Cairbre, Fiacre
A global attractivity result for a class of switching discrete-time systems
(2007)
Solmaz, Selim; Shorten, Robert; O'Cairbre, Fiacre
Abstract:
In this paper we present the global attractivity properties of a class of discrete-time switching systems of the form x(k+1)=Aix(k), Ai A , {A1, ...,Am}, where each constituent matrices Ai Rnn are Schur stable. We show that for a special subset of such switching systems the origin is globally attractive, and it is possible to prove this without requiring the existence of a common quadratic Lyapunov function (CQLF).
http://eprints.nuim.ie/888/
Marked
Mark
A Design Methodology for Switched Discrete Time Linear Systems with Applications to Automotive Roll Dynamics Control
(2008)
Solmaz, Selim; Shorten, Robert; Wulff, Kai; O'Cairbre, Fiacre
A Design Methodology for Switched Discrete Time Linear Systems with Applications to Automotive Roll Dynamics Control
(2008)
Solmaz, Selim; Shorten, Robert; Wulff, Kai; O'Cairbre, Fiacre
Abstract:
In this paper we consider the asymptotic stability of a class of discrete-time switching linear systems, where each of the constituent subsystems is Schur stable. We first present an example to motivate our study, which illustrates that the bilinear transform does not preserve the stability of a class of switched linear systems. Consequently, continuous time stability results cannot be transformed to discrete time analogs using this transformation. We then present a subclass of discrete-time switching systems, that arise frequently in practical applications. We prove that global attractivity for this subclass can be obtained without requiring the existence of a common quadratic Lyapunov function (CQLF). Using this result we present a synthesis procedure to construct switching stabilizing controllers for an automotive control problem, which is related to the stabilization of a vehicle's roll dynamics subject to switches in the center of gravity (CG) height.
http://eprints.nuim.ie/892/
Marked
Mark
On linear co-positive Lyapunov functions for sets of linear positive systems.
(2009)
Knorn, Florian ; Mason, Oliver; Shorten, Robert
On linear co-positive Lyapunov functions for sets of linear positive systems.
(2009)
Knorn, Florian ; Mason, Oliver; Shorten, Robert
Abstract:
In this paper we derive necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for a finite set of linear positive systems. Both the state dependent and arbitrary switching cases are considered. Our results reveal an interesting characterisation of "linear" stability for the arbitrary switching case; namely, the existence of such a linear Lyapunov function can be related to the requirement that a number of extreme systems are Metzler and Hurwitz stable. Examples are given to illustrate the implications of our results.
http://eprints.nuim.ie/1644/
Marked
Mark
Determining the expected variability of immune responses using the Cyton Model
(2008)
Subramanian, Vijay G.; Duffy, Ken R.; Turner, Marian L.; Hodgkin, Philip D.
Determining the expected variability of immune responses using the Cyton Model
(2008)
Subramanian, Vijay G.; Duffy, Ken R.; Turner, Marian L.; Hodgkin, Philip D.
Abstract:
During an adaptive immune response, lymphocytes proliferate for ve to twenty cell divisions, then stop and die over a period of weeks. The cyton model for regulation of lymphocyte proliferation and survival was introduced by Hawkins et al. [17] to provide a framework for understanding this response and its regulation. The model assumes stochastic values for division and survival times for each cell in a responding population. Experimental evidence indicates that the choice of times is drawn from a skewed distribution such as the lognormal, with the fate of individual cells being potentially highly variable. For this reason we calculate the higher moments of the model so that the expected variability can be determined. To do this we formulate a new analytic framework for the cyton model by introducing a generalization to the Bellman-Harris branching process.
http://eprints.nuim.ie/1645/
Marked
Mark
Applications of Linear Co-positive Lyapunov Functions for Switched Linear Positive Systems
(2009)
Knorn, Florian ; Mason, Oliver; Shorten, Robert
Applications of Linear Co-positive Lyapunov Functions for Switched Linear Positive Systems
(2009)
Knorn, Florian ; Mason, Oliver; Shorten, Robert
Abstract:
In this paper we review necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for switched linear positive systems. Both the state dependent and arbitrary switching cases are considered and a number of applications are presented.
http://eprints.nuim.ie/1649/
Marked
Mark
On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics
(2009)
Duffy, Ken R.; Subramanian, Vijay G.
On the impact of correlation between collaterally consanguineous cells on lymphocyte population dynamics
(2009)
Duffy, Ken R.; Subramanian, Vijay G.
Abstract:
During an adaptive immune response, lymphocytes proliferate for five to twenty five cell divisions, then stop and die over a period of weeks. Based on extensive flow cytometry data, Hawkins et al. (PNAS, 2007, 104, 5032{5037) introduced a cell-level stochastic model of lymphocyte population dynamics, called the Cyton Model, that accurately captures mean lymphocyte population size as a function of time. In Subramanian et al. (J. Math. Biol., 2008, 56:6, 861{892), we performed a branching process analysis of the Cyton Model and deduced from parameterizations for in vitro and in vivo data that the immune response is predictable despite each cell's fate being highly variable. One drawback of flow cytometry data is that individual cells cannot be tracked, so that it is not possible to investigate dependencies in the fate of cells within family trees. In the absence of this information, while the Cyton Model abandons one of the usual assumptions of branching processes (the independe...
http://eprints.nuim.ie/1650/
Marked
Mark
Large Deviations Of Max-Weight Scheduling Policies On Convex Rate Regions
(2008)
Subramanian, Vijay G.
Large Deviations Of Max-Weight Scheduling Policies On Convex Rate Regions
(2008)
Subramanian, Vijay G.
Abstract:
We consider a single server discrete-time system with K users where the server picks operating points from a compact, convex and co-ordinate convex set in Rk+. For this system we analyse the performance of a stablising policy that at any given time picks operating points from the allowed rate region that maximise a weighted sum of rate, where the weights depend upon the workloads of the users. Assuming a Large Deviations Principle (LDP) for the arrival processes in the Skorohod space of functions that are right-continuous with left-hand limits we establish an LDP for the workload process using a generalised version of the contraction principle to derive the corresponding rate function. With the LDP result available we then analyse the tail probabilities of the workloads under different buffering scenarios.
http://eprints.nuim.ie/1651/
Marked
Mark
A New Hypothesis for Sleep: Tuning for Criticality
(2009)
Pearlmutter, Barak A.; Conor J. Houghton, Conor J.
A New Hypothesis for Sleep: Tuning for Criticality
(2009)
Pearlmutter, Barak A.; Conor J. Houghton, Conor J.
Abstract:
We propose that the critical function of sleep is to prevent uncontrolled neuronal feedback while allowing rapid responses and prolonged retention of short-term memories. Through learning, the brain is tuned to react optimally to environmental challenges. Optimal behavior often requires rapid responses and the prolonged retention of short-term memories. At a neuronal level, these correspond to recurrent activity in local networks. Unfortunately, when a network exhibits recurrent activity, small changes in the parameters or conditions can lead to runaway oscillations. Thus, the very changes that improve the processing performance of the network can put it at risk of runaway oscillation. To prevent this, stimulus-dependent network changes should be permitted only when there is a margin of safety around the current network parameters. We propose that the essential role of sleep is to establish this margin by exposing the network to a variety of inputs, monitoring for erratic behavior, ...
http://eprints.nuim.ie/1653/
Marked
Mark
Computations of bubble dynamics with heat transfer
(2009)
Senthil Kumar, Sundararaj
Computations of bubble dynamics with heat transfer
(2009)
Senthil Kumar, Sundararaj
http://doras.dcu.ie/14862/
Marked
Mark
Stochastic delay difference and differential equations: applications to financial markets
(2009)
Swords, Catherine
Stochastic delay difference and differential equations: applications to financial markets
(2009)
Swords, Catherine
Abstract:
This thesis deals with the asymptotic behaviour of stochastic difference and functional differential equations of Itˆo type. Numerical methods which both minimise error and preserve asymptotic features of the underlying continuous equation are studied. The equations have a form which makes them suitable to model financial markets in which agents use past prices. The second chapter deals with the behaviour of moving average models of price formation. We show that the asset returns are positively and exponentially correlated, while the presence of feedback traders causes either excess volatility or a market bubble or crash. These results are robust to the presence of nonlinearities in the traders’ demand functions. In Chapters 3 and 4, we show that these phenomena persist if trading takes place continuously by modelling the returns using linear and nonlinear stochastic functional differential equations (SFDEs). In the fifth chapter, we assume that some traders base their demand on th...
http://doras.dcu.ie/14869/
Marked
Mark
On the pathwise large deviations of stochatic differential and functional differential equations with applications to finance
(2009)
Wu, Huizhong
On the pathwise large deviations of stochatic differential and functional differential equations with applications to finance
(2009)
Wu, Huizhong
Abstract:
The thesis deals with the asymptotic behaviour of highly nonlinear stochastic differential equations, as well as linear and nonlinear functional differential equations. Both ordinary functional and neutral equations are analysed. In the first chapter, a class of nonlinear stochastic differential equations which satisfy the Law of the Iterated Logarithm is studied, and the results applied to a financial market model. Mainly scalar equations are considered in the first chapter. The second chapter deals with a more general class of finite-dimensional nonlinear SDEs and SFDEs, employing comparison and time change methods, as well as martingale inequalities, to determine the almost sure rate of growth of the running maximum of functionals of the solution. The third chapter examines the exact almost sure rate of growth of the large deviations for affine stochastic functional differential equations, and for equations with additive noise which are subject to relatively weak nonlinearities a...
http://doras.dcu.ie/14870/
Marked
Mark
On cosmall Abelian groups
(2007)
Goldsmith, Brendan; Kolman, O.
On cosmall Abelian groups
(2007)
Goldsmith, Brendan; Kolman, O.
Abstract:
It is a well-known homological fact that every Abelian group G has the property that Hom(G,−) commutes with direct products. Here we investigate the ‘dual’ property: an Abelian group G is said to be cosmall if Hom(−,G) commutes with direct products. We show that cosmall groups are cotorsion-free and that no group of cardinality less than a strongly compact cardinal can be cosmall. In particular, if there is a proper class of strongly compact cardinals, then there are no cosmall groups.
http://arrow.dit.ie/scschmatart/40
Displaying Results 226 - 250 of 808 on page 10 of 33
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