scholarly journals Rigorous Mathematical Analysis of the Quasispecies Model: From Manfred Eigen to the Recent Developments

2019 ◽  
pp. 27-51
Author(s):  
Alexander S. Bratus ◽  
Artem S. Novozhilov ◽  
Yuri S. Semenov
Keyword(s):  
Mathematical Analysis ◽  
Quasispecies Model ◽  
Recent Developments ◽  
Rigorous Mathematical Analysis

scholarly journals Global Dynamics for an Age-Structured Cholera Infection Model with General Infection Rates

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 2993
Author(s):  
Xin Jiang
Keyword(s):  
Theoretical Analysis ◽  
Mathematical Analysis ◽  
Local Stability ◽  
Infection Model ◽  
Global Behavior ◽  
Uniform Persistence ◽  
Global Dynamics ◽  
Infection Rates ◽  
Age Structured ◽  
Rigorous Mathematical Analysis

This paper studies the global dynamics of a cholera model incorporating age structures and general infection rates. First, we explore the existence and point dissipativeness of the orbit and analyze the asymptotical smoothness. Then, we perform rigorous mathematical analysis on the existence and local stability of equilibria. Based on the uniform persistence, we further investigate the global behavior of the cholera infection model. The results of theoretical analysis are well confirmed by numerical simulations. This research generalizes some known results and provides deeper insights into the dynamics of cholera propagation.

scholarly journals Geometrical Model of Spiking and Bursting Neuron on a Mug-Shaped Branched Manifold

2020 ◽  
Vol 30 (15) ◽  
pp. 2030044
Author(s):  
Mohamed Gheouali ◽  
Tounsia Benzekri ◽  
René Lozi ◽  
Guanrong Chen
Keyword(s):  
Mathematical Analysis ◽  
Phenomenological Model ◽  
Geometrical Model ◽  
Dynamic Motion ◽  
Bursting Neuron ◽  
Theoretical Results ◽  
Rigorous Mathematical Analysis

Based on the Hodgkin–Huxley and Hindmarsh–Rose models, this paper proposes a geometric phenomenological model of bursting neuron in its simplest form, describing the dynamic motion on a mug-shaped branched manifold, which is a cylinder tied to a ribbon. Rigorous mathematical analysis is performed on the nature of the bursting neuron solutions: the number of spikes in a burst, the periodicity or chaoticity of the bursts, etc. The model is then generalized to obtain mixing burst of any number of spikes. Finally, an example is presented to verify the theoretical results.

The Cross-Eye Jamming Mathematical Modeling

2013 ◽  
Vol 344 ◽  
pp. 125-128
Author(s):  
Fei Cao ◽  
Qing Yun Liu ◽  
Fan Wu
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Analysis ◽  
Radar System ◽  
Angular Error ◽  
Simulation Results ◽  
The Cross ◽  
Reasonable Choice ◽  
Rigorous Mathematical Analysis ◽  
Equal Amplitude

A rigorous mathematical analysis of cross-eye jamming in a radar system scenario and an expression for the induced angular error due to the cross-eye jammer are presented. The simulation results show that there is a Doppler difference between jamming and target return. The Doppler difference increases with the decrease of the distance between the monopulse radar and the platform protected by cross-eye jammer. When the power of target return is not small enough with respect to the power of jamming transmitted by one of the two sources, maybe the sign of the indicated angle is uncontrollable. The simulation results also show that although the cross-eye gain is maximized if two jamming signals are equal amplitude and antiphase, it is not a reasonable choice.

Design Formulas for Expansion Bellows

1981 ◽  
Vol 103 (4) ◽  
pp. 881-891 ◽  
Author(s):  
Satish Chand ◽  
S. B. L. Garg
Keyword(s):  
Mathematical Analysis ◽  
Plate Theory ◽  
Axial Loading ◽  
Beam Theory ◽  
Geometric Parameters ◽  
Equivalent Stresses ◽  
Rigorous Mathematical Analysis

In this work the problem for S-type of bellows and U-type of bellows subjected to axial loading is treated by using plate theory and beam theory. The solutions found here are compared with those obtained by rigorous mathematical analysis and simplified expressions are developed for the use of designers. The results for maximum equivalent stresses and axial deflections are plotted for different geometric parameters of bellows.

Computational chemistry from the perspective of numerical analysis

Acta Numerica ◽  
2005 ◽  
Vol 14 ◽  
pp. 363-444 ◽  
Author(s):  
Claude Le Bris
Keyword(s):  
Numerical Analysis ◽  
Numerical Simulations ◽  
Computational Chemistry ◽  
Mathematical Analysis ◽  
New Methods ◽  
Recent Developments ◽  
Open Issues

We present the field of computational chemistry from the standpoint of numerical analysis. We introduce the most commonly used models and comment on their applicability. We briefly outline the results of mathematical analysis and then mostly concentrate on the main issues raised by numerical simulations. A special emphasis is laid on recent results in numerical analysis, recent developments of new methods and challenging open issues.

Investigation on Cyclic Reciprocal Derivative Chronopotentiometry. Part II. Theoretical Equation for an Irreversible Reaction

2000 ◽  
Vol 65 (6) ◽  
pp. 971-978 ◽  
Author(s):  
Shuping Bi ◽  
Jian Chen ◽  
Tao Chen
Keyword(s):  
Transfer Coefficient ◽  
Rate Constant ◽  
Current Density ◽  
Mathematical Analysis ◽  
Electrode Reaction ◽  
Theoretical Equation ◽  
Irreversible Reaction ◽  
Reactant Concentration ◽  
Electrochemical Parameters ◽  
Rigorous Mathematical Analysis

A rigorous mathematical analysis is presented for an irreversible electrode process in the cyclic reciprocal derivative chronopotentiometry. Influences of basic electrochemical parameters, such as transfer coefficient α, rate constant ks, current density j, number of the electrons involved in the electrode reaction n and reactant concentration c0• on the properties of the dt/dE-E chronopotentiogram are described.

Well-posedness of the free surface problem on a Newtonian fluid between cylinders rotating at different speeds

2021 ◽  
pp. 1-26
Author(s):  
Jiaqi Yang
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Newtonian Fluid ◽  
Mathematical Analysis ◽  
Perturbation Series ◽  
Well Posedness ◽  
Centrifugal Forces ◽  
Analysis Theory ◽  
Concentric Cylinders ◽  
Rigorous Mathematical Analysis

When a liquid fills the semi-infinite space between two concentric cylinders which rotate at different steady speeds, how about the shape of the free surface on top of the fluid? The different fluids will lead to a different shape. For the Newtonian fluid, the meniscus descends due to the centrifugal forces. However, for the certain non-Newtonian fluid, the meniscus climbs the internal cylinder. We want to explain the above phenomenon by a rigorous mathematical analysis theory. In the present paper, as the first step, we focus on the Newtonian fluid. This is a steady free boundary problem. We aim to establish the well-posedness of this problem. Furthermore, we prove the convergence of the formal perturbation series obtained by Joseph and Fosdick in Arch. Ration. Mech. Anal. 49 (1973), 321–380.

Tractive efficiency of four-wheel-drive vehicles: An analysis for non-uniform traction conditions

2003 ◽  
Vol 217 (5) ◽  
pp. 363-374 ◽  
Author(s):  
B C Besselink
Keyword(s):  
Mathematical Analysis ◽  
Fixed Ratio ◽  
Graphical Analysis ◽  
The Other ◽  
Speed Ratio ◽  
Road Vehicles ◽  
Wheel Drive ◽  
Four Wheel Drive ◽  
Tractive Efficiency ◽  
Rigorous Mathematical Analysis

An analysis of the tractive efficiency of four-wheel-drive vehicles is conducted from the perspective of maximizing efficiency of slip with respect to non-uniform traction conditions in particular. The analysis is conducted using a more rigorous mathematical analysis than previously and using a thorough graphical analysis to substantiate the mathematical analysis. Previous studies concluded that under all traction conditions efficiency of slip will be a maximum when the slip of each wheel is equal. The analysis revealed that, contrary to the previous literature, efficiency of slip will not be a maximum when the slip of each wheel is equal under non-uniform traction conditions. When applied to a vehicle with an interaxle fixed ratio coupling, this means that the optimum theoretical speed ratio is not always equal to 1. An example of non-uniform traction conditions is the situation where two drive wheels are on soil and the other two are on tarmac. The improvement in the efficiency of slip, in this example, when using the correct theoretical speed ratio (as opposed to that equal to 1) is particularly marked at high drawbar loads. The method by which the correct theoretical speed ratio is to be achieved when non-uniform traction conditions occur is problematic. The drive system would require a drive mechanism and a level of intelligence not currently found in off-road vehicles.

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