Paragraph Of Section Research Articles

On Concentration Phenomena of Least Energy Solutions to Nonlinear Schrödinger Equations with Totally Degenerate Potentials

We study concentration phenomena of the least energy solutions of the following nonlinear Schrödinger equation: \[ h^2 \Delta u - V(x) u + f( u ) = 0 \quad \text{in} \ \mathbb{R}^N, \ u>0, \ u \in H^1(\mathbb{R}^N)\,, \] for a totally degenerate potential $V$. Here $h>0$ is a small parameter, and $f$ is an appropriate, superlinear and Sobolev subcritical nonlinearity. In~[16], Lu and Wei proved that when the parameter $h$ approaches zero, the least energy solutions concentrate at the most centered point of the totally degenerate set $\Omega = \{ x \in \mathbb{R}^N \mid V(x) = \min_{ y \in \mathbb{R}^N } V(y) \}$ when $f(u) = u^p$. In this paper, we show that this kind of result holds for more general $f$. In particular, our proof does not need a so-called uniqueness-nondegeneracy assumption (see, the next-to-last paragraph in Section~1) on the limiting equation (2.6) in Section~2. Furthermore, in~[16] Lu and Wei made a technical assumption for $V$, that is, \[ V(x) - \min_{y \in \mathbb{R}^N} V(y) \geq C d(x, \partial \Omega)^2 \quad \text{for} \ x \in \Omega^{\rm c}\,, \] where $C$ is a positive constant, but our proof does not need this assumption. In our proof, we employ a modification of the argument which has been developed by del Pino and Felmer in~[9] using Schwarz's symmetrization.

Erratum to: The Evil of Death: A Reply to Yi

The original version of this article unfortunately contained a mistake. There were two slight text errors. The correct text information are given below. In the second line of the last paragraph in section Reply to right before the Conclusion, the text should read as: “atypical or, as Yi suggests, are more typical than we appear to suppose”. and In the middle of the same paragraph, the text should read as: “...Note that a proponent of the Brueckner/Fischer approach can accept that it would be rational to regret late birth somewhat, if it really were true that Learning Japanese represents the typical case.” Philosophia (2014) 42:1169 DOI 10.1007/s11406-014-9571-5

Erratum to “Streamlined Approach for Infrapubic Placement of an Inflatable Penile Prosthesis”

With reference to the paper “Streamlined Approach for Infrapubic Placement of an Inflatable Penile Prosthesis”, we want to change in the introduction section paragraph 3 on page 1 to read “our streamlined approach for infrapubic placement of penile prosthesis is a variation of the minimally invasive approach originally published by Perito [1, 2].”

Trial Registration and Wandering Outcomes

Trial Registration and Wandering Outcomes

On the Difference Between Non-Connoting Terms and Rigid Designators: A Reply to Bradley

A main point of my article, as I see it, is that we can solve Putnam's problem, as articulated in the first paragraph of section three, without recourse to the definition of “natural-kind term” as “rigid designator of a natural kind”. I had three main objections to this definition:(a) It makes the classification of a term as a natural-kind term dependent on one's metaphysics, i.e., on the status given to natural kinds. However, Putnam's argument seems to be independent of such metaphysical considerations, and the sort of natural kinds it establishes (if any) should be “read off its face”, not set down in advance (section 2).(b) It permits the derivation of “exotic necessary truths” such as “If water is H20 then necessarily water is H20” (sections 9 and 10).(c) Putnam's main point appears to be about the independence of a term's extension from a linguistic community's beliefs. Why should this point affect the theory of designation? Kripke's argument about names establishes the non-descriptiveness of names while leaving undisturbed the classical conception of names designating individuals. Why should we not take his and Putnam's parallel arguments as establishing the non-descriptiveness (non-connotation) of natural-kind terms while leaving undisturbed the classical conception of general terms designating classes (section 10)?