Hamilton-Jacobi Approach for Power-Law Potentials

The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact analytical solution is determined in terms of $\alpha$, $n$ and the total energy $E$. It is also shown that the non-linear equation of motion can be linearized by constructing a hypergeometric differential equation for the inverse problem $t(q)$. A variable transformation reducing the general problem to that one of a particle subjected to a linear force is also established. For any value of $n$, it leads to a simple harmonic oscillator if $E>0$, an "anti-oscillator" if $E<0$, or a free particle if E=0. However, such a reduction is not possible in the relativistic case. For a bounded relativistic motion, the first order correction to the period is determined for any value of $n$. For $n >> 1$, it is found that the correction is just twice that one deduced for the simple harmonic oscillator ($n=2$), and does not depend on the specific value of $n$.Comment: 12 pages, Late

Just Markets from the Perspective of Catholic Social Teaching

The justice of markets is intricately connected to the treatment of the poor and the disadvantaged in market economies. The increased interest of multinational corporations in low-income market segments affords, on one hand, the opportunity for a more inclusive capitalism, and on the other, the threat of greater exploitation of poor and disadvantaged consumers. This article traces the contributions of Catholic Social Teaching and its basic principles toward providing insight into what constitutes justice in such marketing to the impoverished situations

The Integrative Justice Model for Marketing to the Poor: An Extension of S-D Logic to Distributive Justice and Macromarketing

As multinational corporations (MNCs) increasingly turn their attention to the fast growing markets of China, India, Brazil, and other developing areas, the question of fair treatment of consumers and other residents of those areas is more intensively debated than ever before. In essence, issues of distributive justice come to the fore, that is, are the benefits and burdens of rapid economic development being fairly allocated among the parties and stakeholders to the expanded economic transactions? In response to this question, the authors have postulated a detailed normative model for ethically marketing to impoverished consumer segments; they label their model, the Integrative Justice Model (IJM) for impoverished markets. In this article, the authors show how the IJM, an independently derived model of normative marketing, conforms in its key operational elements to the foundational premises (FPs) of the positive S-D logic and extends the S-D logic perspective to societal and ethical concerns. Furthermore, the authors connect the S-D logic philosophy to macromarketing frameworks such as distributive justice, sustainability, and labor

Marketing to the Poor: An Integrative Justice Model for Engaging Impoverished Marketing Segments

The relatively recent entry of multinational corporations (MNCs) into low-income markets, particularly in developing countries, affords the opportunity for the more inclusive capitalism envisioned by globalists. Alternatively, an expansion of MNC marketing in less developed economies might foreshadow the greater exploitation of disadvantaged consumers predicted by many critics of expanded free trade. To diffuse the charge of “exploitative” marketing, it is imperative that corporate marketing efforts seeking to engage impoverished segments be grounded in a strong ethical framework. This article unveils one such framework—the “integrative justice model” (IJM). The IJM is an aspirational model that outlines how to market ethically to disadvantaged consumers in both developed and developing countries. The authors derive the elements of this model from frameworks of moral philosophy and management theory. Although the IJM is normative in nature, the authors connect it to real-world examples, which provides MNCs that market to the poor practical benchmarks for conducting their business operations with fairness and equity. The article concludes with a discussion of the implications of the IJM for public policy

Gross National Happiness (GNH): Linkages to and Implications for Macromarketing

This theoretical commentary explores the concept of Gross National Happiness (GNH) and connects it with several central macromarketing concepts such as QoL, ethics, the common good, the purpose of market activity as well as the United Nations’ Sustainable Development Goals. The paper portrays GNH as a normative concept that captures collective well-being; it categorizes GNH, at least from the standpoint of Western moral philosophy, as most closely aligned with classical utilitarianism, and it distinguishes GNH from QoL on the basis of its predominantly aspirational and subjective orientation. It asserts that GNH can be seen as one manifestation of the common good, and, in that manner can be perceived as a ‘more ethical’ conception of the purpose of business activity. Finally, it links GNH to promising areas of Macromarketing scholarship. One essential contribution of this commentary is that it differentiates subjective community happiness from more objective measures of QoL familiar to macromarketing studies

Studying light propagation in a locally homogeneous universe through an extended Dyer-Roeder approach

Light is affected by local inhomogeneities in its propagation, which may alter distances and so cosmological parameter estimation. In the era of precision cosmology, the presence of inhomogeneities may induce systematic errors if not properly accounted. In this vein, a new interpretation of the conventional Dyer-Roeder (DR) approach by allowing light received from distant sources to travel in regions denser than average is proposed. It is argued that the existence of a distribution of small and moderate cosmic voids (or "black regions") implies that its matter content was redistributed to the homogeneous and clustered matter components with the former becoming denser than the cosmic average in the absence of voids. Phenomenologically, this means that the DR smoothness parameter (denoted here by $\alpha_E$) can be greater than unity, and, therefore, all previous analyses constraining it should be rediscussed with a free upper limit. Accordingly, by performing a statistical analysis involving 557 type Ia supernovae (SNe Ia) from Union2 compilation data in a flat $\Lambda$CDM model we obtain for the extended parameter, $\alpha_E=1.26^{+0.68}_{-0.54}$ ($1\sigma$). The effects of $\alpha_E$ are also analyzed for generic $\Lambda$CDM models and flat XCDM cosmologies. For both models, we find that a value of $\alpha_E$ greater than unity is able to harmonize SNe Ia and cosmic microwave background observations thereby alleviating the well-known tension between low and high redshift data. Finally, a simple toy model based on the existence of cosmic voids is proposed in order to justify why $\alpha_E$ can be greater than unity as required by supernovae data.Comment: 5 pages, 2 figures. Title modified, results unchanged. It matches version published as a Brief Report in Phys. Rev.