Rotational spectrum of cis–cis HOONO

The pure rotational spectrum of cis-cis peroxynitrous acid, HOONO, has been observed. Over 220 transitions, sampling states up to J(')=67 and K-a(')=31, have been fitted with an rms uncertainty of 48.4 kHz. The experimentally determined rotational constants agree well with ab initio values for the cis-cis conformer, a five-membered ring formed by intramolecular hydrogen bonding. The small, positive inertial defect Delta=0.075667(60) amu A(2) and lack of any observable torsional splittings in the spectrum indicate that cis-cis HOONO exists in a well-defined planar structure at room temperature

Rotational spectroscopy and dipole moment of cis-cis HOONO and DOONO

The rotational spectrum of cis-cis HOONO has been studied over a broad range of frequencies, 13–840 GHz, using pulsed beam Fourier-transform microwave spectroscopy and room-temperature flow cell submillimeter spectroscopy. The rotational spectrum of the deuterated isotopomer, cis-cis DOONO, has been studied over a subset of this range, 84–640 GHz. Improved spectroscopic constants have been determined for HOONO, and the DOONO spectrum is analyzed for the first time. Weak-field Stark effect measurements in the region of 84–110 GHz have been employed to determine the molecular dipole moments of cis-cis HOONO [µa=0.542(8) D,µb=0.918(15) D,µ=1.07(2) D] and DOONO [µa=0.517(9) D,µb=0.930(15) D,µ=1.06(2) D]. The quadrupole coupling tensor in the principal inertial axis system for the 14N nucleus has been determined to be chiaa=1.4907(25) MHz,chibb=–4.5990(59) MHz,chiab=3.17(147) MHz, and chicc=3.1082(59) MHz. Coordinates of the H atom in the center-of-mass frame have been determined with use of the Kraitchman equations, |aH|=0.516 Å and |bH|=1.171 Å. The inertial defects of HOONO and DOONO are consistent with a planar equilibrium structure with significant out-of-plane H atom torsional motion. Comparisons of the present results are made to ab initio calculations

Minimal Nodal Domains for Strictly Elliptic Partial Differential Equations with Homogeneous Boundary Conditions

This work presents a proof of the dependence of the first eigenvalue for uniformly elliptic partial differential equations on the domain in a less abstract setting than that of Ivo Babushka and Rudolf Vyborny in 1965. The proof contained here, under rather mild conditions on the boundary of the domain, �Ω, demonstrates that the first eigenvalue of elliptic partial differential equation [ �� + �� = 0 �� Ω [ � = 0 �� �Ω depends continuously on the domain in the following sense. If a sequence of domains is such that, then the corresponding first eigenvalues satisfy is the first eigenvalue for [ �� + �� = 0 �� Ω [ � = 0 �� �Ω The work also reviews and utilizes the Sturmian comparison results of John G. Heywood, E. S. Noussair, and Charles A. Swanson. For a continuously parameterized family of domains, say with μ ∈ = [a, b], the continuous dependence of the eigenvalue on the domain combined with the Sturmian comparison results provide a theorem that insures, under certain conditions, that the elliptic partial differential equation [ �� = 0 �� Ω [ � = 0 �� �Ω has a solution which is positive on a nodal domain That is there is a least value of μ [a, b] so that a positive solution u exists for [ �� = 0 �� Ωμ [ � = 0 �� �Ωμ Beyond these results the work contains a theorem that shows for certain types of domains, rectangles in , among them, that there is a critical dimension smaller than which, no solution to the problem [ �� + �� = 0 �� Ω [ � = 0 �� �Ω exists when the eigenvalue is fixed. During the investigations taken up in this work, certain observations were made regarding linear approximations to eigenvalue problems in R2 using a standard numerical approximation scheme. One such observation is that if a linear approximation to an eigenvalue problem contains an incorrect estimate for an eigenvalue, the resulting graphical approximation seems to betray whether or not the estimate was low or high. The observations made do not appear to exist in the literature

Studies on Saprolegniaceous Filamentous Fungi

Author Institution: Botany Department, Ohio University, Athens, OhioSeventeen species of saprolegniaceous filamentous fungi from Athens County were isolated, studied, and identified under pure culture conditions. Five of the 17 species have not previously been reported from Ohio (Achlya caroliniana Coker, Saprolegnia kauffmaniana Pieters, S. mixta de Barry, S. hypogyna Pringsh., and S. moniiifera de Barry). Only five of the 17 species have previously been collected in southeastern Ohio. One hundred and twenty collections (15 a month for eight monthsAugust through March 1968) yielded 113 isolates. Seventy-two percent were collected during August through October. Saprolegnia ferax was isolated most frequently. Most species, when grown on sterile hemp seeds in sterile glass-distilled water, initiated production of oogonia and antheridia sooner than those grown in a mixture of one third sterile lake water and two thirds glass-distilled water. Vegetative growth was greater in the latter medium