Non-Linear Affine Embedding of the Dirac Field from the Multiplicity-Free SL(4,R) Unirreps

The correspondence between the linear multiplicity-free unirreps of SL(4, R) studied by Ne'eman and {\~{S}}ija{\~{c}}ki and the non-linear realizations of the affine group is worked out. The results obtained clarify the inclusion of spinorial fields in a non-linear affine gauge theory of gravitation.Comment: 13 pages, plain TeX, macros include

Understanding chemical evolution in resolved galaxies -- I The local star fraction-metallicity relation

This work studies the relation between gas-phase oxygen abundance and stellar-to-gas fraction in nearby galaxies. We first derive the theoretical prediction, and argue that this relation is fundamental, in the sense that it must be verified regardless of the details of the gas accretion and star formation histories. Moreover, it should hold on "local" scales, i.e. in regions of the order of 1 kpc. These predictions are then compared with a set of spectroscopic observations, including both integrated and resolved data. Although the results depend somewhat on the adopted metallicity calibration, observed galaxies are consistent with the predicted relation, imposing tight constraints on the mass-loading factor of (enriched) galactic winds. The proposed parametrization of the star fraction-metallicity relation is able to describe the observed dependence of the oxygen abundance on gas mass at fixed stellar mass. However, the "local" mass-metallicity relation also depends on the relation between stellar and gas surface densities.Comment: 10 pages, 4 figures. Matches accepted version (significant typo corrected

A Novel Hybrid CNN-AIS Visual Pattern Recognition Engine

Machine learning methods are used today for most recognition problems. Convolutional Neural Networks (CNN) have time and again proved successful for many image processing tasks primarily for their architecture. In this paper we propose to apply CNN to small data sets like for example, personal albums or other similar environs where the size of training dataset is a limitation, within the framework of a proposed hybrid CNN-AIS model. We use Artificial Immune System Principles to enhance small size of training data set. A layer of Clonal Selection is added to the local filtering and max pooling of CNN Architecture. The proposed Architecture is evaluated using the standard MNIST dataset by limiting the data size and also with a small personal data sample belonging to two different classes. Experimental results show that the proposed hybrid CNN-AIS based recognition engine works well when the size of training data is limited in siz

The motion of two masses coupled to a massive spring

We discuss the classical motion of a spring of arbitrary mass coupled to two arbitrary massive blocks attached at its ends. A general approach to the problem is presented and some general results are obtained. Examples for which a simple elastic function can be inferred are discussed and the normal modes and normal frequencies obtained. An approximation procedure to the evaluation of the normel frequencies in the case of uniform elastic function and mass density is also discussed.Comment: Standard Latex file plus three eps figure

Effective Potential and Thermodynamics for a Coupled Two-Field Bose Gas Model

We study the thermodynamics of a two-species homogeneous and dilute Bose gas that is self-interacting and quadratically coupled to each other. We make use of field theoretical functional integral techniques and evaluate the one-loop finite temperature effective potential for this system considering the resummation of the leading order temperature dependent as well as infrared contributions. The symmetry breaking pattern associated to the model is then studied by considering different values of self and inter-species couplings. We pay special attention to the eventual appearance of reentrant phases and/or shifts in the observed critical temperatures as compared to the monoatomic (one-field Bose) case.Comment: 21 pages, 4 eps figure

Integrated Planning of Industrial Gas Supply Chains

In this work, we propose a Mixed Integer Linear Programming (MILP) model for optimal planning of industrial gas supply chain, which integrates supply contracts, production scheduling, truck and rail-car scheduling, as well as inventory management under the Vendor Managed Inventory (VMI) paradigm. The objective used here is minimisation of the total operating cost consisting of purchasing of raw material, production, and transportation costs by trucks/rail-cars so as to satisfy customer demands over a given time horizon. The key decisions for production sites include production schedule and purchase schedule of raw material, while the distribution decisions involve customer to plant/depot allocation, quantity transported through rail network, truck delivery amounts, and times. In addition, a relaxation approach is proposed to solve the problem efficiently. An industrial case study is evaluated to illustrate the applicability of the integrated optimisation framework

Gaussian superpositions in scalar-tensor quantum cosmological models

A free scalar field minimally coupled to gravity model is quantized and the Wheeler-DeWitt equation in minisuperspace is solved analytically, exhibiting positive and negative frequency modes. The analysis is performed for positive, negative and zero values of the curvature of the spatial section. Gaussian superpositions of the modes are constructed, and the quantum bohmian trajectories are determined in the framework of the Bohm-de Broglie interpretation of quantum cosmology. Oscillating universes appear in all cases, but with a characteristic scale of the order of the Planck scale. Bouncing regular solutions emerge for the flat curvature case. They contract classically from infinity until a minimum size, where quantum effects become important acting as repulsive forces avoiding the singularity and creating an inflationary phase, expanding afterwards to an infinite size, approaching the classical expansion as long as the scale factor increases. These are non-singular solutions which are viable models to describe the early Universe.Comment: 14 pages, LaTeX, 3 Postscript figures, uses graficx.st

A general treatment of geometric phases and dynamical invariants

Based only on the parallel transport condition, we present a general method to compute Abelian or non-Abelian geometric phases acquired by the basis states of pure or mixed density operators, which also holds for nonadiabatic and noncyclic evolution. Two interesting features of the non-Abelian geometric phase obtained by our method stand out: i) it is a generalization of Wilczek and Zee's non-Abelian holonomy, in that it describes nonadiabatic evolution where the basis states are parallelly transported between distinct degenerate subspaces, and ii) the non-Abelian character of our geometric phase relies on the transitional evolution of the basis states, even in the nondegenerate case. We apply our formalism to a two-level system evolving nonadiabatically under spontaneous decay to emphasize the non-Abelian nature of the geometric phase induced by the reservoir. We also show, through the generalized invariant theory, that our general approach encompasses previous results in the literature

Hierarchical Approach to Integrated Planning of Industrial Gas Supply Chains

In this article, an optimization-based framework is proposed for integrated production and distribution planning of industrial gas supply chains. The main goal is to minimize the overall cost, which is composed of raw material, product sourced from external suppliers, production, truck, and rail-car costs, while satisfying customer demands. The overall problem is formulated as a mixed-integer linear programming (MILP) model while a two-phase hierarchical solution strategy is developed to solve the resulting optimization problem efficiently. The first phase relies on truck scheduling decisions being relaxed, whereas the second phase solves the original model at reduced space by fixing product allocation as determined by phase one. Finally, an industrial-size case study is used to illustrate the applicability and efficiency of the proposed optimization framework