Functions of restricted variation

Preston C. Hammer; John C. Holladay

doi:10.1007/bf02843775

Convergence of Variational Iteration Method for Fractional Delay Integrodifferential-Algebraic Equations

Mathematical Problems in Engineering ◽

10.1155/2017/6749643 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Yayun Fu ◽

Hongliang Liu ◽

Aiguo Xiao

Keyword(s):

Iteration Method ◽

Time Lag ◽

Variational Iteration Method ◽

Good Choice ◽

Algebraic Equations ◽

Science And Engineering ◽

Variational Iteration ◽

Fractional Delay ◽

Restricted Variation ◽

Algebraic Constraint

Fractional order delay integrodifferential-algebraic equations are often used for many practical modeling problems in science and engineering, which have time lag, memory, constraint limit, and so forth. These yield some difficulties in numerical computation. The iterative methods are good choice. In the present paper, we construct variational iteration method for solving them by using the appropriate restricted variation. This overcomes the difficulties caused by limitations of large storage amount and algebraic constraint and extends the previous conclusions.

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You Do Not Mess with the Glia

Neuroglia ◽

10.3390/neuroglia1010014 ◽

2018 ◽

Vol 1 (1) ◽

pp. 193-219 ◽

Cited By ~ 7

Author(s):

Suzana Herculano-Houzel ◽

Sandra Dos Santos

Keyword(s):

Glial Cell ◽

Glial Cells ◽

Expression Profiles ◽

Gene Expression Profiles ◽

Cell Types ◽

Quantitative Studies ◽

Physiological Constraint ◽

Constrained Variation ◽

Restricted Variation ◽

Development And Evolution

Vertebrate neurons are enormously variable in morphology and distribution. While different glial cell types do exist, they are much less diverse than neurons. Over the last decade, we have conducted quantitative studies of the absolute numbers, densities, and proportions at which non-neuronal cells occur in relation to neurons. These studies have advanced the notion that glial cells are much more constrained than neurons in how much they can vary in both development and evolution. Recent evidence from studies on gene expression profiles that characterize glial cells—in the context of progressive epigenetic changes in chromatin during morphogenesis—supports the notion of constrained variation of glial cells in development and evolution, and points to the possibility that this constraint is related to the late differentiation of the various glial cell types. Whether restricted variation is a biological given (a simple consequence of late glial cell differentiation) or a physiological constraint (because, well, you do not mess with the glia without consequences that compromise brain function to the point of rendering those changes unviable), we predict that the restricted variation in size and distribution of glial cells has important consequences for neural tissue function that is aligned with their many fundamental roles being uncovered.

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Restricted variation after projection and the Lipkin-Nogami methods

Physical Review C ◽

10.1103/physrevc.72.064303 ◽

2005 ◽

Vol 72 (6) ◽

Cited By ~ 21

Author(s):

Tomás R. Rodríguez ◽

J. L. Egido ◽

L. M. Robledo

Keyword(s):

Restricted Variation

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Restricted variation in the glycosylation of human α1-acid glycoprotein

Chromatographia ◽

10.1007/bf02275851 ◽

1993 ◽

Vol 37 (3-4) ◽

pp. 144-148 ◽

Cited By ~ 2

Author(s):

M. J. Treuheit ◽

H. B. Halsall

Keyword(s):

Acid Glycoprotein ◽

Restricted Variation

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Restricted variation in data envelopment analysis with undesirable factors in nature

International Journal of Biomathematics ◽

10.1142/s1793524515500345 ◽

2015 ◽

Vol 08 (03) ◽

pp. 1550034 ◽

Cited By ~ 1

Author(s):

Sohrab Kordrostami ◽

Alireza Amirteimoori ◽

Monireh Jahani Sayyad Noveiri

Keyword(s):

Data Envelopment Analysis ◽

Efficient Frontier ◽

Data Envelopment ◽

Standard Data ◽

Weak Disposability ◽

Dea Models ◽

Restricted Environment ◽

Restricted Variation ◽

Decision Making Units ◽

Inputs And Outputs

In standard data envelopment analysis (DEA) models, inefficient decision-making units (DMUs) should change their inputs and outputs arbitrarily to meet the efficient frontier. However, in many real applications of DEA, because of some limitations in resources and DMU's ability, these variations cannot be made arbitrarily. Moreover, in some situations, undesirable factors with different disposability, strong or weak disposability, are found. In this paper, a DEA-based model is proposed to determine the relative efficiency of DMUs in such a restricted environment and in presence of undesirable factors. Indeed, variation levels of inputs and outputs are pre-defined and are considered to evaluate the performance of DMUs. Numerical examples are utilized to demonstrate the approach.

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A Dynamic Model for Motion of an ROV due to On-Board Robotics

Volume 4B: Dynamics, Vibration, and Control ◽

10.1115/imece2017-70110 ◽

2017 ◽

Cited By ~ 1

Author(s):

Andreas Evjenth ◽

Otto Andreas Moe ◽

Iselin Violet Kjelland Schøn ◽

Thomas J. Impelluso

Keyword(s):

Service Industry ◽

Equations Of Motion ◽

New Method ◽

Moving Frame ◽

3D Animation ◽

Remotely Operated Vehicle ◽

Runge Kutta Method ◽

Induced Motion ◽

The Stability ◽

Restricted Variation

A new method in dynamics — the Moving Frame Method (MFM) — is used to conduct the analysis of how a robotic appendage (manipulator) on a Remotely Operated Vehicle (ROV) affects the motion of the ROV. An ROV performs multiple tasks on the seabed in the oil service industry. In most cases, an ROV pilot monitors and adjusts the movement of the vehicle due to induced motion by currents, buoyancy and the manipulators. Simulation data would assist the pilot and improve the stability of the ROV. This paper exploits a new method to analyze the induced movements of the ROV. The method uses the Special Euclidean Group (SE(3)) and the MFM. The method is supplemented with a restricted variation on the angular velocity to extract the equations of motion for the ROV. Then the equations of motion are solved numerically using Runge-Kutta Method and a reconstruction formula (founded upon the Cayley-Hamilton theorem) to secure the 3D rotations of the vehicle. The resulting motion is visualized with selected 2D plots. The 3D animation is displayed on a 3D web page. This paper closes with a summary of the simplifications used in the model and suggestions for advanced work.

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