Mathematical properties of the vacuum polarization function

This paper is an investigation of certain mathematical properties of the vacuum polarization function (s). We show that (s) is a Herglotz function, has no complex zeroes, and belongs to the class of functions called typically real. In addition, we obtain upper bounds on the higher derivatives of (s), at s=0, given that we know the value of the first derivative at that point.Research supported in part by NASA Grant NSG-8035     

The validity of nonlinear geometric optics for weak solutions of conservation laws

The method of weakly nonlinear geometric optics is one of the main formal perturbation techniques used in analyzing nonlinear wave motion for hyperbolic systems. The tacit assumption in using such perturbation methods is that the corresponding solutions of the hyperbolic system remain smooth; since shock waves typically form in such solutions, these assumptions are rarely satisfied in practice. Nevertheless, in a variety of applied contexts, these methods give qualitatively reliable answers for discontinuous weak solutions. Here we give a rigorous proof for the validity of nonlinear geometric optics for general weak solutions of systems of hyperbolic conservation laws in a single space variable. The methods of proof do not mimic the formal construction of weakly nonlinear asymptotics but instead rely on structural symmetries of the approximating equations, stability estimates for intermediate asymptotic times, and the rapid decay in variation of weak solutions for large asymptotic times.Partially supported by NSF Grant No. DMS-8301135Partially supported by NSF Grant No. MCS-81-02360 and ARO Grant No. 483964-25530     

The Hamiltonian structure of general relativistic perfect fluids

We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed.Research supported in part by NSF grant MCS 81-08814(A02)Research supported in part by NSF grant MCS 81-07086     

The effect of glottal angle on intraglottal pressure

Intraglottal pressure distributions depend upon glottal shape, size, and diameter. This study reports the effects of varying glottal angle on intraglottal and transglottal pressures using a three-dimensional Plexiglas model with a glottis having nine symmetric glottal angles and a constant minimal glottal diameter of 0.06 cm. The empirical data were supported by computational results using FLUENT. The results suggested that (1) the greater the convergent glottal angle, the greater outward driving forces (higher intraglottal pressures) on the vocal folds; (2) flow resistance was greatest for the uniform glottis, and least for the 10 degrees divergent glottis; (3) the greatest negative pressure in the glottis and therefore the greatest pressure recovery for diverging glottal shapes occurred for an angle of 10 degrees; (4) the smaller the convergent angle, the greater the flow resistance; (5) FLUENT was highly accurate in predicting the empirical pressures of this model; (6) flow separation locations (given by FLUENT) for the divergent glottis moved upstream for larger flows and larger glottal angles. The results suggest that phonatory efficiency related to aerodynamics may be enhanced with vocal fold oscillations that include large convergent angles during glottal opening and small (5 degrees - 10 degrees) divergent angles during glottal closing.     

High electrocatalytic oxidation of folic acid at carbon paste electrode bulk modified with iron nanoparticle-decorated multiwalled carbon nanotubes and its application in food and pharmaceutical analysis

Ionics - A simple and rapid method was employed for the modification of carbon paste electrode with iron nanoparticle-decorated multiwalled carbon nanotubes (MCPE/Fe-MWCNTs). The synergistic effect...     

Graphs which,with their complements,have certain clique covering numbers

Two common invariants of a graph G are its node clique cover number, θ₀(G), and its edge clique cover number, θ₁(G). We present in this work a characterization of those graphs for which they and their complements, $\text{G}\text{?}$, have θ₀(G)=θ₁(G) and θ₀($\text{G}\text{?}$)=θ₁($\text{G}\text{?}$). Graphs satis ying these conditions are shown to constitute a subset of those graphs which we term C-graphs.     

The personalization of security selection: An application of fuzzy set theory

We apply the theory of fuzzy subsets to the multiple objective decision problem of stock selection. We allow our objectives to have varying degrees of importance. We discuss various criteria used in selecting stocks. We indicate some procedures for subjectively evaluating the membership functions associated with these criteria.     

Observation of persistent α‐helical content and discrete types of backbone disorder during a molten globule to ordered peptide transition via deep‐UV resonance Raman spectroscopy

The molten globule (MG) state can aid in the folding of a protein to a functional structure and is loosely defined as an increase in structural disorder with conservation of the ensemble secondary structure content. Simultaneous observation of persistent secondary structure content with increased disorder has remained experimentally problematic. As a consequence, modeling how the MG state remains stable and how it facilitates proper folding remains difficult due to a lack of amenable spectroscopic techniques to characterize this class of partially unfolded proteins. Previously, deep‐UV resonance Raman (dUVRR) spectroscopy has proven useful in the resolution of global and local structural fluctuations in the secondary structure of proteins. In this work, dUVRR was employed to study the MG to ordered transition of a model four‐helix bundle protein, HP7. Both the average ensemble secondary structure and types of local disorder were monitored, without perturbation of the solvent, pH, or temperature. The MG to ordered transition is induced by stepwise coordination of two heme molecules. Persistent dUVRR spectral features in the amide III region at 1295–1301 and 1335–1338 cm⁻¹ confirm previous observations that HP7 remains predominantly helical in the MG versus the fully ordered state. Additionally, these spectra represent the first demonstration of conserved helical content in a MG protein. With successive heme binding, significant losses are observed in the spectral intensity of the amide III₃ and S regions (1230–1260 and 1390 cm⁻¹, respectively), which are known to be sensitive to local disorder. These observations indicate that there is a decrease in the structural populations able to explore various extended conformations with successive heme binding events. DUVRR spectra indicate that the first heme coordination between two helical segments diminishes exploration of more elongated backbone structural conformations in the inter‐helical regions. A second heme coordination by the remaining two helices further restricts protein motion. Copyright © 2013 John Wiley & Sons, Ltd.     

Two-photon quantum interference from separate nitrogen vacancy centers in diamond

We report on the observation of quantum interference of the emission from two separate nitrogen vacancy (NV) centers in diamond. Taking advantage of optically induced spin polarization in combination with polarization filtering, we isolate a single transition within the zero-phonon line of the nonresonantly excited NV centers. The time-resolved two-photon interference contrast of this filtered emission reaches 66%. Furthermore, we observe quantum interference from dissimilar NV centers tuned into resonance through the dc Stark effect. These results pave the way towards measurement-based entanglement between remote NV centers and the realization of quantum networks with solid-state spins.     

Connectedness percolation of elongated hard particles in an external field

A theory is presented of how orienting fields and steric interactions conspire against the formation of a percolating network of, in some sense, connected elongated colloidal particles in fluid dispersions. We find that the network that forms above a critical loading breaks up again at higher loadings due to interaction-induced enhancement of the particle alignment. Upon approach of the percolation threshold, the cluster dimensions diverge with the same critical exponent parallel and perpendicular to the field direction, implying that connectedness percolation is not in the universality class of directed percolation.