in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...

Large deviation principles are established for the Fleming-Viot processes with neutral mutation and selection, and the corresponding equilibrium measures as the sampling rate goes to 0. All results are rst proved for the nite allele model, and then generalized, through the projective limit technique, to the innnite allele model. Explicit expressions are obtained for the rate functions.

New fixed point results are presented for weakly inward Kakutani condensing maps defined on a Fréchet space E. The proofs rely on the notion of an essential map and viewing E as the projective limit of a sequence of Banach spaces.

New fixed point results are presented for admissible pairs and maps (admissible in the sense of Górniewicz) defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree theory, and on viewing E as the projective limit of a sequence of Banach spaces.

We consider deviations from limit shape induced by uniformly distributed partitions (and strict partitions) of an integer n on the associated Young diagrams. We prove a full large deviation principle, of speed p n. The proof, based on projective limits, uses the representation of the uniform measure on partitions by means of suitably conditioned independent variables.

The paper continues the author’s work in measure and integration, which is an attempt at unified systematization. It establishes projective limit theorems of the Prokhorov and Kolmogorov types in terms of inner premeasures. Then it specializes to obtain the (one-dimensional) Wiener measure on the space of real-valued functions on the positive halfline as a probability measure defined on an imme...

In this paper, we study K3 double structures on minimal rational surfaces [Formula: see text]. The results show there are infinitely many non-split abstract text] parametrized by text], countably of which projective. For exists a unique structure is non-projective (see [J.-M. Drézet, Primitive multiple schemes, preprint (2020), arXiv:2004.04921, to appear in Eur. J. Math.]). We that all project...