A Characterization of Exact Non-atomic Market Games

Continuous exact non-atomic games are naturally associated to certain operators between Banach spaces. It thus makes sense to study games by means of the corresponding operators. We characterize non-atomic exact market games in terms of the properties of the associated operators. We also prove a separation theorem for weak compact sets of countably additive measures, which is of independent interest.

Revisiting modern portfolio theory

This paper revisits Modern Portfolio Theory and derives eleven properties of Efficient Allocations and Portfolios in the presence of leverage. With different degrees of leverage, an Efficient Portfolio is a linear combination of two portfolios that lie in different efficient frontiers - which allows for an attractive reinterpretation of the Separation Theorem. In particular a change in the investor risk-return preferences will leave the allocation between the Minimum Risk and Risk Portfolios completely unaltered - but will change the magnitudes of the tactical risk allocations within the Risk Portfolio. The paper also discusses the role of diversification in an Efficient Portfolio, emphasizing its more tactical, rather than strategic character

Essays on the selection of securities: Decision on acquisition and issuance perspectives and decision rules

This dissertation is a discourse on the capital market and its interactive framework of acquisition and issuance of financial assets that drive the economy from both sides—investors/lenders and issuers/users of capital assets. My work consists of four essays in financial economics that offer a spectrum of revisions to this significant area of study. The first essay is a delineation of the capital market over the past half a century and major developments on capital markets on issues that pertain to the investor's opportunity set and the corporation's capital-raising availability set. This chapter should have merits on two counts: (i) a comprehensive account of capital markets and return-generating assets and (ii) a backdrop against which I present my findings in Chapters 2 through 4. ^ In Chapter 2, I rework on the Markowitz-Roy-Tobin structure of the efficient frontier and of the Separation Theorem. Starting off with a 2-asset portfolio and extending the paradigm to an n-asset portfolio, I bring out the optimal choice of assets for an investor under constrained utility maximization. In this chapter, I analyze the selection and revision-theoretic construct and bring out optimum choices. The effect of a change in perceived risk or return in the mind of an investor is ascertained on the portfolio composition. ^ Chapter 3 takes a look into corporations that issue market securities. The question of how a corporation decides what kinds of securities it should issue in the marketplace to raise funds brings out the classic value invariance proposition of Modigliani and Miller and fills the gap that existed in the literature for almost half a century. I question the general validity in the classic results of Modigliani and Miller and modify the existing literature on the celebrated value invariance proposition. ^ Chapter 4 takes the Modigliani-Miller regime to its correct prescription in the presence of corporate and personal taxes. I show that Modigliani-Miller's age-old proposition needs corrections and extensions, which I derive. ^ My dissertation overall brings all of these corrections and extensions to the existing literature as my findings, showing that capital markets are in an ever-changing state of necessary revision. ^

Separation index of graphs and stacked 2-spheres

In 1987, Kalai proved that stacked spheres of dimension d >= 3 are characterised by the fact that they attain equality in Barnette's celebrated Lower Bound Theorem. This result does not extend to dimension d = 2. In this article, we give a characterisation of stacked 2-spheres using what we call the separation index. Namely, we show that the separation index of a triangulated 2-sphere is maximal if and only if it is stacked. In addition, we prove that, amongst all n-vertex triangulated 2-spheres, the separation index is minimised by some n-vertex flag sphere for n >= 6. Furthermore, we apply this characterisation of stacked 2-spheres to settle the outstanding 3-dimensional case of the Lutz-Sulanke-Swartz conjecture that ``tight-neighbourly triangulated manifolds are tight''. For dimension d >= 4, the conjecture has already been proved by Effenberger following a result of Novik and Swartz. (C) 2015 Elsevier Inc. All rights reserved.

On the Vertex Separation of Cactus Graphs

This paper is part of a work in progress whose goal is to construct a fast, practical algorithm for the vertex separation (VS) of cactus graphs. We prove a \main theorem for cacti", a necessary and sufficient condition for the VS of a cactus graph being k. Further, we investigate the ensuing ramifications that prevent the construction of an algorithm based on that theorem only.

On the Vertex Separation of Maximal Outerplanar Graphs

We investigate the NP-complete problem Vertex Separation (VS) on Maximal Outerplanar Graphs (mops). We formulate and prove a “main theorem for mops”, a necessary and sufficient condition for the vertex separation of a mop being k. The main theorem reduces the vertex separation of mops to a special kind of stretchability, one that we call affixability, of submops.

Evaluation of separation management algorithms in Class G airspace

Use of Unmanned Aerial Vehicles (UAVs) in support of government applications has already seen significant growth and the potential for use of UAVs in commercial applications is expected to rapidly expand in the near future. However, the issue remains on how such automated or operator-controlled aircraft can be safely integrated into current airspace. If the goal of integration is to be realized, issues regarding safe separation in densely populated airspace must be investigated. This paper investigates automated separation management concepts in uncontrolled airspace that may help prepare for an expected growth of UAVs in Class G airspace. Not only are such investigations helpful for the UAV integration issue, the automated separation management concepts investigated by the authors can also be useful for the development of new or improved Air Traffic Control services in remote regions without any existing infrastructure. The paper will also provide an overview of the Smart Skies program and discuss the corresponding Smart Skies research and development effort to evaluate aircraft separation management algorithms using simulations involving realworld data communication channels, and verified against actual flight trials. This paper presents results from a unique flight test concept that uses real-time flight test data from Australia over existing commercial communication channels to a control center in Seattle for real-time separation management of actual and simulated aircraft. The paper also assesses the performance of an automated aircraft separation manager.

Non-adversarial advocates and gatekeepers : lawyers, FDR practitioners and co-operative post-separation parenting

The compulsory dispute resolution requirements in family law parenting cases create new roles and obligations for both lawyers and family dispute resolution (FDR) practitioners. This article will discuss how the legislative provisions impact on both sets of professionals in practice. It will also highlight the increased non-adversarial role of lawyers and a new role for FDR practitioners as “gatekeepers” to family courts in cases requiring FDR certificates.

High-performance ceramic membranes with a separation layer of metal oxide nanofibers

In conventional fabrication of ceramic separation membranes, the particulate sols are applied onto porous supports. Major structural deficiencies under this approach are pin-holes and cracks, and the dramatic losses of flux when pore sizes are reduced to enhance selectivity. We have overcome these structural deficiencies by constructing hierarchically structured separation layer on a porous substrate using lager titanate nanofibers and smaller boehmite nanofibers. This yields a radical change in membrane texture. The resulting membranes effectively filter out species larger than 60 nm at flow rates orders of magnitude greater than conventional membranes. This reveals a new direction in membrane fabrication.

Ceramic membranes for separation of proteins and DNA by in situ growth of alumina nanofibres with a nanomesh of metal oxide nanofibres

Ceramic membranes were fabricated by in situ synthesis of alumina nanofibres in the pores of an alumina support as a separation layer, and exhibited a high permeation selectivity for bovine serum albumin relative to bovine hemoglobin (over 60 times) and can effectively retain DNA molecules at high fluxes.

Porous PLGA microspheres effectively loaded with BSA protein by electrospraying combined with phase separation in liquid nitrogen

Polymer microspheres loaded with bioactive particles, biomolecules, proteins, and/or growth factors play important roles in tissue engineering, drug delivery, and cell therapy. The conventional double emulsion method and a new method of electrospraying into liquid nitrogen were used to prepare bovine serum albumin (BAS)-loaded poly(lactic-co-glycolic acid) (PLGA) porous microspheres. The particle size, the surface morphology and the internal porous structure of the microspheres were observed using scanning electron microscopy (SEM). The loading efficiency, the encapsulation efficiency, and the release profile of the BSA-loaded PLGA microspheres were measured and studied. It was shown that the microspheres from double emulsion had smaller particle sizes (3-50 m), a less porous structure, a poor loading efficiency (5.2 %), and a poor encapsulation efficiency (43.5%). However, the microspheres from the electrospraying into liquid nitrogen had larger particle sizes (400-600 m), a highly porous structure, a high loading efficiency (12.2%), and a high encapsulation efficiency (93.8%). Thus the combination of electrospraying with freezing in liquid nitrogen and subsequent freeze drying represented a suitable way to produce polymer microspheres for effective loading and sustained release of proteins.

Separation management approaches during periods of communication failure

New air traffic automated separation management concepts are constantly under investigation. Yet most of the automated separation management algorithms proposed over the last few decades have assumed either perfect communication or exact knowledge of all aircraft locations. In realistic environments, these idealized assumptions are not valid and any communication failure can potentially lead to disastrous outcomes. This paper examines the separation performance behavior of several popular algorithms during periods of information loss. This comparison is done through simulation studies. These simulation studies suggest that communication failure can cause the performance of these separation management algorithms to degrade significantly. This paper also describes some preliminary flight tests.

Automated centralised separation management with onboard decision support

This paper proposes a novel automated separation management concept in which onboard decision support is integrated within a centralised air traffic separation management system. The onboard decision support system involves a decentralised separation manager that can overrule air traffic management instructions under certain circumstances. This approach allows the advantages of both centralised and decentralised concepts to be combined (and disadvantages of each separation management approach to be mitigated). Simulation studies are used to illustrate the potential benefits of the combined separation management concept.