Empirical forecasting is the science of using past data to predict the future, without physical modeling. For these, probability functions are used, normally bell-shaped Gaussian or Gaussian- like. Taleb in his book the Black Swan introduces for this purpose the concept of scalable functions. Here it is shown that the only scalable functions are power-law functions and they can be treated as one and the same. Moreover, the analytical problems of these functions are discussed. Scalable functions are inadequate for empirical forecasting.
This paper analyses the dynamics of a fishery system in an aquatic environment that consists of two zones: water hyacinth zone and free zone. Fish harvesting is allowed in both the zones and fish migration is allowed from water hyacinth zone to free zone and not back. This paper presents dynamics of the stability when discrete time delay is incorporated in the fish death rate due to oxygen depletion and water pollution caused by water hyacinth. It is shown that the time delay can cause a switch from stable state to unstable state and there by Hopf-bifurcation occurs. Numerical simulations are carried out to validate the analytical findings.
The existence of Paley-Hadamard (4t − 1, 2t − 1, t − 1) difference sets provides a platform for solving the equation δ¯δ = n in the cyclotomic ring Z[ζ4t−1], where ζ4t−1 is root of unity, n > 1 and t > 1 are integers. We look at cases where ⟨n⟩ = ⟨δ⟩⟨¯δ⟩ in Z[ζ4t−1] but δ¯δ = n has trivial solutions. This criterion is combined with other results to conclude non-existence of some difference set parameters.
We consider piecewise defined differential dynamical systems which can be analysed through symbolic dynamics and transition matrices. We have a continuous regime, where the time flow is characterized by an ordinary differential equation (ODE) which has explicit solutions, and the singular regime, where the time flow is characterized by an appropriate transformation. The symbolic codification is given through the association of a symbol for each distinct regular system and singular system. The transition matrices are then determined as linear approximations to the symbolic dynamics. We analyse the dependence on initial conditions, parameter variation and the occurrence of global strange attractors.
This paper contains several generalizations of the theorems for common fixed point of R. Kannan, S. K. Chatterjea and P. V. Koparde & B. B. Waghmode types of mappings. These generalizations are done by using a sequentially convergent mappings. Trough several examples, we have shown that the generalized claims are inapplicable, and that the obtained generalized claims prove the existence of a unique common fixed point of considered mappings.
Cognitive informatics helps in comprehending the software characteristics and its complexity measures can be used to predict critical information about testability of software system. In this paper, a cognitive complexity metric for C++ programming language is formulated. Since C++ is an object – oriented language, the cognitive complexity metric is capable to evaluate any object- oriented language. This paper presents a new cognitive complexity metric named Improved Cognitive Complexity Metric (ICCM) and perform a comparative study of the proposed metric with the existing metric such as NCCOP, CFS, CICM and CPCM. The result shows that the proposed metric performs better than other metrics by giving more information contained in the software and reflecting the understandability of a source code. Also, an attempt has also been made to present the relationship among ICCM, NCCOP, CICM, CFS and CPCM using Pearson correlation coefficient method.