A generalization of rational Bernstein–Bézier curves

This paper is concerned with a generalization of Bernstein–Bézier curves. A one parameter family of rational Bernstein–Bézier curves is introduced based on a de Casteljau type algorithm. A subdivision procedure is discussed, and matrix representation and degree elevation formulas are obtained. We also represent conic sections using rational q-Bernstein–Bézier curves. AMS subject classification (2000)  65D17     

On the Convergence and Iterates of q-Bernstein Polynomials

The convergence properties of q-Bernstein polynomials are investigated. When q1 is fixed the generalized Bernstein polynomials _nf of f, a one parameter family of Bernstein polynomials, converge to f as n→∞ if f is a polynomial. It is proved that, if the parameter 0<q<1 is fixed, then _nf→f if and only if f is linear. The iterates of _nf are also considered. It is shown that _n^Mf converges to the linear interpolating polynomial for f at the endpoints of [0,1], for any fixed q>0, as the number of iterates M→∞. Moreover, the iterates of the Boolean sum of _nf converge to the interpolating polynomial for f at n+1 geometrically spaced nodes on [0,1].     

The Mechanisms of Acid-Catalyzed Hydrolysis of N-(4-Substituted Arylthio) Phthalimides

Abstract

The acid-catalyzed hydrolysis of N-(4-substitutedarylthio)phthalimides was studied in aqueous solutions of sulfuric, perchloric, and hydrochloric acids at 40.0 ± 0.1 °C. Analysis of the data by the excess acidity method, activation parameters, and substituent effects indicates hydrolysis by an A-2 mechanism at low acidity. At higher acidities, a changeover to an A-1 mechanism is observed.

GRAPHICAL ABSTRACT     

Central neurocytoma: proton MR spectroscopy and diffusion weighted MR imaging findings

Purpose

To present proton magnetic resonance spectroscopy and diffusion-weighted imaging (DWI) findings of central neurocytoma (CN).

Methods and Materials

Imaging findings of seven patients with the histopathological diagnosis of CN (five male and two female; age range, 21–28 years of age) were evaluated retrospectively. In addition to conventional magnetic resonance imaging features, we also assessed the metabolite ratios and tumor normalized apparent diffusion coefficient (NADC), which was calculated by dividing the tumor apparent diffusion coefficient (ADC) values by normal ADC. Approval from our institutional review board was obtained for this review.

Results

The tumor choline/creatine ratios were 5.17±2.38, while N-acetyl aspartate/choline and N-acetyl aspartate/creatine ratios were 0.33±0.15 and 1.84±1.38, respectively. On DWI, tumors had heterogeneous hyperintense appearances when compared with the contralateral parietal lobe white matter and tumor NADC values were 0.63±0.05.

Conclusion

Significantly increased choline/creatine and decreased N-acetyl aspartate/choline ratios with lower NADC values in CN resemble high-grade gliomas and complicate the diagnosis. Familarity its physiologic features would help to presurgical diagnosis of ventricular and exraventricular CNs.     

Polymer supported 5,10,15,20-tetrakis(phenoxy acetic acid)porphyrin derivative for separation and preconcentration of d- and f-electron metals

5,10,15,20-tetrakis(phenoxy acetic acid) porphyrin (PAAP) was covalently linked to Merrifield chloromethylated resin. Characterization of PAAP and the modified polymeric matrix were performed by ¹H NMR, FTIR and elemental analysis. The sorbent was used for the separation and enrichment of the d-electron metals (Mn(II), Co(II), Ni(II), Cu(II) and Zn(II)) at pH 6–8 and of the f-electron metals U(VI) and Th(IV) at pH 4–5. The metals ions were preconcentrated with a concentration factor range of 115–215 and then determined by flame atomic absorption spectrometry or visible spectrophotometry using Arsenazo(III). The retained metals were eluted with 2.0 mol L⁻¹ HNO₃ in the case of the d-electron metals and 0.1/0.25 mol L⁻¹ HCl in the case of the f-electron metals. The procedure was validated by analyzing the NIST standard reference material 2709 (San Joaquin Soil). Correspondence: Melek Merdivan, Chemistry Department, Faculty of Arts and Sciences, Dokuz Eylul University, 35160 Buca, Izmir, Turkey     

Partially coherent Airy beam and its propagation in turbulent media

The properties of partially coherent Airy beam propagating in turbulent media are investigated. Firstly the variations in the intensity profile and the location of the Airy beam peak with respect to dislocation and width parameters are examined. On the source plane, it is shown that there is a threshold value of the dislocation parameter which determines whether the beam peak will lie on the negative or positive side of the axis. The changes in source beam power and source beam size with respect to dislocation and width parameters are also examined. Then analysis is made for partially coherent Airy beam propagating in turbulence against variations in propagation distance, dislocation and width parameters, structure constant and partial coherence. It is found that the peak of the Airy beam will always shift to the right for increasing propagation distance. But this shift will become less as the dislocation and width parameters are increased. Finally it is shown that higher levels of turbulence and partial coherence will lead to more spreading and shift the beam peak more toward the on-axis position.     

Scintillation index of elliptical Gaussian beam in turbulent atmosphere

A tensor method is used to formulate the on-axis scintillation index for an elliptical Gaussian beam (EGB; astigmatic Gaussian beam) propagating in a weak turbulent atmosphere. Variations of the on-axis scintillation of an EGB are studied. It is interesting to find that the scintillation index of an EGB can be smaller than that of a circular Gaussian beam in a weakly turbulent atmosphere under certain conditions and is closely related to the ratio of the beam waist size along the long axis to that along the short axis of the EGB, the wavelength, and the structure constant of the turbulent atmosphere.