Two results are obtained that give upper bounds on partial spreads and partial ovoids respectively. The first result is that the size of a partial spread of the Hermitian polar space H(3, q) is at most ( 2p+p 3 )t +1, where q = p, p is a prime. For fixed p this bound is in o(q), which is asymptotically better than the previous best known bound of (q + q + 2)/2. Similar bounds for partial spread...

Let ρC be the regularity of the Hilbert function of a projective space curve C over an algebraically closed field, αI be the initial degree of the defining ideal I of C and βI the least degree t such that the depth of the ideal generated by I≤t is depth(I). Then the Castelnuovo-Mumford regularity reg(C) of C is upper bounded by max{ρC +1, αI +βI −1}. We study in deep and refine the above bound ...

Recently, it was proved that the index of an economy with incomplete real asset markets is typically +1 when the degree of incompleteness, which is defined as the difference between the number of states and the number of securities, is an even number. This paper considers the case where the degree of incompleteness is an odd number and proves that any odd number can be realized as the index of ...

S.M. Lee proposed the conjecture: for any n > 1 and any permutation f in S(n), the permutation graph P (Pn, f) is graceful. For any integer n > 1 and permutation f in S(n), we discuss the gracefulness of the permutation graph P (Pn, f) if f = ∏l−1 k=0(m + 2k, m + 2k + 1), and ∏l−1 k=0(m+4k, m+4k +2)(m+4k +1, m+4k +3) for any positive integers m and l.

http://dx.doi.org/10.1016/j.chb.2014.02.028 0747-5632/ 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +1 646 62

In this brief report, we analyze a generalized theory of massless scalar QED2 and show that, unlike the conventional scalar QED2, it is free from infrared divergence problems. The model is exactly soluble and may describe, in an 1+1 dimensional space-time, noninteracting spin-one tachyons.