On representations of the feasible set in convex optimization

We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any representation of K that satisfies a mild nondegeneracy assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely every KKT point is a minimizer. That is, the KKT optimality conditions are necessary and sufficient as in convex programming where one assumes that the $g_j$ are convex. So in convex optimization, and as far as one is concerned with KKT points, what really matters is the geometry of K and not so much its representation.Comment: to appear in Optimization Letter

Zero modes' fusion ring and braid group representations for the extended chiral su(2) WZNW model

The zero modes' Fock space for the extended chiral $su(2)$ WZNW model gives room to a realization of the Grothendieck fusion ring of representations of the restricted $U_q sl(2)$ quantum universal enveloping algebra (QUEA) at an even ($2h$-th) root of unity, and of its extension by the Lusztig operators. It is shown that expressing the Drinfeld images of canonical characters in terms of Chebyshev polynomials of the Casimir invariant $C$ allows a streamlined derivation of the characteristic equation of $C$ from the defining relations of the restricted QUEA. The properties of the fusion ring of the Lusztig's extension of the QUEA in the zero modes' Fock space are related to the braiding properties of correlation functions of primary fields of the extended $su(2)_{h-2}$ current algebra model.Comment: 36 pages, 1 figure; version 3 - improvements in Sec. 2 and 3: definitions of the double, as well as R- (and M-)matrix changed to fit the zero modes' one

Strong Connections on Quantum Principal Bundles

A gauge invariant notion of a strong connection is presented and characterized. It is then used to justify the way in which a global curvature form is defined. Strong connections are interpreted as those that are induced from the base space of a quantum bundle. Examples of both strong and non-strong connections are provided. In particular, such connections are constructed on a quantum deformation of the fibration $S^2 -> RP^2$. A certain class of strong $U_q(2)$-connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with the q-dependent hermitian metric. A particular form of the Yang-Mills action on a trivial U\sb q(2)-bundle is investigated. It is proved to coincide with the Yang-Mills action constructed by A.Connes and M.Rieffel. Furthermore, it is shown that the moduli space of critical points of this action functional is independent of q.Comment: AMS-LaTeX, 40 pages, major revision including examples of connections over a quantum real projective spac

Bose condensates in a harmonic trap near the critical temperature

The mean-field properties of finite-temperature Bose-Einstein gases confined in spherically symmetric harmonic traps are surveyed numerically. The solutions of the Gross-Pitaevskii (GP) and Hartree-Fock-Bogoliubov (HFB) equations for the condensate and low-lying quasiparticle excitations are calculated self-consistently using the discrete variable representation, while the most high-lying states are obtained with a local density approximation. Consistency of the theory for temperatures through the Bose condensation point requires that the thermodynamic chemical potential differ from the eigenvalue of the GP equation; the appropriate modifications lead to results that are continuous as a function of the particle interactions. The HFB equations are made gapless either by invoking the Popov approximation or by renormalizing the particle interactions. The latter approach effectively reduces the strength of the effective scattering length, increases the number of condensate atoms at each temperature, and raises the value of the transition temperature relative to the Popov approximation. The renormalization effect increases approximately with the log of the atom number, and is most pronounced at temperatures near the transition. Comparisons with the results of quantum Monte Carlo calculations and various local density approximations are presented, and experimental consequences are discussed.Comment: 15 pages, 11 embedded figures, revte

Lattice QCD Constraints on the Nuclear Equation of State

Based on the quasi-particle description of the QCD medium at finite temperature and density we formulate the phenomenological model for the equation of state that exhibits crossover or the first order deconfinement phase transition. The models are constructed in such a way to be thermodynamically consistent and to satisfy the properties of the ground state nuclear matter comply with constraints from intermediate heavy--ion collision data. Our equations of states show quite reasonable agreement with the recent lattice findings on temperature and baryon chemical potential dependence of relevant thermodynamical quantities in the parameter range covering both the hadronic and quark--gluon sectors. The model predictions on the isentropic trajectories in the phase diagram are shown to be consistent with the recent lattice results. Our nuclear equations of states are to be considered as an input to the dynamical models describing the production and the time evolution of a thermalized medium created in heavy ion collisions in a broad energy range from SIS up to LHC.Comment: 13 pages, 11 figure

Critical Reflections on Methodological Challenge in Arts and Dementia Evaluation and Research

Methodological rigour, or its absence, is often a focus of concern for the emerging field of evaluation and research around arts and dementia. However, this paper suggests that critical attention should also be paid to the way in which individual perceptions, hidden assumptions and underlying social and political structures influence methodological work in the field. Such attention will be particularly important for addressing methodological challenges relating to contextual variability, ethics, value judgement, and signification identified through a literature review on this topic. Understanding how, where and when evaluators and researchers experience such challenges may help to identify fruitful approaches for future evaluation. This paper is based upon a presentation on the subject given at the First International Research Conference on the Arts and Dementia: Theory, Methodology and Evidence on 9 March 2017

Tradeoffs and synergies in wetland multifunctionality: A scaling issue

Wetland area in agricultural landscapes has been heavily reduced to gain land for crop production, but in recent years there is increased societal recognition of the negative consequences from wetland loss on nutrient retention, biodiversity and a range of other benefits to humans. The current trend is therefore to re-establish wetlands, often with an aim to achieve the simultaneous delivery of multiple ecosystem services, i.e., multifunctionality. Here we review the literature on key objectives used to motivate wetland re-establishment in temperate agricultural landscapes (provision of flow regulation, nutrient retention, climate mitigation, biodiversity conservation and cultural ecosystem services), and their relationships to environmental properties, in order to identify potential for tradeoffs and synergies concerning the development of multifunctional wetlands. Through this process, we find that there is a need for a change in scale from a focus on single wetlands to wetlandscapes (multiple neighboring wetlands including their catchments and surrounding landscape features) if multiple societal and environmental goals are to be achieved. Finally, we discuss the key factors to be considered when planning for re-establishment of wetlands that can support achievement of a wide range of objectives at the landscape scale

Observing many body effects on lepton pair production from low mass enhancement and flow at RHIC and LHC energies

The $\rho$ spectral function at finite temperature calculated using the real-time formalism of thermal field theory is used to evaluate the low mass dilepton spectra. The analytic structure of the $\rho$ propagator is studied and contributions to the dilepton yield in the region below the bare $\rho$ peak from the different cuts in the spectral function are discussed. The space-time integrated yield shows significant enhancement in the region below the bare $\rho$ peak in the invariant mass spectra. It is argued that the variation of the inverse slope of the transverse mass ($M_T$) distribution can be used as an efficient tool to predict the presence of two different phases of the matter during the evolution of the system. Sensitivity of the effective temperature obtained from the slopes of the $M_T$ spectra to the medium effects are studied