Inflation in Bianchi models and the cosmic no hair theorem in brane world

In this paper, the cosmic no hair theorem for anisotropic Bianchi models which admit inflation with a scalar field is studied in the framework of Brane world. It is found that all Bianchi models except Bianchi type IX, transit to an inflationary regime with vanishing anisotropy. In the Brane world, anisotropic universe approaches the inflationary era much faster than that in the general theory of relativity. The form of the potential does not affect the evolution in the inflationary epoch. However, the late time behaviour is controlled by a constant additive factor in the potential for the inflaton field.Comment: 12 pages, no figures, submitted to Phys. Rev.

The Institutionalist Implications of an Odious Debt Doctrine

Sovereigns incur debts, and creditors look to the law to hold sovereigns to their obligations. In legal terms, the question is whether to recognize and define an odious debt defense through a treaty or national legislative acts, on the one hand, or through the decisions of authoritative dispute-settlement bodies, whether international arbitral organs or domestic courts. Moreover, others may think that odious debt doctrine as a means can optimize the social welfare generated by sovereign-debt contracts. Here, Stephan examines the social welfare in the economic sense but attacks the problem from a different direction and concludes that no satisfactory mechanism exists for instituting an odious debt doctrine

Methodism in Macedonia Between the Two World Wars

After World War I ended, the part of Macedonia commonly called Vardar Macedonia was incorporated into the new Kingdom of Serbs, Croats, and Slovenes (subsequently renamed Yugoslavia). It was officially proclaimed to be a part of Serbia as the Serbian government did not recognize a separate Macedonian nationality. Some 10 stations of the American Board, including the Bitola Girls\u27 School, were in this area. The American Board attempted to maintain a semblance of unity in the Balkan Mission, but Greece, Bulgaria, and Yugoslavia were on such unfriendly terms that this was not feasible. For a while the American Board was planning to establish a strong mission in southern Yugoslavia, and the missionaries in Bulgaria made various recommendations in this direction, primarily suggesting sending out a competent missionary Serbian-speaking couple speaking, since the new government insisted that Serbian be the official language of Macedonia, and tried to obliterate the Macedonian or Bulgarian languages even though they were spoken by the majority

Religion in Eastern Europe After the Fall of Communism: From Euphoria to Anxiety

In the decades prior to the implosion of the communist system, change could be discerned here and there in Eastern Europe. The purpose of this article is to provide a general overview of the most pertinent developments that spurred the transition from communism to post-communism, employing some fairly broad brushstrokes to make my case

Comparative Noninformativities of Quantum Priors Based on Monotone Metrics

We consider a family of prior probability distributions of particular interest, all being defined on the three-dimensional convex set of two-level quantum systems. Each distribution is, following recent work of Petz and Sudar, taken to be proportional to the volume element of a monotone metric on that Riemannian manifold. We apply an entropy-based test (a variant of one recently developed by Clarke) to determine which of two priors is more noninformative in nature. This involves converting them to posterior probability distributions based on some set of hypothesized outcomes of measurements of the quantum system in question. It is, then, ascertained whether or not the original relative entropy (Kullback-Leibler distance) between a pair of priors increases or decreases when one of them is exchanged with its corresponding posterior. The findings lead us to assert that the maximal monotone metric yields the most noninformative (prior) distribution and the minimal monotone (that is, the Bures) metric, the least. Our conclusions both agree and disagree, in certain respects, with ones recently reached by Hall, who relied upon a less specific test criterion than our entropy-based one.Comment: 7 pages, LaTeX, minor changes, to appear in Physics Letters

Two-Qubit Separability Probabilities as Joint Functions of the Bloch Radii of the Qubit Subsystems

We detect a certain pattern of behavior of separability probabilities $p(r_A,r_B)$ for two-qubit systems endowed with Hilbert-Schmidt, and more generally, random induced measures, where $r_A$ and $r_B$ are the Bloch radii ($0 \leq r_A,r_B \leq 1$) of the qubit reduced states ($A,B$). We observe a relative repulsion of radii effect, that is $p(r_A,r_A) < p(r_A,1-r_A)$, except for rather narrow "crossover" intervals $[\tilde{r}_A,\frac{1}{2}]$. Among the seven specific cases we study are, firstly, the "toy" seven-dimensional $X$-states model and, then, the fifteen-dimensional two-qubit states obtained by tracing over the pure states in $4 \times K$-dimensions, for $K=3, 4, 5$, with $K=4$ corresponding to Hilbert-Schmidt (flat/Euclidean) measure. We also examine the real (two-rebit) $K=4$, the $X$-states $K=5$, and Bures (minimal monotone)--for which no nontrivial crossover behavior is observed--instances. In the two $X$-states cases, we derive analytical results, for $K=3, 4$, we propose formulas that well-fit our numerical results, and for the other scenarios, rely presently upon large numerical analyses. The separability probability crossover regions found expand in length (lower $\tilde{r}_A$) as $K$ increases. This report continues our efforts (arXiv:1506.08739) to extend the recent work of Milz and Strunz (J. Phys. A: 48 [2015] 035306) from a univariate ($r_A$) framework---in which they found separability probabilities to hold constant with $r_A$---to a bivariate ($r_A,r_B$) one. We also analyze the two-qutrit and qubit-qutrit counterparts reported in arXiv:1512.07210 in this context, and study two-qubit separability probabilities of the form $p(r_A,\frac{1}{2})$.Comment: 24 pages, 17 figures--revised--to appear in International Journal of Quantum Informatio