scholarly journals Reconstruction of the right-hand part of a distributed differential equation using a positional controlled model

2020 ◽  
Vol 30 (4) ◽  
pp. 533-552
Author(s):  
M.S. Blizorukova ◽  
V.I. Maksimov
Keyword(s):  
Dynamical Property ◽  
Second Order ◽  
Hand Part ◽  
Accuracy Of Measurements ◽  
On Line ◽  
Ill Posed ◽  
The Stability ◽  
The Right ◽  
Stable Reconstruction ◽  
Positional Control

In this paper, we consider the stable reconstruction problem of the unknown input of a distributed system of second order by results of inaccurate measurements of its solution. The content of the problem considered is as follows. We consider a distributed equation of second order. The solution of the equation depends on the input varying in the time. The input, as well as the solution, is not given in advance. At discrete times the solution of the equation is measured. These measurements are not accurate in general. It is required to design an algorithm for approximate reconstruction of the input that has dynamical and stability properties. The dynamical property means that the current values of approximations of the input are produced on-line, and the stability property means that the approximations are arbitrarily accurate for a sufficient accuracy of measurements. The problem refers to the class of inverse problems. The algorithm presented in the paper is based on the constructions of a stable dynamical inversion and on the combination of the methods of ill-posed problems and positional control theory.

TOWARDS THE RIGHT HAMILTONIAN FOR SINGULAR PERTURBATIONS VIA REGULARIZATION AND EXTENSION THEORY

1996 ◽  
Vol 08 (05) ◽  
pp. 715-740 ◽  
Author(s):  
HAGEN NEIDHARDT ◽  
VALENTIN ZAGREBNOV
Keyword(s):  
Operator Method ◽  
Stability Domain ◽  
Extension Theory ◽  
Friedrichs Extension ◽  
Natural Domain ◽  
Abstract Operator ◽  
Adjoint Extension ◽  
Ill Posed ◽  
The Stability ◽  
The Right

For singular potentials in quantum mechanics it can happen that the Schrödinger operator is not esssentially self-adjoint on a natural domain, i.e., each self-adjoint extension is a candidate for the right physical Hamiltonian. Traditional way to single out this Hamiltonian is the removing cut-offs for regularizing potential. Connecting regularization and extension theory we develop an abstract operator method to treat the problem of the right Hamiltonian. We show that, using the notion of the maximal (with respect to the perturbation) Friedrichs extension of unperturbed operator, one can classify the above problem as wellposed or ill-posed depending on intersection of the quadratic form domain of perturbation and deficiency subspace corresponding to restriction of unperturbed operator to stability domain. If this intersection is trivial, then the right Hamiltonian is unique: it coincides with the form sum of perturbation and the Friedrich extension of the unperturbed operator restricted to the stability domain. Otherwise it is not unique: the family of “right Hamiltonians” can be described in terms of symmetric extensions reducing the ill-posed problem to the well-posed problem.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

Pemanfaatan Metil Ester Sulfonat pada Pembuatan Deterjen Cair

2016 ◽  
Vol 7 (14) ◽  
pp. 143-155
Author(s):  
Eldha Sampepana ◽  
Suroto Hadi Saputra
Keyword(s):  
Fatty Acids ◽  
Methyl Ester ◽  
Linear Alkylbenzene Sulfonate ◽  
Emulsion Stability ◽  
Alcohol Sulfate ◽  
Stable Emulsion ◽  
Linear Alkylbenzene ◽  
Alkylbenzene Sulfonate ◽  
The Stability ◽  
The Right

In the manufacture of detergents still using surfactants (which serves as an emulsifier) of crude oil in the form of the AS. (alcohol sulfate) and LAS (linear alkylbenzene sulfonate), where this type of surfactant cannot be degraded by microorganisms when discharged into the environment, causing environmental pollution. Methyl ester sulfonate surfactant is an anionic surfactant which has a composition of C16 - C18 fatty acids are capable of acting against nature deterjensinya, while the C12 - C14 fatty acids contribute to the foaming effect. The purpose of this study was to look for the formulation of methyl ester sulfonate (MES) the right to produce a good detergent by using materials such as methyl ester sulfonate surfactant self-made, methyl ester sulfonate and sodium lauryl market Ester Sulfate (SLS) with a concentration of 15 %, 20 % and 25 %. Detergent results of the study have high detergency ( net ) compared with the detergency of detergent commercial, have a stable emulsion stability, the stability of the foam/foam detergent power made from methyl ester sulfonate surfactant produces less foam, compared with a detergent made from SLS and surfactant SNI 06-4075-1996 standards.

Stability of radical anions derived from substituted 5-nitrofurans investigated by ESR spectroscopy

1985 ◽  
Vol 50 (7) ◽  
pp. 1594-1601 ◽  
Author(s):  
Jiří Klíma ◽  
Larisa Baumane ◽  
Janis Stradinš ◽  
Jiří Volke ◽  
Romualds Gavars
Keyword(s):  
Radical Anion ◽  
High Stability ◽  
Esr Spectroscopy ◽  
Reaction Path ◽  
Order Reaction ◽  
Second Order ◽  
Radical Anions ◽  
Second Order Reaction ◽  
Unpaired Electron Density ◽  
The Stability

It has been found that the decay in dimethylformamide and dimethylformamide-water mixtures of radical anions in five of the investigated 5-nitrofurans is governed by a second-order reaction. Only the decay of the radical anion generated from 5-nitro-2-furfural III may be described by an equation including parallel first- and second-order reactions; this behaviour is evidently caused by the relatively high stability of the corresponding dianion, this being an intermediate in the reaction path. The presence of a larger conjugated system in the substituent in position 2 results in a decrease of the unpaired electron density in the nitro group and, consequently, an increase in the stability of the corresponding radical anions.

Global stability result for parabolic Cauchy problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mourad Choulli ◽  
Masahiro Yamamoto
Keyword(s):  
New York ◽  
Partial Differential Equations ◽  
Global Stability ◽  
Classical Problem ◽  
Stability Result ◽  
Cauchy Problems ◽  
Smooth Solutions ◽  
Linear Partial Differential Equations ◽  
Ill Posed ◽  
The Stability

AbstractUniqueness of parabolic Cauchy problems is nowadays a classical problem and since Hadamard [Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Dover, New York, 1953], these kind of problems are known to be ill-posed and even severely ill-posed. Until now, there are only few partial results concerning the quantification of the stability of parabolic Cauchy problems. We bring in the present work an answer to this issue for smooth solutions under the minimal condition that the domain is Lipschitz.

Convergence and stability analysis of the half thresholding based few-view CT reconstruction

2020 ◽  
Vol 28 (6) ◽  
pp. 829-847
Author(s):  
Hua Huang ◽  
Chengwu Lu ◽  
Lingli Zhang ◽  
Weiwei Wang
Keyword(s):  
Noise Suppression ◽  
Reconstructed Image ◽  
Reference Image ◽  
Projection Data ◽  
Ct Reconstruction ◽  
Reconstruction Algorithms ◽  
Ill Posed ◽  
Thresholding Algorithm ◽  
The Stability ◽  
Well Posed

AbstractThe projection data obtained using the computed tomography (CT) technique are often incomplete and inconsistent owing to the radiation exposure and practical environment of the CT process, which may lead to a few-view reconstruction problem. Reconstructing an object from few projection views is often an ill-posed inverse problem. To solve such problems, regularization is an effective technique, in which the ill-posed problem is approximated considering a family of neighboring well-posed problems. In this study, we considered the {\ell_{1/2}} regularization to solve such ill-posed problems. Subsequently, the half thresholding algorithm was employed to solve the {\ell_{1/2}} regularization-based problem. The convergence analysis of the proposed method was performed, and the error bound between the reference image and reconstructed image was clarified. Finally, the stability of the proposed method was analyzed. The result of numerical experiments demonstrated that the proposed method can outperform the classical reconstruction algorithms in terms of noise suppression and preserving the details of the reconstructed image.

scholarly journals The training schedule affects the stability, not the magnitude, of the interlimb transfer of learned dynamics

2013 ◽  
Vol 110 (4) ◽  
pp. 984-998 ◽  
Author(s):  
Wilsaan M. Joiner ◽  
Jordan B. Brayanov ◽  
Maurice A. Smith
Keyword(s):  
Short Duration ◽  
Dynamic Environment ◽  
Internal Representation ◽  
Motor Adaptation ◽  
Training Period ◽  
Visually Guided ◽  
Brief Training ◽  
Long Duration ◽  
The Stability ◽  
The Right

The way that a motor adaptation is trained, for example, the manner in which it is introduced or the duration of the training period, can influence its internal representation. However, recent studies examining the gradual versus abrupt introduction of a novel environment have produced conflicting results. Here we examined how these effects determine the effector specificity of motor adaptation during visually guided reaching. After adaptation to velocity-dependent dynamics in the right arm, we estimated the amount of adaptation transferred to the left arm, using error-clamp measurement trials to directly measure changes in learned dynamics. We found that a small but significant amount of generalization to the untrained arm occurs under three different training schedules: a short-duration (15 trials) abrupt presentation, a long-duration (160 trials) abrupt presentation, and a long-duration gradual presentation of the novel dynamic environment. Remarkably, we found essentially no difference between the amount of interlimb generalization when comparing these schedules, with 9–12% transfer of the trained adaptation for all three. However, the duration of training had a pronounced effect on the stability of the interlimb transfer: The transfer elicited from short-duration training decayed rapidly, whereas the transfer from both long-duration training schedules was considerably more persistent (<50% vs. >90% retention over the first 20 trials). These results indicate that the amount of interlimb transfer is similar for gradual versus abrupt training and that interlimb transfer of learned dynamics can occur after even a brief training period but longer training is required for an enduring effect.

CRITICAL REVIEW OF EMULSION STABILITY AND CHARACTERIZATION TECHNIQUES IN OIL PROCESSING

2021 ◽  
pp. 1-36
Author(s):  
Vahideh Angardi ◽  
Ali Ettehadi ◽  
Özgün Yücel
Keyword(s):  
Separation Efficiency ◽  
Petroleum Industry ◽  
Cost Effective ◽  
Downstream Processing ◽  
Physical Factors ◽  
Comprehensive Review ◽  
Factors Affecting ◽  
Mathematical Explanations ◽  
The Stability ◽  
The Right

Abstract Effective separation of water and oil dispersions is considered a critical step in the determination of technical and economic success in the petroleum industry over the years. Moreover, a deeper understanding of the emulsification process and different affected parameters is essential for cost-effective oil production, transportation, and downstream processing. Numerous studies conducted on the concept of dispersion characterization indicate the importance of this concept, which deserves attention by the scientific community. Therefore, a comprehensive review study with critical analysis on significant concepts will help readers follow them easily. This study is a comprehensive review of the concept of dispersion characterization and conducted studies recently published. The main purposes of this review are to 1) Highlight flaws, 2) Outline gaps and weaknesses, 3) Address conflicts, 4) Prevent duplication of effort, 5) List factors affecting dispersion. It was found that the separation efficiency and stability of dispersions are affected by different chemical and physical factors. Factors affecting the stability of the emulsions have been studied in detail and will help to look for the right action to ensure stable emulsions. In addition, methods of ensuring stability, especially coalescence are highlighted, and coalescence mathematical explanations of phenomena are presented.

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