Differentiation of two main ammunition brands in Chile by Regularized Discriminant Analysis (RDA) of metals in gunshot residues

Conventionally, chemical patterns of gunshot residues (GSR) can be used for identification of a suspect involved in criminal fire arm incidents. Furthermore, metals composition in GSR is well related with the ammunition brand. In Chile the two main ammunition brands used are FAMAE and CBC. Metals, such as Pb, Ba, Sb, Cu, Zn and Ca are common elements detected in both brands. This work describes the application of both conventional and chemometric analysis of data (Regularized Discriminant Analysis, RDA) for differentiation of ammunition brands according to the metal patterns of GSR collected from shooter individuals. Real samples of GSR were collected from hands (dorsal region) of both shooters and non-shooters. Metals were analyzed using the techniques Atomic Absorption Spectrometry (AAS) and Inductively Coupled Plasma Atomic Emission Spectrometry (ICP-OES). By means of conventional plotting techniques for differentiation, such as binary and ternary plots, differences between the two brands are observed although without quantitative certainty. For the first time, applying chemometric analysis, such as regularized discriminant analysis (RDA), the investigated ammunition brands can be classified and differentiated correctly with 100% certainty.     

Fullerene Derivatives Embedded in Hybrid Sol-Gel Glasses: Nonlinear Optical Properties and Optical Limiting Performances

Hybrid organic-inorganic materials are investigated as suitable materials for inclusion of fullerene derivatives and for fabrication of laser protection devices. A specific synthesis has been developed in order to optimize non-linear optical performances of fullerene derivatives. 3-glicydoxypropyltrymethoxysilane has been used as an inorganic and organic network former to obtain the host material. The sol-gel synthesis consists of the hydrolysis and condensation in acidic conditions of the inorganic network. Epoxy polymerization has been achieved by using zirconium or BF₃ alkoxides precursors. Bulk and multilayer materials doped with a fullerene derivative have been fabricated. They show good optical requirements: high fullerenes concentration, high microstructural homogeneity, high laser damage threshold and high optical limiting efficiency. Optical limiting (OL) mechanisms have been investigated. The most effective in the sol-gel materials is the reverse saturable absorption (RSA) one. However, different mechanisms, like non-linear (NL) scattering and NL refraction contribute to a different extent. Open- and closed-aperture OL and z-scan measurements on sol-gel samples show the contribution of NL scattering and NL refraction at 690 nm. Laser damage threshold has been characterized as a function of the structure of the samples and of the optical configurations (f/66 and f/5).     

Weak Equivalence of Internal Categories

Weak equivalence is defined as equivalence in the bicategory of modules between internal categories. It is known that two categories are weakly equivalent if and only if their Cauchy completions are equivalent. We prove that this condition can be generalized to a suitable notion of intermediate category, stable under composition with weak equivalences. Applications to categorical Morita theory are given.     

Stability of incoherence in a population of coupled oscillators

We analyze a mean-field model of coupled oscillators with randomly distributed frequencies. This system is known to exhibit a transition to collective oscillations: for small coupling, the system is incoherent, with all the oscillators running at their natural frequencies, but when the coupling exceeds a certain threshold, the system spontaneously synchronizes. We obtain the first rigorous stability results for this model by linearizing the Fokker-Planck equation about the incoherent state. An unexpected result is that the system has pathological stability properties: the incoherent state is unstable above threshold, butneutrally stable below threshold. We also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise.     

Relationship between solvation energy, chemical potential and hardness variations

Starting from a density functional theory (DFT) formalism describing the energy change from one ground state representing an isolated solute, to another one representing the same solute in the field of the solvent, it is possible to obtain a simple and useful expression for the solvation energy in terms of the variation of the electronic chemical potential and global hardness associated to the change from gas to solution phase. Since both properties may be obtained from an orbital theory within the approximate Self Consistent Reaction Field (SCRF) methodology, the proposed model is expected to be useful for the analysis of chemical reactivity in solution.     

Correlation Analysis of the Alternating Step Generator

The alternating step generator is a well-known keystream generator consisting of two stop/go clocked LFSRs, LFSR₁ and LFSR₂, whose clocks are controlled by another LFSR, LFSR₃, which is clocked regularly. A probabilistic analysis of this generator is conducted which shows that the posterior probabilites of individual bits of the first derivatives of the regularly clocked LFSR₁ and LFSR₂ sequences, when conditioned on a given segment of the first derivative of the keystream sequence, can be computed efficiently in a number of probabilistic models of interest. The expected values of these probabilities, for a random keystream sequence, are derived by an approximate theoretical analysis and are also verified by systematic computer experiments. It is pointed out that these posterior probabilities can be enhanced in a resynchronization scenario and thus used for a low-complexity fast correlation attack on the two LFSRs. More generally, it is argued that even without resynchronization these probabilities may be significantly different from one half for fast correlation attacks based on iterative decoding algorithms to be successful, although with incresead complexity. A related method for computing the posterior probabilities of individual bits of the LFSR₃ sequence, when conditioned on both the keystream sequence and the LFSR₁ and LFSR₂ sequences, is also developed. As these posterior probabilities are much more different from one half, they can be used for a low-complexity fast correlation attack on LFSR₃, provided that the initial states of LFSR₁ and LFSR₂ are previously reconstructed.     

A note on the existence of the Alizadeh-Haeberly-Overton direction for semidefinite programming

This note establishes a new sufficient condition for the existence and uniqueness of the Alizadeh-Haeberly-Overton direction for semidefinite programming. The work of these authors was based on research supported by the National Science Foundation under grants INT-9600343 and CCR-970048 and the Office of Naval Research under grant N00014-94-1-0340.     

Asymptotic summation of power series

Summary. We give an asymptotic expansion in powers of of the remainder , when the sequence has a similar expansion. Contrary to previous results, explicit formulas for the computation of the coefficients are presented. In the case of numerical series (), rigorous error estimates for the asymptotic approximations are also provided. We apply our results to the evaluation of , which generalizes various summation problems appeared in the recent literature on convergence acceleration of numerical and power series. Received April 22, 1997