Examination of Polish Identity Documents by Laser-Induced Breakdown Spectroscopy

Laser-induced breakdown spectroscopy (LIBS) was applied to the preliminary examination of Polish documents – passports and identity cards – for forensic purposes. Several security features of potentially high discrimination capability were selected at both the passports (Alphagram, serial number, the contour map of Europe, and emblem) and identity cards (kinegram, the date of birth, and emblem). Different elemental compositions were identified after comparing the spectra recorded from various measurement locations. It was possible to identify characteristic atomic emission from several elements (such as Ti, Ca, K, Fe, Cr, Mg, Na, La, Cd, Li, V, Al, Mn, Ni, and Cu) based on the type of document, issue date, and evaluated area. In the case of passports, the potentially good discriminators with unique elemental composition were identified, e.g., the serial number and the contour map of Europe printed with the use of intaglio printing technique. Identity cards with the cover of polycarbonate foil constitute a very difficult sample to analyze because of the foil’s influence on the laser ablation phenomenon. This study presents the potential of LIBS as an effective and useful technique to analyze Polish passports for forensic purposes. Its many advantages provide a good alternative to the analytical methods routinely used for the examination of these objects.     

VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS

The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the issuer is liable for the net loss. In this article, the mathematical foundation for pricing the European passport option is established. The pricing equation which is a fully nonlinear equation is derived using the dynamic programming principle. The comparison principle, uniqueness and convexity preserving of the viscosity solutions of related H J13 equation are proved. A relationship between the passport and lookback options is discussed.