Determination of impurities in graphite using synchrotron radiation based X-ray fluorescence spectrometry.
Determination of impurities namely Ca, Mn, Fe, Ni, Zn, Sr and Pb in graphite by energy dispersive X-ray fluorescence spectrometry is described using microfocused synchrotron radiation. The internal standard and standard addition methodologies were adopted for quantification and the results were compared with tube-based X-ray fluorescence spectrometry. Analysis of the results by the F and t-tests revealed their statistical equivalence. Synchrotron measurements improved the detection limits by an order of magnitude compared to the tube based technique. Cr and Zr, which were below the quantification limit in tube based technique, were also quantified by synchrotron based technique.
Nondestructive analyses of carbonate rocks: applications and potentiality for museum materials
The preciousness of historical artifacts leads to the performance of nondestructive and/or microdestructive analyses, especially when the archeological finds are stored in museums. The PXRF spectrometry represents a powerful technique for the chemometric study of the materials, in alternative to the more usual destructive X-ray-based methods. A large set of limestones belonging to several formations cropping out in the Hyblean area (south-eastern Sicily, Italy) was analyzed by means of a PXRF instrument. The main goal was to test the PXRF potentiality for the discrimination of rocks with similar features and to create a chemical database of carbonate rocks, which were commonly used in the past in the manufacturing of sculptures and stone artifacts. Fluorescence data were processed by means of multivariate statistical analysis. In particular, principal components analysis and linear discriminant analysis were applied. The results allowed us to classify the samples belonging to different formations and to distinguish different rock typologies within each formation. 
 
 
 
Finally, the investigation showed that the analytical PXRF data can be suitable for a substantial characterization of stone materials and this could be extended to museum materials belonging to cultural heritage. Copyright © 2012 John Wiley & Sons, Ltd.
Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type
<jats:p>We consider the discrete Volterra type equation of the form <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:msubsup><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mi>K</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>. We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi mathvariant="normal">o</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math>, for given nonpositive real <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:math>, as a measure of approximation.</jats:p>