We consider the problem of implementing a space-efficient dynamic trie, with an emphasis on good practical performance. For a trie with n nodes with an alphabet of size σ, the informationtheoretic lower bound is n logσ + O(n) bits. The Bonsai data structure is a compact trie proposed by Darragh et al. (Softw., Pract. Exper. 23(3), 1993, pp. 277–291). Its disadvantages include the user having to...

We show for 2 p < 1 and subspaces X of quotients of L p with a 1-unconditional nite-dimensional Schauder decomposition that K (X; ` p) is an M-ideal in L(X; ` p).

Zariski Problem (Cancellation of indeterminates) is settled affirmatively, that is, it is proved that : Let k be an algebraically closed field of characteristic zero and let n, m ∈ N. If R[Y1, . . . , Ym] ∼=k k[X1, . . . , Xn+m] as k-algebras, where Y1, . . . , Ym, X1, . . . , Xn+m are indetermoinates, then R ∼=k k[X1, . . . , Xn]. Zariski Problem is the following : Zariski Problem. Let k be an...

The most luminous X-ray source in the Local Group is associated with the nucleus of M33. This source, M33 X-8, appears modulated by ∼ 20% over a ∼ 106 day period, making it unlikely that the combined emission from unresolved sources could explain the otherwise persistent ∼10erg s X-ray flux (Dubus et al. 1997, Hernquist et al. 1991). We present here high resolution UV imaging of the nucleus wit...

background: vitrification has proven to be more effective than slow freezing methods to cryopreserve mammalian oocytes. the objectives of this study were to evaluate the effects of vitrification on immature and in vitro matured, denuded and cumulus compact goat oocytes and their subsequent fertilization. methods: oocytes were either cryopreserved as immature cumulus compact (imcc) (n=98 exp 1; ...

Let f $f$ be a noncommutative polynomial of degree m ⩾ 1 $m\geqslant 1$ over an algebraically closed field F $F$ characteristic 0. If n − $n\geqslant m-1$ and α , 2 3 $\alpha _1,\alpha _2,\alpha _3$ are nonzero elements from such that + = 0 _1+\alpha _2+\alpha _3=0$ then every trace zero × $n\times n$ matrix can written as A _1 A_1+\alpha _2A_2+\alpha _3A_3$ for some i $A_i$ in the image M ( ) ...

Abstract. Let X ⊂ Pr be a smooth algebraic curve in projective space, over an algebraically closed field of characteristic zero. For each m ∈ N, the m-flexes of X are defined as the points where the osculating hypersurface of degree m has higher contact than expected, and a hypersurface H ⊂ Pr is called a m-Hessian if it cuts X along its m-flexes. When X is a complete intersection, we give an e...

Conscriptions are a model of sequential computations with assumption/commitment specifications in which assumptions can refer to final states, not just to initial states. We show that they instantiate existing algebras for iteration and infinite computations. We use these algebras to derive an approximation order for conscriptions and one for extended conscriptions, which additionally represent...

The Cancellation Problem for Affine Spaces is settled affirmatively, that is, it is proved that : Let k be an algebraically closed field of characteristic zero and let n, m ∈ N. If R[Y1, . . . , Ym] ∼=k k[X1, . . . , Xn+m] as k-algebras, where Y1, . . . , Ym, X1, . . . , Xn+m are indetermoinates, then R ∼=k k[X1, . . . , Xn]. The Cancellation Problem for Affine Spaces (or Zariski Problem) is th...