An extension of a result of Zaharescu on irreducible polynomials

It is well known that if f(x) is a monic irreducible polynomial of degree d with coefficients in a complete valued field (K, ‖), then any monic polynomial of degree d over K which is sufficiently close to f(x) with respect to ‖ is also irreducible over K. In 2004, Zaharescu proved a similar result applicable to separable, irreducible polynomials over valued fields which are not necessarily complete. In this paper, the authors extend Zaharescu’s result to all irreducible polynomials without assuming separability.     

Biodegradable Polymers: Prospects,Problems, and Progress

Abstract

At different times in the history of polymer science specific subjects have come to center stage; for intense investigation because they represent new and important intellectual challenges as well as technological opportunities. In past years the chief incentive for the scientific study of biodegradation of polymers was concern with the problem of preventing or retarding attack on such products by microorganisms, insects, rodents, and other animals. Many research efforts in synthetic polymer chemistry were directed toward the synthesis of polymers resistant to biodegradation. The paramount feature sought by polymer chemists and engineers was stability, and the production of such materials has been very impressive. This is still a very important factor in many applications such as paints, protective coatings, textiles, electrical insulation, and plastic films and sheets used for many applications such as upholstery and floor covering. Fortunately, most synthetic polymers are resistant to biological attack and many of these studies were concerned with choosing additives which would be bioresistant, or with providing protection for the susceptible ingredients in the plastic formulation by the use of fungicides and other biocides. In recent years, however, the picture has changed and there has been a raft of publicity about degradable plastics [1–10].     

Evaluating the Biodegradation of Veterinary Antibiotics Using Kinetics Model and Response Surface Methodology

The inappropriate use and indiscriminate disposal of antibiotics has become a menace worldwide. The incomplete removal of these contaminants from wastewater treatment plants has also contributed to this. This study presents the biodegradation of two veterinary antibiotics; ciprofloxacin (CIP) and enrofloxacin (ENRO). Kinetics models were explored to understand the dynamics of biodegradation in an anaerobic digestion process. This was carried out in batch reactors under various operating conditions: pH, organic loading rate (OLR), and antibiotic concentration. The influence of the parameters was investigated using a response surface methodology (RSM) based on the Box–Behnken experimental design of 15 runs. The data obtained were fitted on a polynomial function model. OLR and pH exhibited a synergistic and antagonistic effect in the response models developed, with a high correlation regression coefficient (R²; 0.9834–0.9875) close to 1 at a 95% confidence level. The optimum conditions obtained from the RSM numerical optimization were pH (6), OLR (2 kgCOD·m⁻³·days⁻¹), and an antibiotic concentration of 75%, which gave the removal of CIP, ENRO, and COD, respectively, as 80%, 83%, and 73% at a desirability function of 85%. The kinetics study shows that the biodegradation of antibiotics was well fitted on a first-order model (R²; 0.9885–0.9978) with rate constants ranging from 0.0695 to 0.96 days⁻¹.     

Very large-core, single-mode, gain-guided, index-antiguided fiber lasers

Lowest-order, single-mode laser oscillation is reported in gain-guided index-antiguided fiber lasers having core diameters from 100 to 400 microm. A model is presented explaining how to select resonator mirrors to assure single-mode operation.     

Spectral narrowing and stabilization of thulium fiber lasers using guided-mode resonance filters

We used guided-mode resonance filters (GMRFs), fabricated using thin-film deposition and chemical etching, as intracavity feedback elements to stabilize and narrow the output spectrum in thulium-doped fiber oscillators operating in the 2?μm wavelength regime, producing linewidths of <700?pm up to 10?W power levels. A Tm fiber-based amplified spontaneous emission source was used to characterize the reflective properties of the GMRFs. Linewidths of 500?pm and a 7.3?dB reduction in transmission were measured on resonances.     

A Uniqueness Problem in Valued function Fields of Conics

Let v₀ be a valuation of a field K₀ with value group G₀. LetK be a function field of a conic over K₀, and let v be an extensionof v₀ to K with value group G such that G/G₀ is not a torsiongroup. Suppose that either (K₀, v₀) is henselian or v₀ is ofrank 1, the algebraic closure of K₀ in K is a purely inseparableextension of K₀, and G₀ is a cofinal subset of G. In this paper,it is proved that there exists an explicitly constructible elementt in K, with v(t) non-torsion modulo G₀ such that the valuationof K₀(t), obtained by restricting v, has a unique extensionto K. This generalizes the result proved by Khanduja in theparticular case, when K is a simple transcendental extensionof K₀ (compare [4]). The above result is an analogue of a resultof Polzin proved for residually transcendental extensions [8].     

Controlled biosynthesis and characterization of poly(3-hydroxybutyrate-co-3-hydroxyvalerate-co-3-hydroxyhexanoate) from mixtures of palm kernel oil and 3HV-precursors

This study investigates the biosynthesis and characterization of P(3HB-co-3HV-co-3HHx) terpolymer from mixtures of palm kernel oil and 3HV-precursors by using recombinant Cupriavidus necator PHB⁻4/pBBREE32d13. Sodium valerate and propionate have been evaluated for the generation of 3HV monomers. The feeding time of these precursors was a crucial factor that significantly affected the 3HV molar fractions, which ranged from 2 to 60 mol%. Sodium valerate was generally the better precursor in initiating the accumulation of 3HV monomers while maintaining high cell dry weight (7.9 g/L) and good PHA accumulation (79 wt%). However, the 3HHx molar fractions in the terpolymers at 72 h were consistent at about 2-7 mol%. P(3HB-co-3HV) copolymers have been known to exhibit approximately the same degree of crystallinity throughout a wide range of 3HV composition. Interestingly, in this study, terpolymers containing 58 mol% 3HB, 39 mol% 3HV and 3 mol% 3HHx showed elastomeric behavior. This study demonstrates the suitability of palm kernel oil as the main carbon source and both sodium propionate and sodium valerate as 3HV-precursors for the synthesis of novel compositions of P(3HB-co-3HV-co-3HHx) terpolymers with interesting properties.