The Numic Spread: A Computer Simulation

We develop a mathematical model for the spread of Numic-speaking peoples across the Great Basin in the second millennium A.D., in accord with the ideas of Bettinger and Baumhoff (1982), who suggested a competitive interaction between the Numic and Prenumic peoples of the region. We construct differential equations representing two competing populations that spread by a diffusion process across an area representing the Great Basin. The demographic variables are fixed to agree with ethnographic data, while the migration rates are fitted to the estimated time for the completion of the spread. The model predicts a spatial distribution of the Numic languages in satisfactory agreement with observations and suggests new avenues of investigation.

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INDUSTRIAL POLLUTION AND ASTHMA: A MATHEMATICAL MODEL

Journal of Biological System ◽

10.1142/s0218339000000225 ◽

2000 ◽

Vol 08 (04) ◽

pp. 347-371 ◽

Cited By ~ 2

Author(s):

MINI GHOSH

Keyword(s):

Mathematical Model ◽

Computer Simulation ◽

Differential Equations ◽

Mathematical Models ◽

Stability Theory ◽

Industrial Pollution ◽

Air Pollutant ◽

Logistic Growth ◽

Nonlinear Mathematical Models

In this paper, some nonlinear mathematical models are proposed and analyzed to study the spread of asthma due to inhaled pollutants from Industry. The following two types of demographics are considered here; (i) population with constant immigration, (ii) population with logistic growth. In each type of demography, the following three cases have been considered regarding the release of pollutant into the environment; (i) when emission of the pollutant into the environment is constant, (ii) when emission of the pollutant is population dependent, and (iii) when emission of the pollutant is periodic. Using stability theory of differential equations and computer simulation, it is shown that due to an increase in the air pollutant, the asthmatic (diseased) population increases in the region under consideration.

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Mathematical model of a drive system with synchronous motors and vertical pumps

E3S Web of Conferences ◽

10.1051/e3sconf/20198402015 ◽

2019 ◽

Vol 84 ◽

pp. 02015

Author(s):

Andrzej Szafraniec

Keyword(s):

Mathematical Model ◽

Computer Simulation ◽

Differential Equations ◽

Power Transformer ◽

Nonlinear Differential Equations ◽

Drive System ◽

Dynamic State ◽

Electrical Load ◽

Synchronous Motors ◽

Electromechanical Transients

The paper presents a mathematical model of an electrical load node consisting of a power transformer and synchronous motors which rotate vertical pumps using non-rigid transmission. Modified principle of Hamilton–Ostrogradsky served as the basis for construction of the model. Using the developed mathematical model of the node, electromechanical transients in the object are studied. The resultant system of dynamic state nonlinear differential equations is introduced in the normal Cauchy’s form. Computer simulation findings are displayed by means of figures; they are under ongoing analysis.

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Glycemia monitoring

Nonlinear Analysis Modelling and Control ◽

10.15388/na.1998.2.0.15282 ◽

1998 ◽

Vol 2 ◽

pp. 23-30

Author(s):

Igor Basov ◽

Donatas Švitra

Keyword(s):

Diabetes Mellitus ◽

Mathematical Model ◽

Numerical Methods ◽

Differential Equations ◽

Blood Sugar ◽

Self Regulation ◽

Physiological System ◽

Non Linear ◽

The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

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Computer Simulation of the Response of Amperometric Biosensors in Stirred and non Stirred Solution

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2003.8.1.15174 ◽

2003 ◽

Vol 8 (1) ◽

pp. 3-18 ◽

Cited By ~ 15

Author(s):

R. Baronas ◽

F. Ivanauskas ◽

J. Kulys

Keyword(s):

Mathematical Model ◽

Computer Simulation ◽

Finite Difference ◽

Mass Transport ◽

Enzyme Reaction ◽

Analyte Concentration ◽

Amperometric Biosensors ◽

Finite Difference Technique ◽

Enzyme Layer ◽

Biosensor Response

A mathematical model of amperometric biosensors has been developed to simulate the biosensor response in stirred as well as non stirred solution. The model involves three regions: the enzyme layer where enzyme reaction as well as mass transport by diffusion takes place, a diffusion limiting region where only the diffusion takes place, and a convective region, where the analyte concentration is maintained constant. Using computer simulation the influence of the thickness of the enzyme layer as well the diffusion one on the biosensor response was investigated. The computer simulation was carried out using the finite difference technique.

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Resource Similarity, Market Commonality, and Spatial Distribution of Hotel Competitive Sets

Journal of Hospitality & Tourism Research ◽

10.1177/1096348020988579 ◽

2021 ◽

pp. 109634802098857

Author(s):

Zvi Schwartz ◽

Timothy Webb

Keyword(s):

Mathematical Model ◽

Spatial Distribution ◽

Performance Evaluation ◽

Critical Role ◽

Principal Agent ◽

Large Dataset ◽

Principal Agent Theory ◽

Agent Theory ◽

Performance And Evaluation

Index scores and competitive sets (compsets) play a critical role in the performance and evaluation of hotels. The reliance on these metrics has drawn skepticism in recent years as competitive sets may be opportunistically chosen, creating bias in performance evaluation. Drawing from the principal–agent theory and the theory of incentives, we explore whether the distance of the competitors chosen for a hotel’s compset influences revenue per available room (RevPAR) index scores. Based on the concepts of resource similarity and market commonality, we develop a novel mathematical model through which we empirically analyze a large dataset of 10,000 compsets. We find evidence that competitor distance influences index performance and that this relationship is bidirectional. Results show that hotels that outperform the competition may use distance to inflate RevPAR indices, while those that underperform may use distance to further reduce scores. These conflicting results may be reflected from the reverse motivations of the stakeholders.

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Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽

10.3390/math9111309 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1309

Author(s):

P. R. Gordoa ◽

A. Pickering

Keyword(s):

Mathematical Model ◽

Partial Differential Equations ◽

Differential Equations ◽

Acoustic Waves ◽

Elliptic Functions ◽

Coupled System ◽

Ultrasonic Waves ◽

Partial Differential ◽

Special Cases ◽

Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

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Design of worst spatial distribution of disturbances for a class of parabolic partial differential equations

Proceedings of the 2005, American Control Conference, 2005. ◽

10.1109/acc.2005.1470583 ◽

2005 ◽

Cited By ~ 5

Author(s):

M.A. Demetriou ◽

J. Borggaard

Keyword(s):

Spatial Distribution ◽

Partial Differential Equations ◽

Differential Equations ◽

Parabolic Partial Differential Equations ◽

Partial Differential

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Mathematical model implementation in conditions of uncertainty and possible risks

Energy and automation ◽

10.31548/energiya2021.04.137 ◽

2021 ◽

pp. 137-145

Author(s):

A. Kravtsov ◽

◽

D. Levkin ◽

O. Makarov ◽

◽

...

Keyword(s):

Thermal Conductivity ◽

Mathematical Model ◽

Differential Equations ◽

Boundary Value Problem ◽

Boundary Value Problems ◽

Layer Structure ◽

Boundary Value ◽

Goal Function ◽

Cauchy Problems ◽

System Of Differential Equations

The article presents the theoretical and methodological principles for forecasting and mathematical modeling of possible risks in technological and biotechnological systems. The authors investigated in details the possible approach to the calculation of the goal function and its parameters. Considerable attention is paid to substantiating the correctness of boundary value problems and Cauchy problems. In mechanics, engineering, and biology, Cauchy problems and boundary value problems of differential equations are used to model physical processes. It is important that differential equations have a single physically sound solution. The authors of this article investigate the specific features of boundary value problems and Cauchy problems with boundary conditions in a two-point medium, and determine the conditions for the correctness of such problems in the spaces of power growth functions. The theory of pseudo-differential operators in the space of generalized functions was used to prove the correctness of boundary value problems. The application of the obtained results will make it possible to guarantee the correctness of mathematical models built in conditions of uncertainty and possible risks. As an example of a computational mathematical model that describes the state of the studied object of non-standard shape, the authors considered the boundary value problem of the system of differential equations of thermal conductivity for the embryo under the action of a laser beam. For such a boundary value problem, it is impossible to guarantee the existence and uniqueness of the solution of the system of differential equations. To be sure of the existence of a single solution, it is necessary either not to take into account the three-layer structure of the microbiological object, or to determine the conditions for the correctness of the boundary value problem. Applying the results obtained by the authors, the correctness of the boundary value problem of systems of differential equations of thermal conductivity for the embryo is proved taking into account the three-layer structure of the microbiological object. This makes it possible to increase the accuracy and speed of its implementation on the computer. Key words: forecasting, risk, correctness, boundary value problems, conditions of uncertainty

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DIFFERENTIAL EQUATIONS FOR TRAIN STARTING WITH ELASTIC CONNECTIONS

Fundamental and Applied Problems of Engineering and Technology ◽

10.33979/2073-7408-2021-346-2-18-26 ◽

2021 ◽

Vol 2 ◽

pp. 18-26

Author(s):

I.P. POPOV

Keyword(s):

Mathematical Model ◽

Differential Equations ◽

Friction Force ◽

Static Friction ◽

Longitudinal Vibrations ◽

Maximum Tension ◽

Inert Mass ◽

The Moment ◽

Elastic Couplings ◽

Selection Of

The starting mode for the train is the most difficult. An effective method of pulling is the selection of coupling clearances. In this case, the cars are set in motion sequentially and the inert mass, as well as the static friction force immediately at the moment of starting, are minimal. This method has two significant drawbacks - a small fixed value of the gaps in the couplings and the shock nature of the impulse transfer. These disadvantages can be avoided by using elastically deformable couplings. The aim of this work is to construct a mathematical model of "easy" starting of a train with elastic couplings. The softening of the train start-off mode is essentially due to the replacement of the simultaneous start-off of the sections with alternate ones. To exclude longitudinal vibrations of the composition, after reaching the maximum tension of the coupling, the possibility of its harmonic compression should be mechanically blocked.

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