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The prehistoric Lowland Maya supported an elaborate civilization, which reached peak population densities in the tropical forests of Guatemala, Belize and southern Mexico during the Classic period between AD 300 and 900. It has been proposed that the Maya turned to labour-intensive construction of raised planting platforms in wetlands for year-round cultivation. Excavations at San Antonio Rio Hondo, northern Belize1, provided the first archaeological data for this hypothesis. In our analysis of data from the San Antonio site, we conclude that the only indisputable evidence that prehistoric wetland cultivation occurred comes from a time before peak population of the Classic period, and that the technique required less labour than previously envisioned. Exploitation of swampy terrain initially involved dry-season cropping without extensive ditching and later ditching, probably for soil drainage.

The purpose of this note is to prove the following theorem for : stimating the norm of an integral operator of a general type. This estimate is needed in the accompanying paper. [3] The scalar case...

An argon ion laser emits several laser lines in the visible region of the optical spectrum. The absorption coefficients of NO/sub 2/ at these laser emissions were measured in a multiple pass absorption cell. A differential technique, in which the ratio of the transmitted intensities of the argon laser emissions is measured, is described to determine the concentration of NO/sub 2/ in a polluted atmosphere over path lengths of several kilometers. Measurement of ratios eliminates interferences from particle scattering and thermal index gradients. Evaluation of the data taken in the 48 meter multipass cell indicates that concentrations of NO/sub 2/ less than one part per million could be determined in a 1 km optical path. (auth)

The principle of this detector is based on the measurement of the intensity of the ultraviolet fluorescence of SO2 produced by absorption of the Zn 2138 A or Cd 2288 A line. The fluorescence intensity was found to be linear from 0.1 to 500 ppm of SO2 in air with the Zn lamp and from 0.1 to 1600 ppm with the Cd lamp. The detection limit at present is about 20 ppb. There is no detectable interference from O3, H2S, NO2, CO2, CO, or H2, although the presence of a large concentration of CS2 (500 times as much as SO2) NO (500 times) or C2H4 (4000 times) interferes with the measurement. The presence of 2% H20 reduces the signal by 25%, while up to 1 % CH4 has almost no effect.

In this paper the existence of a right canonical Wiener-Hopf factorization for a rational matrix function is characterized in terms of a left canonical Wiener-Hopf factorization. Formulas for the factors in a right factorization are given in terms of the formulas for the factors in a given left factorization. Both symmetric and nonsymmetric factorizations are discussed.

The bitangential Nevanlinna-Pick interpolation problem arises in the sensitivity minimization problem of H?-optimal control theory (see [F,FD]) and has been studied in a number of publications (eg. [BH1,BH2, BR1, Fe, K, LA]). Here we review the approach from [BH1,BH2] and summarize results from [BR1] which yield an explicit realization formula (with no recursions) for the linear fractional map which parametrizes all solutions of the problem. We also indicate how one can obtain all sensitivities for stable closed loop systems with H? norm below a prescribed tolerance directly from zero and pole data of the open loop plant for the right half plane - without recourse to explicit inner-outer factorization.

We consider the problem of constructing a regular rational n × n matrix function W(z) = C(zI - A) -1B + D + zE(I - zG)-1F such that WR n + = W1R n + and WR n - = W2R n - . Here R n + (respectively R n - ) is the space of rational ℂn-valued functions analytic inside (respectively outside) a smooth closed con our in the complex plane, and realizations Wj(z) = Cj (zI - Aj)-1Bj + Dj + zEj (I - zGj)-1Fj are given for j = 1, 2. The special case where the contour Γ is the unit circle and W1 (∞) = W2 (∞) = I was studied recently in [BR3]. As applications we consider the model reduction problem from linear systems theory for both the discrete time and continuous time settings and the special case of matrix polynomials.

The goal of this paper is to describe and analyze the set of all unitary n × n matrix valued functions $$ F\left( \varsigma \right) = \sum\limits_{j = - \infty }^\infty {{F_j}{\varsigma ^j}} $$ on the unit circle T•T with prescribed matrix Fourier coefficients Fj =Kj for j < 0. It is known that ‖HK‖ ≤ 1 is a necessary condition for such an F to exist, where HK is the infinite Hankel matrix $$ {\left[ {{K_{ - \left( {j + k - 1} \right)}}} \right]_{J,k = 1,2,...}} $$ acting on l n 2 . With the added assumption that $$ I - H_K^*{H_K} $$ is Fredholm, there is a linear fractional map $$ {T_\Xi }:BL_{S \times S}^\infty \to BL_{n \times n}^\infty $$ (B = unit ball) such that the set of unitary interpolants is precisely all F of the form F = TΞ(G) for a s×s matrix inner function G. The linear fractional map TΞ arises from a 2n × 2n matrix function Ξ which satisfies an identity $$\Xi *J\Xi = \widehat D$$ a.e. on T•T. Here J is the signature matrix $$\left[ {\begin{array}{*{20}{c}} {{I_n}}&0 \\ 0&{ - {I_n}} \end{array}} \right]$$ and D has the form Open image in new window where d is a (n-s) × (n-s) matrix of the form $$ {\left[ d \right]_{ij}} = {\zeta ^j}{\delta _{n + 1 - i,j}}\;\left( {i,j = 1,...,n - s} \right) $$ for negative integers K1, ≤ K2 ≤... ≤ Kn-s< 0. The function Ξ together with the indices {K1, ..., kn-s} can be computed directly from the original data {Kj}j

We discuss basic properties of nonlinear smooth norm-preserving maps on a Hilbert space and nonlinear analogues of various types of operators (Toeplitz, analytic Toeplitz, inner, outer) associated with a shift on a Hilbert space.

Various notions of passivity are introduced for a lossless circuit, or equivalently, for a rational matrix function θ which is J-unitary on the unit circle. These notions, as well as how they are related to each other, are analyzed from several points of view: energy bookkeeping in the circuit, analytic conditions on θ and on the associated scattering matrix U, geometry of shift invariant subspaces, positive definiteness conditions on associated reproducing kernel functions, connections with classical interpolation problems, and state space representations. This gives a circuit theoretic interpretation for several modern approaches to interpolation such as the geometric one of Ball-Helton.

Recently there has been an interesting cross-fertilisation between the areas of mathematical interpolation theory, operator theory and control theory which has led to new results in all areas. In particular the Sarason-Sz. Nagy Foias commutant lifting theorem provides a very broad framework for generalized Nevalinna-Pick interpolation which in turn gives a solution to the H∞-optimal weighted sensitivity problem in control theory. In this paper we give a generalization of this “commutant lifting theorem” for certain classes of nonlinear analytic operators and discuss some possible applications.

Etude d'une extension non lineaire de la theorie classique de l'interpolation de Nevanlinna-Pick

Let H2 (₵k) = H2 ⊗ ₵k be the usual vector-valued Hardy space and let S be the shift operator of multiplication by eit on H2 (₵k).

This report documents the theoretical basis, development, and computational structure of a numerical computer analysis routine incorporated in the US Army Experimental Prototype Automatic Meteorological System (EPAMS) for the estimation of surface layer wind fields at sub-mesoscale resolution (approx. 100 meters) over a limited area in broken topography. The geographically re-locatable analysis exploits detailed topographic information but requires only limited meteorological information. The physically-based analysis uses Gauss' Principle of Least Constraints for a variational adjustment of an initial estimated wind field in a single surface layer to conform with terrain structure, mass conservation, and buoyancy forces. Fields of surface air temperature are also produced. Initial meteorological input is obtained from the EPAMS data base by an automated analysis which is described in detail. The segmentation structure of the computational program levels is presented. Appendices provide user instructions, detailed algorithms, and example wind field estimates. (Author)

Using known results on matrix Nevanlinna-Pick interpolation combined with a spectral factorization algorithm of Youla, we present an algorithm for obtaining all stable closed loop sensitivities having H∞-norm within a prescribed (suboptimal) tolerance for a given open loop plant P(s). Other desirable characteristics for the associated stabilizing compensator (such as suitable roll-off at ∞) can then be sought within this class.

Consider a discrete time, causal, MIMO system whose input-output operator C maps the space of norm square summable RN-valued sequences lN 2[0,?) to itself. Our concern is the feedback systems

The main objective of this article is to develop techniques of robust control and their applications to communication and transportation networks. Three following problems will be studied in detail: (1) Resource Sharing: These systems belong to a class of hybrid systems where the plant to be controlled is a continuous drift free system, and the controller is implemented as a FSM. (2) Admission Control. Ramp metering control problem can be studied in either distributed or lumped parameter setting. These two settings to an isolated case have been studied by the authors and solutions for these have been obtained. (3) Traffic Routing. Traditionally both kinds of network systems have been treated using static optimization methods for congestion control. The traffic routing problem for both types of networks can be solved either in user-equilibrium setting or system-optimal. In user-equilibrium, the aim of the controller is to obtain equal travel times on alternate routes. In system-optimal, the aim is to obtain minimum total travel time on the entire network.

The infrared transmittance of deposited films of tellurium, bismuth, antimony, and magnesium oxide has been measured. These filters are opaque in the visible region and have short wavelength cutoffs varying from 1 to 3 microns. Reflection filters have also been made, for the region from 10μ to 40μ, by roughening the surface of a mirror with emery powder. These filters are used in removing stray radiation from the KBr and KRS-5 regions of the spectrum.

Increased stability for electrodeless discharge lamps used in atomic spectroscopy is attained by mounting a heater coil below the lamp. Heating by convection maintains the lamp at a constant temperature resulting in stable output within 2%.