[en] Central in the paper are two results on the existence of 'economical' embeddings in a Euclidean space. The first result (Corollary 1.4) states the existence of an embedding with image intersecting the large-dimensional planes in sets of 'controllable' dimension. The second result (Corollary 1.6) proves the existence of maps such that each small-dimensional plane contains 'controllably' many points of the image. Well known results of Noebeling-Pontryagin, Roberts, Hurewicz, Boltyanskii, and Goodsell can be obtained as consequences of these results. Their infinite-dimensional version concerning an embedding in a Hilbert space is also established (Theorem 1.8).

[en] Superluminal behavior has been extensively studied in recent years, especially with regard to the topic of superluminality in the propagation of a signal. Particular interest has been devoted to Bessel-X waves propagation, since some experimental results showed that these waves have both phase and group velocities greater that light velocity c. However, because of the lack of an exact definition of signal velocity, no definite answer about the signal propagation (or velocity of information) has been found. The present Letter is a short note that deals in a general way with this vexed question. By analyzing the field of existence of the Bessel X-pulse in pseudo-Euclidean spacetime, it is possible to give a general description of the propagation, and to overcome the specific question related to a definition of signal velocity

[en] Let Csup(n) be a complex euclidean space. A bounded open connected subset D of Csup(n) is called a bounded domain. Bounded homogeneous domains in Csup(n) are studied. Contents: bounded homogeneous domains; j-Lie algebras; Siegel domains; s-structure on a bounded domain. (author)

[en] The one dimensional, linear, half space, abstract transport equation with an accretive, invertible collision operator is shown to be uniquely solvable. An example from multigroup neutron transport is given

[en] The author studies completeness of the wave operators between pairs of spaces not using the subspace of absolute continuity. Rather he works with the orthogonal complement of the eigenvectors, a subspace which is more natural from the viewpoint of physics. Moreover, he also gives sufficient conditions that the singular continuous spectrum be absent. In this case the subspaces mentioned above coincide. (Auth.)

[en] A plausible explanation is given to the 'strange' result that the ground state stochastic process associated to a free scalar field via Nelson's stochastic quantization method coincides with the euclidean Markov field. It is also shown that a positive temperature extension consistent with this result and that of Davidson can be carried out. (author)

[en] A non-Hermitian momentum-space representation of functions of a manifold (curved space) isomorphic to Rⁿ is constructed out of pure plane waves. We prove the covariance of the coordinate- and momentum-space representations. We give the momentum-space representation of the trace of operators. In interacting field theory this representation enables us to calculate the part of the effective action that encodes local properties of a general curved space. Thus the trace anomaly and the beta function can be evaluated. An explicit calculation is displayed at one loop for a scalar field coupled to gravity. In flat space the formalism applies to Cartesian and curvilinear coordinates. Application to the study of the stability of the vacuum of a field theory in curved space is possible

[en] In the present paper, we prove that the family of exponentials associated to the eigenvalues of the perturbed operator T(ε) ≔ T₀ + εT₁ + ε²T₂ + … + ε^kT_k + … forms a Riesz basis in L²(0, T), T > 0, where ε∈C, T₀ is a closed densely defined linear operator on a separable Hilbert space H with domain D(T₀) having isolated eigenvalues with multiplicity one, while T₁, T₂, … are linear operators on H having the same domain D⊃D(T₀) and satisfying a specific growing inequality. After that, we generalize this result using a H-Lipschitz function. As application, we consider a non-selfadjoint problem deduced from a perturbation method for sound radiation

[en] We consider warped products of Riemannian manifolds and some special cases. We give a classification for a class of normally flat Ric-semiparallel submanifolds in Euclidean spaces

No abstract available