Triviality—Quantum Decoherence of Fermionic Quantum Chromodynamics SU(Nc) in?the?Presence of?an?External Strong U(∞) Flavored Constant Noise Field

We consider the problem of infrared divergencies in String theory in Embeddings Manifolds by means of the Nash Theorem of Riemann metrics parametrized by immersions.     

Characterisation of free and glycosidically bound odourant compounds of Aragonez clonal musts by GC-O

To evaluate the potential aroma of Aragonez clonal red musts, several free and glycosidically bound odourant compounds were extracted. Then, the gas chromatography-olfactometry (GC-O) posterior intensity method was used to evaluate their odour intensity and the compounds were identified by gas chromatography-mass spectrometry (GC-MS). A group of eight sniffers evaluated free and bound fractions of Aragonez musts and perceived forty-three and twenty-two odourant peaks respectively. Furaneol (burnt sugar, candy-cotton) and vanillin (vanilla, sweet) were identified in both free and bound fractions of Aragonez musts, indicating their grape-derived origin. Principal component analysis (PCA) was applied to the posterior intensity method data and a relationship between the different odourant compound variables and the free fractions was established. Two principal components (PCs) were found which together explained 100% of the total variance. A large number of potentially important but yet unknown odourants was detected by the GC-O analysis.     

Isometric properties of elementary operators

We consider the elementary operator L, acting on the Hilbert-Schmidt Class C₂(H), given by L(T)=ATB, with A and B bounded operators on H. We establish necessary and sufficient conditions on A and B for L to be a 2-isometry or a 3-isometry. We derive sufficient conditions for L to be an n-isometry. We also give several illustrative examples involving the weighted shift operator on l₂ and the multiplication operator on the Dirichlet space.     

A Feynman Path Integral Representation for?Elastic?Wave?Scattering by?Anisotropic Weakly?Perturbations

We write a space-time Feynman Path Integral representation for scattered elastic wave fields from a weakly anisotropic non-homogeneity.     

Projections and averages of isometries on Lipschitz spaces

We characterize projections on spaces of Lipschitz functions expressed as the average of two and three linear surjective isometries. Generalized bi-circular projections are the only projections on these spaces given as the convex combination of two surjective isometries.     

Absolutely summing polynomials on Banach spaces with unconditional basis

If X is a Banach space with a normalized unconditional Schauder basis (xn), we define whenever and obtain estimates for μX,(xn) when every continuous m-homogeneous polynomial from X into Y is absolutely (q,1) summing. Our results provide new information on coincidence situations between the space of absolutely summing m-homogeneous polynomials and the whole space of continuous m-homogeneous polynomials. In particular, when m=1, we obtain new contributions to the linear theory of absolutely summing operators.     

Qualitative Behavior of Differential Equations Associated with Artificial Neural Networks

We establish conditions under which Oja–Adams' learning models are gradient, semi-gradient, or gradient-like systems. We consider both single and multi-output models. The multi-output learning models are represented by matrix differential equations whose analysis require techniques from matrix calculus. We also derive the stability behavior of these systems while restricted to naturally defined invariant sets.