Oscillatory nature of the Okmok volcano's deformation

It is often very difficult for humans to control cranes due to their inherent oscillatory nature and sluggish response. Tasks are made even harder when the operator moves around the workspace and changes his/her orientation. Traditionally, the driving axes on cranes have been independent of operator orientation and location. When the operators change the direction they are facing, their “Forward” direction is not consistent with “Forward” on the crane control interface. This paper describes two novel ways to reduce this problem and shows their effectiveness in a human operator study.

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On a generalized divisor problem I

Nagoya Mathematical Journal ◽

10.1017/s002776300000814x ◽

2002 ◽

Vol 165 ◽

pp. 71-78 ◽

Cited By ~ 2

Author(s):

Yuk-Kam Lau

Keyword(s):

Error Term ◽

Divisor Problem ◽

Sign Changes ◽

Oscillatory Nature ◽

Dirichlet Divisor Problem

We give a discussion on the properties of Δa(x) (− 1 < a < 0), which is a generalization of the error term Δ(x) in the Dirichlet divisor problem. In particular, we study its oscillatory nature and investigate the gaps between its sign-changes for −½ ≤ a < 0.

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Oscillation criteria for differential equations of second order

Mathematica Slovaca ◽

10.2478/s12175-009-0138-z ◽

2009 ◽

Vol 59 (4) ◽

Cited By ~ 2

Author(s):

A. Nandakumaran ◽

S. Panigrahi

Keyword(s):

Differential Equations ◽

Second Order ◽

Integral Inequalities ◽

Sufficient Condition ◽

Oscillation Criteria ◽

Oscillatory Nature ◽

Non Linear

AbstractIn this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form $$ (r(t)y')' + q(t)y' + p(t)f(y)g(y') = 0, t \geqslant t_0 , $$ where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

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Stability and Response of Systems Satisfying a Second-Order Linear Differential Equation with Time-Dependent Coefficients

Aeronautical Quarterly ◽

10.1017/s0001925900010416 ◽

1957 ◽

Vol 8 (1) ◽

pp. 78-86

Author(s):

A. W. Babister

Keyword(s):

Differential Equation ◽

Singular Point ◽

Linear Differential Equation ◽

Second Order ◽

Time Dependent ◽

Order Linear Differential Equation ◽

Order Linear ◽

Oscillatory Nature ◽

Linear Differential ◽

Image Position

SummaryThe differential equation considered iswhere all the a’s and b’s are real constants.The nature of the solution is investigated in the neighbourhood of the singular point and the conditions are found for logarithmic terms to be absent.The conditions for stability for large values of τ are determined; the system is stable ifare all positive for large values of τ.The form of the response is considered and its oscillatory (or non-oscillatory) nature investigated. The Sonin-Polya theorem is used to determine simple inequalities which must hold between the coefficients of the differential equation in any interval for the relative maxima of | x | to form an increasing or decreasing sequence in that interval.

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Bifurcation control of a minimal model of marine plankton interaction with multiple delays

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2021013 ◽

2021 ◽

Vol 16 ◽

pp. 16

Author(s):

Zhichao Jiang ◽

Maoyan Jie

Keyword(s):

Control Method ◽

Feedback Gain ◽

Multiple Delays ◽

Toxic Substances ◽

Oscillatory Nature ◽

Bifurcation Phenomena ◽

Feedback Control Method ◽

Delay Feedback Control ◽

Three Delays ◽

Delayed Model

Plankton blooms and its control is an intriguing problem in ecology. To investigate the oscillatory nature of blooms, a two-dimensional model for plankton species is considered where one species is toxic phytoplankton and other is zooplankton. The delays required for the maturation time of zooplankton, the time for phytoplankton digestion and the time for phytoplankton cells to mature and release toxic substances are incorporated and the delayed model is analyzed for stability and bifurcation phenomena. It proves that periodic plankton blooms can occur when the delay (the sum of the above three delays) changes and crosses some threshold values. The phenomena described by this mechanism can be controlled through the toxin release rates of phytoplankton. Then, a delay feedback controller with the coefficient depending on delay is introduced to system. It concludes that the onset of the bifurcation can be delayed as negative feedback gain (the decay rate) decreases (increases). Some numerical examples are given to verify the effectiveness of the delay feedback control method and the existence of crossing curve. These results show that the oscillatory nature of blooms can be controlled by human behaviors.

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