
CARMASponsored Seminar Series: Colloquia, Seminars and More.

[Note: events are listed by descending date.]
 CARMA OANT SEMINAR
 Speaker: Assoc Prof Regina Burachik, University of South Australia
 Title: An additive subfamily of enlargements of a maximally monotone Operator
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: SeeVogh (nonAG) [ENQUIRIES]
 Time and Date: 1:30 pm, Mon, 27^{th} Apr 2015
 Abstract:
We introduce a subfamily of additive enlargements of a maximally monotone operator $T$. Our definition is inspired by the seminal
work of Fitzpatrick presented in 1988. These enlargements are a subfamily of the family of enlargements introduced by Svaiter in 2000. For the case $T = \partial f$, we prove that some members of the subfamily are smaller than the $\varepsilon$subdifferential enlargement. For this choice of $T$, we can construct a specific enlargement which coincides with the$\varepsilon$subdifferential. Since these enlargements are all
additive, they can be seen as structurally closer to the $\varepsilon$subdifferential enlargement.
Joint work with Juan Enrique MartínezLegaz (Universitat Autonoma de Barcelona), Mahboubeh Rezaei (University of Isfahan, Iran), and Michel Théra (University of Limoges).
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 CARMA OANT SEMINAR
 Speaker: Dr Dzmitry Badziahin, Department of Mathematical Sciences, Durham University
 Title: On continued fraction expansion of potential counterexamples to mixed Littlewood conjecture
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: SeeVogh (nonAG) [ENQUIRIES]
 Time and Date: 10:00 am, Wed, 5^{th} Nov 2014
 Abstract:
Mixed Littlewood conjecture proposed by de Mathan and Teulie in 2004 states that for every real number $x$ one has $\liminf q * q_D * qx = 0,$
where $q_D$ is a so called pseudo norm which generalises the standard padic norm. In the talk we'll consider the set mad of potential counterexamples to this conjecture. Thanks to the results of Einsiedler and Kleinbock we already know that the Haudorff dimension of mad is zero, so this set is very tiny. During the talk we'll see that the continued fraction expansion of every element in mad should satisfy some quite restrictive conditions. As one of them we'll see that for these expansions, considered as infinite words, the complexity function can neither grow too fast nor too slow.
 SeeVogh meeting number 9743677479.
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 CARMA OANT SEMINAR
 Speaker: Yohei Tachiya, Graduate School of Science and Technology, Hirosaki University
 Title: Algebraic independence results for the generating functions of pattern sequences
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 4:00 pm, Mon, 27^{th} Oct 2014
 Abstract:
We first introduce the notations of pattern sequence, which is defined by
the number of (possibly) overlapping occurrences of a given word in the $\langle q,r\rangle$numeration system. After surveying several properties of pattern sequence,
we will give necessary and sufficient criteria for the algebraic independence
of their generating functions. As applications, we deduce the linear relations between pattern sequences.
The proofs of the theorem and the corollaries are based on Mahler's method.
 SeeVogh meeting 3144213387.
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 CARMA OANT SEMINAR
 Speaker: A/Prof Simon Kristensen, Aarhus University
 Title: Diophantine approximation in positive characteristic
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: SeeVogh (nonAG) [ENQUIRIES]
 Time and Date: 10:00 am, Wed, 22^{nd} Oct 2014
 Abstract:
The completion with respect to the degree valuation of the field of rational functions over a finite field is often a fruitful analogue to consider when one would like to test ideas, methods and conjectures in Diophantine approximation for the real numbers. In many respects, this setting behaves very similarly to the real numbers, and in particular the metric theory of Diophantine approximation in this setup is welldeveloped and and in some respects more is known to be true in this setup than in the real numbers. However, natural analogues of other classical theorems in Diophantine approximation fail spectacularly in positive characteristic. In this talk, I will introduce the topic and give old and new results underpinning the similarities and differences of the theories of Diophantine approximation in positive characteristic and in characteristic zero.
 SeeVogh meeting number 7876118766.
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 CARMA OANT SEMINAR
 Speaker: Assoc Prof Regina Burachik, University of South Australia
 Title: An additive subfamily of enlargements of a maximally monotone operator
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UniSA
 Time and Date: 10:00 am, Wed, 15^{th} Oct 2014
 Abstract:
We introduce a subfamily of enlargements of a maximally monotone operator $T$. Our definition is inspired by a 1988 publication of Fitzpatrick. These enlargements are elements of the family of enlargements $\mathbb{E}(T)$ introduced by Svaiter in 2000. These new enlargements share with the $\epsilon$subdifferential a special additivity property, and hence they can be seen as structurally closer to the $\epsilon$subdifferential. For the case $T=\nabla f$, we prove that some members of the subfamily are smaller than the $\epsilon$subdifferential enlargement. In this case, we construct a specific enlargement which coincides with the $\epsilon$subdifferential.
Joint work with Juan Enrique Martínez Legaz, Mahboubeh Rezaei, and Michel Théra.
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 CARMA OANT SEMINAR
 Joint CARMA OANT and EECS Seminar
 Speaker: A/Prof Christopher Kellett, School of Electrical Engineering and Computer Science, The University of Newcastle
 Title: Converse Theorems in Lyapunov's Second Method and Constructive Methods: Part II
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 10:00 am, Wed, 1^{st} Oct 2014
 Abstract:
More than 120 years after their introduction, Lyapunov's socalled First and Second Methods remain the most widely used tools for stability analysis of nonlinear systems. Loosely speaking, the Second Method states that if one can find an appropriate Lyapunov function then the system has some stability property. A particular strength of this approach is that one need not know solutions of the system in order to make definitive statements about stability properties. The main drawback of the Second Method is the need to find a Lyapunov function, which is frequently a difficult task.
Converse Lyapunov Theorems answer the question: given a particular stability property, can one always (in principle) find an appropriate Lyapunov function? In the first installment of this twopart talk, we will survey the history of the field and describe several such Converse Lyapunov Theorems for both continuous and discretetime systems. In the second instalment we will discuss constructive techniques for numerically computing Lyapunov functions.
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 CARMA OANT SEMINAR
 Joint CARMA OANT and EECS Seminar
 Speaker: A/Prof Christopher Kellett, School of Electrical Engineering and Computer Science, The University of Newcastle
 Title: Converse Theorems in Lyapunov's Second Method and Constructive Methods: Part I
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 10:00 am, Wed, 24^{th} Sep 2014
 Abstract:
More than 120 years after their introduction, Lyapunov's socalled First and
Second Methods remain the most widely used tools for stability analysis of nonlinear
systems. Loosely speaking, the Second Method states that if one can find an appropriate
Lyapunov function then the system has some stability property. A particular strength of
this approach is that one need not know solutions of the system in order to make definitive
statements about stability properties. The main drawback of the Second Method is the
need to find a Lyapunov function, which is frequently a difficult task.
Converse Lyapunov Theorems answer the question: given a particular stability property,
can one always (in principle) find an appropriate Lyapunov function? In the first installment
of this twopart talk, we will survey the history of the field and describe several such Converse
Lyapunov Theorems for both continuous and discretetime systems. In the second instalment
we will discuss constructive techniques for numerically computing Lyapunov functions.
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 CARMA OANT SEMINAR
 Speaker: Christophe Vignat, Tulane University
 Title: An introduction to umbral calculus with applications
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 10:00 am, Wed, 3^{rd} Sep 2014
 Abstract:
Classical umbral calculus was introduced by Blissard in the 1860's and later studied by E. T. Bell and Rota. It is a symbolic computation method that is particularly efficient for proving identities involving elementary special functions such as Bernoulli or Hermite polynomials. I will show the link between this technique and moment representation, and provide examples of its application.
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 CARMA OANT SEMINAR
 Joint CARMA OANT and EECS Seminar
 Speaker: Prof Dr Lars Grüne, Chair of Applied Mathematics, University of Bayreuth
 Title: Economic Model Predictive Control without terminal conditions  theory, applications, and the gap in between
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 4:00 pm, Mon, 1^{st} Sep 2014
 Abstract:
In this talk we consider economic Model Predictive Control (MPC) schemes. "Economic" means that the MPC stage cost models economic considerations (like maximal yield, minimal energy consumption...) rather than merely penalizing the distance to a precomputed steady state or reference trajectory. In order to keep implementation and design simple, we consider schemes without terminal constraints and costs.
In the first (longer) part of the talk, we summarize recent results on the performance and stability properties of such schemes for nonlinear discrete time systems. Particularly, we present conditions under which one can guarantee practical asymptotic stability of the optimal steady state as well as approximately optimal averaged and transient performance. Here, dissipativity of the underlying optimal control problems and the turnpike property are shown to play an important role (this part is based on joint work with Tobias Damm, Marleen Stieler and Karl Worthmann).
In the second (shorter) part of the talk we present an application of an economic MPC scheme to a Smart Grid control problem (based on joint work with Philipp Braun, Christopher Kellett, Steven Weller and Karl Worthmann). While economic MPC shows good results for this control problem in numerical simulations, several aspects of this application are not covered by the available theory. This is explained in the last part of the talk, along with some suggestions on how to overcome this gap.
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 CARMA OANT SEMINAR
 Speaker: Qiji Jim Zhu, Department of Mathematics, Western Michigan University
 Title: Variational Approach to Lagrange Multipliers: Part 2
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Thu, 17^{th} Jul 2014
 Abstract:
Lagrange multiplier method is fundamental in dealing with constrained optimization problems and is also related to many other important results.
In these two talks we first survey several different ideas in proving the Lagrange multiplier rule and then concentrate on the variational approach.
We will first discuss the idea, a variational proof the Lagrange multiplier rule in the convex case and then consider the general case and relationship with other results.
These talks are continuation of the email discussions with Professor Jon Borwein and are very informal.
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 CARMA OANT SEMINAR
 Speaker: Qiji Jim Zhu, Department of Mathematics, Western Michigan University
 Title: Variational Approach to Lagrange Multipliers: Part 1
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Mon, 14^{th} Jul 2014
 Abstract:
Lagrange multiplier method is fundamental in dealing with constrained optimization problems and is also related to many other important results.
In these two talks we first survey several different ideas in proving the Lagrange multiplier rule and then concentrate on the variational approach.
We will first discuss the idea, a variational proof the Lagrange multiplier rule in the convex case and then consider the general case and relationship with other results.
These talks are continuation of the email discussions with Professor Jon Borwein and are very informal.
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 CARMA OANT SEMINAR
 Speaker: Prof David Bailey, Berkeley, California
 Title: Big data computing: Science and pseudoscience
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 3:00 pm, Fri, 11^{th} Jul 2014
 Download: Flyer (416 K)
 Abstract:
The relentless advance of computer technology, a gift of Moore's Law, and the data deluge available via the Internet and other sources, has been a gift to both scientific research and business/industry. Researchers in many fields are hard at work exploiting this data. The discipline of "machine learning," for instance, attempts to automatically classify, interpret and find patterns in big data. It has applications as diverse as supernova astronomy, protein molecule analysis, cybersecurity, medicine and finance. However, with this opportunity comes the danger of "statistical overfitting," namely attempting to find patterns in data beyond prudent limits, thus producing results that are statistically meaningless.
The problem of statistical overfitting has recently been highlighted in mathematical finance. A justpublished paper by the present author, Jonathan Borwein, Marcos Lopez de Prado and Jim Zhu, entitled "PseudoMathematics and Financial Charlatanism," draws into question the present practice of using historical stock market data to "backtest" a new proposed investment strategy or exchangetraded fund. We demonstrate that in fact it is very easy to overfit stock market data, given powerful computer technology available, and, further, without disclosure of how many variations were tried in the design of a proposed investment strategy, it is impossible for potential investors to know if the strategy has been overfit. Hence, many published backtests are probably invalid, and this may explain why so many proposed investment strategies, which look great on paper, later fall flat when actually deployed.
In general, we argue that not only do those who directly deal with "big data" need to be better aware of the methodological and statistical pitfalls of analyzing this data, but those who observe these problems of this sort arising in their profession need to be more vocal about them. Otherwise, to quote our "PseudoMathematics" paper, "Our silence is consent, making us accomplices in these abuses."
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 CARMA OANT SEMINAR
 Speaker: Prof Mark Giesbrecht, University of Waterloo
 Title: Algorithms and statistics for additive polynomials
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Tue, 24^{th} Jun 2014
 Abstract:
The additive or linearized polynomials were introduced by Ore in 1933
as an analogy over finite fields to his theory of difference and
difference equations over function fields. The additive polynomials
over a finite field $F=GF(q)$, where $q=p^e$ for some prime $p$,
are those of the form
$f = f_0 x + f_1 x^p + f_2 x^{p^2} + ... + f_m x^{p^m}$ in $F[x]$
They form a noncommutative lefteuclidean principal ideal domain
under the usual addition and functional composition, and possess a
rich structure in both their decomposition structures and root
geometries. Additive polynomials have been employed in number theory
and algebraic geometry, and applied to constructing errorcorrecting
codes and cryptographic protocols. In this talk we will present fast
algorithms for decomposing and factoring additive polynomials, and
also for counting the number of decompositions with particular degree
sequences.
Algebraically, we show how to reduce the problem of decomposing
additive polynomials to decomposing a related associative algebra, the
eigenring. We give computationally efficient versions of the
JordanHolder and KrullSchmidt theorems in this context to describe
all possible factorization. Geometrically, we show how to compute a
representation of the Frobenius operator on the space of roots, and
show how its Jordan form can be used to count the number of
decompositions. We also describe an inverse theory, from which we can
construct and count the number of additive polynomials with specified
factorization patterns.
Some of this is joint work with Joachim von zur Gathen (Bonn) and
KonstantinZiegler (Bonn).
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 CARMA OANT SEMINAR
 Speaker: Hans Mittelmann, School of Mathematical and Statistical Sciences, Arizona State University
 Title: Computing Strong Bounds in Combinatorial Optimization
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Mon, 24^{th} Feb 2014
 Abstract:
As is wellknown semidefinite relaxations of discrete optimization problems can
yield excellent bounds on their solutions. We present three examples from our
collaborative research. The first addresses the quadratic assignment problem and
a formulation is developed which yields the strongest lower bounds known for
larger dimensions. Utilizing the latest iterative SDP solver and ideas from
verified computing a realistic problem from communications is solved for
dimensions up to 512.
A strategy based on the Lovasz theta function is generalized to compute
upper bounds on the spherical kissing number utilizing SDP relaxations. Multiple
precision SDP solvers are needed and improvements on known results for all
kissing numbers in dimensions up to 23 are obtained. Finally, generalizing ideas
of Lex Schrijver improved upper bounds for general binary codes are obtained
in many cases.
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 CARMA OANT SEMINAR
 Speaker: Oleg Burdakov, Linkoping University
 Title: An approach to solving decomposable optimization problems with coupling constraints
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UniSA
 Time and Date: 3:00 pm, Tue, 10^{th} Dec 2013
 Abstract:
We consider a problem of minimising $f_1(x)+f_2(y)$ over $x \in X \subseteq R^n$ and $y \in Y \subseteq R^m$ subject to a number of extra coupling constraints of the form $g_1(x) g_2(y) \geq 0$. Due to these constraints, the problem may have a large number of local minima. For any feasible combination of signs of $g_1(x)$ and $g_2(y)$, the coupled problem is decomposable, and the resulting two problems are assumed to be easily solved. An approach to solving the coupled problem is presented. We apply it to solving coupled monotonic regression problems arising in experimental psychology.
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 CARMA OANT SEMINAR
 Speaker: Prof Robert Corless, University of Western Ontario
 Title: Highorder, highaccuracy solution of a nonlinear PDE arising in a twodimensional heat transfer model
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UniSA
 Time and Date: 3:00 pm, Mon, 9^{th} Dec 2013
 Abstract:
A classical nonlinear PDE used for modelling heat transfer between concentric cylinders by fluid convection and also for modelling porous flow can be solved by hand using a loworder perturbation method. Extending this solution to higher order using computer algebra is surprisingly hard owing to exponential growth in the size of the series terms, naively computed. In the mid1990's, socalled "Large Expression Management" tools were invented to allow construction and use of socalled "computation sequences" or "straightline programs" to extend the solution to 11th order. The cost of the method was O(N^8) in memory, high but not exponential.
Twenty years of doubling of computer power allows this method to get 15 terms. A new method, which reduces the memory cost to O(N^4), allows us to compute to N=30. At this order, singularities can reliably be detected using the quotientdifference algorithm. This allows confident investigation of the solutions, for different values of the Prandtl number.
This work is joint with Yiming Zhang (PhD Oct 2013).
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 CARMA OANT SEMINAR
 Speaker: Assoc Prof Regina Burachik, University of South Australia
 Title: Interior Epigraph Directions Method for Nonsmooth and Nonconvex Optimization via Generalized Augmented Lagrangian Duality
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UniSA
 Time and Date: 2:00 pm, Tue, 26^{th} Nov 2013
 Abstract:
We propose and study a new method, called the Interior Epigraph Directions (IED)
method, for solving constrained nonsmooth and nonconvex optimization. The IED
method considers the dual problem induced by a generalized augmented Lagrangian
duality scheme, and obtains the primal solution by generating a sequence of
iterates in the interior of the dual epigraph. First, a deflected subgradient
(DSG) direction is used to generate a linear approximation to the dual
problem. Second, this linear approximation is solved using a Newtonlike step.
This Newtonlike step is inspired by the Nonsmooth Feasible Directions Algorithm
(NFDA), recently proposed by Freire and coworkers for solving unconstrained,
nonsmooth convex problems. We have modified the NFDA so that it takes advantage
of the special structure of the epigraph of the dual function. We prove that all
the accumulation points of the primal sequence generated by the IED method are
solutions of the original problem. We carry out numerical experiments by using
test problems from the literature. In particular, we study several instances of
the Kissing Number Problem, previously solved by various approaches such as an
augmented penalty method, the DSG method, as well as the popular differentiable
solvers ALBOX (a predecessor of ALGENCAN), Ipopt and LANCELOT. Our experiments
show that the quality of the solutions obtained by the IED method is comparable
with (and sometimes favourable over) those obtained by the other solvers mentioned.
Joint work with Wilhelm P. Freire and C. Yalcin Kaya.
 Note earlier starting time.
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 CARMA OANT SEMINAR
 Speaker: Dr C. Yalcin Kaya, University of South Australia
 Title: A Numerical Method for Multiobjective Optimal Control
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UniSA
 Time and Date: 2:00 pm, Tue, 19^{th} Nov 2013
 Abstract:
A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multiobjective optimal control problems. First, a suitable scalarization technique is employed for the multiobjective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of singleobjective optimal control problems are solved to obtain points which are spread over the Pareto front. The technique is illustrated on problems involving tumor antiangiogenesis and a fedbatch bioreactor, which exhibit bang–bang, singular and boundary types of optimal control. We illustrate that the Bolza form, the traditional scalarization in optimal control, fails to represent all the compromise, i.e., Pareto optimal, solutions.
Joint work with Helmut Maurer.
C. Y. Kaya and H. Maurer, A numerical method for nonconvex multiobjective optimal control problems, Computational Optimization and Applications, (appeared online: September 2013, DOI 10.1007/s1058901396032)
 Note change of time.
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 CARMA OANT SEMINAR
 Speaker: Dr Victoria MartínMárquez, Department of Mathematical Analysis, Universidad de Sevilla
 Title: Solving Convex Split Feasibility Problems and Applications
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UniSA
 Time and Date: 3:00 pm, Tue, 12^{th} Nov 2013
 Abstract:
The split feasibility problem (SFP) consists in finding a point in a closed convex subset of a Hilbert space such that its image under a bounded linear operator belongs to a closed convex subset of another Hilbert space. Since its inception in 1994 by Censor and Elfving, it has received much attention thanks mainly to its applications to signal processing and image reconstruction. Iterative methods can be employed to solve the SFP. One of the most popular iterative method is Byrne's CQ algorithm. However, this algorithm requires prior knowledge (or at least an estimate) of the norm of the bounded linear operator. We introduce a stepsize selection method so that the implementation of the CQ algorithm does not need any prior information regarding the operator norm. Furthermore, a relaxed CQ algorithm, where the two closed convex sets are both level sets of convex functions, and a Halperntype algorithm are studied under the same stepsize rule, yielding both weak and strong convergence. A more general problem, the Multiplesets split feasibility problem, will be also presented. Numerical experiments are included to illustrate the applications to signal processing and, in particular, to compressed sensing and waveletbased signal restoration.
Based on joint works with G. López and HK Xu.
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 CARMA OANT SEMINAR
 Speaker: Prof Andrew Eberhard, School of Mathematical and Geospatial Sciences, RMIT University
 Title: On the Maximal Extensions of Monotone Operators, Criteria for Maximality, and the Sum Theorem
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Tue, 22^{nd} Oct 2013
 Abstract:
Within a nonzero, real Banach space we study the problem of characterising a maximal extension of a monotone operator in terms of minimality properties of representative functions that are bounded by the Penot and Fitzpatrick functions. We single out a property of the space of representative functions that enable a very compact treatment of maximality and premaximality issues. As this treatment does not assume reflexivity and we characterises this property the existence of a counter example has a number of consequences for the search for a suitable certificate for maximality in nonreflexive spaces. In particular one is lead to conjecture that some extra side condition to the usual CQ is inevitable. We go on to look at the simplest such condition which is boundedness of the domain of the monotone operator and obtain some positive results.
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 CARMA OANT SEMINAR
 Speaker: Dr Thomas Kalinowski, CARMA, The University of Newcastle
 Title: A Social Welfare Optimal Sequential Allocation Procedure
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Tue, 8^{th} Oct 2013
 Abstract:
There exist a variety of mechanisms to share indivisible goods between agents. One of the simplest is to let the agents take turns to pick an item. This mechanism is parameterized by a policy, the order in which agents take turns. A simple model of this mechanism was proposed by Bouveret and Lang in 2011. We show that in their setting the natural policy of letting the agents alternate in picking items is optimal. We also present a number of potential generalizations and extensions.
This is joint work with Nina Narodytska and Toby Walsh.
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 CARMA OANT SEMINAR
 Speaker: Dr Jean Lasserre, LAASCNRS, Université de Toulouse
 Title: Tractable characterizations of nonnegativity on closed sets via Linear Matrix Inequalities
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Tue, 24^{th} Sep 2013
 Abstract:
In many problems in control, optimal and robust control, one has to solve global
optimization problems of the form: $\mathbf{P}:f^\ast=\min_{\mathbf x}\{f(\mathbf x):\mathbf x\in\mathbf K\}$, or, equivalently, $f^\ast=\max\{\lambda:f\lambda\geq0\text{ on }\mathbf K\}$, where $f$ is a polynomial (or even a semialgebraic function) and $\mathbf K$ is a basic semialgebraic set. One may even need solve the "robust" version $\min\{f(\mathbf x):\mathbf x\in\mathbf K;h(\mathbf x,\mathbf u)\geq0,\forall \mathbf u\in\mathbf U\}$ where $\mathbf U$ is a set of parameters. For
instance, some static output feedback problems can be cast as polynomial optimization
problems whose feasible set $\mathbf K$ is defined by a polynomial matrix inequality (PMI). And
robust stability regions of linear systems can be modeled as parametrized polynomial
matrix inequalities (PMIs) where parameters $\mathbf u$ account for uncertainties and (decision)
variables x are the controller coefficients.
Therefore, to solve such problems one needs tractable characterizations of polynomials
(and even semialgebraic functions) which are nonnegative on a set, a topic of independent
interest and of primary importance because it also has implications in many other areas.
We will review two kinds of tractable characterizations of polynomials which are nonnegative on a basic closed semialgebraic set $\mathbf K\subset\mathbb R^n$. The first type of characterization is
when knowledge on $\mathbf K$ is through its defining polynomials, i.e., $\mathbf K=\{\mathbf x:g_j(\mathbf x)\geq 0, j =1,\dots, m\}$, in which case some powerful certificates of positivity can be stated in terms of some sums of squares (SOS)weighted representation. For instance, this allows to define a hierarchy fo semidefinite relaxations which yields a monotone sequence of lower bounds
converging to $f^\ast$ (and in fact, finite convergence is generic). There is also another way
of looking at nonnegativity where now knowledge on $\mathbf K$ is through moments of a measure
whose support is $\mathbf K$. In this case, checking whether a polynomial is nonnegative on $\mathbf K$
reduces to solving a sequence of generalized eigenvalue problems associated with a count
able (nested) family of real symmetric matrices of increasing size. When applied to $\mathbf P$, this
results in a monotone sequence of upper bounds converging to the global minimum, which
complements the previous sequence of upper bounds. These two (dual) characterizations
provide convex inner (resp. outer) approximations (by spectrahedra) of the convex cone
of polynomials nonnegative on $\mathbf K$.
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 CARMA OANT SEMINAR
 Speaker: Dr Hamish Waterer, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: A BucketIndexed Formulation for Nonpreemptive Single Machine Scheduling Problems
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Tue, 17^{th} Sep 2013
 Abstract:
An exact bucket indexed (BI) mixed integer linear programming formulation for nonpreemptive single machine scheduling problems is presented that is a result of an ongoing investigation into strategies to model time in planning applications with greater efficacy. The BI model is a generalisation of the classical time indexed (TI) model to one in which at most two jobs can be processing in each time period. The planning horizon is divided into periods of equal length, but unlike the TI model, the length of a period is a parameter of the model and can be chosen to be as long as the processing time of the shortest job. The two models are equivalent if the problem data are integer and a period is of unit length, but when longer periods are used in the BI model, it can have significantly fewer variables and nonzeros than the TI model at the expense of a greater number of constraints. A computational study using weighted tardiness instances reveals the BI model significantly outperforms the TI model on instances where the mean processing time of the jobs is large and the range of processing times is small, that is, the processing times are clustered rather than dispersed.
Joint work with Natashia Boland and Riley Clement.
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 CARMA OANT SEMINAR
 Speaker: Dr Mumtaz Hussain, CARMA, The University of Newcastle
 Title: Measure theoretic results for small linear forms
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Tue, 10^{th} Sep 2013
 Abstract:
I will talk about the metrical theory of Diophantine approximation associated with linear forms that are simultaneously small in terms of absolute value rather than the classical nearest integer norm. In other words, we consider linear forms which are simultaneously close to the origin. A complete KhintchineGroshev type theorem for monotonic approximating functions is established within the absolute value setup. Furthermore, the Hausdorff measure generalization of the KhintchineGroshev type theorem is obtained. As a consequence we obtain the complete Hausdorff dimension theory. Staying within the absolute value setup, we prove that the corresponding set of badly approximable vectors is of full dimension.
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 CARMA OANT SEMINAR
 Speaker: Prof Wadim Zudilin, CARMA, The University of Newcastle
 Title: Mock theta functions
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Tue, 3^{rd} Sep 2013
 Abstract:
In his deathbed letter to G.H. Hardy, Ramanujan gave a vague definition of a mock modular function: at each root of unity its asymptotics matches the one of a modular form, though a choice of the modular function depends on the root of unity. Recently Folsom, Ono and Rhoades have proved an elegant result about the match for a general family related to Dyson’s rank (mock theta) function and the Andrews—Garvan crank (modular) function. In my talk I will outline some heuristics and elementary ingredients of the proof.
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 CARMA OANT SEMINAR
 Speaker: Prof Frank Garvan, University of Florida
 Title: Dyson's Rank Function and Andrews's SPT Function.
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Tue, 20^{th} Aug 2013
 Abstract:
Let spt(n) denote the number of smallest parts in the partitions of n. In
2008, Andrews found surprising congruences for the sptfunction mod 5, 7 and
13. We discuss new congruences for spt(n) mod powers of 2.
We give new generating function identities for the sptfunction and
Dyson's rank function. Recently with Andrews and Liang we found a sptcrank
function that explains Andrews sptcongruences mod 5 and 7. We extend
these results by finding sptcranks for various overpartitionsptfunctions
of Ahlgren, Bringmann, Lovejoy and Osburn. This most recent work
is joint with Chris JenningsShaffer.
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 CARMA OANT SEMINAR
 Speaker: Assoc. Prof. Brailey Sims, CARMA, The University of Newcastle
 Title: Projections in geodesic metric spaces  Part II
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Tue, 13^{th} Aug 2013
 Abstract:
The feasibility problem associated with nonempty closed
convex sets $A$ and $B$ is to find some $x\in A \cap B$.
Projection algorithms in general aim to compute such a point.
These algorithms play key roles in optimization and have
many applications outside mathematics  for example in medical
imaging.
Until recently convergence results were only available in the setting of linear spaces (more particularly, Hilbert spaces) and where the two sets are closed and convex.
The extension into geodesic metric spaces allows their use in spaces where there is no natural linear
structure, which is the case for instance in tree spaces, state spaces, phylogenomics
and configuration spaces for robotic movements.
After reviewing the pertinent aspects of CAT(0) spaces introduced in Part I, including results for von Neumann's alternating projection method, we will focus on
the DouglasRachford algorithm, in CAT(0) spaces. Two situations arise; spaces with constant curvature and those with nonconstant curvature. A prototypical space of the later kind will be introduced and the behavior of the DouglasRachford algorithm within it examined.
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 CARMA OANT SEMINAR
 Speaker: Assoc. Prof. Brailey Sims, CARMA, The University of Newcastle
 Title: Projections in geodesic metric spaces  Part I
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:30 pm, Mon, 1^{st} Jul 2013
 Abstract:
Geodesic metric spaces provide a setting in which we can develop much of nonlinear, and in particular convex, analysis in the absence of any natural linear structure. For instance, in a state space it often makes sense to speak of the distance between two states, or even a chain of connecting intermediate states, whereas the addition of two states makes no sense at all.
We will survey the basic theory of geodesic metric spaces, and in particular Gromov's so called CAT($\kappa$) spaces. And if there is time (otherwise in a later talk), we will examine some recent results concerning alternating projection type methods, principally the DouglasRachford algorithm, for solving the two set feasibility problem in such spaces.
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 CARMA OANT SEMINAR
 Speaker: Prof Miguel Ángel Goberna Torrent, Departamento de Estadística e Investigación Operativa, University of Alicante
 Title: Voronoi cells of arbitrary sets
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UniSA
 Time and Date: 3:30 pm, Mon, 24^{th} Jun 2013
 Abstract:
Given a set T of the Euclidean space, whose elements are called sites, and a particular site s, the Voronoi cell of s is the set formed by all points closer to s than to any other site. The Voronoi diagram of T is the family of Voronoi cells of all the elements of T. In this talk we show some applications of the Voronoi diagrams of finite and infinite sets and analyze direct and inverse problems concerning the cells. We also discuss the stability of the cells under different types of perturbations and the effect of assigning weights to the sites.
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 CARMA OANT SEMINAR
 Speaker: Prof Jörg Fliege, CORMSIS, University of Southampton
 Title: Optimisation in Space: Problems in Spacecraft Trajectory Optimization
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UniSA
 Time and Date: 11:00 am, Tue, 18^{th} Jun 2013
 Abstract:
In trajectory optimization, the optimal path of a flight system or a group of flight systems is searched for, often in an interplanetary setting: we are in search of trajectories for one or more spacecrafts. On the one hand, this is a welldeveloped field of research, in which commercial software packages are already available for various scenarios. On the other hand, the computation of such trajectories can be rather demanding, especially when lowthrust missions with long travel times (e.g., years) are considered. Such missions invariably involve gravitational slingshot maneuvers at various celestial bodies in order to save propellant or time. Such maneuvers involve vastly different time scales: years of coasting can be followed by course corrections on a daily basis. In this talk, we give an overview over trajectory optimization for space vehicles and highlight some recent algorithmic developments.
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 CARMA OANT SEMINAR
 Speaker: Dr Liangjin Yao, CARMA, The University of Newcastle
 Title: Analysis of the convergence rate for the cyclic projection algorithm applied to semialgebraic convex sets
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:30 pm, Mon, 3^{rd} Jun 2013
 Abstract:
In this talk, we study the rate of convergence of the cyclic projection algorithm applied to finitely many semialgebraic convex sets. We establish an explicit convergence rate estimate which relies on the maximum degree of the polynomials that generate the semialgebraic convex sets and the dimension of the underlying space. We achieve our results by exploiting the algebraic structure of the semialgebraic convex sets.
This is the joint work with Jon Borwein and Guoyin Li.
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 CARMA OANT SEMINAR
 Speaker: Matt Skerritt, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Computation of an Improved Lower Bound to Giuga’s Primality Conjecture
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:30 pm, Mon, 27^{th} May 2013
 Abstract:
Our most recent computations tell us that any counterexample to Giuga’s 1950 primality conjecture must have at least 19,907 digits. Equivalently, any number which is both a Giuga and a Carmichael number must have at least 19,907 digits. This bound has not been achieved through exhaustive testing of all numbers with up to 19,907 digits, but rather through exploitation of the properties of Giuga and Carmichael numbers. We introduce the conjecture and an algorithm for finding lower bounds to a counterexample, then present our recent results and discuss challenges to further computation.
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 CARMA OANT SEMINAR
 Speaker: Mr Matthew Tam, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Cyclic DouglasRachford Iterations
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:30 pm, Mon, 20^{th} May 2013
 Abstract:
In this talk we introduce a DouglasRachford inspired projection algorithm, the cyclic DouglasRachford iteration scheme. We show, unlike the classical DouglasRachford scheme, that the method can be applied directly to convex feasibility problems in Hilbert space without recourse to a product space formulation. Initial results, from numerical experiments comparing our methods to the classical DouglasRachford scheme, are promising.
This is joint work with Prof. Jonathan Borwein.
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 CARMA OANT SEMINAR
 Speaker: Assoc Prof Regina Burachik, University of South Australia
 Title: Conditions for zero duality gap in convex programming
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UniSA
 Time and Date: 3:30 pm, Mon, 13^{th} May 2013
 Abstract:
We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is weaker than all existing constraint qualifications, including the closed epigraph condition. Our dual condition was inspired by, and is weaker than, the socalled Bertsekas’ condition for monotropic programming problems. We give several corollaries of our result and special cases as applications. We pay special attention to the polyhedral and sublinear cases, and their implications in convex optimization.
This research is a joint work with Jonathan M. Borwein and Liangjin Yao.
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 CARMA OANT SEMINAR
 Speaker: Dr Yoshitaka Sasaki, Osaka University of Health and Sport Sciences
 Title: On polyEuler numbers and the related Lfunction
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 3:00 pm, Mon, 4^{th} Mar 2013
 Abstract:
In 1997, Kaneko introduced the polyBernoulli number. PolyEuler numbers are introduced as a generalization of the Euler numbers in a manner similar to the introduction of the polyBernoulli numbers. In my talk, some properties of polyEuler numbers, for example, explicit formulas, sign change, Clausenvon Staudt type formula, combinatorial interpretations and so on are showed.
This research is a joint work with Yasuo Ohno.
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 CARMA OANT SEMINAR
 Speaker: Mr Michael Rose, School of Mathematical and Physical Sciences, The University of Newcastle
 Title: Expectations on Fractal Sets
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 3:00 pm, Mon, 3^{rd} Dec 2012
 Abstract:
Motivated by laboratory studies on the distribution of brain synapses, the
classical theory of box integrals  being expectations on unit hypercubes 
is extended to a new class of fractal "stringgenerated Cantor sets" that
facilitate finetuning of their fractal dimension through a suitable choice
of generating string. Closed forms for certain statistical moments on these
fractal sets will be presented, together with a precision algorithm for
higher embedding dimensions. This is based on joint work with Laur. Prof.
Jon Borwein, Prof. David Bailey and Dr. Richard Crandall.
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 CARMA OANT SEMINAR
 Speaker: Dr Victoria MartínMárquez, Department of Mathematical Analysis, Universidad de Sevilla
 Title: Right Bregman nonexpansive operators in Banach spaces
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 3:00 pm, Mon, 26^{th} Nov 2012
 Abstract:
Nonexpansive operators in Banach spaces are of utmost importance in Nonlinear Analysis and Optimization Theory. We are concerned in this talk with classes of operators which are, in some sense, nonexpansive not with respect to the norm, but with respect to Bregman distances. Since these distances are not symmetric in general, it seems natural to distinguish between left and right Bregman nonexpansive operators. Some left classes have already been studied quite intensively, so this talk is mainly devoted to right Bregman nonexpansive operators and the relationship between both classes.
This talk is based on joint works with Prof. Simeon Reich and Shoham Sabach from TechnionIsrael Institute of Technology, Haifa.
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 CARMA OANT SEMINAR
 Speaker: Dr C. Yalcin Kaya, University of South Australia
 Title: Finding interpolating curves using optimal control
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UniSA
 Time and Date: 3:00 pm, Mon, 5^{th} Nov 2012
 Abstract:
We study the problem of finding an interpolating curve passing through prescribed points in the Euclidean space. The interpolating curve minimizes the pointwise maximum length, i.e., L∞norm, of its acceleration. We reformulate the problem as an optimal control problem and employ simple but effective tools of optimal control theory. We characterize solutions associated with singular (of infinite order) and nonsingular controls. We reduce the infinite dimensional interpolation problem to an ensuing finite dimensional one and derive closed form expressions for interpolating curves. Consequently we devise numerical techniques for finding interpolating curves and illustrate these techniques on examples.
 [Permanent event link]
 CARMA OANT SEMINAR
 Speaker: Dr Francisco Aragón Artacho, CARMA, The University of Newcastle
 Title: Walking on real numbers
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 3:00 pm, Mon, 22^{nd} Oct 2012
 Abstract:
Motivated by the desire to visualise large mathematical data sets, especially in number theory, we offer various tools for representing floating point numbers as planar walks and for quantitatively measuring their “randomness”.
What to expect: some interesting ideas, many beautiful pictures (including a 108gigapixel picture of π), and some easytounderstand maths.
What you won’t get: too many equations, difficult proofs, or any “real walking”.
This is a joint work with David Bailey, Jon Borwein and Peter Borwein.
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 CARMA OANT SEMINAR
 Speaker: Dr Michael Coons, CARMA, The University of Newcastle
 Title: The rationaltranscendental dichotomy of Mahler functions
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 3:00 pm, Mon, 15^{th} Oct 2012
 Abstract:
In this talk, we will show that a Dfinite Mahler function is necessarily rational. This gives a new proof of the rationaltranscendental dichotomy of Mahler functions due to Nishioka. Using our method of proof, we also provide a new proof of a PólyaCarlson type result for Mahler functions due to Randé; that is, a Mahler function which is meromorphic in the unit disk is either rational or has the unit circle as a natural boundary. This is joint work with Jason Bell and Eric Rowland.
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 CARMA OANT SEMINAR
 Speaker: Timothy Trudgian, Australian National University
 Title: By how much does Mertens' conjecture fail?
 Location: Room V206, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 3:00 pm, Mon, 8^{th} Oct 2012
 Abstract:
If some arithmetical sums are small then the complex zeroes of the zetafunction are linearly dependent. Since we don't believe the conclusion we ought not to believe the premise. I will show that the zeroes are 'almost linearly independent' which implies, in particular, that the Mertens conjecture fails more drastically than was previously known.
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 CARMA OANT SEMINAR
 Speaker: Dr Mike Meylan, CARMA, The University of Newcastle
 Title: Linear Water Waves in the TimeDomain
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 3:00 pm, Mon, 17^{th} Sep 2012
 Abstract:
Linear Water Wave theory is one of the most important branches on fluid mechanics. Practically it underpins most of the engineering design of ships, offshore structures, etc. It also has a very rich history in the development of applied mathematics. In this talk I will focus on the connection between solutions in the frequency and timedomains and show
how we can use various formulations to make numerical calculations and to construct approximate solutions. I will illustrate these methods with application to some simple wave scattering problems.
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 CARMA OANT SEMINAR
 Speaker: Dr Liangjin Yao, CARMA, The University of Newcastle
 Title: Legendretype integrands and convex integral functions
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 3:00 pm, Mon, 10^{th} Sep 2012
 Abstract:
In this talk, we study the properties of integral functionals induced on $L_\text{E}^1(S,\mu)$ by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (wellposed). We show that in this generality functions such as the BoltzmannShannon entropy and the FermiDirac entropy are strongly rotund. We also study convergence in measure and give various limiting counterexample.
This is joint work with Jon Borwein.
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 CARMA OANT SEMINAR
 Speaker: Prof David Bailey, Berkeley, California
 Title: Hand to hand combat with thousanddigit integrals
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: UNewcastle [ENQUIRIES]
 Time and Date: 3:00 pm, Mon, 3^{rd} Sep 2012
 Abstract:
A frequent theme of 21st century experimental math is the computer discovery of identities, typically done by means of computing some mathematical entity (a sum, limit, integral, etc) to very high numeric precision, then using the PSLQ algorithm to identify the entity in terms of well known constants.
Perhaps the most successful application of this methodology has been to identify integrals arising in mathematical physics. This talk will present numerous examples of this type, including integrals from quantum field theory, Ising theory, random walks, 3D lattice problems, and even mouse brains. In some cases, it is necessary to compute these integrals to 3000digit precision, and developing techniques to do such computations is a daunting technical challenge.
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