THE STABILITY OF LINEAR MAPPINGS AND SOME PROBLEMS ON ISOMETRIES**It is my pleasure to express my gratitude to the organizing committee of the Conference on Mathematical Analysis and its Applications, Department of Mathematics, Kuwait University, for inviting me to deliver this lecture in Kuwait.

1988 ◽  
pp. 175-184 ◽  
Author(s):  
T.M. RASSIAS
Keyword(s):  
Mathematical Analysis ◽  
Kuwait University ◽  
The Stability

Magneto-viscous resistive tearing of cylindrical flux surfaces

1979 ◽  
Vol 22 (2) ◽  
pp. 329-338 ◽  
Author(s):  
R. J. Hosking
Keyword(s):  
Magnetic Field ◽  
Mathematical Analysis ◽  
Logarithmic Derivative ◽  
Hard Core ◽  
Viscosity Coefficient ◽  
Positive Definite ◽  
Field Curvature ◽  
Large Growth ◽  
The Stability ◽  
High Beta

The stability of cylindrical flux surfaces in the presence of finite resistivity and parallel ion viscosity is reconsidered, and in particular the increment in the logarithmic derivative Δ(Q) over the inner dissipative region. Correction of the viscosity coefficient removes the branch-point behaviour at large growth rates reported earlier. Numerical results for real Q in the high-beta hard-core pinch are supported by mathematical analysis to show that parallel ion viscosity renders Δ(Q) positive definite provided D < 0, with a positive minimum increasing with temperature. This stabilization is associated with coupling of the parallel plasma motion in the presence of magnetic field curvature. The viscous compressible value of Δ(Q) is somewhat less than its inviscid compressible counterpart at small real Q, so that relative to purely compressible theory parallel ion viscosity can be slightly destabilizing.

Effect of Copper on the interaction between the Predator Didinium nasutum and its Prey Paramecium caudatum

1990 ◽  
Vol 47 (6) ◽  
pp. 1122-1127 ◽  
Author(s):  
Christine M. Doucet ◽  
Edward J. Maly
Keyword(s):  
Equilibrium Point ◽  
Mathematical Analysis ◽  
Copper Toxicity ◽  
Copper Stress ◽  
Paramecium Caudatum ◽  
The Stability ◽  
Effect Of Copper ◽  
Predator Efficiency

Tests to determine acute copper toxicity levels demonstrated that the protozoan predator Didinium nasutum were more susceptible to copper stress than its prey Paramecium caudatum Thus we predicted that Paramecium and Didinium densities, at the equilibrium point of their interaction, would be higher at sublethal copper levels due to a decrease in the predator's efficiency. This situation is likely to produce a decrease in the stability of the system. However, isocline analysis did not support the predictions based on the acute lethality tests. Equilibrium densities of both predator and prey did not change at copper levels between 30 and 180 μg/L. The mathematical analysis suggested that the interaction became less stable with increasing copper concentrations. However, stability decreased due to hormesis in Didinium at sublethal copper levels and not due to a reduction in predator efficiency as expected. At 300 μg Cu/L, densities of both species at equilibrium were higher and the stability of the system decreased. This decrease in stability resulted from a reduction in predator efficiency, as 300 μg Cu/L is not sublethal for Didinium.

scholarly journals Characteristics of the Drag Coefficient over a Tropical Environment in Convective Conditions*

2015 ◽  
Vol 72 (12) ◽  
pp. 4903-4913 ◽  
Author(s):  
Piyush Srivastava ◽  
Maithili Sharan
Keyword(s):  
Wind Speed ◽  
Drag Coefficient ◽  
Power Law ◽  
Mathematical Analysis ◽  
Tropical Region ◽  
Convective Conditions ◽  
Similarity Functions ◽  
Regression Curves ◽  
The Stability ◽  
The Tropics

Abstract The turbulent data over a tropical region are utilized to analyze the observational behavior of the drag coefficient with respect to wind speed U and the stability parameter in convective conditions. The drag coefficient is observed to follow the power-law profile with respect to U, with large values in low winds and relatively lower values with moderate-wind conditions. Depending on the stability regimes, regression curves for with U are proposed. The variation of with is bounded by a curve. This curve first shows increasing behavior with until it reaches a peak at and then decreases with increasing instability. A mathematical analysis based on Monin–Obukhov similarity (MOS) reveals that increases monotonically with increasing instability. This suggests that MOS theory is able to capture the increasing nature of in weakly to moderately unstable conditions. However, it is unable to explain the observed decreasing behavior of with in moderately to strongly unstable conditions in the tropics within the framework of commonly used similarity functions.

scholarly journals Mathematical Analysis of a Diarrhoea Model in the Presence of Vaccination and Treatment Waves with Sensitivity Analysis

2021 ◽  
Vol 25 (7) ◽  
pp. 1107-1114
Author(s):  
E.I. Akinola ◽  
B.E. Awoyemi ◽  
I.A. Olopade ◽  
O.D. Falowo ◽  
T.O. Akinwumi
Keyword(s):  
Sensitivity Analysis ◽  
Mathematical Analysis ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Runge Kutta Method ◽  
Modelling Techniques ◽  
Uniqueness And Existence ◽  
The Stability ◽  
Order Four ◽  
Disease Free

In this study, the diarrhoea model is developed based on basic mathematical modelling techniques leading to a system (five compartmental model) of ordinary differential equations (ODEs). Mathematical analysis of the model is then carried out on the uniqueness and existence of the model to know the region where the model is epidemiologically feasible. The equilibrium points of the model and the stability of the disease-free state were also derived by finding the reproduction number. We then progressed to running a global sensitivity analysis on the reproduction number with respect to all the parameters in it, and four (4) parameters were found sensitive. The work was concluded with numerical simulations on Maple 18 using Runge-Kutta method of order four (4) where the values of six (6) parameters present in the model were each varied successively while all other parameters were held constant so as to know the behaviour and effect of the varied parameter on how diarrhoea spreads in the population. The results from the sensitivity analysis and simulations were found to be in sync.

scholarly journals Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jin Woo Jang ◽  
Robert M. Strain ◽  
Tak Kwong Wong
Keyword(s):  
Mathematical Analysis ◽  
Kinetic Equations ◽  
Three Dimensional ◽  
Magnetic Confinement ◽  
Magnetic Potential ◽  
Time Interval ◽  
Finite Time Interval ◽  
Cylindrical Coordinate ◽  
Initial Support ◽  
The Stability

<p style='text-indent:20px;'>Although the nuclear fusion process has received a great deal of attention in recent years, the amount of mathematical analysis that supports the stability of the system seems to be relatively insufficient. This paper deals with the mathematical analysis of the magnetic confinement of the plasma via kinetic equations. We prove the global wellposedness of the <i>Vlasov-Maxwell</i> system in a two-dimensional annulus when a huge (<i>but finite-in-time</i>) external magnetic potential is imposed near the boundary. We assume that the solution is axisymmetric. The authors hope that this work is a step towards a more generalized work on the three-dimensional Tokamak structure. The highlight of this work is the physical assumptions on the external magnetic potential well which remains finite <i>within a finite time interval</i> and from that, we prove that the plasma never touches the boundary. In addition, we provide a sufficient condition on the magnitude of the external magnetic potential to guarantee that the plasma is confined in an annulus of the desired thickness which is slightly larger than the initial support. Our method uses the cylindrical coordinate forms of the <i>Vlasov-Maxwell</i> system.</p>

scholarly journals Lord Robert May of Oxford OM. 8 January 1936—28 April 2020

2021 ◽  
Author(s):  
Lord (John) Krebs ◽  
Michael Hassell ◽  
Sir Charles Godfray
Keyword(s):  
Mathematical Modelling ◽  
Mathematical Analysis ◽  
Royal Society ◽  
Research Agenda ◽  
Ecological Communities ◽  
Population Fluctuations ◽  
Theoretical Physicist ◽  
The Stability ◽  
The Uk ◽  
New Research

Robert May was the leading theoretical ecologist of his generation. He started his career as a theoretical physicist and began the transition to ecology soon after completing a post-doctoral fellowship at Harvard. His mathematical analysis of the stability of ecological communities challenged orthodox views and spawned a new research agenda. He demonstrated that many different patterns of population fluctuations, including chaotic behaviour, could arise from simple mathematical models. Together with R. M. Anderson, he transformed the mathematical modelling of infectious diseases. All of his work was characterized by his remarkable ability to reduce complex problems to their essential simplicities. His achievements were recognized by the award of numerous major international prizes. May also served as the UK government's chief scientific advisor between 1995 and 2000, and as President of the Royal Society between 2000 and 2005.

scholarly journals Ανάλυση της ευστάθειας κατά την ανάπτυξη ελλειψοειδών καρκινικών όγκων

2014 ◽  
Author(s):  
Βασιλική-Χριστίνα Παναγιωτοπούλου
Keyword(s):  
Steady State ◽  
Physical Quantity ◽  
Mathematical Analysis ◽  
Tumour Growth ◽  
Stability Study ◽  
Spherical Case ◽  
Anisotropic Space ◽  
Ellipsoidal Model ◽  
Physical Case ◽  
The Stability

The mathematical analysis of the tumour growth attracted a lot of interest in thelast two decades. However, as of today no generally accepted model for tumourgrowth exists. This is due partially to the incomplete understanding of the relatedpathology as well as the extremely complicated procedure that guides the evolutionof a tumour. Moreover, the growth of a tumour does depend on the available tissuesurrounding the tumour and therefore it represents a physical case which is realisticallymodelled by ellipsoidal geometry. The remarkable aspect of the ellipsoidalshape is that it represents the sphere of the anisotropic space. It provides the appropriategeometrical model for any direction dependent physical quantity. In thepresent work we analyze the stability of a spherical tumour for four continuous modelsof an avascular tumour and the stability study of an ellipsoidal tumour. For allve models, conditions for the stability are stated and the results are implementedThe mathematical analysis of the tumour growth attracted a lot of interest in thelast two decades. However, as of today no generally accepted model for tumourgrowth exists. This is due partially to the incomplete understanding of the relatedpathology as well as the extremely complicated procedure that guides the evolutionof a tumour. Moreover, the growth of a tumour does depend on the available tissuesurrounding the tumour and therefore it represents a physical case which is realisticallymodelled by ellipsoidal geometry. The remarkable aspect of the ellipsoidalshape is that it represents the sphere of the anisotropic space. It provides the appropriategeometrical model for any direction dependent physical quantity. In thepresent work we analyze the stability of a spherical tumour for four continuous modelsof an avascular tumour and the stability study of an ellipsoidal tumour. For allve models, conditions for the stability are stated and the results are implemented numerically. For the spherical cases, it is observed that the steady state radii thatsecure the stability of the tumour are dierent for each of the four models, and thatresults to dierences in the stable and unstable modes. As for the ellipsoidal model,it is shown that, in contrast to the highly symmetric spherical case, where stabilityis possible to be achieved, there are no conditions that secure the stability of anellipsoidal tumour. Hence, as in many physical cases, the observed instability is aconsequence of the lack of symmetry.

STABILITY OF UNCONDITIONAL SCHAUDER DECOMPOSITIONS IN SPACES

2015 ◽  
Vol 92 (3) ◽  
pp. 444-456
Author(s):  
VITALII MARCHENKO
Keyword(s):  
Banach Space ◽  
Hilbert Spaces ◽  
Mathematical Analysis ◽  
Stability Theorem ◽  
Best Constants ◽  
Khintchine Inequality ◽  
The Stability ◽  
Academy Of Sciences

We use the best constants in the Khintchine inequality to generalise a theorem of Kato [‘Similarity for sequences of projections’, Bull. Amer. Math. Soc.73(6) (1967), 904–905] on similarity for sequences of projections in Hilbert spaces to the case of unconditional Schauder decompositions in $\ell _{p}$ spaces. We also sharpen a stability theorem of Vizitei [‘On the stability of bases of subspaces in a Banach space’, in: Studies on Algebra and Mathematical Analysis, Moldova Academy of Sciences (Kartja Moldovenjaska, Chişinău, 1965), 32–44; (in Russian)] in the case of unconditional Schauder decompositions in any Banach space.

Optimal Harvesting Strategy of Inshore-Offshore Species

2013 ◽  
Vol 726-731 ◽  
pp. 1358-1361
Author(s):  
Zai Le He ◽  
Xiang Qing Zhao ◽  
Jing Jing Li
Keyword(s):  
Mathematical Analysis ◽  
Lyapunov Method ◽  
Optimal Harvesting ◽  
Sustainable Harvest ◽  
The Stability

In this paper, we study the optimal harvesting strategy of inshore-offshore species. Firstly, to keep sustainable harvest of inshore-offshore species resources, the stability of the system is discussed by Lyapunov method. Then, the optimal harvesting strategy is obtained by simple mathematical analysis.

scholarly journals Dynamic Spreading Model of Passenger Group Panic considering Official Guidance Information in Subway Emergencies

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Jiayang Li ◽  
Jiafu Tang ◽  
Dan Wang
Keyword(s):  
Mathematical Analysis ◽  
Transmission Dynamics ◽  
Transmission Model ◽  
Rail Transportation ◽  
Spreading Model ◽  
Dynamic Transmission Model ◽  
Fast Pace ◽  
To Come ◽  
The Stability ◽  
Guidance Information

Safety concerns are increasing as rail transportation develops at a fast pace. When emergencies erupt in the course of transportation, panic will spread among passengers. Subway operators should understand how the emotions of passengers spread and how the guidance instructions work, in order to effectively deter the transmission of panic. Based on the models of system dynamics, transmission dynamics, and contagious disease, the essay constructs a dynamic transmission model for passenger panic inside the carriage, incorporating the official guidance instructions. Then, the essay utilizes Routh–Hurwitz criteria and analyzes the stability equilibrium of the dynamic differential equation. Mathematical analysis and simulation tests have verified the validity of the model and stability conditions. Finally, it is proved in the essay by mathematical analysis and simulation tests that official guidance instructions can effectively control the spread of panic and quickly stabilize the system. Thus, the essay helps subway operators to come up with clear official guidance, so as to find quick solutions and prevent escalation of panic due to lack of trust.

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