Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Field-Based Evaluations of Horizontal Flat-Plate Fish Screens

Diversions from streams are often screened to prevent the loss of or injury to fish. Hydraulic criteria meant to protect fish that encounter screens have been developed, but primarily for screens that are vertical to the water flow rather than horizontal. For this reason, we measured selected hydraulic variables and released wild rainbow trout Oncorhynchus mykiss over two types of horizontal flat-plate fish screens in the field. Our goal was to assess the efficacy of these screens under a variety of conditions in the field and provide information that could be used to develop criteria for safe fish passage. We evaluated three different inverted-weir screens over a range of strewn (0.24-1.77 m(3)/s) and diversion flows (0.10-0.31 m(3)/s). Approach velocities (AVs) ranged from 3 to 8 cm/s and sweeping velocities (SVs) from 69 to 143 cm/s. We also evaluated a simple backwatered screen over stream flows of 0.23-0.79 m(3)/s and diversion flows of 0.08-0.32 m(3)/s. The mean SVs for this screen ranged from 15 to 66 cm/s and the mean AVs from 1 to 5 cm/s. The survival rates of fish held for 24 h after passage over these screens exceeded 98%. Overall, the number of fish-screen contacts was low and the injuries related to passage were infrequent and consisted primarily of minor fin injuries. Our results indicate that screens of this type have great potential as safe and effective fish screens for small diversions. Care must be taken, however, to avoid operating conditions that produce shallow or no water over the screen surface, situations of high AVs and low SVs at backwatered screens, and situations producing a localized high AV with spiraling flow.

The Effect of Broadleaf Canopies on Survey-grade Horizontal GPS/GLONASS Measurements

A study was conducted to empirically determine the degradation of survey-grade GPS horizontal position measurements due to the effects of broadleaf forest canopies. The measurements were taken using GPS/GLONASS-capable receivers measuring C/A and P-codes, and carrier phase. Fourteen survey markers were chosen in central Connecticut to serve as reference markers for the study. These markers had varying degrees of sky obstruction due to overhanging tree canopies. Sky obstruction was measured by photographing the sky with a 35mm reflex camera fitted with a hemispherical lens. The negative was scanned and the image mapped using an equal- area projection to remove the distortion caused by the lens. The resulting digital image was thresholded to produce a black-and-white image in which a count of the black pixels is a measure of sky-area obstruction. The locations of the markers were determined independently before the study. During the study, each marker was occupied for four 20-minute sessions over the period of one week in mid-July, 1999. The location of the study markers produced relatively long baselines, as compared with similar studies. We compared the accuracy of GPS-only vs. GPS&GLONASS as a function of sky obstruction. Based on our results, GLONASS observations did not improve or degrade the accuracy of the position measurements. There is a loss of 2mm of accuracy per percent of sky obstruction for both GPS only and GPS&GLONASS.

Technical Efficiency and Stock Market Reaction to Horizontal Mergers

This study examines the relationship between stock market reaction to horizontal merger announcements and technical efficiency levels of the participating firms. The analysis is based on data pertaining to eighty mergers between firms in the U.S. manufacturing industry during the 1990s. We employ Data Envelopment Analysis (DEA) to measure technical efficiency, which capture the firms. competence to produce the maximum output given certain productive resources. Abnormal returns related to the merger announcements provide the investor.s re-evaluation on the future performance of the participating firms. In order to avoid the problem of nonnormality, heteroskedasticity in the regression analysis, bootstrap method is employed for estimations and inferences. We found that there is a significant relationship between technical efficiency and market response. The market apparently welcomes the merger as an arrangement to improve resource utilizations.

Über einige horizontal wachsende Rhizome

Von Fredr. Elfving

Functional architecture of mammalian horizontal cells

In the rabbit retina, there are two kinds of horizontal cells (HCs). The A-type HC is a large axonless cell which contacts cones exclusively. The B-type HC is an axon bearing cell. While the somatic dendrites of B-type HCs also contact cones, the axon expands into an elaborately branched structure, the axon terminal (AT), which contacts a large number of rods. It is difficult to label the different HCs selectively by immunochemical methods. Therefore, we developed dye injection methods to label each type of HC. Then it was possible, (1) to describe the detailed structure of the AT (2) to identify the glutamate receptors mediating cone input to A and B-type HCs and rod input to ATs and (3) to test the hypothesis that the B-type HCs are coupled via Cx57 gap junctions. ^ To obtain well filled examples of single HCs, it was necessary to block gap junction coupling to stop the spread of Neurobiotin through the network. We used dye coupling in A-type HCs to screen a series of potential gap junction antagonists. One of these compounds, meclofenamic acid (MFA), was potent, water soluble and easily reversible. This compound may be a useful tool to manipulate gap junction coupling. ^ In the presence of MFA, Neurobiotin passed down the axon of B-type HCs to reveal the detailed structure of the AT. We observed that only one AT ending entered each rod spherule invagination. This observation was confirmed by calculation and two dye injections. ^ Glutamate is the neurotransmitter used by both rods and cones. AMPA receptors were colocalized with the dendrites of A and B-type HCs at each cone pedicle. In addition, AMPA receptors were located on the AT ending at each rod spherule. Thus rod and cone input to HCs is mediated by AMPA receptors. ^ A-type and B-type HCs may express different connexins because they have different dye-coupling properties. Recently, we found that connexin50 (Cx50) is expressed by A-type HCs. B-type HCs and B-type ATs are also independently coupled. Cx57 was expressed in the OPL and double label studies showed that Cx 57 was colocalized with the AT matrix but not with the somatic dendrites of B-type HCs. ^ In summary, we have identified a useful gap junction antagonist, MFA. There is one AT ending at each rod spherule, rods inputs to ATs is mediated by AMPA receptors and coupling in the AT matrix is mediated by Cx57. This confirms that HCs with different properties use distinct connexins. The properties of ATs described in this research are consistent. The connections and properties reported here suggest that ATs functions as rod HCs and provide a negative feedback signal to rods. ^