We define united K-theory for real C*-algebras, generalizing Bousfield's topological united K-theory. United K-theory incorporates three functors -real K-theory, complex K-theory, and self-conjugate K-theory -and the natural transformations among them. The advantage of united K-theory over ordinary K-theory lies in its homological algebraic properties, which allow us to construct a Künneth-type, non-splitting, short exact sequence whose middle term is the united K-theory of the tensor product of two real C*-algebras A and B which holds as long as the complexification of A is in the bootstrap category N . Since united K-theory contains ordinary K-theory, our sequence provides a way to compute the K-theory of the tensor product of two real C*-algebras.As an application, we compute the united K-theory of the tensor product of two real Cuntz algebras. Unlike in the complex case, it turns out that the isomorphism class of the tensor product O R k+1 ⊗ O R l+1 is not determined solely by the greatest common divisor of k and l. Hence, we have examples of non-isomorphic, simple, purely infinite, real C*-algebras whose complexifications are isomorphic.

We define united KK-theory for real C*-algebras A and B such that A is separable and B is σ-unital,. United KK-theory contains real, complex, and self-conjugate KK-theory; but unlike unaugmented real KK-theory, it admits a universal coefficient theorem. For all separable A and B in which the complexification of A is in the bootstrap category, KK CRT (A, B) can be written as the middle term of a short exact sequence whose outer terms involve the united K-theory of A and B. As a corollary, we prove that united K-theory classifies KKequivalence for real C*-algebras whose complexification is in the bootstrap category.

We prove that the united K-theory functor is a surjective functor from the category of real simple separable purely infinite C * -algebras to the category of countable acyclic CRT-modules. As a consequence, we show that every complex Kirchberg algebra satisfying the universal coefficient theorem is the complexification of a real C * -algebra.

Laser-induced breakdown spectroscopy (LIBS) was carried out on twenty-three low to high alloy steel samples to quantify their concentrations of chromium, nickel, and manganese. LIBS spectral data were correlated to known concentrations of the samples and three calibration methods were compared. A standard LIBS calibration technique using peak area integration normalized by an internal standard was compared to peak area integration normalized by total light and the multivariate statistical technique of partial least squares. For the partial least squares analysis, the PLS-1 algorithm was used, where a predictive model is generated for each element separately. Partial least squares regression coefficients show that the algorithm correctly identifies the atomic emission peaks of interest for each of the elements. Predictive capabilities of each calibration approach were quantified by calculating the standard and relative errors of prediction. The performance of partial least squares is on par with using iron as an internal standard but has the key advantage that it can be applied to samples where the concentrations of all elements are unknown.

We classify real Kirchberg algebras using united Ktheory. Precisely, let A and B be real simple separable nuclear purely infinite C*-algebras that satisfy the universal coefficient theorem such that A C and B C are also simple. In the stable case, A and B are isomorphic if and only if K CRT (A) ∼ = K CRT (B). In the unital case, A and B are isomorphic if and only ifWe also prove that the complexification of such a real C*-algebra is purely infinite, resolving a question left open from [43]. Thus the real C*-algebras classified here are exactly those real C*-algebras whose complexification falls under the classification result of Kirchberg [26] and Phillips [35]. As an application, we find all real forms of the complex Cuntz algebras O n for 2 ≤ n ≤ ∞.