Semi-classical spectral estimates for Schr\"odinger operators at a critical level. Case of a degenerate maximum of the potential

We study the semi-classical trace formula at a critical energy level for a Schr\"odinger operator on $\mathbb{R}^{n}$. We assume here that the potential has a totally degenerate critical point associated to a local maximum. The main result, which establishes the contribution of the associated equilibrium in the trace formula, is valid for all time in a compact subset of $\mathbb{R}$ and includes the singularity in $t=0$. For these new contributions the asymptotic expansion involves the logarithm of the parameter $h$. Depending on an explicit arithmetic condition on the dimension and the order of the critical point, this logarithmic contribution can appear in the leading term.Comment: 27 pages, perhaps to be revise

Contributions of non-extremum critical points to the semi-classical trace formula

We study the semi-classical trace formula at a critical energy level for a $h$-pseudo-differential operator on $\mathbb{R}^{n}$ whose principal symbol has a totally degenerate critical point for that energy. We compute the contribution to the trace formula of isolated non-extremum critical points under a condition of "real principal type". The new contribution to the trace formula is valid for all time in a compact subset of $\mathbb{R}$ but the result is modest since we have restrictions on the dimension.Comment: 24 page

A semi-classical trace formula at a non-degenerate critical level

We study the semi-classical trace formula at a critical energy level for a $h$-pseudo-differential operator whose principal symbol has a unique non-degenerate critical point for that energy. This leads to the study of Hamiltonian systems near equilibrium and near the non-zero periods of the linearized flow. The contributions of these periods to the trace formula are expressed in terms of degenerate oscillatory integrals. The new results obtained are formulated in terms of the geometry of the energy surface and the classical dynamics on this surface.Comment: Repost of a paper published in 2004. 35 page

Spectral fluctuations of Schr\"odinger operators generated by critical points of the potential

Starting from the spectrum of Schr\"odinger operators on $\mathbb{R}^n$, we propose a method to detect critical points of the potential. We argue semi-classically on the basis of a mathematically rigorous version of Gutzwiller's trace formula which expresses spectral statistics in term of classical orbits. A critical point of the potential with zero momentum is an equilibrium of the flow and generates certain singularities in the spectrum. Via sharp spectral estimates, this fluctuation indicates the presence of a critical point and allows to reconstruct partially the local shape of the potential. Some generalizations of this approach are also proposed.\medskip keywords : Semi-classical analysis; Schr\"odinger operators; Equilibriums in classical mechanics.Comment: 18 pages, Final versio

Depression is associated with some patient-perceived cosmetic changes, but not with radiotherapy-induced late toxicity, in long-term breast cancer survivors.: Depression-associated factors in long-term breast cancer survivors

International audienceOBJECTIVE: Although depression is prevalent in long-term breast cancer survivors (LTBCS; ≥5 years since diagnosis), it is underdiagnosed and undertreated. A better understanding of factors associated with depression could improve depression screening, treatment, and prevention in this population. Our study aimed to assess the link between patient and doctor ratings of breast cosmetic outcomes, late radiotherapy toxicity, and depression in LTBCS. METHODS: In all, 214 patients recruited from the ARCOSEIN study were assessed for late radiotherapy toxicity (by using the LENT-SOMA scale) and patient and doctor ratings of breast cosmetic outcomes (mean = 6.7 years since the end of treatment). We reassessed 120 of these patients for depression (HAD) during a second wave of long-term assessment (mean = 8.1 years since the end of treatment). We used univariate analyses and polytomous logistic regression analyses to predict the HAD depression, which was defined as follows: normal, 0-7 points; and significant depression, ≥8 points (8-10 points, possible depression; ≥11 points, probable depression). RESULTS: The mean HAD depression score was 4.5 ± 3.6. 19. 2% of our population had significant depression, 6.7% with probable depression, and 12.5% with possible depression. Significant depression was not associated with late radiotherapy toxicity or initial cancer-related variables. Patients with probable depression reported worse cosmetic outcomes than nondepressed patients in terms of perceived breast largeness (p = 0.04), breast deformation (p = 0.02), and changes in skin pigmentation (p = 0.03). CONCLUSIONS: In LTBCS, depression seems to be more strongly associated with changes in some patients' perceived breast cosmetic outcome than late treatment toxicity or initial cancer-related variables. Copyright © 2012 John Wiley & Sons, Ltd

Mobbing y satisfacción laboral en el personal de una institución militar del Callao, 2022

El presente estudio tuvo la finalidad de establecer la relación entre mobbing y satisfacción laboral en personal de una institución militar del Callao, 2022. El diseño empleado fue correlacional. Se utilizaron como instrumentos la Escala de Mobbing y el Cuestionario de SL-ARG. El muestro es no probabilístico contó con 342 sujetos, de ambos sexos, de edades entre 20 y 65 años. Respecto a los resultados, se encontró una relación estadísticamente significativa entre las variables, con un efecto pequeño (r=-.480; p<.001, r2=.230). Los trabajadores reportaron una mayor frecuencia en el nivel bajo de mobbing (88.3%) y una regular satisfacción laboral (39.8%). No se observaron diferencias significativas respecto al mobbing según el sexo; así mismo, las mujeres reportaron una mayor satisfacción laboral que los varones, como en las áreas de relaciones humanas, supervisión, comunicación y puesto de trabajo. Se concluye que ante mayor mobbing el trabajador percibe una menor satisfacción de su ambiente de trabajo

Structure génétique du cheptel bovin sédentaire du Nord de la Côte d'Ivoire. Perspectives d'avenir en fonction de la diffusion croissante du sang zébu

A l'origine, les savanes du Nord de la Côte-d'Ivoire, largement infestées de glossines et de tiques, étaient essentiellement peuplées de taurins trypanotolérants (Baoulé ou N'Dama suivant les régions considérées). Depuis la sécheresse qui a frappé les régions sahéliennes voisines, des troupeaux de zébus Peul se sont installés dans ces savanes, accélérant un processus de métissage déjà favorisé par les éleveurs-agriculteurs à la recherche d'animaux plus lourds et plus développés tant pour répondre aux besoins de la culture attelée qu'en viande de boucherie. Les auteurs étudient le devenir du patrimoine génétique des races taurines locales au cas où la diffusion du sang zébu continuerait au rythme actuel, ainsi que l'avenir d'un cheptel alors de moins en moins adapté à une sévère pathologie dominée par diverses hématozooses, les trypanosomoses plus particulièrement. Ils discutent des divers aspects de ce problème pour lequel ils proposent les solutions suivantes: promotion des races taurines locales, contrôle de métissage zébu, protection des aires d'élevage où les races N'Dama et Baoulé existent encore à l'état pur. Les solutions, qui tiennent compte des situations locales existantes, sont de nature à réserver l'avenir de l'élevage dans ces régions et à maintenir puis amplifier les courants d'exportation de ces taurin