scholarly journals Square-free values of multivariate polynomials over function fields in linear sparse sets

2016 ◽  
Vol 13 (01) ◽  
pp. 77-108 ◽  
Author(s):  
Shai Rosenberg
Keyword(s):  
Function Fields ◽  
Multivariate Polynomials ◽  
Variable Formula ◽  
Integer Polynomials ◽  
Linear Condition ◽  
Polynomial Formula ◽  
Almost All

Let [Formula: see text] be a square-free polynomial where [Formula: see text] is a field of [Formula: see text] elements. We view [Formula: see text] as a polynomial in the variable [Formula: see text] with coefficients in the ring [Formula: see text]. We study square-free values of [Formula: see text] in sparse subsets of [Formula: see text] which are given by a linear condition. The motivation for our study is an analogue problem of representing square-free integers by integer polynomials, where it is conjectured that setting aside some simple exceptional cases, a square-free polynomial [Formula: see text] takes infinitely many square-free values. Let [Formula: see text] be co-prime to [Formula: see text], and let [Formula: see text]. A consequence of the main result we show is that if [Formula: see text] is sufficiently large with respect to [Formula: see text] and [Formula: see text], then there exist [Formula: see text] such that [Formula: see text] is square-free. Moreover, as [Formula: see text], the last is true for almost all [Formula: see text]. The main result shows that a similar result holds also for other cases. We then generalize the results to multivariate polynomials.

ON SPRINDŽUK’S CLASSIFICATION OF -ADIC NUMBERS

2019 ◽  
pp. 1-11
Author(s):  
YANN BUGEAUD ◽  
GÜLCAN KEKEÇ
Keyword(s):  
Haar Measure ◽  
Complex Numbers ◽  
Integer Polynomials ◽  
Almost All

We carry Sprindžuk’s classification of the complex numbers to the field $\mathbb{Q}_{p}$ of $p$ -adic numbers. We establish several estimates for the $p$ -adic distance between $p$ -adic roots of integer polynomials, which we apply to show that almost all $p$ -adic numbers, with respect to the Haar measure, are $p$ -adic $\tilde{S}$ -numbers of order 1.

scholarly journals Kauffman–Jones polynomial of a curve on a surface

2017 ◽  
Vol 26 (11) ◽  
pp. 1750062
Author(s):  
Shinji Fukuhara ◽  
Yusuke Kuno
Keyword(s):  
Homotopy Class ◽  
Jones Polynomial ◽  
Intersection Number ◽  
Laurent Polynomial ◽  
Computational Results ◽  
Oriented Surface ◽  
Variable Formula ◽  
Polynomial Formula

We introduce a Kauffman–Jones type polynomial [Formula: see text] for a curve [Formula: see text] on an oriented surface, whose endpoints are on the boundary of the surface. The polynomial [Formula: see text] is a Laurent polynomial in one variable [Formula: see text] and is an invariant of the homotopy class of [Formula: see text]. As an application, we obtain an estimate in terms of the span of [Formula: see text] for the minimum self-intersection number of a curve within its homotopy class. We then give a chord diagrammatic description of [Formula: see text] and show some computational results on the span of [Formula: see text].

Habitat Association of Klebsiella Species

1985 ◽  
Vol 6 (2) ◽  
pp. 52-58 ◽  
Author(s):  
Susan T. Bagley
Keyword(s):  
Drinking Water ◽  
Gastrointestinal Tract ◽  
Surface Waters ◽  
Industrial Effluents ◽  
Opportunistic Pathogen ◽  
Habitat Associations ◽  
Habitat Association ◽  
Klebsiella Species ◽  
Almost All ◽  
Polluted Waters

AbstractThe genus Klebsiella is seemingly ubiquitous in terms of its habitat associations. Klebsiella is a common opportunistic pathogen for humans and other animals, as well as being resident or transient flora (particularly in the gastrointestinal tract). Other habitats include sewage, drinking water, soils, surface waters, industrial effluents, and vegetation. Until recently, almost all these Klebsiella have been identified as one species, ie, K. pneumoniae. However, phenotypic and genotypic studies have shown that “K. pneumoniae” actually consists of at least four species, all with distinct characteristics and habitats. General habitat associations of Klebsiella species are as follows: K. pneumoniae—humans, animals, sewage, and polluted waters and soils; K. oxytoca—frequent association with most habitats; K. terrigena— unpolluted surface waters and soils, drinking water, and vegetation; K. planticola—sewage, polluted surface waters, soils, and vegetation; and K. ozaenae/K. rhinoscleromatis—infrequently detected (primarily with humans).

SEM Cold Stage Techniques for the Observation of Vegetative and Floral Apices of Oat (Avena sativa L.) Plants

1977 ◽  
Vol 35 ◽  
pp. 590-591
Author(s):  
B. K. Kirchoff ◽  
L.F. Allard ◽  
W.C. Bigelow
Keyword(s):  
Critical Point ◽  
Avena Sativa ◽  
Substantial Improvement ◽  
Fresh Tissue ◽  
Cold Stage ◽  
Critical Point Drying ◽  
Almost All ◽  
Cell Collapse ◽  
Conductive Paint ◽  
Carbon Based

In attempting to use the SEM to investigate the transition from the vegetative to the floral state in oat (Avena sativa L.) it was discovered that the procedures of fixation and critical point drying (CPD), and fresh tissue examination of the specimens gave unsatisfactory results. In most cases, by using these techniques, cells of the tissue were collapsed or otherwise visibly distorted. Figure 1 shows the results of fixation with 4.5% formaldehyde-gluteraldehyde followed by CPD. Almost all cellular detail has been obscured by the resulting shrinkage distortions. The larger cracks seen on the left of the picture may be due to dissection damage, rather than CPD. The results of observation of fresh tissue are seen in Fig. 2. Although there is a substantial improvement over CPD, some cell collapse still occurs.Due to these difficulties, it was decided to experiment with cold stage techniques. The specimens to be observed were dissected out and attached to the sample stub using a carbon based conductive paint in acetone.

Electron microscopy studies of plasma-sprayed materials

1983 ◽  
Vol 41 ◽  
pp. 70-71
Author(s):  
K.R. Subramanian ◽  
A.H. King ◽  
H. Herman
Keyword(s):  
Plasma Spraying ◽  
Substrate Surface ◽  
Flame Temperature ◽  
Ceramic Coatings ◽  
Metallic Substrates ◽  
Hot Plasma ◽  
Almost All ◽  
Plasma Sprayed ◽  
Hostile Environments ◽  
Plasma Spraying Process

Plasma spraying is a technique which is used to apply coatings to metallic substrates for a variety of purposes, including hardfacing, corrosion resistance and thermal barrier applications. Almost all of the applications of this somewhat esoteric fabrication technique involve materials in hostile environments and the integrity of the coatings is of paramount importance: the effects of process variables on such properties as adhesive strength, cohesive strength and hardness of the substrate/coating system, however, are poorly understood.Briefly, the plasma spraying process involves forming a hot plasma jet with a maximum flame temperature of approximately 20,000K and a gas velocity of about 40m/s. Into this jet the coating material is injected, in powder form, so it is heated and projected at the substrate surface. Relatively thick metallic or ceramic coatings may be speedily built up using this technique.

Vacuum System to Minimize the Specimen Contamination of High-Performance EM

1977 ◽  
Vol 35 ◽  
pp. 68-69
Author(s):  
N. Yoshimura ◽  
K. Shirota ◽  
T. Etoh
Keyword(s):  
Electron Microscope ◽  
High Speed ◽  
High Performance ◽  
High Vacuum ◽  
Vacuum System ◽  
Pump System ◽  
Pumping System ◽  
Diffusion Pump ◽  
Almost All ◽  
Cascade Type

One of the most important requirements for a high-performance EM, especially an analytical EM using a fine beam probe, is to prevent specimen contamination by providing a clean high vacuum in the vicinity of the specimen. However, in almost all commercial EMs, the pressure in the vicinity of the specimen under observation is usually more than ten times higher than the pressure measured at the punping line. The EM column inevitably requires the use of greased Viton O-rings for fine movement, and specimens and films need to be exchanged frequently and several attachments may also be exchanged. For these reasons, a high speed pumping system, as well as a clean vacuum system, is now required. A newly developed electron microscope, the JEM-100CX features clean high vacuum in the vicinity of the specimen, realized by the use of a CASCADE type diffusion pump system which has been essentially improved over its predeces- sorD employed on the JEM-100C.

Quantitative Freeze Fracture Studies of Gap Junctions in Somatic Cell Hybrids, Their Parents, and Revertants

1976 ◽  
Vol 34 ◽  
pp. 218-219
Author(s):  
W. J. Larsen ◽  
R. Azarnia ◽  
W. R. Loewenstein
Keyword(s):  
Gap Junctions ◽  
Striated Muscle ◽  
Freeze Fracture ◽  
Cell Movement ◽  
Dye Molecules ◽  
Somatic Cell Hybrids ◽  
Cell Coupling ◽  
Normal Cells ◽  
Mediate Cell ◽  
Almost All

Although the physiological significance of the gap junction remains unspecified, these membrane specializations are now recognized as common to almost all normal cells (excluding adult striated muscle and some nerve cells) and are found in organisms ranging from the coelenterates to man. Since it appears likely that these structures mediate the cell-to-cell movement of ions and small dye molecules in some electrical tissues, we undertook this study with the objective of determining whether gap junctions in inexcitable tissues also mediate cell-to-cell coupling.To test this hypothesis, a coupling, human Lesh-Nyhan (LN) cell was fused with a non-coupling, mouse cl-1D cell, and the hybrids, revertants, and parental cells were analysed for coupling with respect both to ions and fluorescein and for membrane junctions with the freeze fracture technique.

Analytical Electron Microscopy Study of Second-Phase Particles in 7075 and 7475 Aluminum Alloys

1985 ◽  
Vol 43 ◽  
pp. 348-349
Author(s):  
M. Raghavan ◽  
J. Y. Koo ◽  
J. W. Steeds ◽  
B. K. Park
Keyword(s):  
Aluminum Alloys ◽  
Silicon Oxide ◽  
Analytical Electron Microscopy ◽  
Microscopy Study ◽  
Electron Microscopy Study ◽  
Partial Substitution ◽  
Second Phase ◽  
X Ray ◽  
Second Phase Particles ◽  
Almost All

X-ray microanalysis and Convergent Beam Electron Diffraction (CBD) studies were conducted to characterize the second phase particles in two commercial aluminum alloys -- 7075 and 7475. The second phase particles studied were large (approximately 2-5μm) constituent phases and relatively fine ( ∼ 0.05-1μn) dispersoid particles, Figures 1A and B. Based on the crystal structure and chemical composition analyses, the constituent phases found in these alloys were identified to be Al7Cu2Fe, (Al,Cu)6(Fe,Cu), α-Al12Fe3Si, Mg2Si, amorphous silicon oxide and the modified 6Fe compounds, in decreasing order of abundance. The results of quantitative X-ray microanalysis of all the constituent phases are listed in Table I. The data show that, in almost all the phases, partial substitution of alloying elements occurred resulting in small deviations from the published stoichiometric compositions of the binary and ternary compounds.

High-resolution scanning electron microscopy in biology

1990 ◽  
Vol 48 (3) ◽  
pp. 14-15
Author(s):  
Keiichi Tanaka
Keyword(s):  
High Resolution ◽  
Immunoglobulin M ◽  
Metal Coating ◽  
Biological Macromolecules ◽  
Ultrahigh Resolution ◽  
Preparation Methods ◽  
Low Contrast ◽  
Almost All ◽  
Charging Effect ◽  
Scanning Electron

With the development of scanning electron microscope (SEM) with ultrahigh resolution, SEM became to play an important role in not only cytology but also molecular biology. However, the preparation methods observing tiny specimens with such high resolution SEM are not yet established.Although SEM specimens are usually coated with metals for getting electrical conductivity, it is desirable to avoid the metal coating for high resolution SEM, because the coating seriously affects resolution at this level, unless special coating techniques are used. For avoiding charging effect without metal coating, we previously reported a method in which polished carbon plates were used as substrate. In the case almost all incident electrons penetrate through the specimens and do not accumulate in them, when the specimens are smaller than 10nm. By this technique some biological macromolecules including ribosomes, ferritin, immunoglobulin G were clearly observed.Unfortunately some other molecules such as apoferritin, thyroglobulin and immunoglobulin M were difficult to be observed only by the method, because they had very low contrast and were easily damaged by electron beam.

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