Abstract Let $f: X \to B$ be a relatively minimal fibration of maximal Albanese dimension from variety $n \ge 2$ to curve B defined over an algebraically closed field characteristic zero. We prove that $K_{X/B}^n 2n! \chi _f$ . It verifies conjectural formulation Barja in [2]. Via the strategy outlined [4], it also leads new proof Severi inequality for varieties dimension. Moreover, when equali...

In this paper, we determine the $L^p(\mathbb{R})\times L^q(\mathbb{R})\rightarrow L^r(\mathbb{R})$ boundedness of bilinear Hilbert transform $H_{\gamma}(f,g)$ along a convex curve $\gamma$ $$H_{\gamma}(f,g)(x):=\mathrm{p.\,v.}\int_{-\infty}^{\infty}f(x-t)g(x-\gamma(t)) \,\frac{\textrm{d}t}{t},$$ where $p$, $q$, and $r$ satisfy $\frac{1}{p}+\frac{1}{q}=\frac{1}{r}$, $r>\frac{1}{2}$, $p>1$, $q>1$...

1. Motivation. Let J0(N) denote the Jacobian of the modular curve X0(N) parametrizing pairs of N -isogenous elliptic curves. The simple factors of J0(N) have real multiplication, that is to say that the endomorphism ring of a simple factor A contains an order in a totally real number field of degree dimA. We shall sometimes abbreviate “real multiplication” to “RM” and say that A has maximal RM ...

the paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. attention goes to the number of limit cycles produced by the period annulus under perturbations. by using the appropriate p...

Relatively extremal knots are the relative minima of the ropelength functional in the C1 topology. They are the relative maxima of the thickness (normal injectivity radius) functional on the set of curves of …xed length, and they include the ideal knots. We prove that a C1;1 relatively extremal knot in Rn either has constant maximal (generalized) curvature, or its thickness is equal to half of ...

In this survey, we review the historical development for Carleson problem about a.e. pointwise convergence in five aspects: generalized Schrödinger operators along vertical lines; arbitrary single curves; a family of restricted upper bounds p Lp-Schrödinger maximal estimates; and rate curves. Finally, list some open problems which need to be addressed.

We show that the fundamental group of the complement of any irreducible tame torus sextics in P is isomorphic to Z2 ∗ Z3 except one class. The exceptional class has the configuration of the singularities {C3,9, 3A2} and the fundamental group is bigger than Z2 ∗ Z3. In fact, the Alexander polynomial is given by (t 2 − t + 1). For the proof, we first reduce the assertion to maximal curves and the...

Cumulative dose-response curves to carbachol given by aerosol were established using plethysmographic measurements of specific airways resistance (SRaw) in 10 patients with asthma and five healthy subjects. Two experiments were performed--a control test and one in which maximal respiratory manoeuvres (MRM) (two maximal inspirations and two maximal expirations) were made before each carbachol in...