This paper may be viewed as a corrigendum as well as an extension of the paper by (Czumaj et al., Theoret. Comput. Sci. 262 (1–2), (2001) 569–582) where they deal with the variable length scheduling problem (VLSP) with parameters k1; k2, denoted VLSP(k1; k2). In the current paper, we >rst discuss an error in the analysis of one of the approximation algorithms described in (Czumaj et al., Theore...

A binary sequence satisfies a one-dimensional (d; k) run length constraint if every run of zeros has length at least d and at most k. A two-dimensional binary pattern is (d1; k1; d2; k2)-constrained if it satisfies the one-dimensional (d1; k1) run length constraint horizontally and the one-dimensional (d2; k2) run length constraint vertically. For given d1; k1; d2, and k2, the asymmetric two-di...

To gain insight into the physiological role of a kidney-specific chloride channel, CLC-K2, the exact intrarenal localization was determined by in situ hybridization. In contrast to the inner medullary localization of CLC-K1, the signal of CLC-K2 in our in situ hybridization study was highly evident in the superficial cortex, moderate in the outer medulla, and absent in the inner medulla. To ide...

We prove the inequality E[(X/μ)k]≤(k/μlog(1+k/μ))k≤exp(k2/(2μ)) for sub-Poissonian random variables X, such as Binomially or Poisson distributed variables, with mean μ. The asymptotic behaviour E[(X/μ)k]=1+O(k2/μ) matches a lower bound of 1+Ω(k2/μ) small k2/μ. This improves over previous uniform raw moment bounds by factor exponential in k.

For a number field F , it is proved that the K2-semigroup K2(F,F++) defined in [R.V. Moody, J. Morita, J. Algebra 229 (2000) 1] has similar properties to the positive K2 group K + 2 (F) introduced by Gras in [J. Number Theory 23 (1986) 322].  2003 Elsevier Inc. All rights reserved.

Let E be an elliptic curve, K1 its Kummer curve E/{±1}, E its square product, and K2 the split Kummer surface E /{±1}. The addition law on E gives a large endomorphism ring, which induce endomorphisms of K2. With a view to the practical applications to scalar multiplication on K1, we study the explicit arithmetic of K2.

OBJECTIVE Sorafenib is an oral multikinase inhibitor that has been proven effective as a single-agent therapy in hepatocellular carcinoma, and there is a strong rationale for investigating its use in combination with other agents. Vitamin K2 is nearly non-toxic to humans and has been shown to inhibit the growth of hepatocellular carcinoma. In this study, we evaluated the effects of a combinatio...

We give improved solutions for the problem of generating the k smallest spanning trees in a graph and in the plane. Our algorithm for general graphs takes time O(m log β(m,n) + k2); for planar graphs this bound can be improved to O(n+ k2). We also show that the k best spanning trees for a set of points in the plane can be computed in time O(min(k2n + n log n, k2 + kn log(n/k))). The k best orth...