Recovering memory kernels in parabolic transmission problems in infinite time intervals: the non-accessible case

2010 ◽  
Vol 18 (4) ◽  
Author(s):  
Jaan Janno ◽  
Alfredo Lorenzi
Keyword(s):  
Infinite Time ◽  
Time Intervals ◽  
Transmission Problems

Optimization of discounted income for a structured population exposed to harvesting

2021 ◽  
pp. 15-25
Author(s):  
Anastasia V. Egorova
Keyword(s):  
Time Moment ◽  
Renewable Resource ◽  
Optimal Harvesting ◽  
Infinite Time ◽  
System Of Difference Equations ◽  
Time Intervals ◽  
Homogeneous Population ◽  
Structured Population ◽  
The Cost ◽  
Conventional Unit

A structured population the individuals of which are divided into n age or typical groups x_1,…,x_n. is considered. We assume that at any time moment k, k = 0,1,2… the size of the population x(k) is determined by the normal autonomous system of difference equations x(k+1)=F(x(k)), where F(x)=col(f_1 (x),…,〖 f〗_n (x) ) are given vector functions with real non-negative components f_i (x), i=1,…n. We investigate the case when it is possible to influence the population size by means of harvesting. The model of the exploited population under discussion has the form x(k+1)=F((1-u(k) )x(k) ), where u(k)= (u_1 (k),…,u_n (k))∈〖[0; 1]〗^n is a control vector, which can be varied to achieve the best result of harvesting the resource. We assume that the cost of a conventional unit of each of n classes is constant and equals to C_i≥0, i=1,…,n. To determine the cost of the resource obtained as the result of harvesting, the discounted income function is introduced into consideration. It has the form H_α (u ̅,x(0))=∑_(j=0)^∞▒〖∑_(i=1)^n▒〖C_i x_i (j) u_i (j) e^(-αj) 〗,〗 where α>0 is the discount coefficient. The problem of constructing controls on finite and infinite time intervals at which the discounted income from the extraction of a renewable resource reaches the maximal value is solved. As a corollary, the results on the construction of the optimal harvesting mode for a homogeneous population are obtained (that is, for n = 1).

Arrow-type sufficient conditions for optimality of age-structured control problems

2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Vladimir Krastev
Keyword(s):  
Boundary Conditions ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Infinite Time ◽  
Time Intervals ◽  
Sufficient Conditions For Optimality ◽  
Age Structured

AbstractWe consider a class of age-structured control problems with nonlocal dynamics and boundary conditions. For these problems we suggest Arrow-type sufficient conditions for optimality of problems defined on finite as well as infinite time intervals. We examine some models as illustrations (optimal education and optimal offence control problems).

Rotational Characteristics of the Green Solar Corona: 1947-1991

1994 ◽  
Vol 144 ◽  
pp. 139-141 ◽  
Author(s):  
J. Rybák ◽  
V. Rušin ◽  
M. Rybanský
Keyword(s):  
Solar Corona ◽  
World Wide ◽  
Rotation Period ◽  
Original Data ◽  
Coronal Emission ◽  
Time Intervals ◽  
Data Set ◽  
The World ◽  
Coronal Emission Line ◽  
Homogeneous Data

AbstractFe XIV 530.3 nm coronal emission line observations have been used for the estimation of the green solar corona rotation. A homogeneous data set, created from measurements of the world-wide coronagraphic network, has been examined with a help of correlation analysis to reveal the averaged synodic rotation period as a function of latitude and time over the epoch from 1947 to 1991.The values of the synodic rotation period obtained for this epoch for the whole range of latitudes and a latitude band ±30° are 27.52±0.12 days and 26.95±0.21 days, resp. A differential rotation of green solar corona, with local period maxima around ±60° and minimum of the rotation period at the equator, was confirmed. No clear cyclic variation of the rotation has been found for examinated epoch but some monotonic trends for some time intervals are presented.A detailed investigation of the original data and their correlation functions has shown that an existence of sufficiently reliable tracers is not evident for the whole set of examinated data. This should be taken into account in future more precise estimations of the green corona rotation period.

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