Modeling of hydrogen ground state rotational and vibrational temperatures in kinetic plasmas

A dipole-quadrupole electron-impact excitation model, consistent with molecular symmetry rules, is presented to fit ro-vibronic spectra of the hydrogen Fulcher-α Q-branch line emissions for passively measuring the rotational temperature of hydrogen neutral molecules in kinetic plasmas with the coronal equilibrium approximation. A quasi-rotational temperature and quadrupole contribution factor are adjustable parameters in the model. Quadrupole excitation is possible due to a violation of the 1st Born approximation for low to medium energy electrons (up to several hundred eV). The Born-Oppenheimer and Franck-Condon approximations are implicitly shown to hold. A quadrupole contribution of 10% is shown to fit experimental data at several temperatures from different experiments with electron energies from several to 100 eV. A convenient chart is produced to graphically determine the vibrational temperature of the hydrogen molecules from diagonal band intensities, if the ground state distribution is Boltzmann. Hydrogen vibrational modes are long-lived, surviving up to thousands of wall collisions, consistent with multiple other molecular dynamics computational results. The importance of inter-molecular collisions during a plasma pulse is also discussed.     

Strictly Order-Preserving Maps into Z, II. A 1979 Problem of Erné

A lattice L is constructed with the property that every interval has finite height, but there exists no strictly order-preserving map from L to Z. A 1979 problem of Erné (posed at the 1981 Banff Conference on Ordered Sets) is thus solved. It is also shown that if a poset P has no uncountable antichains, then it admits a strictly order-preserving map into Z if and only if every interval has finite height.     

POLYMERS DERIVED FROM HEXAFLUOROACETONE

Abstract

The continuing demand for polymeric materials with a unique combination of properties has brought forth a sizable research effort concerning the use of trifluoromethyl substituents, particularly the 1,1,1,3,3,3-hexafluoroisopropylidene (HFIP) function derived from the incorporation of hexafluoroacetone (HFA) into the monomer. This work had its beginnings approximately 25 years ago when Rogers briefly reported in a patent the preparation of polyimides (PIs) from an hexafluoroisopropylidenebrideged diamine [1,2]. Since then numerous efforts have been made toward the synthesis, characterization, and evaluation of CF₃-containing polymers. Much of this information is found in patents, indicating the importance of these polymers to industry. At the present time, at least 11 known classes of polymers containing pendant or backbone-incorporated bis-trifluoromethyl groups have been reported. These polymers show promise as film formers, gas separation membranes, seals, soluble polymers, coatings, and in other high-temperature applications. Frequently the polymer properties imparted by the inclusion of the HFIP function encompass: increased solubility, flame resistance, glass transition temperature, thermal stability, oxidation resistance, and environmental stability; decreased color, crystallinity, dielectric constant, and water absorption.     

The uniqueness of the core

Simple proofs are given for two theorems of Duffus and Rival: If a finite poset is dismantled by irreducibles as much as possible, the subposet one finally obtains is unique up to isomorphism. If one dismantles by doubly irreducibles, the subposet is unique.     

Magnetic linear dichroism in the angular dependence of core-level photoemission from (Ga,Mn)As using hard x rays

We report a study of the electronic properties of the ferromagnetic semiconductor (Ga,Mn)As using magnetic linear dichroism in the angular dependence of Mn 2p photoemission under hard x-ray excitation. Bulk plasmon loss satellites demonstrate that the probed Mn ions are incorporated deep within the GaAs lattice, while the observed large dichroism indicates that the spectra originate from ferromagnetic substitutional Mn. Simulations of the spectra using an Anderson impurity model show that the ferromagnetic Mn 3d electrons of substitutional Mn in (Ga,Mn)As are intermediate between localized and delocalized.     

Distributive lattices of small width, II: A problem from Stanley's 1986 text Enumerative Combinatorics

In Richard P. Stanley's 1986 text, Enumerative Combinatorics, the following problem is posed: Fix a natural number k. Consider the posets P of cardinality n such that, for 0<i<n, P has exactly k order ideals (down-sets) of cardinality i. Let fk(n) be the number of such posets. What is the generating function ∑f₃(n)xn?In this paper, the problem is solved.     

Principles and applications of ENDOR spectroscopy for structure determination in solution and disordered matrices

Both electron paramagnetic resonance (EPR) and electron nuclear double resonance (ENDOR) spectroscopies are extremely powerful and versatile methods for the characterisation of paramagnetic systems in biology, chemistry, and physics. However, by comparison to EPR, ENDOR remains a less widely used technique. In this tutorial review the basic principles of continuous wave ENDOR are described. The theory of orientation selective ENDOR, for structure determination in frozen solutions and powders, is then described. A range of examples, illustrating the type of information obtained from the ENDOR spectrum, is finally presented.     

Partitioning a Planar Graph of Girth 10 into a Forest and a Matching

We prove that any finite planar graph with girth at least 10 can have its edges partitioned to form two graphs on the same vertices, one of which is a forest, and the other of which is a matching. Several related results are also demonstrated.     

New measurement of (g−2) of the Muon

The g-factor anomaly, a≡(g?2)/2, has been measured for μ⁺ in the new Muon Storage Ring at CERN. The result is a = (1 165 895 ± 27) × 10^?9. This is (13 ± 29) × 10^?9 below the theoretical value which includes sixth-order QED terms and a hadronic contribution of (73 ± 10) × 10^?9.