In this paper, we study an excision theorem of the dihedral and reflexive (co)homology theory of associative algebras. That is, for such an extension, we obtain a six-term exact sequence in the dihedral cohomology. Also, we present and prove the relation between cyclic and dihedral cohomology of algebras and some examples.
Abstract Let be a real hypersurface in a Sasakian space form . In this paper, we prove that if holds on , then is a Hopf hypersurface, where and denote the Jacobi operator structure and the induced operator from the Lie derivative with respect to the induced normal vector field , respectively. We characterize such the Hopf hypersurfaces of .
In this paper, we obtain a closed formula for the Kostant's partition function for the Lie algebras sl(4)(C) Received 20 August 2020 and sp(6)(C): Using this function, one can compute the weight multiplicity of irreducible representations Accepted 18 February 2021 of the Lie algebras sl(4)(C) and sp(6)(C).
In this article, we have suggested a class of estimators for the estimation of the population variance of the variable of interest.The proposed estimators used some certain known information of the auxiliary variable, such as kurtosis, coefficient of variation, and the minimum and maximum values.The properties of the suggested class of estimators such as the bias and mean squared error (MSE) are obtained up to the first order of approximation.In order to check the performances of the estimators and to verify the theoretical results, we conducted a simulation study.The results of the simulation study show that the proposed class of estimators have lower MSE than other existing estimators.This holds for all simulation scenarios.In the application part, we used data from Statistical Bureau of Pakistan, and from the Textbook of Cochran, which also confirms that the suggested class of estimators is more efficient than the usual unbiased variance estimator, ratio estimator, traditional regression estimator, and other existing estimators in survey literature.
This study attempts to put forward a framework that can be utilized to model the dynamics of the underlying returns on asset. The intention is to probe the dynamic connection between volatility of stock returns and trading volume of the Nairobi Securities Exchange (NSE20) index. The consequence of incorporating trading volume in the equation for conditional variance of the generalized autoregressive conditional heteroscedasticity (GARCH) model on volatility persistence is investigated. Further, this study brings into play GARCH, GARCH-M, and EGARCH models conditioned to normal, student-t and generalized error distributions to model the dynamic structure of the NSE20 index for the period 2 January 2001 to 31 December 2017. The results disclose some well-known stylized facts of returns on stock, for instance, volatility clustering, heavy tails, leverage effects, and leptokurtic distribution. The estimates of parameters of the three models, that is, GARCH (1, 1), GARCH-M (1, 1), and EGARCH models report that the correlation between stock returns volatility and trading volume is positive and statistically significant. Moreover, estimates of the coefficients of EGARCH (1, 1) model report an increased measure of persistence on volatility as well as volatility asymmetry and the absence of leverage effect in the returned volatility. Also, the estimates of GARCH (1, 1) and GARCH-M (1, 1) parameters report that volatility persistence dwindles after trading volume is incorporated in the equation for the conditional variance.
