New methods based on ℋ-tensors for identifying positive definiteness of homogeneous polynomial forms

2019 ◽  
Vol 68 (12) ◽  
pp. 2473-2483
Author(s):  
Deshu Sun
Keyword(s):  
Homogeneous Polynomial ◽  
Positive Definiteness ◽  
New Methods

A CLASS OF MODIFIED BFGS METHODS WITH FUNCTION VALUE INFORMATION FOR UNCONSTRAINED OPTIMIZATION

2013 ◽  
Vol 30 (06) ◽  
pp. 1350024 ◽  
Author(s):  
HAO LIU ◽  
HAI-JUN WANG ◽  
XIAO-YAN QIAN ◽  
QING-SHENG SHI
Keyword(s):  
Superlinear Convergence ◽  
Positive Definiteness ◽  
Standard Test ◽  
Test Problems ◽  
Convergence Properties ◽  
Interpolation Model ◽  
New Methods ◽  
Quadratic Interpolation ◽  
Global And Local ◽  
Quasi Newton

Based on some new interpolation conditions, a quadratic interpolation model is constructed to approximate the objective function, and then a class of modified BFGS methods with function value information is presented. The new methods satisfy some new weak secant equations and there is a parameter γ in the update formulae which ranges from zero to one. The global and local superlinear convergence properties of the new modified BFGS methods are proved. Numerical results for standard test problems from CUTE are reported, which indicate that all the methods in the proposed class perform well. Ensuring the sufficient positive definiteness of the updating matrices, an adaptive BFGS quasi-Newton method by dynamically choosing the parameter γ is proposed, which may be competitive with other BFGS modifications.

scholarly journals An optimal $ Z $-eigenvalue inclusion interval for a sixth-order tensor and its an application

2021 ◽  
Vol 7 (1) ◽  
pp. 967-985
Author(s):  
Tinglan Yao ◽  
Keyword(s):  
Homogeneous Polynomial ◽  
Symmetric Tensor ◽  
Positive Definiteness ◽  
Polynomial Systems ◽  
Sixth Order ◽  
Invariant Polynomial ◽  
Sufficient Condition ◽  
Order Tensor ◽  
Inclusion Interval ◽  
Time Invariant

<abstract><p>An optimal $ Z $-eigenvalue inclusion interval for a sixth-order tensor is presented. As an application, a sufficient condition for the positive definiteness of a sixth-order real symmetric tensor (also a homogeneous polynomial form) is obtained, which is used to judge the asymptotically stability of time-invariant polynomial systems.</p></abstract>

scholarly journals New iterative codes for 𝓗-tensors and an application

2016 ◽  
Vol 14 (1) ◽  
pp. 212-220 ◽  
Author(s):  
Feng Wang ◽  
Deshu Sun
Keyword(s):  
Homogeneous Polynomial ◽  
Sufficient Conditions ◽  
Symmetric Tensor ◽  
Positive Definiteness ◽  
Polynomial Form ◽  
Numerical Examples ◽  
Even Order

AbstractNew iterative codes for identifying 𝓗 -tensor are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor, i.e., an even-degree homogeneous polynomial form are given. Advantages of results obtained are illustrated by numerical examples.

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.

F. New Methods of Disinfection and Sterilization

2000 ◽  
Vol 12 (4) ◽  
pp. 380-380
Author(s):  
Kazuei Ogoshi ◽  
Taiji Akamatsu ◽  
Hiroyasu Iishi ◽  
Daizo Saito ◽  
Nobuhiro Sakaki ◽  
...  
Keyword(s):  
New Methods
Sign in / Sign up

Export Citation Format

Share Document