Let P be a polytope with rational vertices. A classical theorem of Ehrhart states that the number of lattice points in the dilations P (n) = nP is a quasi-polynomial in n. We generalize this theorem by allowing the vertices of P (n) to be arbitrary rational functions in n. In this case we prove that the number of lattice points in P (n) is a quasi-polynomial for n sufficiently large. Our work w...

The distance-3 cyclic lowest-density MDS array code (called the C-Code) is a good candidate for RAID 6 because of its optimal storage efficiency, optimal update complexity, optimal length, and cyclic symmetry. In this paper, the underlying connections between C-Codes (or quasi-C-Codes) and starters in group theory are revealed. It is shown that each C-Code (or quasi-C-Code) of length 2n can be ...

The elastic pressure/volume (P/V) curve obtained by the multiple linear regression (MLR) technique using a new model, was compared with the quasi-static P/V points obtained by the rapid airway occlusion technique. Seven infants were studied during mechanical ventilation using a pressure controlled mode. The resistive pressure was subtracted from airway opening pressure, thus determining the ela...

The Schatten-p quasi-norm (0<p<1) is usually used to replace the standard nuclear norm in order to approximate the rank function more accurately. However, existing Schattenp quasi-norm minimization algorithms involve singular value decomposition (SVD) or eigenvalue decomposition (EVD) in each iteration, and thus may become very slow and impractical for large-scale problems. In this paper, we fi...

In this paper, we investigate approximation of quasi-projection operators in Besov spaces B p,q, μ > 0, 1 ≤ p, q ≤ ∞. Suppose I is a countable index set. Let (φi)i∈I be a family of functions in Lp(IR), and let (φ̃i)i∈I be a family of functions in Lp̃(IR), where 1/p+ 1/p̃ = 1. Let Q be the quasi-projection operator given by

We construct nontrivial homomorphisms from the quasi group of some cubic surfaces over Fp into a group. We show experimentally that the homomorphisms constructed are the only possible ones and that there are no nontrivial homomorphisms in the other cases. Thereby, we follow the classification of cubic surfaces, due to A.Cayley. 1 The quasi group of a cubic surface 1.1. –––– According to Yu. I. ...

‎A topological space is called submaximal if each of its dense subsets is open and is called nodec if each of its nowhere dense ea subsets is closed‎. ‎Here‎, ‎we study a variety of spaces some of which have already been studied in $C(X)$‎. ‎Among them are‎, ‎most importantly‎, ‎quasi $P$-spaces and pointwise quasi $P$-spaces‎. ‎We obtain some new useful topological characterizations of quasi $...

We study the approximation of d-dimensional integrals. We present sufficient conditions for fast quasi-Monte Carlo convergence. They apply to isotropic and non-isotropic problems and, in particular, to a number of problems in computational finance. We show that the convergence rate of quasi-Monte Carlo is of order n−1+p{logn} −1/2 with p ≥ 0. This is a worst case result. Compared to the expecte...

Quasi-abelian codes constitute an important class of linear codes containing theoretically and practically interesting codes such as quasi-cyclic codes, abelian codes, and cyclic codes. In particular, the sub-class consisting of 1-generator quasi-abelian codes contains large families of good codes. Based on the well-known decomposition of quasi-abelian codes, the characterization and enumeratio...