The true order of magnitude of Lamé rounding error sums

2002 ◽  
Vol 79 (6) ◽  
pp. 534-542
Author(s):  
G. Kuba
Keyword(s):  
Rounding Error ◽  
Order Of Magnitude ◽  
True Order

Lattice points in bodies of rotation with a dent

2016 ◽  
Vol 12 (02) ◽  
pp. 567-583
Author(s):  
Werner Georg Nowak
Keyword(s):  
Lattice Points ◽  
Real Parameter ◽  
General Body ◽  
Convex Case ◽  
Order Of Magnitude ◽  
True Order

In the sense of the theory of lattice points in large bodies, a fairly general body of rotation [Formula: see text] in [Formula: see text] is considered whose convexity is being hampered by a “dent” (see Fig. 1). It turns out that, for [Formula: see text] a large real parameter, the true order of magnitude of the lattice discrepancy of [Formula: see text] essentially can be evaluated, contrary to the convex case.

scholarly journals On the distribution of reducible polynomials

2009 ◽  
Vol 59 (3) ◽  
Author(s):  
Gerald Kuba
Keyword(s):  
Irreducible Factor ◽  
Order Of Magnitude ◽  
True Order

AbstractLet ℛn(t) denote the set of all reducible polynomials p(X) over ℤ with degree n ≥ 2 and height ≤ t. We determine the true order of magnitude of the cardinality |ℛn(t)| of the set ℛn(t) by showing that, as t → ∞, t 2 log t ≪ |ℛ2(t)| ≪ t 2 log t and t n ≪ |ℛn(t)| ≪ t n for every fixed n ≥ 3. Further, for 1 < n/2 < k < n fixed let ℛk,n(t) ⊂ ℛn(t) such that p(X) ∈ ℛk,n(t) if and only if p(X) has an irreducible factor in ℤ[X] of degree k. Then, as t → ∞, we always have t k+1 ≪ |ℛk,n(t)| ≪ t k+1 and hence |ℛn−1,n (t)| ≫ |ℛn(t)| so that ℛn−1,n (t) is the dominating subclass of ℛn(t) since we can show that |ℛn(t)∖ℛn−1,n (t)| ≪ t n−1(log t)2.On the contrary, if R ns(t) is the total number of all polynomials in ℛn(t) which split completely into linear factors over ℤ, then t 2(log t)n−1 ≪ R ns(t) ≪ t 2 (log t)n−1 (t → ∞) for every fixed n ≥ 2.

A controller for safe, convenient operation of LaB6 emitters on electron-beam instruments

1983 ◽  
Vol 41 ◽  
pp. 408-409
Author(s):  
W. J. Abramson ◽  
H. W. Estry ◽  
L. F. Allard
Keyword(s):  
Electron Beam ◽  
Control System ◽  
Thermal Shock ◽  
Appropriate Care ◽  
Electron Guns ◽  
Tungsten Filaments ◽  
Order Of Magnitude ◽  
Main Components

LaB6 emitters are becoming increasingly popular as direct replacements for tungsten filaments in the electron guns of modern electron-beam instruments. These emitters offer order of magnitude increases in beam brightness, and, with appropriate care in operation, a corresponding increase in source lifetime. They are, however, an order of magnitude more expensive, and may be easily damaged (by improper vacuum conditions and thermal shock) during saturation/desaturation operations. These operations typically require several minutes of an operator's attention, which becomes tedious and subject to error, particularly since the emitter must be cooled during sample exchanges to minimize damage from random vacuum excursions. We have designed a control system for LaBg emitters which relieves the operator of the necessity for manually controlling the emitter power, minimizes the danger of accidental improper operation, and makes the use of these emitters routine on multi-user instruments.Figure 1 is a block schematic of the main components of the control system, and Figure 2 shows the control box.

Novel magneto-optical recording materials: Bi-substituted garnet films

1991 ◽  
Vol 49 ◽  
pp. 776-777
Author(s):  
Takao Suzuki ◽  
Hossein Nuri
Keyword(s):  
Grain Size ◽  
Amorphous Film ◽  
Nitrogen Atmosphere ◽  
Optical Recording ◽  
Garnet Film ◽  
Media Noise ◽  
Garnet Films ◽  
Order Of Magnitude ◽  
A New Technique ◽  
A Current

For future high density magneto-optical recording materials, a Bi-substituted garnet film ((BiDy)3(FeGa)5O12) is an attractive candidate since it has strong magneto-optic effect at short wavelengths less than 600 nm. The signal in read back performance at 500 nm using a garnet film can be an order of magnitude higher than a current rare earth-transition metal amorphous film. However, the granularity and surface roughness of such crystalline garnet films are the key to control for minimizing media noise.We have demonstrated a new technique to fabricate a garnet film which has much smaller grain size and smoother surfaces than those annealed in a conventional oven. This method employs a high ramp-up rate annealing (Γ = 50 ~ 100 C/s) in nitrogen atmosphere. Fig.1 shows a typical microstruture of a Bi-susbtituted garnet film deposited by r.f. sputtering and then subsequently crystallized by a rapid thermal annealing technique at Γ = 50 C/s at 650 °C for 2 min. The structure is a single phase of garnet, and a grain size is about 300A.

Atomic-level imaging of the surface structure of Ag2O

1984 ◽  
Vol 42 ◽  
pp. 656-657
Author(s):  
William Krakow
Keyword(s):  
High Vacuum ◽  
Atomic Level ◽  
Ultra High Vacuum ◽  
Research Groups ◽  
Resolution Electron ◽  
Surface Reconstructions ◽  
Order Of Magnitude ◽  
High Resolution Electron Microscope ◽  
Saturated Structure ◽  
Transmission And Reflection

In recent years electron microscopy has been used to image surfaces in both the transmission and reflection modes by many research groups. Some of this work has been performed under ultra high vacuum conditions (UHV) and apparent surface reconstructions observed. The level of resolution generally has been at least an order of magnitude worse than is necessary to visualize atoms directly and therefore the detailed atomic rearrangements of the surface are not known. The present author has achieved atomic level resolution under normal vacuum conditions of various Au surfaces. Unfortunately these samples were exposed to atmosphere and could not be cleaned in a standard high resolution electron microscope. The result obtained surfaces which were impurity stabilized and reveal the bulk lattice (1x1) type surface structures also encountered by other surface physics techniques under impure or overlayer contaminant conditions. It was therefore decided to study a system where exposure to air was unimportant by using a oxygen saturated structure, Ag2O, and seeking to find surface reconstructions, which will now be described.

Near-field scanning optical microscopy

1986 ◽  
Vol 44 ◽  
pp. 642-643
Author(s):  
E. Betzig ◽  
A. Harootunian ◽  
M. Isaacson ◽  
A. Lewis
Keyword(s):  
Near Field ◽  
Optical Microscope ◽  
Visible Radiation ◽  
Field Methods ◽  
Optical Elements ◽  
Optical Region ◽  
Order Of Magnitude ◽  
Nondestructive Imaging ◽  
Scanning Optical Microscopy ◽  
Near Field Scanning

In general, conventional methods of optical imaging are limited in spatial resolution by either the wavelength of the radiation used or by the aberrations of the optical elements. This is true whether one uses a scanning probe or a fixed beam method. The reason for the wavelength limit of resolution is due to the far field methods of producing or detecting the radiation. If one resorts to restricting our probes to the near field optical region, then the possibility exists of obtaining spatial resolutions more than an order of magnitude smaller than the optical wavelength of the radiation used. In this paper, we will describe the principles underlying such "near field" imaging and present some preliminary results from a near field scanning optical microscope (NS0M) that uses visible radiation and is capable of resolutions comparable to an SEM. The advantage of such a technique is the possibility of completely nondestructive imaging in air at spatial resolutions of about 50nm.

Detection, Averaging, and 3D Reconstruction of Biological Specimens on Hypercubes (Transputer-based) Computers

1990 ◽  
Vol 48 (1) ◽  
pp. 454-455
Author(s):  
Jose-Maria Carazo ◽  
I. Benavides ◽  
S. Marco ◽  
J.L. Carrascosa ◽  
E.L. Zapata
Keyword(s):  
3D Reconstruction ◽  
3D Structure ◽  
Three Dimensional ◽  
Software Tools ◽  
Mapping Method ◽  
Computer Architectures ◽  
Parallel Computer ◽  
Reconstruction Process ◽  
Computing Power ◽  
Order Of Magnitude

Obtaining the three-dimensional (3D) structure of negatively stained biological specimens at a resolution of, typically, 2 - 4 nm is becoming a relatively common practice in an increasing number of laboratories. A combination of new conceptual approaches, new software tools, and faster computers have made this situation possible. However, all these 3D reconstruction processes are quite computer intensive, and the middle term future is full of suggestions entailing an even greater need of computing power. Up to now all published 3D reconstructions in this field have been performed on conventional (sequential) computers, but it is a fact that new parallel computer architectures represent the potential of order-of-magnitude increases in computing power and should, therefore, be considered for their possible application in the most computing intensive tasks.We have studied both shared-memory-based computer architectures, like the BBN Butterfly, and local-memory-based architectures, mainly hypercubes implemented on transputers, where we have used the algorithmic mapping method proposed by Zapata el at. In this work we have developed the basic software tools needed to obtain a 3D reconstruction from non-crystalline specimens (“single particles”) using the so-called Random Conical Tilt Series Method. We start from a pair of images presenting the same field, first tilted (by ≃55°) and then untilted. It is then assumed that we can supply the system with the image of the particle we are looking for (ideally, a 2D average from a previous study) and with a matrix describing the geometrical relationships between the tilted and untilted fields (this step is now accomplished by interactively marking a few pairs of corresponding features in the two fields). From here on the 3D reconstruction process may be run automatically.

The Effect of Adrenaline Infusions on Blood Coagulation in Normal and Haemophilia B Dogs

1966 ◽  
Vol 15 (03/04) ◽  
pp. 349-364 ◽  
Author(s):  
A.H Özge ◽  
H.C Rowsell ◽  
H.G Downie ◽  
J.F Mustard
Keyword(s):  
Body Weight ◽  
Factor Viii ◽  
Factor Ix ◽  
Clotting Factor ◽  
Blood Ph ◽  
Order Of Magnitude ◽  
Dose Dependent ◽  
Generation Test ◽  
Plasma Activity

SummaryThe addition of trace amounts of adrenaline to whole blood in plasma in vitro increased factor VIII, factor IX and whole plasma activity in the thromboplastin generation test. This was dose dependent.Adrenaline infusions less than 22 (μg/kg body weight in normal dogs accelerated clotting, increased factor IX, factor VIII and whole plasma activity in the thromboplastin generation test and caused a fall in blood pH. In a factor IX deficient dog, there was no increase in factor IX activity. After adrenaline infusions, however, the other changes occurred and were of the same order of magnitude as in the normal. Adrenaline in doses greater than 22 μg/kg body weight did not produce as great an effect on clotting in normal or factor IX deficient dogs. The platelet count in the peripheral blood was increased following the infusion of all doses of adrenaline. These observations suggest that the accelerating effect of adrenaline on clotting is not mediated through increase in activity of a specific clotting factor.

Development of a method for multielemental determination in water by EDXRF with radioisotopic source of 238Pu.

2019 ◽  
Vol 7 (2A) ◽  
Author(s):  
Camilo Fuentes Serrano ◽  
Juan Reinaldo Estevez Alvares ◽  
Alfredo Montero Alvarez ◽  
Ivan Pupo Gonzales ◽  
Zahily Herrero Fernandez ◽  
...  
Keyword(s):  
Thin Layer ◽  
Expanded Uncertainty ◽  
Considerable Decrease ◽  
X Ray ◽  
Precipitation Efficiency ◽  
Method Of Determination ◽  
Sensitivity Curves ◽  
Order Of Magnitude ◽  
Metrological Parameters

A method for determination of Cr, Fe, Co, Ni, Cu, Zn, Hg and Pb in waters by Energy Dispersive X Ray Fluorescence (EDXRF) was implemented, using a radioisotopic source of 238Pu. For previous concentration was employed a procedure including a coprecipitation step with ammonium pyrrolidinedithiocarbamate (APDC) as quelant agent, the separation of the phases by filtration, the measurement of filter by EDXRF and quantification by a thin layer absolute method. Sensitivity curves for K and L lines were obtained respectively. The sensitivity for most elements was greater by an order of magnitude in the case of measurement with a source of 238Pu instead of 109Cd, which means a considerable decrease in measurement times. The influence of the concentration in the precipitation efficiency was evaluated for each element. In all cases the recoveries are close to 100%, for this reason it can be affirmed that the method of determination of the studied elements is quantitative. Metrological parameters of the method such as trueness, precision, detection limit and uncertainty were calculated. A procedure to calculate the uncertainty of the method was elaborated; the most significant source of uncertainty for the thin layer EDXRF method is associated with the determination of instrumental sensitivities. The error associated with the determination, expressed as expanded uncertainty (in %), varied from 15.4% for low element concentrations (2.5-5 μg/L) to 5.4% for the higher concentration range (20-25 μg/L).

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