scholarly journals Recent developments in the theory of function spaces

1986 ◽  
pp. 95-106
Author(s):  
H. Triebel
Keyword(s):  
Function Spaces ◽  
Recent Developments

scholarly journals Continuity envelopes of spaces of generalised smoothness: a limiting case; embeddings and approximation numbers

2005 ◽  
Vol 3 (1) ◽  
pp. 33-71 ◽  
Author(s):  
António M. Caetano ◽  
Dorothee D. Haroske
Keyword(s):  
Asymptotic Behaviour ◽  
Function Spaces ◽  
Approximation Numbers ◽  
Local Growth ◽  
Recent Developments ◽  
Limiting Case ◽  
Growth Envelopes

Continuity envelopes for the spaces of generalised smoothnessBpq(s,Ψ)(ℝn)andFpq(s,Ψ)(ℝn)are studied in the so-called supercriticals=1+n/p, paralleling recent developments for a corresponding limiting case for local growth envelopes of spaces of such a type. In addition, the power of the concept is used in proving conditions for some embeddings between function spaces to hold, as well as in the study of the asymptotic behaviour of approximation numbers of related embeddings.

scholarly journals Recent Developments on Fixed Point Theory in Function Spaces and Applications to Control and Optimization Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-2
Author(s):  
Hemant Kumar Nashine ◽  
Mujahid Abbas ◽  
Marlène Frigon ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Optimization Problems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Function Spaces ◽  
Recent Developments

scholarly journals GENERALIZED FRACTAL TRANSFORMS AND SELF-SIMILARITY: RECENT RESULTS AND APPLICATIONS

2011 ◽  
Vol 30 (2) ◽  
pp. 63 ◽  
Author(s):  
Davide La Torre ◽  
Edward R. Vrscay
Keyword(s):  
Image Processing ◽  
Image Analysis ◽  
Image Coding ◽  
Function Spaces ◽  
Base Space ◽  
Self Similarity ◽  
Fractal Image ◽  
Fractal Image Coding ◽  
Recent Developments ◽  
Image Function

Most practical as well as theoretical works in image processing and mathematical imaging consider images as real-valued functions, u : X → ℝg, where X denotes the base space or pixel space over which the images are defined and ℝg ⊂ ℝ is a suitable greyscale space. A variety of function spaces ℱ(X) may be considered depending on the application. Fractal image coding seeks to approximate an image function as a union of spatially-contracted and greyscale-modified copies of subsets of itself, i.e., u ≈ Tu, where T is the so-called Generalized Fractal Transform (GFT) operator. The aim of this paper is to show some recent developments of the theory of generalized fractal transforms and how they can be used for the purpose of image analysis (compression, denoising). This includes the formulation of fractal transforms over various spaces of multifunctions, i.e., set-valued and measure-valued functions. The latter may be useful in nonlocal image processing.

scholarly journals A Survey on Function Spaces of John–Nirenberg Type

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2264
Author(s):  
Jin Tao ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Systematic Review ◽  
Function Spaces ◽  
Side Length ◽  
Open Questions ◽  
Recent Developments

In this systematic review, the authors give a survey on the recent developments of both the John–Nirenberg space JNp and the space BMO as well as their vanishing subspaces such as VMO, XMO, CMO, VJNp, and CJNp on Rn or a given cube Q0⊂Rn with finite side length. In addition, some related open questions are also presented.

Trends in Electron Energy Loss Spectroscopy

1977 ◽  
Vol 35 ◽  
pp. 228-229
Author(s):  
C. Colliex ◽  
P. Trebbia
Keyword(s):  
Energy Loss ◽  
Electron Energy ◽  
Electron Energy Loss Spectroscopy ◽  
Materials Science ◽  
Analytical Technique ◽  
Recent Developments ◽  
Quantitative Results ◽  
Electron Microscopes ◽  
Electron Energy Loss ◽  
Primary Electrons

The physical foundations for the use of electron energy loss spectroscopy towards analytical purposes, seem now rather well established and have been extensively discussed through recent publications. In this brief review we intend only to mention most recent developments in this field, which became available to our knowledge. We derive also some lines of discussion to define more clearly the limits of this analytical technique in materials science problems.The spectral information carried in both low ( 0<ΔE<100eV ) and high ( >100eV ) energy regions of the loss spectrum, is capable to provide quantitative results. Spectrometers have therefore been designed to work with all kinds of electron microscopes and to cover large energy ranges for the detection of inelastically scattered electrons (for instance the L-edge of molybdenum at 2500eV has been measured by van Zuylen with primary electrons of 80 kV). It is rather easy to fix a post-specimen magnetic optics on a STEM, but Crewe has recently underlined that great care should be devoted to optimize the collecting power and the energy resolution of the whole system.

Filaments and membranes in the mitotic apparatus

1983 ◽  
Vol 41 ◽  
pp. 544-547
Author(s):  
Kent McDonald
Keyword(s):  
Intermediate Filaments ◽  
Mitotic Spindle ◽  
Mitotic Apparatus ◽  
Light Microscope Level ◽  
Microtubule Associated Proteins ◽  
Recent Developments ◽  
Associated Proteins ◽  
Force Generator ◽  
Spindle Function ◽  
Antibody Technology

At the light microscope level the recent developments and interest in antibody technology have permitted the localization of certain non-microtubule proteins within the mitotic spindle, e.g., calmodulin, actin, intermediate filaments, protein kinases and various microtubule associated proteins. Also, the use of fluorescent probes like chlorotetracycline suggest the presence of membranes in the spindle. Localization of non-microtubule structures in the spindle at the EM level has been less rewarding. Some mitosis researchers, e.g., Rarer, have maintained that actin is involved in mitosis movements though the bulk of evidence argues against this interpretation. Others suggest that a microtrabecular network such as found in chromatophore granule movement might be a possible force generator but there is little evidence for or against this view. At the level of regulation of spindle function, Harris and more recently Hepler have argued for the importance of studying spindle membranes. Hepler also believes that membranes might play a structural or mechanical role in moving chromosomes.

Software pattern recognition applied to nanodiffraction patterns from a STEM instrument

1986 ◽  
Vol 44 ◽  
pp. 694-695
Author(s):  
G.Y. Fan ◽  
J.M. Cowley
Keyword(s):  
Image Processing ◽  
Pattern Recognition ◽  
Computer Software ◽  
Processing System ◽  
Light Level ◽  
Host Computer ◽  
Low Light ◽  
Image Processing System ◽  
Recent Developments ◽  
On Line

In recent developments, the ASU HB5 has been modified so that the timing, positioning, and scanning of the finely focused electron probe can be entirely controlled by a host computer. This made the asynchronized handshake possible between the HB5 STEM and the image processing system which consists of host computer (PDP 11/34), DeAnza image processor (IP 5000) which is interfaced with a low-light level TV camera, array processor (AP 400) and various peripheral devices. This greatly facilitates the pattern recognition technique initiated by Monosmith and Cowley. Software called NANHB5 is under development which, instead of employing a set of photo-diodes to detect strong spots on a TV screen, uses various software techniques including on-line fast Fourier transform (FFT) to recognize patterns of greater complexity, taking advantage of the sophistication of our image processing system and the flexibility of computer software.

High-resolution microscopy of twin boundaries in gold

1987 ◽  
Vol 45 ◽  
pp. 260-261
Author(s):  
William Krakow ◽  
David A. Smith
Keyword(s):  
High Resolution ◽  
Specimen Preparation ◽  
Gold Films ◽  
Boundary Area ◽  
Transmission Electron ◽  
Recent Developments ◽  
Tilt Boundaries ◽  
High Resolution Microscopy ◽  
Twist Boundaries

Recent developments in specimen preparation, imaging and image analysis together permit the experimental determination of the atomic structure of certain, simple grain boundaries in metals such as gold. Single crystal, ∼125Å thick, (110) oriented gold films are vapor deposited onto ∼3000Å of epitaxial silver on (110) oriented cut and polished rock salt substrates. Bicrystal gold films are then made by first removing the silver coated substrate and placing in contact two suitably misoriented pieces of the gold film on a gold grid. Controlled heating in a hot stage first produces twist boundaries which then migrate, so reducing the grain boundary area, to give mixed boundaries and finally tilt boundaries perpendicular to the foil. These specimens are well suited to investigation by high resolution transmission electron microscopy.

Recent developments in automated Transmission Electron MI

1989 ◽  
Vol 47 ◽  
pp. 46-47
Author(s):  
W.J. de Ruijter ◽  
P. Rez ◽  
David J. Smith
Keyword(s):  
Image Analysis ◽  
Computer Image ◽  
Lens Design ◽  
Computer Image Analysis ◽  
Transmission Electron ◽  
Resolution Electron ◽  
Recent Developments ◽  
On Line ◽  
Routine Procedures ◽  
Near Future

There is growing interest in the on-line use of computers in high-resolution electron n which should reduce the demands on highly skilled operators and thereby extend the r of the technique. An on-line computer could obviously perform routine procedures hand, or else facilitate automation of various restoration, reconstruction and enhan These techniques are slow and cumbersome at present because of the need for cai micrographs and off-line processing. In low resolution microscopy (most biologic; primary incentive for automation and computer image analysis is to create a instrument, with standard programmed procedures. In HREM (materials researc computer image analysis should lead to better utilization of the microscope. Instru (improved lens design and higher accelerating voltages) have improved the interpretab the level of atomic dimensions (approximately 1.6 Å) and instrumental resolutior should become feasible in the near future.

Sign in / Sign up

Export Citation Format

Share Document