acase@tulane.edu

acase@tulane.edu

We consider the Cauchy problem(UNFORMATTED TABLE OR EQUATION FOLLOWS)$$\eqalign{u\sp\prime(t)&= \int\sbsp{0}{t}\ K(t - s)Au(s)ds,\quad t\geq 0\cr u(0)&= f,\cr}\leqno(P)$$(TABLE/EQUATION ENDS)and we are interested in continuous dependence of solutions $u(t) = U(t)f$ on A and K, where $\{U(t)\}\sb{t\geq 0}$ is the resolvent family for (P) Given a family of operators $\{A\sb{n}\}$ and a family of scalar kernels $\{ K\sb{n}\}$, we study the family of Cauchy problems(UNFORMATTED TABLE OR EQUATION FOLLOWS)$$\eqalign{u\sbsp{n}{\prime}(t)&= \int\sbsp{0}{t}\ K\sb{n}(t - s)A\sb{n}u\sb{n}(s)ds,\quad t\geq 0\cr u\sb{n}(0)&= f\sb{n}.\cr}\leqno(Pn)$$(TABLE/EQUATION ENDS)We show that under certain stability conditions for $\{ A\sb{n}\}$ and $\{ K\sb{n}\},$ if $A\sb{n} \to A\sb{o}$ and if $K\sb{n} \to K\sb{o},$ in a certain sense, then $u\sb{n}(t) \to u\sb{o}(t).$ Our result is a partial extension of the Trotter-Neveu-Kato theorem to integro-differential equations / acase@tulane.edu

acase@tulane.edu

Ludwig Feuerbach's most significant accomplishment was his development of a detailed projection theory to explain how religious and idealistic thought had produced an understanding of human nature and its potential for full realization; he proposed that ethicists adopt the innate humanistic drive as an explicit ethical norm and also that they adopt a naturalistic standpoint; this would encourage direct involvement in social and political change as the only legitimate form of morality. The genesis of this point of view is explained in order to demonstrate that Feuerbach's philosophy--and particularly his ethics--is more systematic than most critics have recognized, and thereby show that the widespread acceptance of the standard Marxist critique--which has effectively eclipsed the real significance of Feuerbach's accomplishments--is not justifiable. The chief reason that Feuerbach's philosophy is considered as valuable is based on the historical function it served as a transition from Hegelian idealism to Marxist materialism; in fact, it is precisely his synthesis of humanistic ethics and naturalism that makes his thought important in the present age, in which many regard these two options as exclusive and incompatible This critique begins by relating Feuerbach's epic of the origin and development of human mental activity and western culture. Projection and alienation are traced through two kinds of nature religion, two kinds of Christianity, Hegelian philosophy, and political ideology. Clarification of the continuity within these six stages reveals a systematic structure that has been missed by Feuerbach's critics. This makes possible a cogent analysis of Feuerbach's materialistic explanation of human nature, which focuses on his concept of species-being; therein one may find affinities to subsequently developed aspects of Lamarckian and Darwinian models of description as well as epistemological conclusions which he drew from his theory of human nature. His ethical humanism is then explicated and analyzed, beginning with his demonstration of the materialistic basis of altruistic tendencies among humans, and leading to his program for correcting the previous misdirection of these tendencies so that they might function more directly in social and political settings. Negative Marxian critiques of Feuerbach's work are then assessed, with attention given to the numerous misrepresentations therein of Feuerbach's actual thought and to the contradictions that developed in Marx's own ethical positions. The conclusion describes the nature of Feuerbach's ethical system, indicates the distinctiveness of his thought, and points to the promise of Feuerbach's approach for ethical philosophizing in the future. The interdisciplinary work now being done among sociobiologists is discussed there as the most contemporary attempt to utilize the methods prescribed by Feuerbach / acase@tulane.edu

We obtain asymptotics for eigenvalues of an operator which acts on bounded measurable functions vanishing outside some bounded domain in ${\rm \IR}\sp{r}$. The operator we consider is associated with a pure jump Markov process in the sense that the infinitesimal generator of the process acts on functions in the same way that the operator does. The asymptotics of the eigenvalues bear a resemblance to those found by A. D. Wentzell and M. I. Freidlin for a second order elliptic differential operator with a small parameter in the higher derivatives In a recent manuscript Professor Wentzell obtained asymptotics for the first eigenvalue of a process, possibly having jumps, assumed to have certain large deviations properties. We show that the pure jump Markov process we are treating has the large deviations behavior assumed in Professor Wentzell's paper, and thus obtain asymptotics for the first eigenvalue of our operator. We obtain asymptotics for additional eigenvalues of our operator by exploiting the large deviations properties of the associated Markov process / acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu

acase@tulane.edu