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1.
Steven P. Lalley 《Transactions of the American Mathematical Society》1997,349(11):4355-4365
An algorithm is given for computing the Hausdorff dimension of the set(s) of real numbers with representations , where each , a finite set of ``digits', and is a Pisot number. The Hausdorff dimension is shown to be , where is the top eigenvalue of a finite 0-1 matrix , and a simple algorithm for generating from the data is given.
2.
K. Jarosz 《Proceedings of the American Mathematical Society》1997,125(10):3129-3130
Let be a compact subset of the complex plane and let We show that the maximal ideal space of Banach algebras of Lipschitz functions, which are analytic on , coincides with
3.
Yoshiaki Fukuma 《Transactions of the American Mathematical Society》1996,348(10):4185-4197
Let be a smooth projective surface over and an ample Cartier divisor on . If the Kodaira dimension or , the author proved , where . If , then the author studied with . In this paper, we study the polarized surface with , , and .
4.
Robert D. Thompson 《Transactions of the American Mathematical Society》1998,350(5):1931-1944
In this paper we analyze the localization of , the fiber of the double suspension map , with respect to . If four cells at the bottom of , the th extended power spectrum of the Moore spectrum, are collapsed to a point, then one obtains a spectrum . Let be the James-Hopf map followed by the collapse map. Then we show that the secondary suspension map has a lifting to the fiber of and this lifting is shown to be a -periodic equivalence, hence an -equivalence.
5.
If and are positive integers with and , then the equation of the title possesses at most one solution in positive integers and , with the possible exceptions of satisfying , and . The proof of this result relies on a variety of diophantine approximation techniques including those of rational approximation to hypergeometric functions, the theory of linear forms in logarithms and recent computational methods related to lattice-basis reduction. Additionally, we compare and contrast a number of these last mentioned techniques.
6.
Yann Bugeaud 《Proceedings of the American Mathematical Society》1997,125(11):3203-3208
One of the purposes of this note is to correct the proof of a recent result of Y. Guo & M. Le on the equation . Moreover, we prove that the diophantine equation , , , , , gcd, , has only finitely many solutions, all of which satisfying .
7.
Let be a compact metric space, and let be a calibrated thin -ideal. Then is . This solves an open problem, which was posed by Kechris, Louveau and Woodin. Using our result we obtain a new proof of Kaufman's theorem concerning -sets and -sets.
8.
Zoran Spasojevic 《Proceedings of the American Mathematical Society》1996,124(12):3857-3865
For a partial order , let denote the statement that for every -increasing -sequence there is a -decreasing -sequence on top of such that is an -gap in . The main result of this paper is that . It is also shown, as a corollary, that but .
9.
10.
Sy D. Friedman W. Hugh Woodin 《Proceedings of the American Mathematical Society》1996,124(7):2211-2213
We show that the supremum of the lengths of prewellorderings of the reals can be , with inaccessible to reals, assuming only the consistency of an inaccessible.
11.
It is proved that there are precisely 4204 pairwise non-isomorphic Steiner systems invariant under the group and which can be constructed using only short orbits.
It is further proved that there are precisely 38717 pairwise non-isomorphic Steiner systems invariant under the group and which can be constructed using only short orbits.
12.
Michael J. Puls 《Proceedings of the American Mathematical Society》1998,126(3):721-728
Let be a discrete group, the group ring of over and the Lebesgue space of with respect to Haar measure. It is known that if is torsion free elementary amenable, and , then . We will give a sufficient condition for this to be true when , and in the case we will give sufficient conditions for this to be false when .
13.
It is shown that the suspension order of the -fold cartesian product of real projective -space is less than or equal to the suspension order of the -fold symmetric product of and greater than or equal to , where and satisfy and . In particular has suspension order , and for fixed the suspension orders of the spaces are unbounded while their stable suspension orders are constant and equal to .
14.
Yin Xi Huang 《Proceedings of the American Mathematical Society》1997,125(11):3347-3354
We study the nonlinear eigenvalue problem
where , is a bounded smooth domain in . We prove that the first and the second variational eigenvalues of (1) are continuous functions of . Moreover, we obtain the asymptotic behavior of the first eigenvalue as and .
15.
Chih-Nung Hsu 《Proceedings of the American Mathematical Society》1998,126(3):647-652
Let be the finite field with elements and let denote the ring of polynomials in one variable with coefficients in . Let be a monic polynomial irreducible in . We obtain a bound for the least degree of a monic polynomial irreducible in ( odd) which is a quadratic non-residue modulo . We also find a bound for the least degree of a monic polynomial irreducible in which is a primitive root modulo .
16.
J. H. E. Cohn. 《Mathematics of Computation》1997,66(219):1347-1351
An effective method is derived for solving the equation of the title in positive integers and for given completely, and is carried out for all . If is of the form , then there is the solution , ; in the above range, except for with solution , , there are no other solutions.
17.
W. G. Dwyer 《Proceedings of the American Mathematical Society》1998,126(7):2159-2167
We show that for the mod group cohomology of is not detected on diagonal matrices.
18.
Masayoshi Hata 《Transactions of the American Mathematical Society》1998,350(6):2311-2327
We shall show that the numbers and
are linearly independent over for any natural number . The key is to construct explicit Padé-type approximations using Legendre-type polynomials.
are linearly independent over for any natural number . The key is to construct explicit Padé-type approximations using Legendre-type polynomials.
19.
Christopher J. Bishop 《Proceedings of the American Mathematical Society》1996,124(9):2695-2701
We show that a function on the unit disk extends continuously to , the maximal ideal space of iff it is uniformly continuous (in the hyperbolic metric) and close to constant on the complementary components of some Carleson contour.
20.
We characterize weak compactness and weak conditional compactness of subsets of in terms of regular methods of summability. We also study when these results still hold using only convergence in the sense of Cesàro.