scholarly journals COMPACT CARDINALS AND EIGHT VALUES IN CICHOŃ’S DIAGRAM

2018 ◽  
Vol 83 (2) ◽  
pp. 790-803 ◽  
Author(s):  
JAKOB KELLNER ◽  
ANDA RAMONA TĂNASIE ◽  
FABIO ELIO TONTI
Keyword(s):  
Cichoń’S Diagram ◽  
Image Position ◽  
Strongly Compact Cardinals

AbstractAssuming three strongly compact cardinals, it is consistent that$${\aleph _1} < add\left( {\cal N} \right) < cov\left( {\cal N} \right) &#x003C; \mathfrakb &#x003C; \mathfrakd < non\left( {\cal N} \right) < cof\left( {\cal N} \right) < {2^{{\aleph _0}}}.$$Under the same assumption, it is consistent that$${\aleph _1} < add\left( {\cal N} \right) < cov\left( {\cal N} \right) < non\left( {\cal M} \right) < cov\left( {\cal M} \right) < non\left( {\cal N} \right) < cof\left( {\cal N} \right) < {2^{{\aleph _0}}}.$$

scholarly journals THE STRONG TREE PROPERTY AT SUCCESSORS OF SINGULAR CARDINALS

2014 ◽  
Vol 79 (01) ◽  
pp. 193-207 ◽  
Author(s):  
LAURA FONTANELLA
Keyword(s):  
Singular Limit ◽  
Inaccessible Cardinal ◽  
Tree Property ◽  
Supercompact Cardinals ◽  
Singular Cardinals ◽  
Image Position ◽  
Strongly Compact Cardinals

Abstract An inaccessible cardinal is strongly compact if, and only if, it satisfies the strong tree property. We prove that if there is a model of ZFC with infinitely many supercompact cardinals, then there is a model of ZFC where ${\aleph _{\omega + 1}}$ has the strong tree property. Moreover, we prove that every successor of a singular limit of strongly compact cardinals has the strong tree property.

scholarly journals COHERENT SYSTEMS OF FINITE SUPPORT ITERATIONS

2018 ◽  
Vol 83 (1) ◽  
pp. 208-236 ◽  
Author(s):  
VERA FISCHER ◽  
SY D. FRIEDMAN ◽  
DIEGO A. MEJÍA ◽  
DIANA C. MONTOYA
Keyword(s):  
Three Dimensional ◽  
Finite Support ◽  
Coherent Systems ◽  
Cichoń’S Diagram ◽  
Image Position ◽  
Generic Extensions

AbstractWe introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. We use them to produce models of new constellations in Cichoń’s diagram, in particular, a model where the diagram can be separated into 7 different values. Furthermore, we show that this constellation of 7 values is consistent with the existence of a ${\rm{\Delta }}_3^1$ well-order of the reals.

ON ${\omega _1}$-STRONGLY COMPACT CARDINALS

2014 ◽  
Vol 79 (01) ◽  
pp. 266-278 ◽  
Author(s):  
JOAN BAGARIA ◽  
MENACHEM MAGIDOR
Keyword(s):  
Measurable Cardinal ◽  
Second Order ◽  
Singular Cardinal ◽  
Strongly Compact Cardinal ◽  
Compact Cardinal ◽  
Relational Structures ◽  
Uncountable Cardinal ◽  
Image Position ◽  
Strongly Compact Cardinals ◽  
Order Reflection

Abstract An uncountable cardinal κ is called ${\omega _1}$ -strongly compact if every κ-complete ultrafilter on any set I can be extended to an ${\omega _1}$ -complete ultrafilter on I. We show that the first ${\omega _1}$ -strongly compact cardinal, ${\kappa _0}$ , cannot be a successor cardinal, and that its cofinality is at least the first measurable cardinal. We prove that the Singular Cardinal Hypothesis holds above ${\kappa _0}$ . We show that the product of Lindelöf spaces is κ-Lindelöf if and only if $\kappa \ge {\kappa _0}$ . Finally, we characterize ${\kappa _0}$ in terms of second order reflection for relational structures and we give some applications. For instance, we show that every first-countable nonmetrizable space has a nonmetrizable subspace of size less than ${\kappa _0}$ .

Simple Identification of Electron Diffraction Ring Patterns

1969 ◽  
Vol 27 ◽  
pp. 160-161
Author(s):  
Carolyn Nohr ◽  
Ann Ayres
Keyword(s):  
Electron Microscope ◽  
Electron Diffraction ◽  
Diffraction Ring ◽  
Image Position

Texts on electron diffraction recommend that the camera constant of the electron microscope be determine d by calibration with a standard crystalline specimen, using the equation

Atomic orientation effects in proton stopping at low velocity

1983 ◽  
Vol 41 ◽  
pp. 708-709
Author(s):  
Kin Lam
Keyword(s):  
Polycrystalline Material ◽  
Charged Particles ◽  
Target Material ◽  
Stopping Power ◽  
Low Velocity ◽  
Electronic Density ◽  
Interatomic Distances ◽  
Frame Work ◽  
Image Position ◽  
Atomic Orientation

The energy of moving ions in solid is dependent on the electronic density as well as the atomic structural properties of the target material. These factors contribute to the observable effects in polycrystalline material using the scanning ion microscope. Here we outline a method to investigate the dependence of low velocity proton stopping on interatomic distances and orientations.The interaction of charged particles with atoms in the frame work of the Fermi gas model was proposed by Lindhard. For a system of atoms, the electronic Lindhard stopping power can be generalized to the formwhere the stopping power function is defined as

A Magnetic Spectrometer for a Scanning Transmission Electron Microscope

1974 ◽  
Vol 32 ◽  
pp. 436-437
Author(s):  
A. Kosiara ◽  
J. W. Wiggins ◽  
M. Beer
Keyword(s):  
Scanning Transmission Electron Microscope ◽  
Magnetic Spectrometer ◽  
Fringe Field ◽  
Curvature Radius ◽  
Magnetic Pole ◽  
Quadrupole Field ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Under Construction ◽  
Image Position

A magnetic spectrometer to be attached to the Johns Hopkins S. T. E. M. is under construction. Its main purpose will be to investigate electron interactions with biological molecules in the energy range of 40 KeV to 100 KeV. The spectrometer is of the type described by Kerwin and by Crewe Its magnetic pole boundary is given by the equationwhere R is the electron curvature radius. In our case, R = 15 cm. The electron beam will be deflected by an angle of 90°. The distance between the electron source and the pole boundary will be 30 cm. A linear fringe field will be generated by a quadrupole field arrangement. This is accomplished by a grounded mirror plate and a 45° taper of the magnetic pole.

Optimizing conditions for x-ray microchemical analysis in analytical electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 548-549 ◽  
Author(s):  
N. J. Zaluzec
Keyword(s):  
Solid Angle ◽  
Analytical Electron Microscopy ◽  
Incident Beam ◽  
Thin Foil ◽  
Experimental Conditions ◽  
X Ray ◽  
Microchemical Analysis ◽  
Analytical Electron ◽  
Image Position ◽  
Incident Beam Energy

The ultimate sensitivity of microchemical analysis using x-ray emission rests in selecting those experimental conditions which will maximize the measured peak-to-background (P/B) ratio. This paper presents the results of calculations aimed at determining the influence of incident beam energy, detector/specimen geometry and specimen composition on the P/B ratio for ideally thin samples (i.e., the effects of scattering and absorption are considered negligible). As such it is assumed that the complications resulting from system peaks, bremsstrahlung fluorescence, electron tails and specimen contamination have been eliminated and that one needs only to consider the physics of the generation/emission process.The number of characteristic x-ray photons (Ip) emitted from a thin foil of thickness dt into the solid angle dΩ is given by the well-known equation

X-ray microanalysis of thin specimens in the transmission electron microscope at voltages up to 1000 Kv.

1978 ◽  
Vol 36 (1) ◽  
pp. 540-541
Author(s):  
G. Cliff ◽  
M.J. Nasir ◽  
G.W. Lorimer ◽  
N. Ridley
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Weight Fraction ◽  
Present Series ◽  
Constant Independent ◽  
X Ray ◽  
Transmission Electron ◽  
Series Of Experiments ◽  
Image Position ◽  
X Ray Absorption

In a specimen which is transmission thin to 100 kV electrons - a sample in which X-ray absorption is so insignificant that it can be neglected and where fluorescence effects can generally be ignored (1,2) - a ratio of characteristic X-ray intensities, I1/I2 can be converted into a weight fraction ratio, C1/C2, using the equationwhere k12 is, at a given voltage, a constant independent of composition or thickness, k12 values can be determined experimentally from thin standards (3) or calculated (4,6). Both experimental and calculated k12 values have been obtained for K(11<Z>19),kα(Z>19) and some Lα radiation (3,6) at 100 kV. The object of the present series of experiments was to experimentally determine k12 values at voltages between 200 and 1000 kV and to compare these with calculated values.The experiments were carried out on an AEI-EM7 HVEM fitted with an energy dispersive X-ray detector.

SEM analysis of the change in the reaction rates with deposit structures in the copper-iron cementation system

1978 ◽  
Vol 36 (1) ◽  
pp. 456-457
Author(s):  
V. Annamalai ◽  
L.E. Murr
Keyword(s):  
Structural Characteristics ◽  
Secondary Electron Emission ◽  
Copper Deposit ◽  
Reaction Rates ◽  
Sem Analysis ◽  
Experimental Conditions ◽  
Major Drawback ◽  
Emission Mode ◽  
Scrap Iron ◽  
Image Position

Economical recovery of copper metal from leach liquors has been carried out by the simple process of cementing copper onto a suitable substrate metal, such as scrap-iron, since the 16th century. The process has, however, a major drawback of consuming more iron than stoichiometrically needed by the reaction.Therefore, many research groups started looking into the process more closely. Though it is accepted that the structural characteristics of the resultant copper deposit cause changes in reaction rates for various experimental conditions, not many systems have been systematically investigated. This paper examines the deposit structures and the kinetic data, and explains the correlations between them.A simple cementation cell along with rotating discs of pure iron (99.9%) were employed in this study to obtain the kinetic results The resultant copper deposits were studied in a Hitachi Perkin-Elmer HHS-2R scanning electron microscope operated at 25kV in the secondary electron emission mode.

Toward High-Resolution Low-Voltage SEM

1988 ◽  
Vol 46 ◽  
pp. 218-219
Author(s):  
Zhifeng Shao
Keyword(s):  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Limiting Factor ◽  
Operating Voltage ◽  
Probe Radius ◽  
Non Local ◽  
Electron Microscopes ◽  
Image Position ◽  
Scanning Electron Microscopes

Recently, low voltage (≤5kV) scanning electron microscopes have become popular because of their unprecedented advantages, such as minimized charging effects and smaller specimen damage, etc. Perhaps the most important advantage of LVSEM is that they may be able to provide ultrahigh resolution since the interaction volume decreases when electron energy is reduced. It is obvious that no matter how low the operating voltage is, the resolution is always poorer than the probe radius. To achieve 10Å resolution at 5kV (including non-local effects), we would require a probe radius of 5∽6 Å. At low voltages, we can no longer ignore the effects of chromatic aberration because of the increased ratio δV/V. The 3rd order spherical aberration is another major limiting factor. The optimized aperture should be calculated as

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