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Different classes of phenomenological universalities of environment dependent growths have been proposed. The logistic as well as environment dependent West-type allometry based biological growth can be explained in this proposed framework of phenomenological description. It is shown that logistic and environment dependent West-type growths are phenomenologically identical in nature. However there is a difference between them in terms of coefficients involved in the phenomenological descriptions. It is also established that environment independent and enviornment dependent biological growth processes lead to the same West-type biological growth equation. Involuted Gompertz function, used to describe biological growth processes undergoing atrophy or a demographic and economic system undergoing involution or regression, can be addressed in this proposed environment dependent description. In addition, some other phenomenological descriptions have been examined in this proposed framework and graphical representations of variation of different parameters involved in the description are executed.
In this communication, the incorrectness of phenomenological approach to the logistic growth equation, proposed by Castorina et al. is presented in detail. The correct phenomenological approach to logistic growth equation is also proposed here. It is
We study some statistical properties for the behavior of the average squared velocity -- hence the temperature -- for an ensemble of classical particles moving in a billiard whose boundary is time dependent. We assume the collisions of the particles
Dripping water from a faucet is a typical example exhibiting rich nonlinear phenomena. For such a system, the time stamps at which water drops separate from the faucet can be directly observed in real experiments, and the time series of intervals tau
Numerical experiments of the statistical evolution of an ensemble of non-interacting particles in a time-dependent billiard with inelastic collisions, reveals the existence of three statistical regimes for the evolution of the speeds ensemble, namely
Let $G$ be a virtually special group. Then the residual finiteness growth of $G$ is at most linear. This result cannot be found by embedding $G$ into a special linear group. Indeed, the special linear group $text{SL}_k(mathbb{Z})$, for $k > 2$, has residual finiteness growth $n^{k-1}$.