We prove that for a solution (M, g(t)), t ∈ [0, T ), where T < ∞, to the Ricci flow on a complete non-compact Riemannian manifold with the Ricci curvature tensor uniformly bounded by some constant C on M × [0, T ), the curvature tensor stays uniformly bounded on M × [0, T ).

Little work has been done in garbage collection algorithms for distributed shared memory systems. Mosaic is a safe and complete garbage collection system that collects garbage in object systems that are implemented above page-based distributed shared memory systems. It is non-intrusive in its impact on application performance. Mosaic partitions the virtual address space into separately managed ...

We give a example of non nilpotent faithful representation of a filiform Lie algebra. This gives one counter-example of the conjecture saying that every affine connection on a filiform Lie group is complete. 1. Affine connection on a nilpotent Lie algebra 1.1. Affine connection on nilpotent Lie algebras. Definition 1. Let g be a n-dimensional Lie algebra over R. It is called affine if there is ...

Objective(s)Distinction of hydatidiform moles from non-molar specimens and subclassification of hydatidiform moles as complete and partial are important for clinical practice, but diagnosis based solely on histomorphology suffers from poor interobserver reproducibility. Nowadays, pathologists rely on molecular techniques, however these methods are technically difficult, relatively expensive, an...

We describe prime ideals of height 2 minimally generated by 3 elements in a Gorenstein, Nagata local ring of Krull dimension 3 and multiplicity at most 3. This subject is related to a conjecture of Y. Shimoda and to a long-standing problem of J. Sally.

Rfam is a comprehensive collection of non-coding RNA (ncRNA) families, represented by multiple sequence alignments and profile stochastic context-free grammars. Rfam aims to facilitate the identification and classification of new members of known sequence families, and distributes annotation of ncRNAs in over 200 complete genome sequences. The data provide the first glimpses of conservation of ...

We prove that a complete family of linearly non-degenerate rational curves of degree e > 2 in P has at most n−1 moduli. For e = 2 we prove that such a family has at most n moduli. It is unknown whether or not this is the best possible result. The general method involves exhibiting a map from the base of a family X to the Grassmaninian of e-planes in P and analyzing the resulting map on cohomology.

The Non-Identity Check problem asks whether a given a quantum circuit is far away from the identity or not. It is well known that this problem is QMA-Complete [14]. In this note, it is shown that the Non-Identity Check problem remains QMA-Complete for circuits of short depth. Specifically, we prove that for constant depth quantum circuit in which each gate is given to at least Ω(log n) bits of ...

In this paper, we study the volume growth property of a non-compact complete Riemannian manifold X . We improve the volume growth theorem of Calabi (1975) and Yau (1976), Cheeger, Gromov and Taylor (1982). Then we use our new result to study gradient Ricci solitons. We also show that on X , for any q ∈ (0,∞), every non-negative L subharmonic function is constant under a natural decay condition ...