On a restriction problem of de Leeuw type for Laguerre multipliers

In 1965 K. de Leeuw \cite{deleeuw} proved among other things in the Fourier transform setting: {\it If a continuous function $m(\xi _1, \ldots ,\xi _n)$ on ${\bf R}^n$ generates a bounded transformation on $L^p({\bf R}^n),\; 1\le p \le \infty ,$ then its trace $\tilde{m}(\xi _1, \ldots ,\xi _m)=m(\xi _1, \ldots ,\xi _m,0,\ldots ,0), \; m<n,$ generates a bounded transformation on $L^p({\bf R}^m)$. } In this paper, the analogous problem is discussed in the setting of Laguerre expansions of different orders

Ultraspherical multipliers revisited

Sufficient ultraspherical multiplier criteria are refined in such a way that they are comparable with necessary multiplier conditions. Also new necessary conditions for Jacobi multipliers are deduced which, in particular, imply known Cohen type inequalities. Muckenhoupt's transplantation theorem is used in an essential way

Intra-cavity spectroscopy using amplified spontaneous emission in fiber lasers

Fiber laser sources offer interesting possibilities for gas sensors since they can operate over an extended wavelength range, encompassing the near-IR absorption lines of a number of important gases but a major problem is that overtone absorption lines of gases in the near-IR are relatively weak. In order to enhance sensitivity, we present here a simple method of intra-cavity absorption spectroscopy (ICAS) which makes use of the amplified spontaneous emission (ASE) already present within a fiber laser cavity. The ASE also provides a convenient broadband source for the simultaneous interrogation of several gases within the gain-bandwidth of the fiber laser. The key principle is based on adjusting the cavity attenuation to select an appropriate inversion level where the fiber gain curve is flat. Under this condition, the ASE undergoes multiple circulations within the fiber laser cavity, enhancing the effective path-length of a gas cell placed within the laser cavity. A theoretical model of system operation is given and we have experimentally demonstrated the principle of operation with acetylene and carbon dioxide using a simple erbium fiber laser system containing a 6 cm path-length, fiber coupled, intra-cavity, micro-optic gas cell. We have experimentally simultaneously observed 16 absorption lines for 1% acetylene gas in the 1530 nm region and detected the very weak carbon dioxide lines in this same wavelength region. A path length enhancement of in the linear regime has been demonstrated transforming the 6 cm micro-optic cell into an effective path length of m. We also demonstrate how the enhancement factor may be calibrated by use of a simple fiber-optic interferometer. Apart from the OSA, all components are inexpensive and the system is very simple to construct and operate

Social Welfare and Coercion in Public Finance

This paper develops an expanded framework for social planning in which the existence of coercion is explicitly acknowledged. Key issues concern the precise definition of coercion for individuals and in the aggregate, its difference from redistribution, and its incorporation into normative analysis. We explore modifications to traditional rules for optimal fiscal policy in the presence of coercion constraints and determine the degree of coercion implied by traditional social planning. The paper maps the trade-off between social welfare and aggregate coercion and explores its implications for normative policy and the comparative evaluation of institutions, including competitive democracy.coercion, redistribution, social planning, optimal fiscal policy, marginal cost of funds, public goods, collective choice

Calculation of the Two-body T-matrix in Configuration Space

A spectral integral method (IEM) for solving the two-body Schroedinger equation in configuration space is generalized to the calculation of the corresponding T-matrix. It is found that the desirable features of the IEM, such as the economy of mesh-points for a given required accuracy, are carried over also to the solution of the T-matrix. However the algorithm is considerably more complex, because the T-matrix is a function of two variables r and r', rather than only one variable r, and has a slope discontinuity at r=r'. For a simple exponential potential an accuracy of 7 significant figures is achieved, with the number N of Chebyshev support points in each partition equal to 17. For a potential with a large repulsive core, such as the potential between two He atoms, the accuracy decreases to 4 significant figures, but is restored to 7 if N is increased to 65.Comment: 22 pages, 1 table 8 figure

The sanction for religious education based on the function of religion in social evolution

Thesis (Ph.D.)--Boston Universit

Nutrient Levels and Organic Matter Decomposition in Response to Prescribed Burns in Mid-Atlantic Coastal Marshes

Prescribed winter burning is a commonly used management practice in coastal marshes along the Atlantic Coast. I conducted a manipulative field study to explore the mechanisms by which fire increases plant productivity. I found that prescribed fire does not provide a fertilization effect for vegetation through ash deposition due to the low amounts of nutrients in ash. Modeling biomass nutrient stocks in other marshes with similar vegetation types shows that this lack of a fertilization effect likely exists across all coastal marsh types. Through the mechanism of canopy removal, organic matter decomposition rates in marsh areas tended to decrease later in the growing season, corresponding with a decrease in porewater ammonium and phosphate, which were taken up in much higher quantities in the biomass. These effects were stronger and more consistent in areas dominated by the sedge species, as these areas showed more of a biomass response to canopy removal

A study of the evaporation of organic liquids and mixtures of organic liquids

The purpose of this thesis is to make a study of the evaporation of organic solvents. The relative rates of evaporation of the single substances and binary and ternary mixtures are to be considered. A study of the changes in composition of binary and ternary mixtures that occur on evaporation are to be made. Information on the evaporation of organic liquids is important in relation to lacquers, and for that reason the solvents used in this work are liquids commonly used in making lacquers --Introduction, page 2