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.     

Pharmacological distribution diagrams: a tool for de novo drug design

BACKGROUND: There is no empirical data available on attitudes concerning AIDS and habits towards HIV infected patients of physicians in general or private practice. In this study results of a self-evaluation are presented. METHODS: 178 physicians working with out-patients in different medical fields were randomly selected for a cross sectional study and interviewed using a standardised questionnaire. RESULTS: 89% think that they are sufficiently informed about AIDS (in the USA 20%). They regarded the risk of infection to be lower than the Anglo-American physicians. They believed there is a lack of interchange of information between colleagues regarding the degree of infectiousness of referred patients. A third of the physicians fear that other patients will go elsewhere if they find out that their physician is treating AIDS patients. 54% would hold special clinic sessions for HIV-patients outside the normal schedule for practice times. 89% believed that HIV patients were partly to blame for their illness. CONCLUSIONS: Although the physicians recognise the problem of HIV-infection, they partly deny the real necessities and facts. A reason for this could be the emotions underlying the general attitude to everything pertaining to HIV-disease. Attitudes to HIV-disease and the dealing with it in daily practice must be considered on the basis of individual emotional motives.     

Ascitic fluid analysis in hepatocellular carcinoma

BACKGROUND: Ascites in patients with hepatocellular carcinoma (HCC) is a poorly characterized subgroup of malignancy-related ascites. Not only the underlying liver disease, but also the tumor growth and spread contributes to the ascites formation. The authors differentiated ascites in HCC from other types of ascites. METHODS: The authors analyzed the ascitic fluid of 185 consecutive patients (89 liver cirrhosis, 33 HCC, 31 peritoneal carcinomatosis, 22 liver metastases, 10 spontaneous bacterial peritonitis). RESULTS: Each subgroup showed a typical pattern. Compared with the cirrhotic patients, those with HCC showed a higher frequency of positive cytologic findings (4 of 33 versus 0/89, P < 0.004), elevated fibronectin concentration (10/33 versus 8/89, P < 0.004), and elevated polymorphonuclear cell count (10/33 versus 5/89 P < 0.004). CONCLUSIONS: A significant number of patients with ascites and HCC patients showed signs of peritoneal infiltration with positive cytologic findings and increased concentration of fibronectin. Moreover, neutrocytic ascites without signs of superinfection is relatively common (30%).     

Deploying deep learning approaches to left ventricular non-compaction measurement

The Journal of Supercomputing - Left ventricular non-compaction (LVNC) is a rare cardiomyopathy characterized by abnormal trabeculations in the left ventricle cavity. Although traditional computer...     

Ion‐exchange resins. II. Acrylamide crosslinked copolymers as precursors for some ion exchangers

Crosslinked copolymers of acrylamide (AA) and ethylacrylate and some ion exchangers derived from them containing either primary amine groups, obtained by the Hofmann degradation of the amide groups, or carboxylic groups, obtained by the alkaline hydrolysis of the ester groups, were studied. Divinylbenzene and N,N′‐methylenebisacrylamide were used as crosslinkers. The starting copolymers and the corresponding ion exchangers were characterized by IR spectroscopy, swelling behavior, and thermogravimetric analysis. The ion‐exchanger properties were correlated with the crosslinker nature and the chemical reactions performed on the AA copolymers. The average molecular weight between two crosslinks, determined from the swelling data in water, was compared with that calculated on the basis of the copolymerization stoichiometry only for the carboxylic cation exchangers. In this way, the preservation of the crosslink density after the hydrolysis was revealed. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 2701–2707, 2003     

Dielectric behavior of PVDF/POMA blends that have a low doped POMA content

The real (ε′) and imaginary (ε″) components of the complex permittivity of blends of PVDF [poly(vinylidene fluoride)] with POMA [poly(o‐methoxyaniline)] doped with toluenosulfonic acid (TSA) containing 1, 2.5, and 5 wt % POMA–TSA were determined in the frequency interval between 10² and 3 × 10⁶ Hz and in the temperature range from ?120 up to 120°C. It was observed that the values of ε′ and ε″ had a greater increase with the POMA–TSA content and with a temperature in the region of frequencies below 10 kHz. This effect decreased with frequency and it was attributed to interfacial polarization. This polarization was caused by the blend heterogeneity, formed by conductive POMA–TSA agglomerates dispersed in an insulating matrix of PVDF. The equation of Maxwell–Garnett, modified by Cohen, was used to evaluate the permittivity and conductivity behavior of POMA–TSA in the blends. A strong decrease was observed in POMA–TSA conductivity in the blend, which was bigger the lower the POMA–TSA content in the blend. This decrease could have been caused either by the POMA dedoping during the blend preparation process or by its dispersion into the insulating matrix. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 752–758, 2003     

Miscibility and morphology of poly(vinylidene fluoride)/poly[(vinylidene fluoride)‐ran‐trifluorethylene] blends

This study presents an investigation of the effect of the different crystalline phases of each blend component on miscibility when blending poly(vinylidene fluoride) (PVDF) and its copolymer poly[(vinylidene fluoride)‐ran‐trifluorethylene] [P(VDF–TrFE)] containing 72 mol % of VDF. It was found that, when both components crystallized in their ferroelectric phase, the PVDF showed a strong effect on the crystallinity and phase‐transition temperature of the copolymer, indicating partial miscibility in the crystalline state. On the other hand, immiscibility was observed when both components, after melting, were crystallized in their paraelectric phase. In this case, however, a decrease in crystallization temperatures suggested a strong interaction between monomers in the liquid state. Blend morphologies indicated that, in spite of the lack of miscibility in the crystalline state, there is at least miscibility between PVDF and P(VDF–TrFE) in the liquid state, and that a very intimate mixture of the two phases on the lamellar level can be maintained upon crystallization. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 1362–1369, 2002     

Manganese ferrite nanoparticles synthesized through a nanocasting route as a highly active Fenton catalyst

Spinel ferrite MnFe₂O₄ nanoparticles were synthesized by means of a nanocasting technique using a low-cost mesoporous silica gel as a hard template. The magnetic nanoparticles, of <10 nm diameter and with a surface area of around 100 m²/g, were tested as a heterogeneous Fenton catalyst for the decomposition of hydrogen peroxide under neutral and basic conditions. This catalyst shows a much higher activity than previous heterogeneous catalysts reported in the literature, which is mainly ascribed to its small particle size. Furthermore, the magnetic catalyst can be easily separated from the reaction medium by means of an external magnetic field. The effects of residual silica and the purity of the catalyst (hematite formation) on catalytic activity have been studied and correlated. The results obtained show this catalyst to be a suitable candidate for the removal of pollutants in wastewaters by means of the Fenton heterogeneous reaction.