Real Even Symmetric Ternary Forms

AbstractLet Sen,m denote the set of all real symmetric forms of degree m=2d. Let PSen,m and ΣSen,m denote the cones of positive semidefinite (psd) and sum of squares (sos) elements of Sen,m, respectively. For m=2 or 4, these cones coincide. For m=6, they do not, and were analyzed in Even Symmetric Sextics, by M. D. Choi, T. Y. Lam, and B. Reznick (1987, Math. Z.195, pp. 559–580).We present an easily checked, necessary and sufficient condition for an even symmetric n-ary octic to be in PSen,8 and for an even symmetric ternary decic to be in PSe3,10; we also show that there is no corresponding condition for even symmetric ternary forms of degree greater than 10. We proceed to discuss the extremal elements of the cones PSe3,8 and PSe3,10. This leads to the question: how many of these extremal forms have sos representations? We prove that PSe3,8=ΣSe3,8 and demonstrate that PSe3,10\ΣSe3,10 is nonempty, providing many new examples of psd forms which are not sos.We give a graphic representation of ternary forms which also indicates whether or not an element of Se3,8 or Se3,10 is psd. We interpret elements of PSe3,m as inequalities; in particular, we give all symmetric polynomial inequalities of degree ≤5 satisfied by the sides of a triangle

Globular Clusters in NGC 1275

We present the results of a deep photometric study of the outer halo of NGC 1275, the highly active cD galaxy at the center of the Perseus cluster. We find a modest excess of faint ($R > 22.5$) starlike objects in its halo, indicating a population of old-halo globular clusters. However, the total estimated cluster population corresponds to a specific frequency of $S_N = 4.4 \pm 1.2$, no larger than that of normal giant ellipticals and three times lower than that of other central cD galaxies such as M87. We discuss several ideas for the origin of this galaxy. Our results reinforce the view that high $S_N$ (ie: highly efficient globular cluster formation) is not associated with cooling flows, or with recent starburst or merger phenomena.Comment: 25 pages, latex, postscript figures, tarred, Unix compressed, postscript version of paper and figures available at http://www.physics.mcmaster.ca/Grads/DKaisler/office.htm

FACTORS INFLUENCING RATES OF ADOPTION OF TRICHOMONIASIS VACCINE BY NEVADA RANGE CATTLE PRODUCERS

Tritrichimonas foetus vaccine has been marketed since 1989 to combat the trichomoniasis disease that causes reproductive failure and considerable economic loss to Nevada ranchers. An ex post technology adoption model is estimated to examine the possible adoption rate, to identify the factors that may influence the adoption behavior, and to test how the probability of adoption for five possible adopter groups would change due to changes in various ranch specific factors. Results indicate that use of computers, veterinary checkup of herd, and herd size influence the probability of adoption. Model results show that cooperative extension programs enhance the rate of adoption.Livestock Production/Industries,

On the Formation of Galaxy Halos: Comparing NGC 5128 and the Local Group Members

The metallicity distribution function (MDF) for the old red-giant stars in the halo of NGC 5128, the nearest giant elliptical galaxy, is virtually identical with the MDF for the old-disk stars in the LMC and also strongly resembles the halo MDF in M31. These galaxies all have high mean halo metallicities ( ~ -0.4$) with very small proportions of low-metallicity stars. These observations reinforce the view that metal-rich halos are quite normal for large galaxies of all types. Such systems are unlikely to have built up by accretion of pre-existing, gas-free small satellite galaxies, unless these satellites had an extremely shallow mass distribution (d log N / d log M > -1). We suggest that the halo of NGC 5128 is more likely to have assembled from hierarchical merging of gas-rich lumps in which the bulk of star formation took place during or after the merger stage.Comment: 10 pages, LaTeX, plus 3 figures in separate postscript files; Astronomical Journal, in press for December 200

Ptf1a is expressed transiently in all types of amacrine cells in the embryonic zebrafish retina.

BACKGROUND: The vertebrate retina is composed of five major types of neurons: three excitatory (photoreceptors, bipolar cells and ganglion cells) and two inhibitory (horizontal and amacrine cells). The transcription factor Ptf1a (pancreas transcription factor 1a) is important for the normal development of the inhibitory retinal neurons. RESULTS: Using a transgenic Ptf1a:GFP reporter and in situ hybridization in the zebrafish retina, we show that ptf1a message is transiently expressed in all amacrine and horizontal cells within hours after the terminal division of multipotent progenitors at the apical surface of the retinal neuroepithelium, and remains on as these cells migrate to their final laminar location. The message then shuts off, but we can follow the stable Ptf1a:GFP protein for up to 120 hours post-fertilization. A variety of anatomically and neurochemically distinct subtypes of amacrine cells can already be distinguished at this embryonic time point. CONCLUSION: The timing of Ptf1a expression suggests that it is involved in the very early stages or steps in the differentiation of amacrine cells, which, due to the perdurance of the Ptf1a:GFP, can be seen to rapidly diversify into a large number of subtypes. This work sets the stage for future studies looking at genetic specification of amacrine subtypes.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

COMPUTABLE GENERAL EQUILIBRIUM MODELING OF RANGELAND FIRES IN NORTHERN NEVADA

Resource /Energy Economics and Policy,

RANGELAND FIRES IN NORTHERN NEVADA: AN APPLICATION OF COMPUTABLE GENERAL EQUILIBRIUM MODELING

Resource /Energy Economics and Policy,

intraoperative Radiotherapy for Breast Cancer

Intraoperative radiotherapy (IORT) for early stage breast cancer is a technique for partial breast irradiation. There are several technologies in clinical use to perform breast IORT. Regardless of technique, IORT generally refers to the delivery of a single dose of radiation to the periphery of the tumor bed in the immediate intraoperative time frame, although some protocols have performed IORT as a second procedure. There are two large prospective randomized trials establishing the safety and efficacy of breast IORT in early stage breast cancer patients with sufficient follow-up time on thousands of women. The advantages of IORT for partial breast irradiation include: direct visualization of the target tissue ensuring treatment of the high-risk tissue and eliminating the risk of marginal miss; the use of a single dose coordinated with the necessary surgical excision thereby reduc- ing omission of radiation and the selection of mastectomy for women without access to a radiotherapy facility or unable to undergo several weeks of daily radiation; favorable toxicity profiles; patient convenience and cost savings; radiobiological and tumor micro- environment conditions which lead to enhanced tumor control. The main disadvantage of IORT is the lack of final pathologic information on the tumor size, histology, margins, and nodal status. When unexpected findings on final pathology such as positive margins or positive sentinel nodes predict a higher risk of local or regional recurrence, additional whole breast radiation may be indicated, thereby reducing some of the convenience and low-toxicity advantages of sole IORT. However, IORT as a tumor bed boost has also been studied and appears to be safe with acceptable toxicity. IORT has potential efficacy advantages related to overall survival related to reduced cardiopulmonary radia- tion doses. It may also be very useful in specific situations, such as prior to oncoplastic reconstruction to improve accuracy of adjuvant radiation delivery, or when used as a boost in higher risk patients to improve tumor control. Ongoing international clinical trials are studying these uses and follow-up data are accumulating on completed studies