Although Bayes’s theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes’s theorem sometimes generates sensible procedures from improper priors, Pitman’s estimator being a good example. However, improper priors may also lead to Bayes procedures that are paradoxical or otherwise unsatisfactory, prompting some authors to insist that al...

In this work we generalize the celebrated Rees’s theorem for arbitrary ideals in a local ring by using the Achilles-Manaresi multiplicity sequence as a generalization of the Hilbert-Samuel multiplicity.

We give a quantitative version of Roth’s Theorem over an arbitrary number field, similar to that given by Bombieri and van der Poorten. Introduction. Let K/Q be a number field, with [K : Q] = d. Let MK be a complete set of inequivalent absolute values on K, normalized so that the absolute logarithmic height is given by h : K → [0,∞), h(x) = ∑

A theorem of S. Warschawski on the derivative of a holomorphic function mapping conformally the circle onto a simply-connected domain bounded by the piecewise-Lyapunov Jordan curve is extended to domains with a non-Jordan boundary having interior cusps of a certain type. 2000 Mathematics Subject Classification: 3OC35.

In a paper recently published in the Rendiconti del Circolo Matemático di Palermo (vol. 33, 1912, pp. 375-407) and entitled Sur un théorème de Géométrie, Poincaré enunciated a theorem of great importance, in particular for the restricted problem of three bodies; but, having only succeeded in treating a variety of special cases after long-continued efforts, he gave out the theorem for the consid...

f3 real. (See, for instance, [1], p. 224, ex. 4.) We offer the following proof whic h, although it also uses Bieberbach's result, is considerably different. PROOF: Let cP (z) J~ . Then cP sends the open unit disk into itself. Let cP 1= cP and inductively 1 a? define cPn=cP OcPlI t. If cPll(Z)=An,1 z+AIl,z Z2+ . .. ,it is clear that A"'=M' A I ,2= M' AII ,I = A", AIl I,t, and A II ,2 = AI ,I A n...

In the first section we review the beautiful combinatorial theory of Ramsey as well as the history of Szemerédi’s theorem. In Section 2 we give a sketch of Ruzsa’s modern proof of Freiman’s theorem on sumsets which plays an important role in Gowers’ quantitative proof of Szemerédi’s theorem. In the last section we deduce Roth’s theorem (Szemerédi’s theorem in the case k=3) from the Triangle Rem...

In our last lecture, we studied two root-finding methods that each took in a polynomial f(x) and an interval [a, b], and returned a root of that function on that interval. This was great for the problem we asked at the start of the class — how to find a root of a quintic polynomial — but is not necessarily so great for many other problems we may want to study. For example, we may want to find a...

in this paper‎, ‎using a generalized dunkl translation operator‎, ‎we obtain a generalization of titchmarsh's theorem for the dunkl transform for functions satisfying the$(psi,p)$-lipschitz dunkl condition in the space $mathrm{l}_{p,alpha}=mathrm{l}^{p}(mathbb{r},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.

in this paper, we investigate the concept of topological stationary for locally compact semigroups. in [4], t. mitchell proved that a semigroup s is right stationary if and only if m(s) has a left invariant mean. in this case, the set of values ?(f) where ? runs over all left invariant means on m(s) coincides with the set of constants in the weak* closed convex hull of right translates of f. th...