Computing Minimal Multi-Homogeneous Bezout Numbers Is Hard

The multi-homogeneous Bezout number is a bound for the number of solutions of a system of multi-homogeneous polynomial equations, in a suitable product of projective spaces. Given an arbitrary, not necessarily multi-homogeneous, system, one can ask for the optimal multi-homogenization that would minimize the Bezout number. In this paper it is proved that the problem of computing, or even estimating, the optimal multi-homogeneous Bezout number is actually NP-hard. In terms of approximation theory for combinatorial optimization, the problem of computing the best multi-homogeneous structure does not belong to APX, unless P = NP. Moreover, polynomial-time algorithms for estimating the minimal multi-homogeneous Bezout number up to a fixed factor cannot exist even in a randomized setting, unless BPP ⫆ NP.     

Electrical properties and positron annihilation study of (Ba<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ho<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>)TiO<Subscript>3</Subscript> ceramics

DC resistivity, dielectric constant, dielectric loss and positron annihilation spectra of (Ba_1−x Ho _x )TiO₃ ceramics have been measured as a function of holmium concentration x. It has been found that the DC resistivity of (Ba_1−x Ho _x )TiO₃ is strongly dependent on the Ho content: it decreases three orders of magnitude and reaches a minimum at x = 0.4%. Doping with 0.6% holmium increases the permittivity of BaTiO₃ by approximately three times (from ∼1,300 to ∼4,000), with only a slight increase in the corresponding dielectric loss. The local electron density and defect concentration estimated using positron annihilation technique conforms well to the features found in the dielectric and resistivity measurements. The results have been discussed in terms of a mixed compensation model.     

A Study of Integrated Document and Connection Caching in the WWW

Document caching and connection caching are extensively studied problems. In document caching, one has to maintain caches containing documents accessible in a network. In connection caching, one has to maintain a set of open network connections that handle data transfer. Previous work investigated these two problems separately while in practice the problems occur together: In order to load a document, one has to establish a connection between network nodes if the required connection is not already open. In this paper we present the first study that integrates document and connection caching. We first consider a very basic model in which all documents have the same size and the cost of loading a document or establishing a connection is equal to 1. We present deterministic and randomized online algorithms that achieve nearly optimal competitive ratios unless the size of the connection cache is extremely small. We then consider general settings where documents have varying sizes. We investigate a FAULT model in which the loading cost of a document is 1 as well as a BIT model in which the loading cost is equal to the size of the document.     

Preliminary<Emphasis Type="Italic">in vitro</Emphasis> and<Emphasis Type="Italic">in vivo</Emphasis> characterizations of a sol-gel derived bioactive glass-ceramic system

This study investigates quantitatively and qualitatively the sol-gel derived bioactive glass-ceramic system (BGS)—apatite-wollastonite (AW) type granules in the size range of 0.5–1 mm, as an effective graft material for bone augmentation and restoration. Scanning electron micrographs (SEM) of the sintered granules revealed the rough material surface with micropores in the range 10–30 μm. X-ray diffraction (XRD) pattern of the granules revealed the presence of crystalline phases of the hydroxyapatite and wollastonite, and the functional groups of the silicate and phosphates were identified by Fourier transform infrared spectroscopy (FT-IR). Thein vitro cell culture studies with L929 mouse fibroblast cell line showed very few cells adhered on the BGS disc after 24 h. This could be due to the highly reactive surface of the disc concomitant with the crystallization but not due to the cytotoxicity of the material, since the cellular viability (MTT assay) with the material was 80‰ Cytotoxicity and cytocompatibility studies proved that the material was non-toxic and biocompatible. After 12 weeks of implantation of the BGS granules in the tibia bone of New Zealand white rabbits, the granules were found to be well osteointegrated, as observed in the radiographs. Angiogram with barium sulphate and Indian ink after 12 weeks showed the presence of microcapillaries in the vicinity of the implant site implicating high vascularity. Gross observation of the implant site did not show any inflammation or necrosis. SEM of the implanted site after 24 weeks revealed good osteointegration of the material with the newly formed bone and host bone. New bone was also observed within the material, which was degrading. Histological evaluation of the bone healing with the BGS granules in the tibial defect at all time intervals was without inflammation or fibrous tissue encapsulation. After 2 weeks the new bone was observed as a trabeculae network around the granules, and by 6 weeks the defect was completely closed with immature woven bone. By 12 weeks mature woven bone was observed, and new immature woven bone was seen within the cracks of the granules. After 24 weeks the defect was completely healed with lamellar bone and the size of the granules decreased. Histomorphometrically the area percentage of new bone formed was 67.77% after 12 weeks and 63.37% after 24 weeks. Less bone formation after 24 weeks was due to an increased implant surface area contributed by the material degradation and active bone remodeling. The osteostimulative and osteoconductive potential of the BGS granules was established by tetracycline labelling of the mineralizing areas by 2 and 6 weeks. This sol-gel derived BGS granules proved to be bioactive and resorbable which in turn encouraged active bone formation.     

Vibrational analysis of functionalized polyolefins/poly(vinylchloride) blends

Polyolefins functionalized with diethylmaleate were mixed with poly(vinylchloride) (PVC) in different compositions. Intermolecular interactions involving the carbonyl groups of the side chains of the functionalized polyolefins and methine hydrogens of PVC were investigated by means of infrared spectroscopy. The major flexibility of the ester groups attached to the backbone chains, with respect to polyesters, seems to increase the capability of such groups to interact with groups of more polar polymers, thus allowing prediction of easier miscibility, which however also depends on the starting polyolefin structure and function-alization degree.