scholarly journals Some new results on the weaving of K-g-frames in Hilbert spaces

2021 ◽  
Vol 19 (1) ◽  
pp. 1315-1329
Author(s):  
Zhong-Qi Xiang
Keyword(s):  
Hilbert Spaces ◽  
Perturbation Result ◽  
New Methods ◽  
Whole Space ◽  
New Perturbation

Abstract In this paper, we provide some conditions for a K-woven pair of K-g-frames to be preserved under an operator and particularly, we report that applying two different operators to a K-woven pair of K-g-frames can leave them K-woven. Several new methods on the construction of K-woven pair of K-g-frames are also given. We end the paper with a new perturbation result on the weaving of K-g-frames, which shows that, under the perturbation condition involved in one known result on this topic, two K-g-frames can be K-woven in the whole space, not merely in the subspace Range(K).

scholarly journals Some New Characterizations andg-Minimality and Stability ofg-Bases in the Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xunxiang Guo
Keyword(s):  
Hilbert Spaces ◽  
Frame Theory ◽  
Schauder Basis ◽  
Simple Condition ◽  
Similar Role ◽  
Perturbation Result

The concept ofg-basis in the Hilbert spaces is introduced by Guo (2012) who generalizes the Schauder basis in the Hilbert spaces.g-basis plays the similar role ing-frame theory to that the Schauder basis plays in frame theory. In this paper, we establish some important properties ofg-bases in the Hilbert spaces. In particular, we obtain a simple condition under which some important properties established in Guo (2012) are still true. With these conditions, we also establish some new interesting properties ofg-bases which are related tog-minimality. Finally, we obtain a perturbation result aboutg-bases.

scholarly journals Finding Minimum Norm Fixed Point of Nonexpansive Mappings and Applications

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Xue Yang ◽  
Yeong-Cheng Liou ◽  
Yonghong Yao
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Minimum Norm ◽  
New Methods

We construct two new methods for finding the minimum norm fixed point of nonexpansive mappings in Hilbert spaces. Some applications are also included.

FUSION FRAMES AND g-FRAMES IN HILBERT C*-MODULES

2008 ◽  
Vol 06 (03) ◽  
pp. 433-446 ◽  
Author(s):  
AMIR KHOSRAVI ◽  
BEHROOZ KHOSRAVI
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Hilbert Spaces ◽  
Frame Theory ◽  
Fusion Frames ◽  
Perturbation Result ◽  
Fusion Frame

The notion of frame has some generalizations such as frames of subspaces, fusion frames and g-frames. In this paper, we introduce fusion frames and g-frames in Hilbert C*-modules and we show that they share many useful properties with their corresponding notions in Hilbert space. We also generalize a perturbation result in frame theory to g-frames in Hilbert spaces. We also show that tensor product of fusion frames (g-frames) is a fusion frame (g-frame) and tensor product of resolution of identity is a resolution of identity.

g-FRAMES AND MODULAR RIESZ BASES IN HILBERT C*-MODULES

2012 ◽  
Vol 10 (02) ◽  
pp. 1250013 ◽  
Author(s):  
AMIR KHOSRAVI ◽  
BEHROOZ KHOSRAVI
Keyword(s):  
Hilbert Spaces ◽  
Riesz Basis ◽  
Riesz Bases ◽  
Parseval Frame ◽  
C Algebra ◽  
Perturbation Result ◽  
Natural Way

In this paper we introduce modular Riesz basis, modular g-Riesz basis in Hilbert C*-modules in a very natural way and we show that they share many properties with Riesz basis and g-Riesz basis in Hilbert spaces. We also found that by using the fact that every finitely or countably generated Hilbert C*-module over a unital C*-algebra has a standard Parseval frame, we characterize g-frames, modular Riesz bases and modular g-Riesz bases. Finally we obtain a perturbation result for modular g-Riesz bases.

Replication of Wet Objects and Cells

1974 ◽  
Vol 32 ◽  
pp. 102-103
Author(s):  
S. Basu ◽  
D. F. Parsons
Keyword(s):  
Water Vapor Pressure ◽  
High Vacuum ◽  
Polystyrene Latex ◽  
Vacuum System ◽  
Saturated Water Vapor ◽  
Replication Method ◽  
New Methods ◽  
Saturated Water ◽  
Water Vapors ◽  
Intermediate Chamber

We are approaching the invasiveness of cancer cells from the studies of their wet surface morphology which should distinguish them from their normal counterparts. In this report attempts have been made to provide physical basis and background work to a wet replication method with a differentially pumped hydration chamber (Fig. 1) (1,2), to apply this knowledge for obtaining replica of some specimens of known features (e.g. polystyrene latex) and finally to realize more specific problems and to improvize new methods and instrumentation for their rectification. In principle, the evaporant molecules penetrate through a pair of apertures (250, 350μ), through water vapors and is, then, deposited on the specimen. An intermediate chamber between the apertures is pumped independently of the high vacuum system. The size of the apertures is sufficiently small so that full saturated water vapor pressure is maintained near the specimen.

A Freeze Shadow Technique for the Preparation of Soft Paint Latexes for Electron Microscopy

1977 ◽  
Vol 35 ◽  
pp. 314-315
Author(s):  
Earl R. Walter ◽  
Glen H. Bryant
Keyword(s):  
Sample Preparation ◽  
High Vacuum ◽  
Vacuum System ◽  
Latex Particles ◽  
New Methods ◽  
Diffusion Pump ◽  
Film Forming ◽  
Routine Basis ◽  
Distribution Studies ◽  
Preparation Techniques

With the development of soft, film forming latexes for use in paints and other coatings applications, it became desirable to develop new methods of sample preparation for latex particle size distribution studies with the electron microscope. Conventional latex sample preparation techniques were inadequate due to the pronounced tendency of these new soft latex particles to distort, flatten and fuse on the substrate when they dried. In order to avoid these complications and obtain electron micrographs of undistorted latex particles of soft resins, a freeze-dry, cold shadowing technique was developed. The method has now been used in our laboratory on a routine basis for several years.The cold shadowing is done in a specially constructed vacuum system, having a conventional mechanical fore pump and oil diffusion pump supplying vacuum. The system incorporates bellows type high vacuum valves to permit a prepump cycle and opening of the shadowing chamber without shutting down the oil diffusion pump. A baffeled sorption trap isolates the shadowing chamber from the pumps.

Directional observation on lipid of male nectary of Lindera megaphylla hemsl. by the rapid embedding method with polyethylene glycol (PEG)

1990 ◽  
Vol 48 (3) ◽  
pp. 718-719
Author(s):  
Dai Dalin ◽  
Guo Jianmin
Keyword(s):  
Electron Microscope ◽  
Polyethylene Glycol ◽  
Chemical Reaction ◽  
Traditional Method ◽  
Osmium Tetroxide ◽  
Unsaturated Lipid ◽  
Embedding Method ◽  
Long Period ◽  
New Methods

Lipid cytochemistry has not yet advanced far at the EM level. A major problem has been the loss of lipid during dehydration and embedding. Although the adoption of glutaraldehyde and osmium tetroxide accelerate the chemical reaction of lipid and osmium tetroxide can react on the double bouds of unsaturated lipid to from the osmium black, osmium tetroxide can be reduced in saturated lipid and subsequently some of unsaturated lipid are lost during dehydration. In order to reduce the loss of lipid by traditional method, some researchers adopted a few new methods, such as the change of embedding procedure and the adoption of new embedding media, to solve the problem. In a sense, these new methods are effective. They, however, usually require a long period of preparation. In this paper, we do research on the fiora nectary strucure of lauraceae by the rapid-embedding method wwith PEG under electron microscope and attempt to find a better method to solve the problem mentioned above.

Confronting the grey zone after severe brain injury

2019 ◽  
Vol 3 (6) ◽  
pp. 707-711 ◽  
Author(s):  
Andrew Peterson ◽  
Adrian M. Owen
Keyword(s):  
Brain Injury ◽  
Ethical Issues ◽  
Vegetative State ◽  
Clinical Care ◽  
Grey Zone ◽  
Severe Brain Injury ◽  
New Methods ◽  
Legal Decision Making ◽  
Technological Developments ◽  
The Brain

In recent years, rapid technological developments in the field of neuroimaging have provided several new methods for revealing thoughts, actions and intentions based solely on the pattern of activity that is observed in the brain. In specialized centres, these methods are now being employed routinely to assess residual cognition, detect consciousness and even communicate with some behaviorally non-responsive patients who clinically appear to be comatose or in a vegetative state. In this article, we consider some of the ethical issues raised by these developments and the profound implications they have for clinical care, diagnosis, prognosis and medical-legal decision-making after severe brain injury.

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