22 research outputs found
Isoparametric foliation and Yau conjecture on the first eigenvalue
A well known conjecture of Yau states that the first eigenvalue of every
closed minimal hypersurface in the unit sphere is just its
dimension . The present paper shows that Yau conjecture is true for minimal
isoparametric hypersurfaces. Moreover, the more fascinating result of this
paper is that the first eigenvalues of the focal submanifolds are equal to
their dimensions in the non-stable range.Comment: to appear in J.Diff.Geo
Isoparametric functions and exotic spheres
The first part of the paper is to improve the fundamental theory of
isoparametric functions on general Riemannian manifolds. Next we focus our
attention on exotic spheres, especially on "exotic" 4-spheres (if exist) and
the Gromoll-Meyer sphere. In particular, as one of main results we prove: there
exists no properly transnormal function on any exotic 4-sphere if it exists.
Furthermore, by projecting an -invariant isoparametric function on
, we construct a properly transnormal but not an isoparametric function
on the Gromoll-Meyer sphere with two points as the focal varieties.Comment: 21 pages, to appear in Journal f\"ur die reine und angewandte
Mathematik (Crelles Journal
Topology of Blow-ups and Enumerative Geometry
Let M be the blow--up of a manifold M along a submanifold X. In this paper we
present closed formulae for the integral cohomology and the total Chern class
of M. As applications we compute the cohomology of the varieties of complete
conics and complete quadrices in 3--space, and justify two enumerative results
due to Schubert.Comment: 30 page
Expert Consensus on Microtransplant for Acute Myeloid Leukemia in Elderly Patients -Report From the International Microtransplant Interest Group
Recent studies have shown that microtransplant (MST) could improve outcome of patients with elderly acute myeloid leukemia (EAML). To further standardize the MST therapy and improve outcomes in EAML patients, based on analysis of the literature on MST, especially MST with EAML from January 1st, 2011 to November 30th, 2022, the International Microtransplant Interest Group provides recommendations and considerations for MST in the treatment of EAML. Four major issues related to MST for treating EAML were addressed: therapeutic principle of MST (1), candidates for MST (2), induction chemotherapy regimens (3), and post-remission therapy based on MST (4). Others included donor screening, infusion of donor cells, laboratory examinations, and complications of treatment
Generalizations of RSA Public Key Cryptosystem
In this paper, for given N = pq with p and q different odd primes, and m = 1, 2, , we give a public key cryptosystem. When m = 1 the system is just the famous RSA system. And when m 2, the system is usually more secure than the one with m = 1