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Coil migration is a rare complication of vascular embolization. This report describes 3 cases of peripheral pseudoaneurysm embolization with the use of Penumbra packing coils in which coils migrated into the lumens of adjacent viscera: 2 into the duodenum and 1 into the vagina. The coils passed spontaneously in 2 cases and required endoscopic removal in the third. There were no immediate or delayed bleeding or infectious complications following migration. The majority of previously reported coil migration cases have occurred following treatment of pseudoaneurysms adjacent to air-filled structures, and this observation is an important consideration during pretreatment planning.

We introduce the notion of caliber, cal (A, B), of a strictly increasing sequence of natural numbers A with respect to another one B, as the limit inferior of the ratio of the nth term of A to that of B. We further consider the limit superior t(A) of the average order of the number of representations of an integer as a sum of two elements of A. We give some basic properties of each notion and we relate the two together, thus yielding a generalization, of the form t(A) ≤ t(B)/ cal (A, B), of a result of Cassels specific to the case where A is an additive basis of the natural numbers and B is the sequence of perfect squares. We also provide some formulas for the computation of t(A) in a large class of cases, and give some examples.

We consider and study formal power series, that we call supported series, with real coefficients which are either zero or bounded below by some positive constant. The sequences of such coefficients have a lot of similarity with sequences of natural numbers considered in additive number theory. It is this analogy that we pursue, thus establishing many properties and giving equivalent statements to the well-known Erdös-Turán conjectures in terms of supported series and extending to them a version of Erdös-Fuchs theorem.

Let denote the inverse limit of all finite cyclic groups. Let F, G and H be abelian groups with H ≤ G. Let FβH denote the abelian group (F × H, +β), where +βis defined by (a, x) +β (b, y) = (a + b, x + y + β(a) + β(b) — β(a + b)) for a certain β : F G linear mod H meaning that β(0) = 0 and β(a) + β(b) — β(a + b) ∈ H for all a, b in F. In this paper we show that the following hold: (1) The additive group of any nonstandard model ℤ* of the ring ℤ is isomorphic to (ℤ*+/H)βH for a certain β : ℤ*+/H linear mod H. (2) is isomorphic to (ℤ+/H )βH for some β : /H ℚ linear mod H, though is not the additive group of any model of Th(ℤ, +, ×) and the exact sequence H /H is not splitting.

Soit T une partie non bornee de R + avec 0 appartenant a T. A chaque fonction croissante f: T → R + nous associons le couple r(f) = (s(f), i(f)) ou s(f) = lim sup t→+ ∞ f(t)/t et i(f) = lim inf t→+ ∞ f(t)/t appartiennent a R + U {+∞}. Nous decrivons l'ensemble R(f) = {r(g); g: T → R, g et f - g croissantes}. Ce travail unifie et prolonge des resultats obtenus sur les densites des parties de N, d'une part, et les limites des moyennes des fonctions positives, d'autre part.

LetWbe an algebraically closed field of characteristic zero, and letKbe an algebraically closed field of characteristic zero, complete for an ultrametric absolute value. LetQnbe the polynomialxn−xn−1+kfor any constantk≠0, (n−1)n−1/nn. LetTn(k) be the set ofndistinct zeros ofQn. For everyn⩾9, we show thatTn(k) is ann-point unique range set (ignoring multiplicities) for bothW[x] and the set A(K) of entire functions inK. However, for everyn>0, we also show thatTn(k) is not a unique range set (counting or ignoring multiplicities) forW(x) and therefore, is also not a unique range set for the set of p-adic meromorphic functions (this was also separately found by Chung-Chun Yang and Xin-Hou Hua). In the same way, we show that there exist no bi-urs for p-adic meromorphic functions of the form ({a,b,c}, {ω}). Moreover, for everyn⩾5, we show that the only linear fractional functions preserving a setTn(k) is the identity, something which was asked (in particular) in Boutabaa and Escassut, “On Uniqueness of p-adic Meromorphic Functions,”Proc. Amer. Math. Soc.(1988).

This is a contribution to the algebraic study of an Australian kinship system known as the ‘Murngin system’. It is shown how the introduction of hypergroups and semi-direct products of groups can shed new light on some aspects of this particular system and further enhance the abstract theory of kinship.

We show that the following property (LN) holds in the basic Cohen model as sketched by Jech: The order topology of any linearly ordered set is normal. This proves the independence of the axiom of choice from LN in ZF, and thus settles a question raised by G. Birkhoff (1940) which was partly answered by van Douwen (1985).

We give a lower bound to the maximal number of representations by an additive basis of the natural numbers, in conjunction with a celebrated conjecture of Erdős and Turan.

The doubling time (DT) of human prostatic cancer is calculated for the first time; its various parameters and the relative importance of each are reviewed. A crude volume-doubling time (DTcv), a theoretical doubling of the number of cells (DTt), and an annual doubling rate (ADR), are defined and calculated for each of 12 patients who had undergone needling of the prostate for diagnostic purposes and in whom tumor cells were implanted in the track of the biopsy needle and had grown into a subcutaneous perineal nodule. The harmonic average DTcv was six days and DTt eight days, and the average ADR was 45 doublings per year. From the study of the calculated DTs and ADRs, it became obvious that the 12 patients fell into three distinct groups: Group I = slow tumor growth rate, an average ADR of 9 doublings per year, and a harmonic average DTt of forty days; Group II = medium tumor growth rate, an average ADR of 35 doublings/year, and a harmonic average DTt of ten days; and Group III = rapid tumor growth rate, an average ADR of 100 doublings/year, and a harmonic average DTt of four days.

RésuméParmi d'autres résultats, on montre en particulier que les D-hypergroupes ne forment pas une classe élémentaire, autrement dit, que la structure de D-hypergroupe ne peut pas être caractérisée par un système d'axiomes du premier ordre, dans le langage des hypergroupes.AbstractAmong other results, it is shown that the class of D-hypergroups is not an elementary class in the sense of model theory.

We give equivalent formulations of the Erdős–Turan conjecture on the unboundedness of the number of representations of the natural numbers by additive bases of order two of N . These formulations allow for a quantitative exploration of the conjecture. They are expressed through some functions of x∈ N reflecting the behavior of bases up to x. We examine some properties of these functions and give numerical results showing that the maximum number of representations by any basis is ⩾6.