Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface

A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively

Total Positivity of the Cubic Trigonometric Bézier Basis

Within the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric Bézier basis with two shape parameters λ and μ given in Han et al. (2009) forms an optimal normalized totally positive basis for λ,μ∈(-2,1]. Moreover, we show that for λ=-2 or μ=-2 the basis is not suited for curve design from the blossom point of view. In order to compute the corresponding cubic trigonometric Bézier curves stably and efficiently, we also develop a new corner cutting algorithm

Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application

Four new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class of C1 continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing a C1 positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, the G1 continuous conditions are deduced for the joining of two patches

The Effect of Recycling Flux on the Performance and Microbial Community Composition of a Biofilm Hydrolytic-Aerobic Recycling Process Treating Anthraquinone Reactive Dyes

Synthetic dyes are extensively used and rarely degraded. Microbial decomposition is a cost-effective alternative to chemical and physical degradation processes. In this study, the decomposition of simulated anthraquinone reactive dye (Reactive Blue 19; RB19) at a concentration of 400-mg/L in wastewater by a biofilm hydrolytic-aerobic recycling system was investigated over a range of recycling fluxes. The 16S rDNA-based fingerprint technique was also used to investigate the microbial community composition. Results indicated that the recycling flux was a key factor that influenced RB19 degradation. The RB19 and COD removal efficiency could reach values as high as 82.1% and 95.4%, respectively, with a recycling flux of 10 mL/min. Molecular analysis indicated that some strains were similar to Aeromonadales, Tolumonas, and some uncultured clones were assumed to be potential decolorization bacteria. However, the microbial community composition in the reactors remained relatively stable at different recycling fluxes. This study provided insights on the decolorization capability and the population dynamics during the decolorization process of anthraquinone dye wastewater.National Natural Science Foundation of China[40801195, 41071302]; State Key Lab of Urban Water Resource and Environment (HIT)[QA200809

Spectroscopic super-resolution fluorescence cell imaging using ultra-small Ge quantum dots

QMUL/CSC scholarship (2011611045); BBSRC grant (BB/J001473/1)

C1 triangular Coons surface construction and image interpolation based on new Side-Side and Side-Vertex interpolation operators.

In this paper, a new class of rational quadratic/linear trigonometric Hermite functions with two shape parameters is proposed. Based on these Hermite functions, new improved first class of Side-Side (FCSS), second class of Side-Side (SCSS), first class of Side-Vertex (FCSV) and second class of Side-Vertex (SCSV) interpolation operators are proposed respectively, which can be used to construct C1 Coons surfaces over triangular domain. By altering the values of two shape parameters, the shape of the Coons surface patch can be adjusted flexibly, but without affecting the function values and partial derivatives of the boundaries. For constructing the triangular surface patches with the center of mass passing through a fixed point, we also give a center of mass function value control method, by which we can solve the corresponding shape parameter values. Moreover, we also apply these four improved interpolation operators to image interpolation. Compared with some widely used image interpolation methods, our methods achieve competitive performance

A Class of Trigonometric Bernstein-Type Basis Functions with Four Shape Parameters

In this work, a family of four new trigonometric Bernstein-type basis functions with four shape parameters is constructed, which form a normalized basis with optimal total positivity. Based on the new basis functions, a kind of trigonometric Bézier-type curves with four shape parameters, analogous to the cubic Bézier curves, is constructed. With appropriate choices of control points and shape parameters, the resulting trigonometric Bézier-type curves can represent exactly any arc of an ellipse or parabola. The four shape parameters have tension control roles on adjusting the shape of resulting curves. Moreover, a new corner cutting algorithm is also proposed for calculating the trigonometric Bézier-type curves stably and efficiently

Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface

A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively