Selfconsistent Approximations in Mori's Theory

The constitutive quantities in Mori's theory, the residual forces, are expanded in terms of time dependent correlation functions and products of operators at $t=0$, where it is assumed that the time derivatives of the observables are given by products of them. As a first consequence the Heisenberg dynamics of the observables are obtained as an expansion of the same type. The dynamic equations for correlation functions result to be selfconsistent nonlinear equations of the type known from mode-mode coupling approximations. The approach yields a neccessary condition for the validity of the presented equations. As a third consequence the static correlations can be calculated from fluctuation-dissipation theorems, if the observables obey a Lie algebra. For a simple spin model the convergence of the expansion is studied. As a further test, dynamic and static correlations are calculated for a Heisenberg ferromagnet at low temperatures, where the results are compared to those of a Holstein Primakoff treatment.Comment: 51 pages, Latex, 3 eps figures included, elsart and epsf style files included, also available at http://athene.fkp.physik.th-darmstadt.de/public/wolfram.html and ftp://athene.fkp.physik.th-darmstadt.de/pub/publications/wolfram

Statistically derived contributions of diverse human influences to twentieth-century temperature changes

The warming of the climate system is unequivocal as evidenced by an increase in global temperatures by 0.8 °C over the past century. However, the attribution of the observed warming to human activities remains less clear, particularly because of the apparent slow-down in warming since the late 1990s. Here we analyse radiative forcing and temperature time series with state-of-the-art statistical methods to address this question without climate model simulations. We show that long-term trends in total radiative forcing and temperatures have largely been determined by atmospheric greenhouse gas concentrations, and modulated by other radiative factors. We identify a pronounced increase in the growth rates of both temperatures and radiative forcing around 1960, which marks the onset of sustained global warming. Our analyses also reveal a contribution of human interventions to two periods when global warming slowed down. Our statistical analysis suggests that the reduction in the emissions of ozone-depleting substances under the Montreal Protocol, as well as a reduction in methane emissions, contributed to the lower rate of warming since the 1990s. Furthermore, we identify a contribution from the two world wars and the Great Depression to the documented cooling in the mid-twentieth century, through lower carbon dioxide emissions. We conclude that reductions in greenhouse gas emissions are effective in slowing the rate of warming in the short term.F.E. acknowledges financial support from the Consejo Nacional de Ciencia y Tecnologia (http://www.conacyt.gob.mx) under grant CONACYT-310026, as well as from PASPA DGAPA of the Universidad Nacional Autonoma de Mexico. (CONACYT-310026 - Consejo Nacional de Ciencia y Tecnologia; PASPA DGAPA of the Universidad Nacional Autonoma de Mexico

Actions of the braid group, and new algebraic proofs of results of Dehornoy and Larue

This article surveys many standard results about the braid group with emphasis on simplifying the usual algebraic proofs. We use van der Waerden's trick to illuminate the Artin-Magnus proof of the classic presentation of the algebraic mapping-class group of a punctured disc. We give a simple, new proof of the Dehornoy-Larue braid-group trichotomy, and, hence, recover the Dehornoy right-ordering of the braid group. We then turn to the Birman-Hilden theorem concerning braid-group actions on free products of cyclic groups, and the consequences derived by Perron-Vannier, and the connections with the Wada representations. We recall the very simple Crisp-Paris proof of the Birman-Hilden theorem that uses the Larue-Shpilrain technique. Studying ends of free groups permits a deeper understanding of the braid group; this gives us a generalization of the Birman-Hilden theorem. Studying Jordan curves in the punctured disc permits a still deeper understanding of the braid group; this gave Larue, in his PhD thesis, correspondingly deeper results, and, in an appendix, we recall the essence of Larue's thesis, giving simpler combinatorial proofs.Comment: 51`pages, 13 figure

Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force

We study the competitive action of magnetic field, Coulomb repulsion and space curvature on the motion of a charged particle. The three types of interaction are characterized by three basic lengths: l_{B} the magnetic length, l_{0} the Bohr radius and R the radius of the sphere. The energy spectrum of the particle is found by solving a Schr\"odinger equation of the Heun type, using the technique of continued fractions. It displays a rich set of functioning regimes where ratios \frac{R}{l_{B}} and \frac{R}{l_{0}} take definite values.Comment: 12 pages, 5 figures, accepted to JOPA, november 200

Biomedical Ph.D. Students Enrolled in Two Elite Universities in the United Kingdom and the United States Report Adopting Multiple Learning Relationships

Objective: The ability to form multiple learning relationships is a key element of the doctoral learning environment in the biomedical sciences. Of these relationships, that between student and supervisor has long been viewed as key. There are, however, limited data to describe the student perspective on what makes this relationship valuable. In the present study, we discuss the findings of semi-structured interviews with biomedical Ph.D. students from the United Kingdom and the United States to: i) determine if the learning relationships identified in an Australian biomedical Ph.D. cohort are also important in a larger international student cohort; and ii) improve our understanding of student perceptions of value in their supervisory relationships. Study Design 32 students from two research intensive universities, one in the United Kingdom (n = 17), and one in the United States (n = 15) were recruited to participate in a semi-structured interview. Verbatim transcripts were transcribed, validated and analysed using a Miles and Huberman method for thematic analysis. Results: Students reported that relationships with other Ph.D. students, post-doctoral scientists and supervisors were all essential to their learning. Effective supervisory relationships were perceived as the primary source of high-level project guidance, intellectual support and confidence. Relationships with fellow students were viewed as essential for the provision of empathetic emotional support. Technical learning was facilitated, almost exclusively, by relationships with postdoctoral staff. Conclusions: These data make two important contributions to the scholarship of doctoral education in the biomedical sciences. Firstly, they provide further evidence for the importance of multiple learning relationships in the biomedical doctorate. Secondly, they clarify the form of a ‘valued’ supervisory relationship from a student perspective. We conclude that biomedical doctoral programs should be designed to contain a minimum level of formalised structure to promote the development of multiple learning relationships that are perceived as key to student learning

A 2.5-GHz asymmetric multilevel outphasing power amplifier in 65-nm CMOS

We present a high-efficiency transmitter based on asymmetric multilevel outphasing (AMO). AMO transmitters improve their efficiency over LINC (linear amplification using nonlinear components) transmitters by switching the output envelopes of the power amplifiers among a discrete set of levels. This minimizes the occurrence of large outphasing angles, reducing the energy lost in the power combiner. We demonstrate this concept with a 2.5-GHz, 20-dBm peak output power transmitter using 2-level AMO designed in a 65-nm CMOS process. To the authors' knowledge, this IC is the first integrated implementation of the AMO concept. At peak output power, the measured power-added efficiency is 27.8%. For a 16-QAM signal with 6.1dB peak-to-average power ratio, the AMO prototype improves the average efficiency from 4.7% to 10.0% compared to the standard LINC system

An algorithm to obtain global solutions of the double confluent Heun equation

A procedure is proposed to construct solutions of the double confluent Heun equation with a determinate behaviour at the singular points. The connection factors are expressed as quotients of Wronskians of the involved solutions. Asymptotic expansions are used in the computation of those Wronskians. The feasibility of the method is shown in an example, namely, the Schroedinger equation with a quasi-exactly-solvable potential

On conformal measures and harmonic functions for group extensions

We prove a Perron-Frobenius-Ruelle theorem for group extensions of topological Markov chains based on a construction of $\sigma$-finite conformal measures and give applications to the construction of harmonic functions.Comment: To appear in Proceedings of "New Trends in Onedimensional Dynamics, celebrating the 70th birthday of Welington de Melo

Sign Rules for Anisotropic Quantum Spin Systems

We present new and exact ``sign rules'' for various spin-s anisotropic spin-lattice models. It is shown that, after a simple transformation which utilizes these sign rules, the ground-state wave function of the transformed Hamiltonian is positive-definite. Using these results exact statements for various expectation values of off-diagonal operators are presented, and transitions in the behavior of these expectation values are observed at particular values of the anisotropy. Furthermore, the effects of sign rules in variational calculations and quantum Monte Carlo calculations are considered. They are illustrated by a simple variational treatment of a one-dimensional anisotropic spin model.Comment: 4 pages, 1 ps-figur