Analyticity and uniform stability in the inverse spectral problem for Dirac operators

We prove that the inverse spectral mapping reconstructing the square integrable potentials on [0,1] of Dirac operators in the AKNS form from their spectral data (two spectra or one spectrum and the corresponding norming constants) is analytic and uniformly stable in a certain sense.Comment: 19 page

Boundary relations and generalized resolvents of symmetric operators

The Kre\u{\i}n-Naimark formula provides a parametrization of all selfadjoint exit space extensions of a, not necessarily densely defined, symmetric operator, in terms of maximal dissipative (in \dC_+) holomorphic linear relations on the parameter space (the so-called Nevanlinna families). The new notion of a boundary relation makes it possible to interpret these parameter families as Weyl families of boundary relations and to establish a simple coupling method to construct the generalized resolvents from the given parameter family. The general version of the coupling method is introduced and the role of boundary relations and their Weyl families for the Kre\u{\i}n-Naimark formula is investigated and explained.Comment: 47 page

Inverse spectral problems for Dirac operators with summable matrix-valued potentials

We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in[1,\infty)$. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest a method for reconstructing the potential from the corresponding spectral data.Comment: 32 page

Integrated Microfluidic Platform for Oral Diagnostics

While many point-of-care (POC) diagnostic methods have been developed for blood-borne analytes, development of saliva-based POC diagnostics is in its infancy. We have developed a portable microfluidic device for detection of potential biomarkers of periodontal disease in saliva. The device performs rapid microfluidic chip-based immunoassays (<3–10 min) with low sample volume requirements (10 ΜL) and appreciable sensitivity (nM–pM). Our microfluidic method facilitates hands-free saliva analysis by integrating sample pretreatment (filtering, enrichment, mixing) with electrophoretic immunoassays to quickly measure analyte concentrations in minimally pretreated saliva samples. The microfluidic chip has been integrated with miniaturized electronics, optical elements, such as diode lasers, fluid-handling components, and data acquisition software to develop a portable, self-contained device. The device and methods are being tested by detecting potential biomarkers in saliva samples from patients diagnosed with periodontal disease. Our microchip-based analysis can readily be extended to detection of biomarkers of other diseases, both oral and systemic, in saliva and other oral fluids.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73594/1/annals.1384.004.pd

Space-Time Diffusion of Ground and Its Fractal Nature

We present evidences of the diffusive motion of the ground and tunnels and show that if systematic movements are excluded then the remaining uncorrelated component of the motion obeys a characteristic fractal law with the displacement variance dY^2 scaling with time- and spatial intervals T and L as dY^2 \propto T^(Alpha)L^(Gamma) with both exponents close to 1. We briefly describe experimental methods of the mesa- and microscopic ground motion detection used in the measurements at the physics research facilities sensitive to the motion, particularly, large high energy elementary particle accelerators. A simple mathematical model of the fractal motion demonstrating the observed scaling law is also presented and discussed.Comment: 83 pages, 46 fig

Jets Produced in π^-, π^+, and Proton Interactions at 200 GeV on Hydrogen and Aluminum Targets

This paper presents results from an experiment on the production of jets (groups of particles) with high p_⊥ produced in 200-GeV/c interactions. Results are presented on the comparison of jet cross sections on aluminum and hydrogen targets. The jet fragmentation distributions are also examined. Both the cross section and the jet structure are found to depend strongly on the beam and target types

Measurement of Forward Jets Produced in High-Transverse-Momentum Hadron-Proton Collisions

A measurement of charged-particle production is reported for the forward region in events triggered by high-transverse-momentum (p⊥) jets and single particles. The momentum distributions of forward-going particles are observed to scale in a simple p⊥-dependent longitudinal variable. Forward-going (beam) jets are observed to be tilted away from the original direction by an amount which agrees with muon-pair data when interpreted in a parton (quantum-chromodynamics) model

Observation of the Production of Jets of Particles at High Transverse Momentum and Comparison with Inclusive Single-Particle Reactions

Data are presented on production by 200-GeV/c hadrons incident on beryllium of both single particles and jets (groups of particles) with high p_T (transverse momentum). The experiment was performed in a wide-aperture multiparticle spectrometer at Fermilab. The jet and single-particle cross sections have a similar shape from p_T=3 to 5 GeV/c but the jet cross section is over two orders of magnitude larger. The distributions of charged-particle momenta show striking similarities to those observed in lepton-induced processes

Experimental Tests of Quantum Chromodynamics in High-p_⊥ Jet Production in 200-GeV/c Hadron-Proton Collisions

Data on inclusive jet production in the transverse-momentum (p_⊥) range 0-8 GeV/c for 200-GeV/c p, π^-, π^+, K^-, K^+, and p incident on a hydrogen target are presented. The jet cross section is fully corrected for losses and biases, and compared with the predictions of a model based on quantum chromodynamics. Both the absolute cross section and the inclusive charged-particle distributions inside and outside the jet are in qualitative agreement with the model