Photographic quantification of water quality in mixing zones

A method was developed to quantitatively delineate waste concentrations throughout waste effluent mixing zones on the basis of densitometric measurements extracted from aerial photography. A mixing zone is the extent of a receiving water body ultilized to dilute a waste discharge to a concentration characteristic of a totally mixed condition. Simultaneously-acquired color infrared photography and suspended solids water samples were used to quantitatively delineate the mixing zone resulting from the discharge of a paper mill effluent. Digital scanning microdensitometer data was used to estimate and delineate suspended solids concentrations on the basis of a semi-empirical model. Photographic photometry, when predicated on a limited amount of ground sampling, can measure and delineate mixing zone waste distributions in more detail then conventional surface measuring techniques. The method has direct application to: (1) the establishment of definite and rational water quality guidelines; (2) the development of sampling and surveillance programs for use by governmental and private agencies; and (3) the development of design and location criteria for industrial and municipal waste effluent outfalls

Interdisciplinary research on the application of ERTS-1 data to the regional land use planning process

The author has identified the following significant results. Although the degree to which ERTS-1 imagery can satisfy regional land use planning data needs is not yet known, it appears to offer means by which the data acquisition process can be immeasurably improved. The initial experiences of an interdisciplinary group attempting to formulate ways of analyzing the effectiveness of ERTS-1 imagery as a base for environmental monitoring and the resolution of regional land allocation problems are documented. Application of imagery to the regional planning process consists of utilizing representative geographical regions within the state of Wisconsin. Because of the need to describe and depict regional resource complexity in an interrelatable state, certain resources within the geographical regions have been inventoried and stored in a two-dimensional computer-based map form. Computer oriented processes were developed to provide for the economical storage, analysis, and spatial display of natural and cultural data for regional land use planning purposes. The authors are optimistic that the imagery will provide revelant data for land use decision making at regional levels

The use of ERTS-1 data for the inventory of critical land resources for regional land use planning

Computer-generated spatial and statistical comparisons of critical land resource data derived from conventional sources, RB-57 photographs, and ERTS images, for an eastern Wisconsin test site, suggest that certain critical land resource data can be mapped from ERTS images on a statewide basis. This paper presents one of the biotic resources, wetlands, as an example of the use of ERTS imagery to inventory land resources

Snow wetness measurements for melt forecasting

A microwave technique for directly measuring snow pack wetness in remote installations is described. The technique, which uses satellite telemetry for data gathering, is based on the attenuation of a microwave beam in transmission through snow

Multiple solutions to a magnetic nonlinear Choquard equation

We consider the stationary nonlinear magnetic Choquard equation [(-\mathrm{i}\nabla+A(x))^{2}u+V(x)u=(\frac{1}{|x|^{\alpha}}\ast |u|^{p}) |u|^{p-2}u,\quad x\in\mathbb{R}^{N}%] where $A\$is a real valued vector potential, $V$ is a real valued scalar potential$,$ $N\geq3$, $\alpha\in(0,N)$ and $2-(\alpha/N) <p<(2N-\alpha)/(N-2)$. \ We assume that both $A$ and $V$ are compatible with the action of some group $G$ of linear isometries of $\mathbb{R}^{N}$. We establish the existence of multiple complex valued solutions to this equation which satisfy the symmetry condition $$u(gx)=\tau(g)u(x)\text{\ \ \ for all}g\in G,\text{}x\in\mathbb{R}^{N},$$ where $\tau:G\rightarrow\mathbb{S}^{1}$ is a given group homomorphism into the unit complex numbers.Comment: To appear on ZAM

The Ljapunov-Schmidt reduction for some critical problems

This is a survey about the application of the Ljapunov-Schmidt reduction for some critical problems

Measurements of Anisotropy in the Cosmic Microwave Background Radiation at 0.5 Degree Angular Scales Near the Star Gamma Ursae Minoris

We present results from a four frequency observation of a 6 x 0.6 degree strip of the sky centered near the star Gamma Ursae Minoris during the fourth flight of the Millimeter-wave Anisotropy eXperiment (MAX). The observation was made with a 1.4 degree peak-to-peak sinusoidal chop in all bands. The FWHM beam sizes were 0.55 +/- 0.05 degrees at 3.5 cm-1 and 0.75 +/-0.05 degrees at 6, 9, and 14 cm-1. During this observation significant correlated structure was observed at 3.5, 6 and 9 cm-1 with amplitudes similar to those observed in the GUM region during the second and third flights of MAX. The frequency spectrum is consistent with CMB and inconsistent with thermal emission from interstellar dust. The extrapolated amplitudes of synchrotron and free-free emission are too small to account for the amplitude of the observed structure. If all of the structure is attributed to CMB anisotropy with a Gaussian autocorrelation function and a coherence angle of 25', then the most probable values of DeltaT/TCMB in the 3.5, 6, and 9 cm-1 bands are 4.3 (+2.7, -1.6) x 10-5, 2.8 (+4.3, -1.1) x 10-5, and 3.5 (+3.0, -1.6) x 10-5 (95% confidence upper and lower limits), respectively.Comment: 16 pages, postscrip

Measurements of Anisotropy in the Cosmic Microwave Background Radiation at Degree Angular Scales Near the Stars Sigma Hercules and Iota Draconis

We present results from two four-frequency observations centered near the stars Sigma Hercules and Iota Draconis during the fourth flight of the Millimeter-wave Anisotropy eXperiment (MAX). The observations were made of 6 x 0.6-degree strips of the sky with 1.4-degree peak to peak sinusoidal chop in all bands. The FWHM beam sizes were 0.55+/-0.05 degrees at 3.5 cm-1 and a 0.75+/-0.05 degrees at 6, 9, and 14 cm-1. Significant correlated structures were observed at 3.5, 6 and 9 cm-1. The spectra of these signals are inconsistent with thermal emission from known interstellar dust populations. The extrapolated amplitudes of synchrotron and free-free emission are too small to account for the amplitude of the observed structures. If the observed structures are attributed to CMB anisotropy with a Gaussian autocorrelation function and a coherence angle of 25', then the most probable values are DT/TCMB = (3.1 +1.7-1.3) x 10^-5 for the Sigma Hercules scan, and DT/TCMB = (3.3 +/- 1.1) x 10^-5 for the Iota Draconis scan (95% confidence upper and lower limits). Finally a comparison of all six MAX scans is presented.Comment: 13 pages, postscript file, 2 figure

Dvoretzky type theorems for multivariate polynomials and sections of convex bodies

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, and the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture