Let Tn be the semigroup of full transformation on a nite set n. Then, a map ∈ Tn is said to be a contraction, if for all x; y ∈ Xn, |x − y| ≤ |x − y|. Let CTn denote the subsemigroup of all contraction maps in Tn. In this paper we calculated the rank of the subsemigroup of CTn generated by elements of defect one, where the defect of ∈ CTn is dened to be the cardinality of the set Xn\im(∝) and rank of a semigroup is the smallest number of generators for the semigroup.
This article deals with the evaluation of some integrals involving error-, exponential- and algebraic functions with an objective to derive explicit expressions for the second and third order correction terms in the approximation of the modified error function, playing important role in the study of Stefan problem. The results obtained here appear to be new and resolve the lack of desired monotonicity property in the results presented by Ceretania et al.. Results derived here seem to be useful for the researchers working with Stefan problems.
Aims/ objectives: The study seeks to analyze the correlation of some selected stock returns with respect to both time and frequency domain, and also to forecast returns using Wavelet Coherence and Wavelet-ARIMA model as alternative to Pearson correlation and ARIMA model respectively. Study Design: Financial Mathematics. Place and Duration of Study: August 2016 to July 2017 , Department of Mathematics, Kwame Nkrumah University of Science and Technology. Methodology: We transform data using the Haar Wavelet as the basis function. Results: Results revealed interesting dynamics of correlations altering in time and across frequencies continually between paired returns. Furthermore, Wavelet-Arima method was found to be more appropriate for forecast with minimal error measure of forecast values. Conclusion: Given the heterogeneous trading behavior in stock markets, investors operate at different frequencies for their trade and investment preferences. Thus, apart from the time domain, there is a frequency domain, which represents various investment horizons.
In this paper, Darbo's and Rothe's xed point theorems is used to prove the existence of monotonic solutions for the nonlinear quadratic fractional order integral equation of the following type x(t) = h(t) + Gx(t)Jα a(t)f(H1x(t),H2x(t)), t ∈ [1, e], α > 0, where a belongs to appropriate Orlicz space. Here Jα stands the Hadamard-type fractional integral operator.
This paper proposes a modified Gompertz model with a constant free term based on the classical Gompertz model. Different from the three-sum method for determining the parameters of classical Gompertz model, this paper construct an optimization problem with the help of nonlinear least squares method. Moreover, employing the Levenberg-Marquardt method and the MATLAB software, the numerilal solution of the optimization problem is found. A numerilal example is provided in this paper. Finally, this paper uses this model to forecast the consumption level of Chinese rural residents, and the results illustrate the modified Gompertz model provides accurate prediction.