Symmetries and reversing symmetries of polynomial automorphisms of the plane

The polynomial automorphisms of the affine plane over a field K form a group which has the structure of an amalgamated free product. This well-known algebraic structure can be used to determine some key results about the symmetry and reversing symmetry groups of a given polynomial automorphism.Comment: 27 pages, AMS-Late

The structure of reversing symmetry groups

We present some of the group theoretic properties of reversing symmetry groups, and classify their structure in simple cases that occur frequently in several well-known groups of dynamical systems.Comment: 12 page

New Estimates of Federal Government Tangible Capital and Net Investment

Government capital formation raises a number of issues important to national economic well-being, yet the U.S., unlike most advanced countries, does not account for capital in its formal budget documents. We estimate depreciation of government capital using a methodology developed by Hulten and Wykoff which is based on used asset price data. We estimate a federal government net nonresidential capital stock of over $800 billion in 1984, more than 20% higher than estimated by the BEA. We also find much larger net federal investment since World War II than the BEA. The behavior of military and civilian structures and equipment is also examined.We analyze the potential importance of these results for measuring the net national savings rate, national wealth, the trend in government capital formation relative to private capital formation, and the relationship between net investment and deficits.

15N NMR study of a mixture of uniformly labeled tRNAs

15N NMR spectra were taken of 15N-enriched tRNA extracted from bakers yeast; ammonium sulfate was used as a nitrogen source. The increase in the degree of denaturation of tRNA, which occurs with increase in temperature from 30 degrees C to 70 degrees C, resulted in no large changes in 15N chemical shifts at acidic and neutral pH but quite pronounced changes in proton-15N nuclear Overhauser effects

Flight Attitude and Acceleration Data Recorder

This document outlines the design and implementation of a low-cost, low-power acceleration data recorder for utility category gliders. Working from literature and experience, we have built a recorder that can accurately measure the forces and angle experienced by a glider in flight. The recorder is able to record and display acceleration force and angular rates of turn as well as display and analyze post-flight data utilizing software created for a personal digital assistant and personal computer

Symmetries and reversing symmetries of area-preserving polynomial mappings in generalised standard form

We determine the symmetries and reversing symmetries within G, the group of real planar polynomial automorphisms, of area-preserving nonlinear polynomial maps L in generalised standard form, L: x'=x+p(y), y'=y+q(x'), where p and q are polynomials. We do this by using the amalgamated free product structure of G. Our results lead to normal forms for polynomial maps in generalised standard form and to a classification of the group structures of the reversing symmetry groups for such maps.Comment: 22 page

Conformational Preferences of 3-(Dimethylazinoyl)propanoic Acid as a Function of pH and Solvent; Intermolecular versus Intramolecular Hydrogen Bonding

The conformational equilibrium of 3-(dimethylazinoyl)propanoic acid (DMAPA, azinoyl = N^+(O^−) has a weak pH-dependence in D_2O, with a slight preference for trans in alkaline solutions. The acid ionization constants of the protonated amine oxide and carboxylic functional groups as determined by NMR spectroscopy were 7.9 × 10^(−4) and 6.3 × 10^(−6), respectively. The corresponding value of K_1/K_2 of 1.3 × 10^2 is not deemed large enough to provide experimental NMR evidence for a significant degree of intramolecular hydrogen bonding in D_2O. Conformational preferences of DMAPA are mostly close to statistical (gauche/trans = 2/1) in other protic solvents, e.g., alcohols. However, the un-ionized form of DMAPA appears to be strongly intramolecularly hydrogen-bonded and gauche in aprotic solvents

Periodic orbits of linear endomorphisms on the 2-torus and its lattices

Counting periodic orbits of endomorphisms on the 2-torus is considered, with special focus on the relation between global and local aspects and between the dynamical zeta function on the torus and its analogue on finite lattices. The situation on the lattices, up to local conjugacy, is completely determined by the determinant, the trace and a third invariant of the matrix defining the toral endomorphism.Comment: 22 page

Reversing and extended symmetries of shift spaces

The reversing symmetry group is considered in the setting of symbolic dynamics. While this group is generally too big to be analysed in detail, there are interesting cases with some form of rigidity where one can determine all symmetries and reversing symmetries explicitly. They include Sturmian shifts as well as classic examples such as the Thue–Morse system with various generalisations or the Rudin–Shapiro system. We also look at generalisations of the reversing symmetry group to higher-dimensional shift spaces, then called the group of extended symmetries. We develop their basic theory for faithful ℤd-actions, and determine the extended symmetry group of the chair tiling shift, which can be described as a model set, and of Ledrappier’s shift, which is an example of algebraic origin