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1.
Dusan Repovs Arkadij B. Skopenkov Evgenij V. Scepin 《Proceedings of the American Mathematical Society》1996,124(4):1219-1226
We give the characterization of -homogeneous compacta in : Let be a locally compact (possibly nonclosed) subset of . Then is -homogeneous if and only if is a -submanifold of .
2.
Osamu Saeki Kazuhiro Sakuma 《Transactions of the American Mathematical Society》1996,348(7):2585-2606
We give two congruence formulas concerning the number of non-trivial double point circles and arcs of a smooth map with generic singularities --- the Whitney umbrellas --- of an -manifold into , which generalize the formulas by Szücs for an immersion with normal crossings. Then they are applied to give a new geometric proof of the congruence formula due to Mahowald and Lannes concerning the normal Euler number of an immersed -manifold in . We also study generic projections of an embedded -manifold in into and prove an elimination theorem of Whitney umbrella points of opposite signs, which is a direct generalization of a recent result of Carter and Saito concerning embedded surfaces in . The problem of lifting a map into to an embedding into is also studied.
3.
Martin Bridgeman 《Proceedings of the American Mathematical Society》1998,126(1):221-224
A well-known result states that, if a curve in has geodesic curvature less than or equal to one at every point, then is embedded. The converse is obviously not true, but the embeddedness of a curve does give information about the curvature. We prove that, if is a convex embedded curve in , then the average curvature (curvature per unit length) of , denoted , satisfies . This bound on the average curvature is tight as for a horocycle.
4.
Michael Marsalli 《Proceedings of the American Mathematical Society》1997,125(3):779-784
Let be a von Neumann algebra with a faithful, finite, normal tracial state , and let be a finite, maximal subdiagonal algebra of . Let be the closure of in the noncommutative Lebesgue space . Then possesses several of the properties of the classical Hardy space on the circle, including a commutant lifting theorem, some results on Toeplitz operators, an factorization theorem, Nehari's Theorem, and harmonic conjugates which are bounded.
5.
Kanghui Guo 《Proceedings of the American Mathematical Society》1997,125(5):1329-1340
A uniform estimate of Bessel functions is obtained, which is used to get a characterization of the measures on the unit sphere of in terms of the mixed norm of the Fourier transform of the measures.
6.
Christine Scharlach Luc Vrancken 《Proceedings of the American Mathematical Society》1998,126(1):213-219
For (positive) definite surfaces in there is a canonical choice of a centroaffine normal plane bundle, which induces a centroaffine invariant Ricci-symmetric connection . We classify all surfaces in with planar -geodesics. It turns out that the resulting class of surfaces is umbilical with projectively flat induced connection and flat normal plane bundle.
7.
Victoria Paolantoni 《Proceedings of the American Mathematical Society》1998,126(6):1733-1738
Let be a smooth real hypersurface of and a compact submanifold of . We generalize a result of A. Boggess and R. Dwilewicz giving, under some geometric conditions on and , an estimate of the submeanvalue on of any function on a neighbourhood of , by the norm of on a neighbourhood of in .
8.
Let be the \u{C}ech-Stone remainder . We show that there exists a large class of images of such that whenever is a subset of of cardinality at most the continuum, then is again an image of . The class contains all separable compact spaces, all compact spaces of weight at most and all perfectly normal compact spaces.
9.
Sanxing Wu 《Proceedings of the American Mathematical Society》1997,125(10):3119-3123
We derive a sufficient condition for a radially symmetric function which is positive somewhere to be a conformal curvature on . In particular, we show that every nonnegative radially symmetric continuous function on is a conformal curvature.
10.
Let be a finite nonzero Borel measure in satisfying for all and and some . If the Riesz -transform
is essentially bounded, then is an integer. We also give a related result on the -boundedness.
11.
Arthur Baragar 《Proceedings of the American Mathematical Society》1998,126(3):637-644
We discuss Manin and Batyrev's notion of the arithmetic stratification of a variety, and, for an irreducible surface embedded in , compare it with the spectrum of degrees of rational curves on . We study this spectrum for the class of K3 surfaces generated by smooth (2,2,2) forms in .
12.
S. M. Bhatwadekar Amartya K. Dutta 《Transactions of the American Mathematical Society》1997,349(8):3303-3319
In this paper we study the kernel of a non-zero locally nilpotent -derivation of the polynomial ring over a noetherian integral domain containing a field of characteristic zero. We show that if is normal then the kernel has a graded -algebra structure isomorphic to the symbolic Rees algebra of an unmixed ideal of height one in , and, conversely, the symbolic Rees algebra of any unmixed height one ideal in can be embedded in as the kernel of a locally nilpotent -derivation of . We also give a necessary and sufficient criterion for the kernel to be a polynomial ring in general.
13.
Jen-Tseh Chang James W. Cogdell 《Proceedings of the American Mathematical Society》1999,127(4):1251-1256
We compute the -homology for a class of representations of
and which admit a Whittaker model. They are all completely reducible.
and which admit a Whittaker model. They are all completely reducible.
14.
Meng-Kiat Chuah 《Proceedings of the American Mathematical Society》1996,124(11):3481-3491
Let be a compact semi-simple Lie group, and let be a maximal unipotent subgroup of the complexified group . In this paper, we classify all the -invariant Kaehler structures on . For each Kaehler structure , let be the line bundle with connection whose curvature is . We then study the holomorphic sections of , which constitute a -representation space.
15.
Czeslaw Bessaga Tadeusz Dobrowolski 《Proceedings of the American Mathematical Society》1997,125(1):259-268
It is shown that
- (1)
- a locally compact convex subset of a topological vector space that admits a sequence of continuous affine functionals separating points of affinely embeds into a Hilbert space;
- (2)
- an infinite-dimensional locally compact convex subset of a metric linear space has a central point;
- (3)
- every -compact locally convex metric linear space topologically embeds onto a pre-Hilbert space.
16.
P. M. Gadea J. Muñ oz Masqué 《Proceedings of the American Mathematical Society》1996,124(5):1437-1443
Let be a finite-dimensional commutative algebra over and let , and be the ring of -differentiable functions of class , the ring of real analytic mappings with values in and the ring of -analytic functions, respectively, defined on an open subset of . We prove two basic results concerning -differentiability and -analyticity: ) , ) if and only if is defined over .
17.
Douglas R. Farenick Phillip B. Morenz 《Transactions of the American Mathematical Society》1997,349(5):1725-1748
18.
We consider the Hausdorff measures , , defined on with the topology induced by the metric
for all . We study its properties, their relation to the ``Lebesgue measure" defined on by R. Baker in 1991, and the associated Hausdorff dimension. Finally, we give some examples.
19.
The root count developed by Bernshtein, Kushnirenko and Khovanskii only counts the number of isolated zeros of a polynomial system in the algebraic torus . In this paper, we modify this bound slightly so that it counts the number of isolated zeros in . Our bound is, apparently, significantly sharper than the recent root counts found by Rojas and in many cases easier to compute. As a consequence of our result, the Huber-Sturmfels homotopy for finding all the isolated zeros of a polynomial system in can be slightly modified to obtain all the isolated zeros in .
20.
We consider the homotopy type of classifying spaces , where is a finite -group, and we study the question whether or not the mod cohomology of , as an algebra over the Steenrod algebra together with the associated Bockstein spectral sequence, determine the homotopy type of . This article is devoted to producing some families of finite 2-groups where cohomological information determines the homotopy type of .