On the Decomposition of Clifford Algebras of Arbitrary Bilinear Form

Clifford algebras are naturally associated with quadratic forms. These algebras are Z_2-graded by construction. However, only a Z_n-gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V) \bigwedge V and an ordering, guarantees a multi-vector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomorphism theorem cannot be generalized to algebras if the Z_n-grading or other structures are added, e.g., a linear form. We work with pairs consisting of a Clifford algebra and a linear form or a Z_n-grading which we now call 'Clifford algebras of multi-vectors' or 'quantum Clifford algebras'. It turns out, that in this sense, all multi-vector Clifford algebras of the same quadratic but different bilinear forms are non-isomorphic. The usefulness of such algebras in quantum field theory and superconductivity was shown elsewhere. Allowing for arbitrary bilinear forms however spoils their diagonalizability which has a considerable effect on the tensor decomposition of the Clifford algebras governed by the periodicity theorems, including the Atiyah-Bott-Shapiro mod 8 periodicity. We consider real algebras Cl_{p,q} which can be decomposed in the symmetric case into a tensor product Cl_{p-1,q-1} \otimes Cl_{1,1}. The general case used in quantum field theory lacks this feature. Theories with non-symmetric bilinear forms are however needed in the analysis of multi-particle states in interacting theories. A connection to q-deformed structures through nontrivial vacuum states in quantum theories is outlined.Comment: 25 pages, 1 figure, LaTeX, {Paper presented at the 5th International Conference on Clifford Algebras and their Applications in Mathematical Physics, Ixtapa, Mexico, June 27 - July 4, 199

Stacking sequences for extensionally isotropic, fully isotropic and quasi-homogeneous orthotropic laminates

Stacking sequence listings are presented for fully uncoupled Extensionally Isotropic (EILs), Fully Isotropic (FILs) and Quasi-Homogeneous Orthotropic (QHOLs) angle-ply Laminates, with up to 21 plies. All are sub-sets of a definitive list of Fully Orthotropic Laminates (FOLs), containing generally non-symmetric stacking sequences that are characterized in terms of angle- and cross-ply sub-sequence symmetries. Dimensionless parameters are given for each stacking sequence, from which the ABD matrix is readily derived. Expressions relating these dimensionless parameters to the well-known lamination parameters are also given, together with graphical representations of the feasible domains for Pi/3 and Pi/4 EILs and angle-ply QHOLs containing two and three ply orientations. The feasible domain for Pi/3 FILs is represented graphically by a single point, whereas the domain for angle-ply QHOLs containing four ply orientations is represented by a single stacking sequence

Asia-Pacific Regional Integration Index: Construction, Interpretation, and Comparison

We develop an index to measure the degree of regional integration in Asia and the Pacific (48 economies in six subregions). The index comprises 26 indicators in six dimensions of regional integration, i.e., trade and investment, money and finance, regional value chains, infrastructure and connectivity, free movement of people, and institutional and social integration. We use principal component analysis to apportion a weight to each dimension and indicator to construct composite indexes. The resulting indexes help assess the state of regional integration on diverse socioeconomic dimensions, evaluate progress against goals, identify strengths and weaknesses, and track progress. Cross-country, cross-regional comparisons also allow policy makers to prioritize areas for further efforts

Double Counting Ambiguities in the Linear Sigma Model

We study the dynamical consequences imposed on effective chiral field theories such as the quark-level SU(2) linear $\sigma$ model (L$\sigma$M) due to the fundamental constraints of massless Goldstone pions, the normalization of the pion decay constant and form factor, and the pion charge radius. We discuss quark-level double counting L$\sigma$M ambiguities in the context of the Salam-Weinberg $Z = 0$ compositeness condition. Then SU(3) extensions to the kaon are briefly considered.Comment: 23 pages To be published in Journal of Physics

Does Income Inequality Lead to Terrorism? Evidence from the Post-9/11 Era

We study the influence of income inequality on terrorism. Using cross-national data for 79 countries for the 2002-2012 period, we show that endogeneity matters to the inequalityterrorism relationship, e.g., because of the distributional effects of terrorism. Once endogeneity is properly accounted for by means of an instrumental-variable approach, higher levels of income inequality result in more terrorist activity. This finding is robust to different definitions of the dependent variable, different estimation techniques and different instruments for income inequality. Our finding that inequality fuels terrorism is consistent with relative deprivation theory which argues that conflict results from frustration over the actual distribution of economic resources within a society