A second order minimality condition for the Mumford-Shah functional

A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\Gamma)$, $\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.Comment: 30 page

Improved Understanding of Atomic Ordering in Y4SixAl2- xO9- xNxMaterials Using a Combined Solid-State NMR and Computational Approach

Ceramics based around silicon aluminum oxynitrides are of both fundamental structural chemistry and technological interest. Certain oxynitride crystal structures allow very significant compositional variation through extensive Si/N exchange for Al/O, which implies a degree of atomic ordering. In this study, solid-state 29Si MAS NMR and variable field 1D and 2D 27Al MAS NMR measurements are combined with density functional theory calculations of both the structural and NMR interaction parameters for various points across the Y4Si2O7N2-Y4Al2O9 compositional range. This series provides numerous possibilities for significant variation of atomic ordering in the local ditetrahedral (Si,Al)2O7-xNx units. The two slightly structurally inequivalent aluminum sites in Y4Al2O9 are unambiguously assigned to the observed resonances. Computational findings on Y4Si2O7N2 demonstrate that the single observed 29Si NMR resonance covers a range of local inequivalent silicon environments. For the first time, the MAS NMR and neutron diffraction data from the Y4SiAlO8N structure have been directly reconciled, thus establishing aspects of atomic order and disorder that characterize this system. This comparison suggests that, although the diffraction data indicates long-range structural order supporting a highly crystalline character, the short-range information afforded by the solid-state NMR measurements indicates significant atomic disorder throughout the (Si,Al)2O7-xNx units

The resultant on compact Riemann surfaces

We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential theory and give explicit formulas for the algebraic dependence between two meromorphic functions on a compact Riemann surface. As a particular application, the exponential transform of a quadrature domain in the complex plane is expressed in terms of the resultant of two meromorphic functions on the Schottky double of the domain.Comment: 44 page

Critical properties of 1-D spin 1/2 antiferromagnetic Heisenberg model

We discuss numerical results for the 1-D spin 1/2 antiferromagnetic Heisenberg model with next-to-nearest neighbour coupling and in the presence of an uniform magnetic field. The model develops zero frequency excitations at field dependent soft mode momenta. We compute critical quantities from finite size dependence of static structure factors.Comment: talk given by H. Kr{\"o}ger at Heraeus Seminar Theory of Spin Lattices and Lattice Gauge Models, Bad Honnef (1996), 20 pages, LaTeX + 18 figures, P

Understanding preventive behaviors among mid-Western African-American men: a pilot qualitative study of prostate screening

http://dx.doi.org/10.1016/j.jomh.2011.03.00

Probing exotic phenomena at the interface of nuclear and particle physics with the electric dipole moments of diamagnetic atoms: A unique window to hadronic and semi-leptonic CP violation

The current status of electric dipole moments of diamagnetic atoms which involves the synergy between atomic experiments and three different theoretical areas -- particle, nuclear and atomic is reviewed. Various models of particle physics that predict CP violation, which is necessary for the existence of such electric dipole moments, are presented. These include the standard model of particle physics and various extensions of it. Effective hadron level combined charge conjugation (C) and parity (P) symmetry violating interactions are derived taking into consideration different ways in which a nucleon interacts with other nucleons as well as with electrons. Nuclear structure calculations of the CP-odd nuclear Schiff moment are discussed using the shell model and other theoretical approaches. Results of the calculations of atomic electric dipole moments due to the interaction of the nuclear Schiff moment with the electrons and the P and time-reversal (T) symmetry violating tensor-pseudotensor electron-nucleus are elucidated using different relativistic many-body theories. The principles of the measurement of the electric dipole moments of diamagnetic atoms are outlined. Upper limits for the nuclear Schiff moment and tensor-pseudotensor coupling constant are obtained combining the results of atomic experiments and relativistic many-body theories. The coefficients for the different sources of CP violation have been estimated at the elementary particle level for all the diamagnetic atoms of current experimental interest and their implications for physics beyond the standard model is discussed. Possible improvements of the current results of the measurements as well as quantum chromodynamics, nuclear and atomic calculations are suggested.Comment: 46 pages, 19 tables and 16 figures. A review article accepted for EPJ

Sexuality, disability, and reproductive issues through the lifespan

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45558/1/11195_2005_Article_BF01102578.pd