A Time-Dependent Dirichlet-Neumann Method for the Heat Equation

We present a waveform relaxation version of the Dirichlet-Neumann method for parabolic problem. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain decomposition, and the iteration involves subdomain solves with Dirichlet boundary conditions followed by subdomain solves with Neumann boundary conditions. However, each subdomain problem is now in space and time, and the interface conditions are also time-dependent. Using a Laplace transform argument, we show for the heat equation that when we consider finite time intervals, the Dirichlet-Neumann method converges, similar to the case of Schwarz waveform relaxation algorithms. The convergence rate depends on the length of the subdomains as well as the size of the time window. In this discussion, we only stick to the linear bound. We illustrate our results with numerical experiments.Comment: 9 pages, 5 figures, Lecture Notes in Computational Science and Engineering, Vol. 98, Springer-Verlag 201

Error bounds for the asymptotic expansion of the Hurwitz zeta function

In this paper, we reconsider the large-$a$ asymptotic expansion of the Hurwitz zeta function $\zeta(s,a)$. New representations for the remainder term of the asymptotic expansion are found and used to obtain sharp and realistic error bounds. Applications to the asymptotic expansions of the polygamma functions, the gamma function, the Barnes $G$-function and the $s$-derivative of the Hurwitz zeta function $\zeta(s,a)$ are provided. A detailed discussion on the sharpness of our error bounds is also given.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1606.07961, accepted for publication in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science

Effective actions on the squashed three-sphere

The effective actions of a scalar and massless spin-half field are determined as functions of the deformation of a symmetrically squashed three-sphere. The extreme oblate case is particularly examined as pertinant to a high temperature statistical mechanical interpretation that may be relevant for the holographic principle. Interpreting the squashing parameter as a temperature, we find that the effective `free energies' on the three-sphere are mixtures of thermal two-sphere scalars and spinors which, in the case of the spinor on the three-sphere, have the `wrong' thermal periodicities. However the free energies do have the same leading high temperature forms as the standard free energies on the two-sphere. The next few terms in the high-temperature expansion are also explicitly calculated and briefly compared with the Taub-Bolt-AdS bulk result.Comment: 23 pages, JyTeX. Conclusion slightly amended, one equation and minor misprints correcte

Leser-Trélat syndrome in patients affected by six multiple metachronous primitive cancers

Leser-Trélat syndrome is characterized by the eruptive appearance of multiple seborrheic keratoses in association with underlying malignant disease. Usually, the sign of Leser-Trélat is associated with adenocarcinoma, most frequently of the colon, breast, or stomach, but also of the lung, kidney, liver, and pancreas. Herein, we present a case that we believe is the first report of the sign of Leser-Trélat in association with occult gastric adenocarcinoma and the anamnestic oncologic history of five other multiple primitive cancers. Epidermal growth factor receptor (EGFR) immunohistochemical expression analysis of multiple seborrheic keratoses revealed an intense membranous staining in the basal keratinocytes and in all the upper epidermal layers. Patients with the sign of Leser-Trélat should undergo a diagnostic screening programme for malignant disease along with patients with known Leser-Trélat syndrome who present with a recent acute and florid eruption of their seborrheic keratoses. We propose the importance of combining the molecular features of multiple seborrheic keratoses with EGFR immunohistochemistry analyses to determine the likelihood of Leser-Trélat syndrome and the consequent high risk of underlying multiple visceral malignancies

Multidimensional Gaussian sums arising from distribution of Birkhoff sums in zero entropy dynamical systems

A duality formula, of the Hardy and Littlewood type for multidimensional Gaussian sums, is proved in order to estimate the asymptotic long time behavior of distribution of Birkhoff sums $S_n$ of a sequence generated by a skew product dynamical system on the $\mathbb{T}^2$ torus, with zero Lyapounov exponents. The sequence, taking the values $\pm 1$, is pairwise independent (but not independent) ergodic sequence with infinite range dependence. The model corresponds to the motion of a particle on an infinite cylinder, hopping backward and forward along its axis, with a transversal acceleration parameter $\alpha$. We show that when the parameter $\alpha /\pi$ is rational then all the moments of the normalized sums $E((S_n/\sqrt{n})^k)$, but the second, are unbounded with respect to n, while for irrational $\alpha /\pi$, with bounded continuous fraction representation, all these moments are finite and bounded with respect to n.Comment: To be published in J. Phys.

First Production and Detection of Cold Antihydrogen Atoms

The ATHENA experiment recently produced the first atoms of cold antihydrogen. This paper gives a brief review of how this was achieved.Comment: Invited talk at Int. Conf. on Low Energy Antiprotons 2003 (LEAP03), to be published in NIM

Producing Slow Antihydrogen for a Test of CPT Symmetry with ATHENA

The ATHENA experiment at the Antiproton Decelerator facility at CERN aims at testing CPT symmetry with antihydrogen. An overview of the experiment, together with preliminary results of development towards the production of slow antihydrogen are reported.The ATHENA experiment at the Antiproton Decelerator facility at CERN aims at testing CPT symmetry with antihydrogen. An overview of the experiment, together with preliminary results of development towards the production of slow antihydrogen are reported.The ATHENA experiment at the Antiproton Decelerator facility at CERN aims at testing CPT symmetry with antihydrogen. An overview of the experiment, together with preliminary results of development towards the production of slow antihydrogen are reported.The ATHENA experiment at the Antiproton Decelerator facility at CERN aims at testing CPT symmetry with antihydrogen. An overview of the experiment, together with preliminary results of development towards the production of slow antihydrogen are reported

University–industry linkages and academic engagements: individual behaviours and firms’ barriers. Introduction to the special section

The article introduces the special section on “University–industry linkages and academic engagements: Individual behaviours and firms’ barriers”. We first revisit the latest developments of the literature and policy interest on university–industry research. We then build upon the extant literature and unpack the concept of academic engagement by further exploring the heterogeneity of UI linkages along a set of dimensions and actors involved. These are: (1) Incentives and behaviours of individual academic entrepreneurs; (2) Firms’ barriers to cooperation with public research institutions; (3) Individual behaviours, incentives and organizational bottlenecks in late developing countries. We summarize the individual contributions along these dimensions. There are overlooked individual characteristics that affect the degree of engagement of academics and scholars in cooperating with other organizations, of which gender and the non-academic background of individuals are most crucial. The notion of academic engagement should be enlarged to aspects that go beyond the commercialization or patenting of innovation, but embrace social and economic impact more at large. From the perspective of the firm, barriers to innovation might exert an effect on the likelihood to cooperate with universities and public research institutes, most especially to cope with lack of finance or access to frontier knowledge. We finally propose a research agenda that addresses the challenges ahead

Dynamics of antiproton cooling in a positron plasma during antihydrogen formation

Abstract We demonstrate cooling of 10 4 antiprotons in a dense, cold plasma of ∼10 8 positrons, confined in a nested cylindrical Penning trap at about 15 K. The time evolution of the cooling process has been studied in detail, and several distinct types of behavior identified. We propose explanations for these observations and discuss the consequences for antihydrogen production. We contrast these results with observations of interactions between antiprotons and "hot" positrons at about 3000 K, where antihydrogen production is strongly suppressed