A comment on "Intergenerational equity: sup, inf, lim sup, and lim inf"

We reexamine the analysis of Chambers (Social Choice and Welfare, 2009), that produces a characterization of a family of social welfare functions in the context of intergenerational equity: namely, those that coincide with either the sup, inf, lim sup, or lim inf rule. Reinforcement, ordinal covariance, and monotonicity jointly identify such class of rules. We show that the addition of a suitable axiom to this three properties permits to characterize each particular rule. A discussion of the respective distinctive properties is provided.Social welfare function; Intergenerational equity; Lim sup ; Lim inf

The effect of Nafion film on the cathode catalyst layer performance in a low-Pt PEM fuel cell

A single--pore model for performance of the cathode catalyst layer (CCL) in a PEM fuel cell is developed. The model takes into account oxygen transport though the CCL depth and through the thin Nafion film, separating the pore from Pt/C species. Analytical solution to model equations reveals the limiting current density $j_N^{\rm lim}$ due to oxygen transport through the Nafion film. Further, $j_N^{\rm lim}$ linearly depends of the CCL thickness, i.e., the thinner the CCL, the lower $j_N^{\rm lim}$. This result may explain unexpected lowering of low--Pt loaded catalyst layers performance, which has been widely discussing in literature.Comment: 11 page

On the convergence of continued fractions at Runckel's points and the Ramanujan conjecture

We consider the limit periodic continued fractions of Stieltjes $$\frac{1}{1-} \frac{g_1 z}{1-} \frac{g_2(1-g_1) z}{1-} \frac{g_3(1-g_2)z}{1-...,}, z\in \mathbb C, g_i\in(0,1), \lim\limits_{i\to \infty} g_i=1/2, \quad (1)$$ appearing as Shur--Wall $g$-fraction representations of certain analytic self maps of the unit disc $|w|< 1$, $w \in \mathbb C$. We precise the convergence behavior and prove the general convergence [2, p. 564 ] of (1) at the Runckel's points of the singular line $(1,+\infty)$ It is shown that in some cases the convergence holds in the classical sense. As a result a counterexample to the Ramanujan conjecture [1, p. 38-39] stating the divergence of a certain class of limit periodic continued fractions is constructed.Comment: 8 page

Passage of Lévy Processes across Power Law Boundaries at Small Times

We wish to characterize when a Lévy process Xt crosses boundaries like tκ, κ > 0, in a one- or two-sided sense, for small times t; thus, we inquire when lim.supt↓0 |Xt|/tκ, lim supt↓0, Xt/tκ and/or lim inft↓0 Xt/tκ are almost surely (a.s.) finite or infinite. Necessary and sufficient conditions are given for these possibilities for all values of κ > 0. This completes and extends a line of research, going back to Blumenthal and Getoor in the 1960s. Often (for many values of κ), when the lim sups are finite a.s., they are in fact zero, but the lim sups may in some circumstances take finite, nonzero, values, a.s. In general, the process crosses one- or two-sided boundaries in quite different ways, but surprisingly this is not so for the case κ = 1/2, where a new kind of analogue of an iterated logarithm law with a square root boundary is derived. An integral test is given to distinguish the possibilities in that case.Supported in part by ARC Grants DP0210572 and DP0664603

Review of A to Zoo: Subject Access to Children\u27s Picture Books

This article is a book review of A to Zoo: Subject Access to Children\u27s Picture Books, by Carolyn W. Lima and John A. Lim

Review of A to Zoo: Subject Access to Children\u27s Picture Books

This article is a book review of A to Zoo: Subject Access to Children\u27s Picture Books, by Carolyn W. Lima and John A. Lim