scholarly journals Continuous- discrete mathematical model for control of growth of a plant population in a given time period under a given budget

2018 ◽  
Vol 2 (2) ◽  
Author(s):  
Dilip Kumar Bhattacharya
Keyword(s):  
Discrete Model ◽  
Continuous Model ◽  
Plant Population ◽  
Logistic Growth ◽  
Initial Population ◽  
Growth Equation ◽  
Time Period ◽  
Net Profit ◽  
Discrete Mathematical Model ◽  
The Given

The paper discusses an economically viable way of controlling biomass of a vegetable plant population under the use of fertilizer in a given span of time under a given budget of expenditure. The span of time is divided in some suitable consecutive periods of equal duration P, called cohorts. The treatment is done on the available population of plant at the beginning of each cohort for a suitable time; the continuous dynamics in the change of biomass for this time period is governed by an ordinary differential equation involving total effort exerted in treating the initial population. Taking this improved value at the end of the time period as the initial value, the biomass of the population is allowed to move under its normal continuous dynamics given by Logistic growth equation for the rest of the time of that cohort.  The final concentration of the biomass at the end of the first cohort is obtained by following the above two types of dynamics. This is also considered as the starting biomass for the next cohort. The same process adopted for the first cohort is repeated for calculating the improvement of the biomass in the second cohort and the whole process is repeated till the end of the final cohort is reached. Next an objective function is formed for the given span of time. This measures the net profit in getting improvement in the weight of the biomass less the cost involved in the process of improving the weight of the biomass for the given period of time. As the analysis is done in considering different cohorts at regular intervals of time, so it is a discrete model. As within each cohort, the dynamics takes place continuously, so it is a continuous model too. As a whole, the model is found to be a continuous- discrete model. Hence method of optimal control for continuous-discrete model is used to determine how the treatment at the starting of each cohort be adjusted, depending on the allocated budget, so that the total net profit is maximum.

The Ideology of Socialism and the Armenian Political Parties

wisdom ◽  
2020 ◽  
Vol 15 (2) ◽  
pp. 107-113
Author(s):  
Gegham HOVHANNISYAN
Keyword(s):  
Political Parties ◽  
Political Life ◽  
The Political ◽  
Political Organizations ◽  
Social Democrats ◽  
Time Period ◽  
The Social ◽  
Political Forces ◽  
The 19Th Century ◽  
The Given

The article covers the manifestations and peculiarities of the ideology of socialism in the social-political life of Armenia at the end of the 19th century and the beginning of the 20th century. General characteristics, aims and directions of activity of the political organizations functioning in the Armenian reality within the given time-period, whose program documents feature the ideology of socialism to one degree or another, are given (Hunchakian Party, Dashnaktsutyun, Armenian Social-democrats, Specifics, Socialists-revolutionaries). The specific peculiarities of the national-political life of Armenia in the given time-period and their impact on the ideology of political forces are introduced.

Utilization of remote sensing for estimation of scale of cutting and growing of forest zones

2017 ◽  
Vol 920 (2) ◽  
pp. 57-60
Author(s):  
F.E. Guliyeva
Keyword(s):  
Remote Sensing ◽  
Fixed Time ◽  
Time Interval ◽  
Time Points ◽  
Average Value ◽  
Time Period ◽  
Remote Estimation ◽  
The Given ◽  
Forest Cutting

The study of results of relevant works on remote sensing of forests has shown that the known methods of remote estimation of forest cuts and growth don’t allow to calculate the objective average value of forests cut volume during the fixed time period. The existing mathematical estimates are not monotonous and make it possible to estimate primitively the scale of cutting by computing the ratio of data in two fixed time points. In the article the extreme properties of the considered estimates for deforestation and reforestation models are researched. The extreme features of integrated averaged values of given estimates upon limitations applied on variables, characterizing the deforestation and reforestation processes are studied. The integrated parameter, making it possible to calculate the averaged value of estimates of forest cutting, computed for all fixed time period with a fixed step is suggested. It is shown mathematically that the given estimate has a monotonous feature in regard of value of given time interval and make it possible to evaluate objectively the scales of forest cutting.

scholarly journals Spatiotemporal Patterns Formed by a Discrete Nutrient-Phytoplankton Model with Time Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Feifan Zhang ◽  
Wenjiao Zhou ◽  
Lei Yao ◽  
Xuanwen Wu ◽  
Huayong Zhang
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Numerical Simulations ◽  
Functional Response ◽  
Bifurcation Analysis ◽  
Discrete Model ◽  
Continuous Model ◽  
Spatiotemporal Patterns ◽  
Homogeneous Steady State ◽  
Simulation Results

In this research, a continuous nutrient-phytoplankton model with time delay and Michaelis–Menten functional response is discretized to a spatiotemporal discrete model. Around the homogeneous steady state of the discrete model, Neimark–Sacker bifurcation and Turing bifurcation analysis are investigated. Based on the bifurcation analysis, numerical simulations are carried out on the formation of spatiotemporal patterns. Simulation results show that the diffusion of phytoplankton and nutrients can induce the formation of Turing-like patterns, while time delay can also induce the formation of cloud-like pattern by Neimark–Sacker bifurcation. Compared with the results generated by the continuous model, more types of patterns are obtained and are compared with real observed patterns.

Progress curve analysis of qRT-PCR reactions using the logistic growth equation

2011 ◽  
Vol 27 (5) ◽  
pp. 1407-1414 ◽  
Author(s):  
Meile Liu ◽  
Claudia Udhe-Stone ◽  
Chetan T. Goudar
Keyword(s):  
Curve Analysis ◽  
Logistic Growth ◽  
Growth Equation ◽  
Qrt Pcr ◽  
Progress Curve

scholarly journals The Model of Sociological Education in the USSR (the Late 1950s — Early 1980s)

2021 ◽  
pp. 112-117
Author(s):  
Sergei V. Kozin ◽  
Zhanna B. Litvinova
Keyword(s):  
Sociological Research ◽  
Scientific Publications ◽  
Mutual Exchange ◽  
Research Areas ◽  
Time Period ◽  
The Given ◽  
Soviet Sociology

The article provides an analysis of foreign and Soviet scientific publications devoted to the problem of sociological education, the “revival” of Soviet sociology, as well as to the role and place of sociology among the sciences, in society and education. The given study covers the time period of the late 1950s — early 1980s and briefly describes the education of the population of the USSR at that time. Looking through the works on Soviet sociology, the authors show that sociology was introduced not only into the research areas of specific universities and laboratories, but also into many other branches and spheres of activity, as well as into the authorities’ activity. The authors of the article purposefully focus on the role of consolidation and mutual exchange of sociological research from various sociological services.

scholarly journals Extended logistic growth model for heterogeneous populations

2017 ◽  
Author(s):  
Wang Jin ◽  
Scott W McCue ◽  
Matthew J Simpson
Keyword(s):  
Cell Proliferation ◽  
Growth Model ◽  
Numerical Solutions ◽  
Cellular Level ◽  
Logistic Growth ◽  
Logistic Growth Model ◽  
Living Tissues ◽  
Discrete Mathematical Model ◽  
The Continuum

AbstractCell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.

scholarly journals CULTURAL HERITAGE MONUMENT DOCUMENTATION THROUGH ADAPTIVE PARAMETRIC DESIGN PROCESS

2021 ◽  
Vol XLVI-M-1-2021 ◽  
pp. 769-776
Author(s):  
G. Tryfonos ◽  
M. Ioannides ◽  
A. G. Anastasi ◽  
V. A. Apostolou ◽  
P. P. Pieri ◽  
...  
Keyword(s):  
Cultural Heritage ◽  
Parametric Design ◽  
3D Models ◽  
Building Information Modelling ◽  
3D Data ◽  
Time Period ◽  
Building Information ◽  
Game Developers ◽  
The Given ◽  
The City

Abstract. The paper presents a novel adaptive parametric documentation, modelling and sharing methodology, which aims to achieve a continuous holistic documentation, data processing and sharing process for cultural heritage community, such as architects, engineers, archaeologists, conservators, programmers, fabricators, contest creators, game developers, scholars and common citizens. Thus, the use of advance parametric and building information modelling software allows the processing and specification of all data by creating the 3D models needed for the multidisciplinary experts. Two Cypriot case studies from the medieval time period have been chosen for the development, and evaluation of our proposed methodology in order to investigate the process of modelling and sharing all the given metadata and 3D data. The first one is the Asinou Church, a UNESCO Heritage stone monument in the Troodos Mountains with a unique interior and the Kolossi Castle, a former Crusader stronghold on the west of the city of Limassol on the island of Cyprus.

scholarly journals Psi-Caputo Logistic Population Growth Model

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Muath Awadalla ◽  
Yves Yannick Yameni Noupoue ◽  
Kinda Abu Asbeh
Keyword(s):  
Population Growth ◽  
Fractional Derivative ◽  
Carrying Capacity ◽  
Chinese Population ◽  
Logistic Model ◽  
Logistic Equation ◽  
Logistic Growth ◽  
Growth Equation ◽  
Uniqueness Of The Solution ◽  
Better Than

This article studies modeling of a population growth by logistic equation when the population carrying capacity K tends to infinity. Results are obtained using fractional calculus theories. A fractional derivative known as psi-Caputo plays a substantial role in the study. We proved existence and uniqueness of the solution to the problem using the psi-Caputo fractional derivative. The Chinese population, whose carrying capacity, K, tends to infinity, is used as evidence to prove that the proposed approach is appropriate and performs better than the usual logistic growth equation for a population with a large carrying capacity. A psi-Caputo logistic model with the kernel function x + 1 performed the best as it minimized the error rate to 3.20% with a fractional order of derivative α  = 1.6455.

scholarly journals Variation in Marginal Response to Nitrogen Fertilizer between Locations

2000 ◽  
Vol 32 (2) ◽  
pp. 363-372 ◽  
Author(s):  
Dale K. Graybeal
Keyword(s):  
North Carolina ◽  
Nitrogen Fertilizer ◽  
Logistic Growth ◽  
Growth Equation ◽  
Finite Sample ◽  
Dummy Variable ◽  
Bootstrap Simulation ◽  
Sample Covariance ◽  
The Mean ◽  
Parameter Values

AbstractA logistic growth equation with time and location varying parameters was used to model corn response to applied nitrogen. A nonlinear dummy-variable regression model provided a parsimonious representation of site and time effects on parameter values. The model was used to test for the equality of the mean marginal product of nitrogen fertilizer between locations on the coastal plain of North Carolina. Monte Carlo simulation and bootstrap simulation were used to construct finite sample covariance estimates. Results support rejection of the hypothesis that mean marginal products are equal when nitrogen is applied at 168 kg/ac. A comparison of bootstrapped errors and asymptotic errors suggests that results based on asymptotic theory are fairly reliable in this case.

scholarly journals Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Zhaofeng An ◽  
Suxia Zhang ◽  
Jinhu Xu
Keyword(s):  
Public Health ◽  
Health Education ◽  
Differential Equations ◽  
Discrete Model ◽  
Public Health Education ◽  
Continuous Model ◽  
Basic Reproductive Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Nsfd Scheme

In this paper, an alcoholism model of SEAR type with different susceptibilities due to public health education is investigated, with the form of continuous differential equations as well as discrete differential equations by applying the Mickens nonstandard finite difference (NSFD) scheme to the continuous equations. Threshold dynamics of the continuous model are performed by constructing Lyapunov functions. The analysis of a discrete model indicates that the alcohol-free equilibrium is globally asymptotically stable if the basic reproductive number R0<1, and conversely, the alcohol-present equilibrium is globally asymptotically stable if R0>1, revealing the consistency and efficiency of the discrete model to preserve the dynamical properties of the corresponding continuous model. In addition, stability preserving and the impact of the parameters related with public health education are conducted by numerical simulations.

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