Search results for "Pure Mathematics"

ACL homeomorphisms and linear dilatation

2001

We establish an integrability condition on the linear dilatation to guarantee ACL.

Permutation invariant functionals of Lévy processes

2017

Darboux integrable system with a triple point and pseudo-abelian integrals

2016

We study pseudo-abelian integrals associated with polynomial perturbations of Dar-boux integrable system with a triple point. Under some assumptions we prove the local boundedness of the number of their zeros. Assuming that this is the only non-genericity, we prove that the number of zeros of the corresponding pseudo-abelian integrals is bounded uniformly for nearby Darboux integrable foliations.

A singular elliptic equation and a related functional

2021

We study a class of Dirichlet boundary value problems whose prototype is [see formula in PDF] where 0 < p < 1 and f belongs to a suitable Lebesgue space. The main features of this problem are the presence of a singular term |u|p−2u and a datum f which possibly changes its sign. We introduce a notion of solution in this singular setting and we prove an existence result for such a solution. The motivation of our notion of solution to problem above is due to a minimization problem for a non–differentiable functional on [see formula in PDF] whose formal Euler–Lagrange equation is an equation of that type. For nonnegative solutions a uniqueness result is obtained.

Periodic Controls in Step 2 Strictly Convex Sub-Finsler Problems

2020

We consider control-linear left-invariant time-optimal problems on step 2 Carnot groups with a strictly convex set of control parameters (in particular, sub-Finsler problems). We describe all Casimirs linear in momenta on the dual of the Lie algebra. In the case of rank 3 Lie groups we describe the symplectic foliation on the dual of the Lie algebra. On this basis we show that extremal controls are either constant or periodic. Some related results for other Carnot groups are presented. peerReviewed

Meridianos distintos (Jīng Bié) y sistema linfático, comparación anatómica y funcional

2016

The analysis of possible meeting points between Chinese and Western medicine makes an addition to the gradual progress towards mutual understanding and synergy of both disciplines. The description of trajectories and functions of the Divergent Channels seems to suggest certain parallels regarding western anatomy and lymph system function. From the anatomical perspective, the trajectory of the JīngBie resembles the arrangement and energy flux direction to the lymph system. Besides, the position of the main JīngBie points, such as “Departure points” and “Window of Heaven points” tends to match regions with a high presence of lymph nodes. Also, the JīngBie functions resemble the physiology of …

On the minimal number of singular fibers with non-compact Jacobians for families of curves over P1

2016

Abstract Let f : X → P 1 be a non-isotrivial family of semi-stable curves of genus g ≥ 1 defined over an algebraically closed field k. Denote by s nc the number of the singular fibers whose Jacobians are non-compact. We prove that s nc ≥ 5 if k = C and g ≥ 5 ; we also prove that s nc ≥ 4 if char ( k ) > 0 and the relative Jacobian of f is non-smooth.

OPERADS AND JET MODULES

2005

Let $A$ be an algebra over an operad in a cocomplete closed symmetric monoidal category. We study the category of $A$-modules. We define certain symmetric product functors of such modules generalising the tensor product of modules over commutative algebras, which we use to define the notion of a jet module. This in turn generalises the notion of a jet module over a module over a classical commutative algebra. We are able to define Atiyah classes (i.e. obstructions to the existence of connections) in this generalised context. We use certain model structures on the category of $A$-modules to study the properties of these Atiyah classes. The purpose of the paper is not to present any really de…

Projective models of K3 surfaces with an even set

2006

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a carefull analysis of the divisors contained in the Picard lattice we study their projective models, giving necessary and sufficient conditions to have an even set. Moreover we investigate their relation with K3 surfaces with a Nikulin involution.

Varieties of algebras with pseudoinvolution and polynomial growth

2017

Let A be an associative algebra with pseudoinvolution (Formula presented.) over an algebraically closed field of characteristic zero and let (Formula presented.) be its sequence of (Formula presented.) -codimensions. We shall prove that such a sequence is polynomially bounded if and only if the variety generated by A does not contain five explicitly described algebras with pseudoinvolution. As a consequence, we shall classify the varieties of algebras with pseudoinvolution of almost polynomial growth, i.e. varieties of exponential growth such that any proper subvariety has polynomial growth and, along the way, we shall give also the classification of their subvarieties. Finally, we shall de…