Counting integral ideals in a number field

Let K   be an algebraic number field. We discuss the problem of counting the number of integral ideals below a given norm and obtain effective error estimates. The approach is elementary and follows a classical line of argument of Dedekind and Weber. The novelty here is that explicit error estimates can be obtained by fine tuning this classical argument without too much difficulty. The error estimate is sufficiently strong to give the analytic continuation of the Dedekind zeta function to the left of the line R(s)=1$\mathfrak{R}(s)=1$ as well as explicit bounds for the residue of the zeta function at s=1$s=1$.     

Phase holdups in three-phase fluidized beds in the presence of disc promoter

Three-phase fluidized beds are found to have wide applications in process industries. The present investigation essentially comprises of the studies on gas holdup, liquid holdup and bed porosity in three-phase fluidized beds with coaxially placed disc promoter. Holdup data were obtained from bed expansion and pressure drop measurements. Analysis of the data was done to elucidate the effects of dynamic and geometric parameters on gas holdup, liquid holdup and bed porosity. Data were correlated and useful equations were obtained from empirical modeling.     

Spectroscopic studies on Fe and Mn doped SrB4O7 glasses

EPR and optical absorption studies on Fe³⁺ and Mn²⁺ doped strontium tetraborate (SrB₄O₇) glasses are carried out at room temperature. The EPR spectrum of the Fe³⁺ doped glass consists of signals with g-values 9.04, 4.22 and 2.04, whereas the EPR spectrum of Mn²⁺ doped glass exhibits a characteristic hyperfine sextet around g=2.0. The spectroscopic analyses of the obtained results confirmed distorted octahedral site symmetry for the Fe³⁺ and Mn²⁺ impurity ions. Crystal field and Racah parameters evaluated from optical absorption spectra are: Dq=790, B=700 and C=3000 cm⁻¹ for Fe³⁺doped glass and Dq=880, B=700 and C=2975 cm⁻¹ for Mn²⁺ doped glass.     

Metal-sensitive and thermostable trypsin from the crevalle jack (<Emphasis Type="Italic">Caranx hippos</Emphasis>) pyloric caeca: purification and characterization

Background

Over the past decades, the economic development and world population growth has led to increased for food demand. Increasing the fish production is considered one of the alternatives to meet the increased food demand, but the processing of fish leads to by-products such as skin, bones and viscera, a source of environmental contamination. Fish viscera have been reported as an important source of digestive proteases with interesting characteristics for biotechnological processes. Thus, the aim of this study was to purify and to characterize a trypsin from the processing by-products of crevalle jack (Caranx hippos) fish.

Results

A 27.5 kDa trypsin with N-terminal amino acid sequence IVGGFECTPHVFAYQ was easily purified from the pyloric caeca of the crevalle jack. Its physicochemical and kinetic properties were evaluated using N-α-benzoyl-_DL-arginine-p-nitroanilide (BApNA) as substrate. In addition, the effects of various metal ions and specific protease inhibitors on trypsin activity were determined. Optimum pH and temperature were 8.0 and 50°C, respectively. After incubation at 50°C for 30 min the enzyme lost only 20% of its activity. K _m , k_cat, and k _cat /K _m values using BApNA as substrate were 0.689 mM, 6.9 s^-1, and 10 s^-1 mM^-1, respectively. High inhibition of trypsin activity was observed after incubation with Cd²⁺, Al³⁺, Zn²⁺, Cu²⁺, Pb²⁺, and Hg²⁺ at 1 mM, revealing high sensitivity of the enzyme to metal ions.

Conclusions

Extraction of a thermostable trypsin from by-products of the fishery industry confirms the potential of these materials as an alternative source of these biomolecules. Furthermore, the results suggest that this trypsin-like enzyme presents interesting biotechnological properties for industrial applications.

     

An efficient synthesis of 2-benzoxepines from Morita-Baylis-Hillman adducts using heterogeneous recyclable catalysts

2-Benzoxepines have efficiently been synthesized from Morita-Baylis-Hillman adducts, alkyl 3-aryl-3-hydroxy-2-methylenepropanoates by treatment with HCHO catalyzed by silica supported perchloric acid (HClO4.SiO2) or Amberlyst-15 in CH2Cl2 under reflux for a short period of time (1.5-2.5 h). The catalyst can be recovered and recycled. The antibacterial properties of the new 2-benzoxepines were studied but no activity was found.