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Remembering German-Australian Colonial Entanglements emphatically promotes a critical and nuanced understanding of the complex entanglement of German colonial actors and activities within Australian colonial institutions and different imperial ideologies. Case studies ranging from the German reception of James Cook’s voyages through to the legacies of 19th- and 20th-century settler colonialism foreground the highly ambiguous roles played by explorers, missionaries, intellectuals and other individuals, as well as by objects and things that travelled between worlds – ancestral human remains, rare animal skins, songs, and even military tanks. The chapters foreground the complex relationship between science, religion, art and exploitation, displacement and annihilation.
This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.
In a bounded domain with smooth boundary in R^3 we consider the stationary Maxwell equations
for a function u with values in R^3 subject to a nonhomogeneous condition
(u,v)_x = u_0 on
the boundary, where v is a given vector field and u_0 a function on the boundary. We specify this problem within the framework of the Riemann-Hilbert boundary value problems for the Moisil-Teodorescu system. This latter is proved to satisfy the Shapiro-Lopaniskij condition if an only if the vector v is at no point tangent to the boundary. The Riemann-Hilbert problem for the Moisil-Teodorescu system fails to possess an adjoint boundary value problem with respect to the Green formula, which satisfies the Shapiro-Lopatinskij condition. We develop the construction of Green formula to get a proper concept of adjoint boundary value problem.
This essay reads Sam Selvon’s novel The Lonely Londoners (1956) as a milestone in the decolonisation of British fiction. After an introduction to Selvon and the core composition of the novel, it discusses the ways in which the narrative takes on issues of race and racism, how it in the tradition of the Trinidadian carnival confronts audiences with sexual profanation and black masculine swagger, and not least how the novel, especially through its elaborate use of creole Englishes, reimagines London as a West Indian metropolis. The essay then turns more systematically to the ways in which Selvon translates Western literary models and their isolated subject positions into collective modes of narrative performance taken from Caribbean orature and the calypsonian tradition. The Lonely Londoners breathes entirely new life into the ossified conventions of the English novel, and imbues it with unforeseen aesthetic, ethical, political and epistemological possibilities.
We consider the Navier-Stokes equations in the layer R^n x [0,T] over R^n with finite T > 0. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form (I+K) u = f, where K is a compact continuous operator in anisotropic normed Hölder spaces weighted at the point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all t in [0,T]. On using the particular properties of the de Rham complex we conclude that the Fréchet derivative (I+K)' is continuously invertible at each point of the Banach space under consideration and the map I+K is open and injective in the space. In this way the Navier-Stokes equations prove to induce an open one-to-one mapping in the scale of Hölder spaces.
We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called "fast convergence rates" depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the L^2 (prediction) norm as well as for the stronger Hilbert norm, if the true
regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available.
Convoluted Brownian motion
(2016)
In this paper we analyse semimartingale properties of a class of Gaussian periodic processes, called convoluted Brownian motions, obtained by convolution between a deterministic function and a Brownian motion. A classical
example in this class is the periodic Ornstein-Uhlenbeck process. We compute their characteristics and show that in general, they are neither
Markovian nor satisfy a time-Markov field property. Nevertheless, by enlargement
of filtration and/or addition of a one-dimensional component, one can in some case recover the Markovianity. We treat exhaustively the case of the bidimensional trigonometric convoluted Brownian motion and the higher-dimensional monomial convoluted Brownian motion.
Recollecting Bones
(2016)
In the same “guarded, roundabout and reticent way” which Lindsay Barrett invokes for Australian conversations about imperial injustice, Germans, too, must begin to more systematically explore, in Paul Gilroy’s words, “the connections and the differences between anti-semitism and anti-black and other racisms and asses[s] the issues that arise when it can no longer be denied that they interacted over a long time in what might be seen as Fascism’s intellectual, ethical and scientific pre-history” (Gilroy 1996: 26). In the meantime, we need to care for the dead. We need to return them, first, from the status of scientific objects to the status of ancestral human beings, and then progressively, and proactively, as close as possible to the care of those communities from whom they were stolen.