Microwave spectrum and structure of cyanamide: Semirigid bender treatment

An extensive study of the microwave spectrum of cyanamide has been undertaken, the analysis being based in part on semirigidbender calculations by the methods of Bunker and Szalay. Inversion lines of NH₂CN, $\text{K}{}_{\mathrm{?1}}\text{= 2}{}^{\mathrm{a}}\text{Q}$ branches and a number of vibrational satellites of the J = 2?1 transition were observed. A two-vibrational-state Hamiltonian was used to fit simultaneously the 0⁺ and 0^? microwave data and yielded rotational constants X, Y, Z, D_J, D_JK, d₁, H_JK as well as the inversion splitting and the μ_yz-connecting matrix element. Vibrational satellite data of seven isotopic species and infrared frequencies of NH₂CN were included in the semirigid bender calculations: The NCN spine is nonlinear by ca. 5° in the equilibrium structure of the molecule. Also, $\text{r}{}_{\mathrm{<mtext>NH</mtext>}}\text{A}\text{?}\text{= 0.9994 + 0.0144?}{}^2$; <HNH/2 = 60.39° ? 0.1134?²; $\text{r}{}_{\mathrm{<mtext>NC</mtext>}}\text{A}\text{?}\text{= 1.3301 + 0.0327?}{}^2$ (? is the inversion angle in rad); $\text{r}{}_{\mathrm{<mtext>CN</mtext>}}\text{= 1.1645}\text{A}\text{?}$ fixed. The inclusion of the NC bond flexing was necessary in order to reproduce the observed vibrational satellite patterns of NH₂CN, NHDCN, and ND₂CN. The barrier to inversion of the amino group is 510 ± 6 cm^?1 with minima at ±45.0 ±0.2°. The inversion dipole moment is 0.91 ± 0.02 Debye.     

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.