Weighted estimates for solutions of the ∂\partial -equation for lineally convex domains of finite type and applications to weighted bergman projections

In this paper we obtain sharp weighted estimates for solutions of the $\partial$-equation in a lineally convex domains of finite type. Precisely we obtain estimates in spaces of the form L p ({\Omega},$\delta$ $\gamma$), $\delta$ being the distance to the boundary, with gain on the index p and the exponent $\gamma$. These estimates allow us to extend the L p ({\Omega},$\delta$ $\gamma$) and lipschitz regularity results for weighted Bergman projection obtained in [CDM14b] for convex domains to more general weights

Estimates for some Weighted Bergman Projections

In this paper we investigate the regularity properties of weighted Bergman projections for smoothly bounded pseudo-convex domains of finite type in $\mathbb{C}^{n}$. The main result is obtained for weights equal to a non negative rational power of the absolute value of a special defining function $\rho$ of the domain: we prove (weighted) Sobolev-$L^{p}$ and Lipchitz estimates for domains in $\mathbb{C}^{2}$ (or, more generally, for domains having a Levi form of rank $\geq n-2$ and for "decoupled" domains) and for convex domains. In particular, for these defining functions, we generalize results obtained by A. Bonami & S. Grellier and D. C. Chang & B. Q. Li. We also obtain a general (weighted) Sobolev-$L^{2}$ estimate.Comment: Final version. To appear in Complex Variables and Elliptic Equation

Estimates for the Bergman and Szegö projections for pseudoconvex domains of finite type with locally diagonalizable Levi form

In this paper, we give precise isotropic and non-isotropic estimates for the Bergman and Szegö projections of a bounded pseudoconvex domain whose boundary points are all of finite type and with locally diagonalizable Levi form. Additional local results on estimates of invariant metrics are also given

Approximation par des fonctions holomorphes a croissance controleé

Let $\Omega$ be a bounded pseuco-convex domain in $\Bbb C^n$ with a \Cal C^{\infty} boundary, and let $S$ be the set of strictly pseudo-convex points of $\partial\Omega$. In this paper, we study the asymptotic behaviour of holomorphic functions along normals arising from points of $S$. We extend results obtained by M. Ortel and W. Schneider in the unit disc and those of A. Iordan and Y. Dupain in the unit ball of $\Bbb C^n$. We establish the existence of holomorphic functions of given growth having a "prescribed behaviour" on almost all normals arising from points of $S$

The Science of Running

Running is the most primitive of all types of muscular activity. It is man's oldest racial movement. The effects of running are physiologically more far-reaching than any other form of physical activity. Running does not overdevelop or hyper-trophy any muscular groups. It normally develops in the safest way the very dynamos of life, the heart, lungs and vascular system. Running awakens the most primitive urges and joys of life, because there still exist in the neurones of man the remnants of his ancestral flights in chasing, hunting and catching. When youth and man run they wildly and joyously recapitulate the story of their long distant past. The recorded history of the art shows Pheidippides, the greatest runner of all time, performing a deed unbeatable up to modern times. Two great athletic deeds he is honoured with. Not only did he run from Athens to Sparta in two days, a distance of 152 miles, but he bore the message of the Greeks' victory over the Persians from the battlefield of Marathon to the City of Athens. It is not recorded in what time he did this 26 miles, but the distance was run so swiftly that it was the cause of his death, for he only had time to utter the words " Rejoice, we conquer " and he collapsed

Newly identified LMO3-BORCS5 fusion oncogene in Ewing sarcoma at relapse is a driver of tumor progression

International audienceRecently, we detected a new fusion transcript LMO3-BORCS5 in a patient with Ewing sarcoma within a cohort of relapsed pediatric cancers. LMO3-BORCS5 was as highly expressed as the characteristic fusion oncogene EWS/FLI1. However, the expression level of LMO3-BORCS5 at diagnosis was very low. Sanger sequencing depicted two LMO3-BORCS5 variants leading to loss of the functional domain LIM2 in LMO3 gene, and disruption of BORCS5. In vitro studies showed that LMO3-BORCS5 (i) increases proliferation, (ii) decreases expression of apoptosis-related genes and treatment sensitivity, and (iii) downregulates genes involved in differentiation and upregulates proliferative and extracellular matrix-related pathways. Remarkably, in vivo LMO3-BORCS5 demonstrated its high oncogenic potential by inducing tumors in mouse fibroblastic NIH-3T3 cell line. Moreover, BORCS5 probably acts, in vivo, as a tumor-suppressor gene. In conclusion, functional studies of fusion oncogenes at relapse are of great importance to define mechanisms involved in tumor progression and resistance to conventional treatments

Many Faces of Entropy or Bayesian Statistical Mechanics

Some 80-90 years ago, George A. Linhart, unlike A. Einstein, P. Debye, M. Planck and W. Nernst, has managed to derive a very simple, but ultimately general mathematical formula for heat capacity vs. temperature from the fundamental thermodynamical principles, using what we would nowadays dub a "Bayesian approach to probability". Moreover, he has successfully applied his result to fit the experimental data for diverse substances in their solid state in a rather broad temperature range. Nevertheless, Linhart's work was undeservedly forgotten, although it does represent a valid and fresh standpoint on thermodynamics and statistical physics, which may have a significant implication for academic and applied science.Comment: submitte