Search results for "Geometry"

Bifurcations of Links of Periodic Orbits in Non-Singular Systems with Two Rotational Symmetries on S3

1997

A topological characterization of all possible links composed of the periodic orbits of a Non Singular Morse-Smale flow on S3 has been made by M. Wada. The presence of symmetry forces the appearance of given types of links. In this paper we introduce a geometrical tool to represent these type of links when a symmetry around two axes is considered on NMS systems: mosaics. On the other hand, we use mosaics to study what kind of bifurcation can occur in this type of system maintaining the symmetry.

Rank two aCM bundles on the del Pezzo fourfold of degree 6 and its general hyperplane section

2018

International audience; In the present paper we completely classify locally free sheaves of rank 2 with vanishing intermediate cohomology modules on the image of the Segre embedding $\mathbb{P}^2$ x $\mathbb{P}^2 \subseteq \mathbb{P}^8$ and its general hyperplane sections.Such a classification extends similar already known results regarding del Pezzo varieties with Picard numbers 1 and 3 and dimension at least 3.

Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces

2003

Let M(d,n) be the moduli stack of hypersurfaces of degree d > n in the complex projective n-space, and let M(d,n;1) be the sub-stack, parameterizing hypersurfaces obtained as a d fold cyclic covering of the projective n-1 space, ramified over a hypersurface of degree d. Iterating this construction, one obtains M(d,n;r). We show that M(d,n;1) is rigid in M(d,n), although the Griffiths-Yukawa coupling degenerates for d<2n. On the other hand, for all d>n the sub-stack M(d,n;2) deforms. We calculate the exact length of the Griffiths-Yukawa coupling over M(d,n;r), and we construct a 4-dimensional family of quintic hypersurfaces, and a dense set of points in the base, where the fibres ha…

Specialization of cycles and the K-theory elevator

2017

A general specialization map is constructed for higher Chow groups and used to prove a "going-up" theorem for algebraic cycles and their regulators. The results are applied to study the degeneration of the modified diagonal cycle of Gross and Schoen, and of the coordinate symbol on a genus-2 curve.

Forcing for First-Order Languages from the Perspective of Rasiowa–Sikorski Lemma

2017

The paper is concerned with the problem of building models for first-order languages from the perspective of the classic paper of Rasiowa and Sikorski [9]. The central idea, developed in this paper, consists in constructing first-order models from individual variables. The key notion of a Rasiowa–Sikorski set of formulas for an arbitrary countable language L is examined. Each Rasiowa–Sikorski set defines a countable model for L . Conversely, every countable model for L is determined by a Rasiowa–Sikorski set. The focus is on constructing Rasiowa–Sikorski sets by applying forcing techniques restricted to Boolean algebras arising from the subsets of the set of atomic formulas of L .

On saturated formations of finite groups with a restricted cover and avoidance property

1994

A rigidity theorem for Lagrangian deformations

2005

We consider deformations of singular Lagrangian varieties in symplectic manifolds. We prove that a Lagrangian deformation of a Lagrangian complete intersection is analytically rigid provided that this is the case infinitesimally. This result is given as a consequence of the coherence of the direct image sheaves of relative infinitesimal Lagrangian deformations.

Rejoinder on: Natural Induction: An Objective Bayesian Approach

2009

Giron and Moreno. We certainly agree with Professors Giron and Moreno on the interest in sensitivity of any Bayesian result to changes in the prior. That said, we also consider of considerable pragmatic importance to be able to single out a unique, particular prior which may reasonably be proposed as the reference prior for the problem under study, in the sense that the corresponding posterior of the quantity of interest could be routinely used in practice when no useful prior information is available or acceptable. This is precisely what we have tried to do for the twin problems of the rule of succession and the law of natural induction. The discussants consider the limiting binomial versi…

Complex powers of elliptic pseudodifferential operators

1986

The aim of this paper is the construction of complex powers of elliptic pseudodifferential operators and the study of the analytic properties of the corresponding kernels kS (x,y). For x=y, the case of principal interest, the domain of holomorphy and the singularities of kS (x,x) are shown to depend on the asymptotic expansion of the symbol. For classical symbols, kS (x,x) is known to be meromorphic on ℂ with simple poles in a set of equidistant points on the real axis. In the more general cases considered here, the singularities may be distributed over a half plane and kS (x,x) can not always be extended to337-2. An example is given where kS (x,x) has a vertical line as natural boundary.

Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences

2022

With more than 50 years of literature, fuzzy logic has gradually progressed from an emerging field to a developed research domain, incorporating the sub-domain of mathematical fuzzy logic (MFL) [...]