Two New Proofs of Afriat's Theorem

Two New Proofs of Afriat's Theore

On renormalizability of the massless Thirring model

We discuss the renormalizability of the massless Thirring model in terms of the causal fermion Green functions and correlation functions of left-right fermion densities. We obtain the most general expressions for the causal two-point Green function and correlation function of left-right fermion densities with dynamical dimensions of fermion fields, parameterised by two parameters. The region of variation of these parameters is constrained by the positive definiteness of the norms of the wave functions of the states related to components of the fermion vector current. We show that the dynamical dimensions of fermion fields calculated for causal Green functions and correlation functions of left-right fermion densities can be made equal. This implies the renormalizability of the massless Thirring model in the sense that the ultra-violet cut-off dependence, appearing in the causal fermion Green functions and correlation functions of left-right fermion densities, can be removed by renormalization of the wave function of the massless Thirring fermion fields only.Comment: 17 pages, Latex, the contribution of fermions with opposite chirality is added,the parameterisation of fermion determinant by two parameters is confirmed,it is shown that dynamical dimensions of fermion fields calculated from different correlation functions can be made equal.This allows to remove the dependence on the ultra-violet cut-off by the renormalization of the wave function of Thirring fermion fields onl

Massless Thirring model in canonical quantization scheme

It is shown that the exact solvability of the massless Thirring model in the canonical quantization scheme originates from the intrinsic linearizability of its Heisenberg equations in the method of dynamical mappings. The corresponding role of inequivalent representations of free massless Dirac field is elucidated.Comment: 10 page

Near-optimal modified base stock policies for the capacitated inventory problem with stochastic demand and fixed cost

In this study, we investigate a single-item, periodic-review inventory problem where the production capacity is limited and unmet demand is backordered. We assume that customer demand in each period is a stationary, discrete random variable. Linear holding and backorder cost are charged per unit at the end of a period. In addition to the variable cost charged per unit ordered, a positive fixed ordering cost is incurred with each order given. The optimization criterion is the minimization of the expected cost per period over a planning horizon. We investigate the infinite horizon problem by modeling the problem as a discrete-time Markov chain. We propose a heuristic for the problem based on a particular solution of this stationary model, and conduct a computational study on a set of instances, providing insight on the performance of the heuristic. © 2014 World Scientific Publishing Co

Group Theory Approach to Band Structure: Scarf and Lame Hamiltonians

The group theoretical treatment of bound and scattering state problems is extended to include band structure. We show that one can realize Hamiltonians with periodic potentials as dynamical symmetries, where representation theory provides analytic solutions, or which can be treated with more general spectrum generating algebraic methods. We find dynamical symmetries for which we derive the transfer matrices and dispersion relations. Both compact and non-compact groups are found to play a role.Comment: 4 pages + 2 figs. Revtex/epsf. To appear: Phys Rev Lett, v.83 199

Shape invariant potential formalism for photon-added coherent state construction

An algebro-operator approach, called shape invariant potential method, of constructing generalized coherent states for photon-added particle system is presented. Illustration is given on Poschl-Teller potential

‘We’ll be okay together’: navigating challenges as queer university students in Aotearoa New Zealand

Queer university students face multiple stressors which can contribute to mental health difficulties, including minority stressors unique to their queer identities. However, there is little literature exploring stressors faced by queer individuals in university settings. The aim of this study was to qualitatively explore the current challenges and strengths faced by queer university students in Aotearoa New Zealand, in order to contextualise their mental health experiences. Twenty-eight queer students participated across 12 focus groups or interviews. Two queer researchers thematically analysed the data. Three themes were interpreted from the data: ‘That’s not feminine enough’: the impact of societal ideologies on queer students; ‘There’s one rainbow person in the room’: Tokenism, social isolation, and then finding community; and ‘You know what it’s like to not be heard’: The transformation of challenges into strengths. The findings illustrate how queer university students make meaning of their challenges, and the strengths they develop to mitigate these. Educational institutions are highlighted as important sites of systemic change, to reduce minority stressors in students’ lives

‘Is it worth potentially dealing with someone who won't get it?’: LGBTQA+ university students’ perspectives on mental health care

LGBTQA+ university students have unique mental health needs and high rates of mental distress compared to their cisgender heterosexual peers; however, it is likely that many LGBTQA+ individuals remain untreated or receive inappropriate or insensitive care. The aim of this study was to explore the experiences and preferences in mental health care of LGBTQA+ university students in Aotearoa New Zealand. Twenty-eight young adults participated across 12 focus groups or interviews in which they were asked about their experiences and preferences. We used thematic analysis to identify patterns of meaning in the data. Researchers developed three themes of I can do this on my own, but others should seek help; you have to be lucky to access mental health care; and ‘therapists just need to be a bit more like up with the programme’. The results of this study mirror those found in more general studies of LGBTQA+ mental healthcare experiences, however, also adds to considerations for university campus healthcare services. The findings of this study should be considered by all mental health providers working with LGBTQA+ young adult university students

WARNING: Physics Envy May Be Hazardous To Your Wealth!

The quantitative aspirations of economists and financial analysts have for many years been based on the belief that it should be possible to build models of economic systems - and financial markets in particular - that are as predictive as those in physics. While this perspective has led to a number of important breakthroughs in economics, "physics envy" has also created a false sense of mathematical precision in some cases. We speculate on the origins of physics envy, and then describe an alternate perspective of economic behavior based on a new taxonomy of uncertainty. We illustrate the relevance of this taxonomy with two concrete examples: the classical harmonic oscillator with some new twists that make physics look more like economics, and a quantitative equity market-neutral strategy. We conclude by offering a new interpretation of tail events, proposing an "uncertainty checklist" with which our taxonomy can be implemented, and considering the role that quants played in the current financial crisis.Comment: v3 adds 2 reference

Massless Metric Preheating

Can super-Hubble metric perturbations be amplified exponentially during preheating ? Yes. An analytical existence proof is provided by exploiting the conformal properties of massless inflationary models. The traditional conserved quantity \zeta is non-conserved in many regions of parameter space. We include backreaction through the homogeneous parts of the inflaton and preheating fields and discuss the role of initial conditions on the post-preheating power-spectrum. Maximum field variances are strongly underestimated if metric perturbations are ignored. We illustrate this in the case of strong self-interaction of the decay products. Without metric perturbations, preheating in this case is very inefficient. However, metric perturbations increase the maximum field variances and give alternative channels for the resonance to proceed. This implies that metric perturbations can have a large impact on calculations of relic abundances of particles produced during preheating.Comment: 8 pages, 4 colour figures. Version to appear in Phys. Rev. D. Contains substantial new analysis of the ranges of parameter space for which large changes to the inflation-produced power spectrum are expecte