Inverse spectral problem for singular AKNS operator on [0,1]

We consider an inverse spectral problem for a class of singular AKNS operators $H\_a, a\in\N$ with an explicit singularity. We construct for each $a\in\N$, a standard map $\lambda^a\times\kappa^a$ with spectral data $\lambda^a$ and some norming constant $\kappa^a$. For $a=0$, $\lambda^a\times\kappa^a$ was known to be a local coordinate system on \lr\times\lr. Using adapted transformation operators, we extend this result to any non-negative integer $a$, give a description of isospectral sets and we obtain a Borg-Levinson type theorem.Comment: 31 page

On the symplectic phase space of KdV

We prove that the Birkhoff map \Om for KdV constructed on H^{-1}_0(\T) can be interpolated between H^{-1}_0(\T) and L^2_0(\T). In particular, the symplectic phase space H^{1/2}_0(\T) can be described in terms of Birkhoff coordinates. As an application, we characterize the regularity of a potential q\in H^{-1}(\T) in terms of the decay of the gap lengths of the periodic spectrum of Hill's operator on the interval $[0,2]$

Cop Confidential: Police Supervision and Sub-Culture

Law enforcement first-line supervision is the key management element in the daily functioning of American police organizations. This qualitative study examines supervision from the viewpoint of the patrol sergeant supervisor. In this study, supervisors discussed their beliefs on the care of officers, organizational development, politics, community, administration, and their supervisor peer group. Using an inductive model of data collection, this thick-description ethnographic study exposed a Multiple Constituency Model consisting of people and interests requiring the time, favor, and expertise of the first-line supervisor. Supervisors discussed dilemmas of decision-making, police agency structure, leadership strategies, and peer supervisor and subordinate relationships. The relationships within the Multiple Constituency Model each required negotiations and resolutions with supervisors. Strain in some of the relationships is seen through sub-cultural issues in policing and through the idealized thoughts of supervisors. By understanding these dynamics, law enforcement administrators may be able work with supervisors for better organizational outcomes

Analysis of the adhesive damage for different shapes and types patch’s in Aircraft Structures corroded with an inclined crack

In this study, the finite element method is used to analyze the effect of corrosion and the behavior of inclined cracks of an aluminum plate Al 2024 -T3 under thermomechanical loading.  The effects of the inclination of the crack and the effect of temperature for and different types and shapes of adhesives are highlighted.  The results obtained show the increase of the crack inclination leads to a decrease of the damaged area and the damaged area ratio of the adhesive.  In addition, the ratio DR increases with increasing temperature variation ΔT.  The best performing patch shape that gave interesting results during this analysis is the circular and for type the Boron/epoxy is the best

Finite element analysis of the interface defect in ceramic-metal assemblies: Alumina-Silver

The realization of a connection between a ceramic and a metal is always accompanied by the creation of a multi-axial stress field. Different physical and mechanical origins explain the genesis of stresses at the bonding interface in the ceramic and metal at the bond formation of ceramic-metal. In this study, a finite element model is developed to analyze numerically the effect of the sites of alumina grains snatches on the distribution and stresses level of the interface with the silver. The analysis has been extended to the effect of alumina grains-alumina grains interaction, alumina grains size and form

Probabilistic Elastic-plastic Fracture Mechanics Analysis of Propagation of Cracks in Pipes under Internal Pressure

This study presents a three dimensional finite element method analysis of semi-elliptical surface cracks in pipes under internal pressure load. In the elastic–plastic case, estimates of the J-integral are presented for various ratios including crack depth to pipe thickness (a/t) and strain hardening index in the (R-O) Ramberg-Osgood (n).  Finally, failure probability is accessed by a statistical analysis for uncertainties in loads and material properties, and structural reliability and crack size. The Monte Carlo method is used to predict the distribution function of the mechanical response. According to the obtained results, we note that the stress variation and the crack size are important factors influencing on the distribution function of (J/Je)