On the notions of facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem

We investigate three competing notions that generalize the notion of a facet of finite-dimensional polyhedra to the infinite-dimensional Gomory-Johnson model. These notions were known to coincide for continuous piecewise linear functions with rational breakpoints. We show that two of the notions, extreme functions and facets, coincide for the case of continuous piecewise linear functions, removing the hypothesis regarding rational breakpoints. We then separate the three notions using discontinuous examples.Comment: 18 pages, 2 figure

Approximation of corner polyhedra with families of intersection cuts

We study the problem of approximating the corner polyhedron using intersection cuts derived from families of lattice-free sets in $\mathbb{R}^n$. In particular, we look at the problem of characterizing families that approximate the corner polyhedron up to a constant factor, which depends only on $n$ and not the data or dimension of the corner polyhedron. The literature already contains several results in this direction. In this paper, we use the maximum number of facets of lattice-free sets in a family as a measure of its complexity and precisely characterize the level of complexity of a family required for constant factor approximations. As one of the main results, we show that, for each natural number $n$, a corner polyhedron with $n$ basic integer variables and an arbitrary number of continuous non-basic variables is approximated up to a constant factor by intersection cuts from lattice-free sets with at most $i$ facets if $i> 2^{n-1}$ and that no such approximation is possible if $i \leq 2^{n-1}$. When the approximation factor is allowed to depend on the denominator of the fractional vertex of the linear relaxation of the corner polyhedron, we show that the threshold is $i > n$ versus $i \leq n$. The tools introduced for proving such results are of independent interest for studying intersection cuts

Thermodynamics of phase transition in higher dimensional AdS black holes

We investigate the thermodynamics of phase transition for $(n+1)$ dimensional Reissner Nordstrom (RN)-AdS black holes using a grand canonical ensemble. This phase transition is characterized by a discontinuity in specific heat. The phase transition occurs from a lower mass black hole with negative specific heat to a higher mass black hole with positive specific heat. By exploring Ehrenfest's scheme we show that this is a second order phase transition. Explicit expressions for the critical temperature and critical mass are derived. In appropriate limits the results for $(n+1)$ dimensional Schwarzschild AdS black holes are obtained.Comment: LaTex, 11 pages, 5 figures, To appear in JHE

The structure of the infinite models in integer programming

The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper we study the relationships between these two descriptions. Our results have implications for corner polyhedra. One consequence is that nonnegative, continuous valid functions suffice to describe corner polyhedra (with or without rational data)

Removal and degradation of mixed dye pollutants by integrated adsorption-photocatalysis technique using 2-D MoS2/TiO2 nanocomposite

Two-dimensional (2D) Molybdenum disulfide (MoS2) has become one of the most exciting areas of research for adsorbents due to its high surface area and abundant active sites. Mainly, 2D MoS2 show promising removal of textile dye pollutants by adsorption process, but it show high affinity for anionic type of dyes, that limits its performance in mixed dye pollutants treatment. Herein, we demonstrate an integrated approach to remove mixed dye pollutants (anionic and cationic) concurrently by combining adsorption and photocatalysis process. We synthesize MoS2/TiO2 nanocomposites for different weight percentages 2.5, 5, 10, 20, 30 and 50 wt% of pre-synthesized flower-like MoS2 nanoparticle by a two-step hydrothermal method. We demonstrate a new process of two-stage adsorption/photocatalysis using high wt% of MoS2 (Stage-I) and low wt% of MoS2 (Stage-II) nanocomposites. The proposed two-stage integrated adsorption and photocatalysis process using 50% and 2.5% of MoS2 coated TiO2, respectively showed complete removal of methylene blue dye ∼5 times faster than conventional single-stage (adsorption or photocatalysis) water treatment process. Furthermore, the feasibility of the proposed two-stage method in mixed dye pollutants removal (anionic and cationic) testified, which showed excellent performance even in doubling the dye pollutant concentration. This work brings a deeper insight into understanding the morphology and concentration of 2-D MoS2 in MoS2/TiO2 nanocomposite in tackling mixed dye pollutants and the possibilities of applying in textile dyeing industries wastewater treatment plants

Brexit or Brand it? The Effects of Attitude Towards Brexit and Reshored Brands on Consumer Purchase Intention

Copyright © 2022 The Authors. Brexit has caused a seismic shift in the British socio-economic and political landscapes, creating widespread uncertainties, while simultaneously giving hope and national pride to millions. The decision by a number of organizations to reshore their production has opened a new era for business management that challenges the axiomatic assumption of the benefits of offshored production. Although reshoring predates Brexit, the link between the two in the British context is not just serendipitous and they are argued to have reasonable interlinkages. However, there is inadequate empirical evidence to suggest that British consumers’ attitude towards Brexit has any effect on their intention to purchase reshored brands. Through a mixed-methods study comprising a survey of 415 respondents and 20 in-depth interviews, this paper addresses this research gap. Findings suggest that corporate social responsibility (CSR) and consumer reshoring sentiment (CRS) have positive effects on consumers’ attitude towards reshored brands. Despite CRS's positive influence on attitude towards Brexit, the latter does not have any significant effects on the intention to purchase a reshored brand, which is positively influenced by the attitude towards the same brand. As such, companies should enhance the image of their brands and CSR in order to harness the benefits of reshoring.University of Western Australia, as part of the Wiley – The University of Western Australia agreement via the Council of Australian University Librarians

Entangled Dilaton Dyons

Einstein-Maxwell theory coupled to a dilaton is known to give rise to extremal solutions with hyperscaling violation. We study the behaviour of these solutions in the presence of a small magnetic field. We find that in a region of parameter space the magnetic field is relevant in the infra-red and completely changes the behaviour of the solution which now flows to an $AdS_2\times R^2$ attractor. As a result there is an extensive ground state entropy and the entanglement entropy of a sufficiently big region on the boundary grows like the volume. In particular, this happens for values of parameters at which the purely electric theory has an entanglement entropy growing with the area, $A$, like $A \log(A)$ which is believed to be a characteristic feature of a Fermi surface. Some other thermodynamic properties are also analysed and a more detailed characterisation of the entanglement entropy is also carried out in the presence of a magnetic field. Other regions of parameter space not described by the $AdS_2\times R^2$ end point are also discussed.Comment: Some comments regarding comparison with weakly coupled Fermi liquid changed, typos corrected and caption of a figure modifie

Thermodynamics of Large N Gauge Theories with Chemical Potentials in a 1/D Expansion

In order to understand thermodynamical properties of N D-branes with chemical potentials associated with R-symmetry charges, we study a one dimensional large N gauge theory (bosonic BFSS type model) as a first step. This model is obtained through a dimensional reduction of a 1+D dimensional SU(N) Yang-Mills theory and we use a 1/D expansion to investigate the phase structure. We find three phases in the \mu-T plane. We also show that all the adjoint scalars condense at large D and obtain a mass dynamically. This dynamical mass protects our model from the usual perturbative instability of massless scalars in a non-zero chemical potential. We find that the system is at least meta-stable for arbitrary large values of the chemical potentials in D \to \infty limit. We also explore the existence of similar condensation in higher dimensional gauge theories in a high temperature limit. In 2 and 3 dimensions, the condensation always happens as in one dimensional case. On the other hand, if the dimension is higher than 4, there is a critical chemical potential and the condensation happens only if the chemical potentials are below it.Comment: 37 pages, 4 figures; v2: minor corrections, references added; v3: minor corrections, to appear in JHE