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1.
Daniel M. Oberlin 《Proceedings of the American Mathematical Society》2006,134(11):3201-3209
We prove an estimate for the spherical average operator in if . This leads to a lower bound for the Hausdorff dimension of unions of certain collections of spheres and to a Strichartz-type estimate for solutions of the wave equation.
2.
Ailana Fraser 《Proceedings of the American Mathematical Society》2007,135(11):3733-3744
We prove Morse index estimates for the area functional for minimal surfaces that are solutions to the free boundary problem in -convex domains in manifolds of nonnegative complex sectional curvature.
3.
Martha Alvarez Montserrat Corbera Joaquin Delgado Jaume Llibre 《Proceedings of the American Mathematical Society》2005,133(2):529-536
In the -body problem a central configuration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for and for 4$"> that if masses are located at fixed points in the plane, then there are only a finite number of ways to position the remaining th mass in such a way that they define a central configuration. Lindstrom leaves open the case . In this paper we prove the case using as variables the mutual distances between the particles.
4.
Alexander M. Meadows 《Proceedings of the American Mathematical Society》2007,135(5):1411-1417
We give conditions under which bounded solutions to semilinear elliptic equations on domains of are continuous despite a possible infinite singularity of . The conditions do not require a minimization or variational stability property for the solutions. The results are used in a second paper to show regularity for a familiar class of equations.
5.
Arno van den Essen Peter van Rossum 《Transactions of the American Mathematical Society》2004,356(5):1691-1703
This paper studies coordinates in two variables over a -algebra. It gives several ways to characterize such coordinates. Also, various results about coordinates in two variables that were previously only known for fields, are extended to arbitrary -algebras.
6.
F. Cabello Sá nchez J. M. F. Castillo N. J. Kalton D. T. Yost 《Transactions of the American Mathematical Society》2003,355(11):4523-4541
If is a separable Banach space, we consider the existence of non-trivial twisted sums , where or For the case we show that there exists a twisted sum whose quotient map is strictly singular if and only if contains no copy of . If we prove an analogue of a theorem of Johnson and Zippin (for ) by showing that all such twisted sums are trivial if is the dual of a space with summable Szlenk index (e.g., could be Tsirelson's space); a converse is established under the assumption that has an unconditional finite-dimensional decomposition. We also give conditions for the existence of a twisted sum with with strictly singular quotient map.
7.
David Eisenbud Jerzy Weyman 《Transactions of the American Mathematical Society》2003,355(11):4451-4473
Let be a map of free modules over a commutative ring . Fitting's Lemma shows that the ``Fitting ideal,' the ideal of minors of , annihilates the cokernel of and is a good approximation to the whole annihilator in a certain sense. In characteristic 0 we define a Fitting ideal in the more general case of a map of graded free modules over a -graded skew-commutative algebra and prove corresponding theorems about the annihilator; for example, the Fitting ideal and the annihilator of the cokernel are equal in the generic case. Our results generalize the classical Fitting Lemma in the commutative case and extend a key result of Green (1999) in the exterior algebra case. They depend on the Berele-Regev theory of representations of general linear Lie superalgebras. In the purely even and purely odd cases we also offer a standard basis approach to the module when is a generic matrix.
8.
Clemens Fuchs Attila Petho Robert F. Tichy 《Transactions of the American Mathematical Society》2003,355(11):4657-4681
Let be a field of characteristic and let be a linear recurring sequence of degree in defined by the initial terms and by the difference equation
with . Finally, let be an element of . In this paper we are giving fairly general conditions depending only on on , and on under which the Diophantine equation
has only finitely many solutions . Moreover, we are giving an upper bound for the number of solutions, which depends only on . This paper is a continuation of the work of the authors on this equation in the case of second-order linear recurring sequences.
with . Finally, let be an element of . In this paper we are giving fairly general conditions depending only on on , and on under which the Diophantine equation
has only finitely many solutions . Moreover, we are giving an upper bound for the number of solutions, which depends only on . This paper is a continuation of the work of the authors on this equation in the case of second-order linear recurring sequences.
9.
Frances Hammock Peter Luthy Alexander M. Meadows Phillip Whitman 《Proceedings of the American Mathematical Society》2007,135(5):1419-1430
We show partial regularity of bounded positive solutions of some semilinear elliptic equations in domains of . As a consequence, there exists a large variety of nonnegative singular solutions to these equations. These equations have previously been studied from the point of view of free boundary problems, where solutions additionally are stable for a variational problem, which we do not assume.
10.
Julio C. Rebelo 《Transactions of the American Mathematical Society》2004,356(11):4543-4557
We consider subgroups of -diffeomorphisms of the circle which act transitively on -tuples of points. We show, in particular, that these subgroups are dense in the group of homeomorphisms of . A stronger result concerning -approximations is obtained as well. The techniques employed in this paper rely on Lie algebra ideas and they also provide partial generalizations to the differentiable case of some results previously established in the analytic category.
11.
Let be an odd prime and , positive integers. In this note we prove that the problem of the determination of the integer solutions to the equation can be easily reduced to the resolution of the unit equation over . The solutions of the latter equation are given by Wildanger's algorithm.
12.
We prove Olenik-type decay estimates for entropy solutions of strictly hyperbolic systems of balance laws built out of a wave-front tracking procedure inside which the source term is treated as a nonconservative product localized on a discrete lattice.
13.
H. H. Edwards P. Mikusinski M. D. Taylor 《Proceedings of the American Mathematical Society》2005,133(5):1505-1513
A measure, , on is said to be -invariant if its value for any Borel set is invariant with respect to the symmetries of the unit square. A function, , generated in a certain way by a measure, , on is shown to be a measure of concordance if and only if the generating measure is positive, regular, -invariant, and satisfies certain inequalities. The construction examined here includes Blomqvist's beta as a special case.
14.
Fabio Nicola 《Proceedings of the American Mathematical Society》2003,131(9):2841-2848
We are concerned with the so-called -pseudo-differential calculus. We describe the spectrum of the unital and commutative -algebra given by the norm closure of the space of -order pseudo-differential operators modulo compact operators; other related algebras are also considered. Finally, their -theory is computed.
15.
E. N. Dancer 《Transactions of the American Mathematical Society》2005,357(3):1225-1243
In this paper, we study bounded solutions of on (where and sometimes ) and show that, for most 's, the weakly stable and finite Morse index solutions are quite simple. We then use this to obtain a very good understanding of the stable and bounded Morse index solutions of on with Dirichlet or Neumann boundary conditions for small .
16.
Octavian Cornea 《Proceedings of the American Mathematical Society》2004,132(9):2769-2781
In this note we use Morse theory to produce new obstructions to the existence of thickenings of -complexes in low codimension. The obstructions are expressed as nonexistence of solutions to an equation of type with a Ganea-Hopf type invariant.
17.
Siddhartha Gadgil 《Proceedings of the American Mathematical Society》2004,132(12):3705-3714
We show that an oriented elliptic -manifold admits a universally tight positive contact structure if and only if the corresponding group of deck transformations on (after possibly conjugating by an isometry) preserves the standard contact structure.
We also relate universally tight contact structures on -manifolds covered by to the isomorphism .
The main tool used is equivariant framings of -manifolds.
18.
Lin Chen Ruan Yingbin Yan Zikun 《Proceedings of the American Mathematical Society》2003,131(9):2753-2759
We prove that if are injective, then is subscalar if and only if is subscalar. As corollaries, it is shown that -hyponormal operators and log-hyponormal operators are subscalar; also w-hyponormal operators with Ker Kerand their generalized Aluthge transformations are subscalar.
19.
Ales Vavpetic Antonio Viruel 《Transactions of the American Mathematical Society》2005,357(11):4517-4532
We study the mod cohomology of the classifying space of the projective unitary group . We first prove that conjectures due to J.F. Adams and Kono and Yagita (1993) about the structure of the mod cohomology of the classifying space of connected compact Lie groups hold in the case of . Finally, we prove that the classifying space of the projective unitary group is determined by its mod cohomology as an unstable algebra over the Steenrod algebra for 3$">, completing previous work by Dwyer, Miller and Wilkerson (1992) and Broto and Viruel (1998) for the cases .
20.
To supplement existing data, solutions of are tabulated for primes with and . For , five new solutions 2^{32}$"> are presented. One of these, for , also satisfies the ``reverse' congruence . An effective procedure for searching for such ``double solutions' is described and applied to the range , . Previous to this, congruences are generally considered for any and fixed prime to see where the smallest prime solution occurs.