First-order fractionally integrated non-separable spatial autoregressive (FINSSAR(1,1)) model and some of its properties

Spatial modelling has its applications in many fields. There exist in the literature a class of models known as the fractionally integrated separable spatial autoregressive (FISSAR) model. In this paper the objective of our research is to develop a non-separable counterpart of the FISSAR model. We term this model as the fractionally integrated non-separable spatial autoregressive (FINSSAR) model. The FINSSAR model is a more general model as it encompasses the FISSAR and the standard separable autoregressive (SSAR) models. The theoretical autocovariance function and the spectral function of the model are obtained and some numerical results is presented. This model may be able to model many type of real phenomen

Autocovariance function of the Fractionally Integrated Separable Spatial ARMA (FISSARMA) models

Spatial modeling is important in many fields and there are various kinds of spatial models. One of such models is known as the fractionally integrated separable spatial ARMA (FISSARMA) model. In the area of time series analysis, Sowell (19927. Sowell, F. (1992). Maximum likelihood estimation of stationary univariate fractionally integrated time series models. J. Econ. 53:165–188.[CrossRef], [Web of Science ®]View all references) has established the autocovariance function of the long-memory models using hypergeometric function. In this paper we will extend Sowell’s work for FISSARMA models

Some properties of the normalized periodogram of a fractionally integrated separable spatial ARMA (FISSARMA) model

In this article, we study the properties of the normalized periodogram of the Fractionally Integrated Separable Spatial ARMA (FISSARMA) models. In particular, we establish the asymptotic mean of the normalised periodogram and the asymptotic second-order moments of the normalised Fourier coefficients. We also establish the asymptotic distribution of the normalised periodogram. Some numerical results are also provided

Estimation of the memory parameters of the fractionally integrated separable spatial autoregressive (FISSAR(1,1)) model : a simulation study.

In this article, we implement the regression method for estimating (d1,d2) of the FISSAR(1,1) model. It is also possible to estimate d1 and d2 by Whittle’s method. We also compute the estimated bias, standard error, and root mean square error by a simulation study. A comparison was made between the regression method of estimating d1 and d2 to that of the Whittle’s method. It was found in this simulation study that the regression method of estimation was better when compare with the Whittle’s estimator, in the sense that it had smaller root mean square errors (RMSE) values

An Efficient Synthesis of Tetrahydrobenzo[ b

Tetrahydrobenzo[b]pyran derivatives were efficiently synthesized by the reaction of appropriated aromatic aldehydes, malononitrile and dimedone in the presence of SiO2-Pr-SO3H as a nanoporous and recoverable solid acid catalyst, in good to excellent yields. Single crystal x-ray analysis conclusively confirmed the structure of the 2-amino-3-cyano-7,7-dimethyl-4-(4-methylphenyl)-5-oxo-4H-5,6,7,8-tetrahydro-benzopyran

A Review of Coronavirus Disease (COVID-19) in Children

Abstract: Since December 2019, an outbreak of coronavirus disease 2019 (COVID-19) with a high morbidity and mortality rate has spread globally and affected all age groups. Children can carry and transmit the novel coronavirus, but usually do not develop severe disease. The number of children who contracted coronavirus disease 2019 has increased significantly; however, compared to adults, there have been fewer reported cases of COVID-19 in the pediatric population. This review is mainly about the epidemiological features, clinical findings, laboratory tests, imaging, and treatment recommendations in children with COVID-19 disease

A first-order spatial integer-valued autoregressive SINAR(1,1) model.

Binomial thinning operator has a major role in modeling one-dimensional integer-valued autoregressive time series models. The purpose of this article is to extend the use of such operator to define a new stationary first-order spatial non negative, integer-valued autoregressive SINAR (1,1) model. We study some properties of this model like the mean, variance and autocorrelation function. Yule-Walker estimator of the model parameters is also obtained. Some numerical results of the model are presented and, moreover, this model is applied to a real data set

Effect of Benzyltrimethylammonium Ion as a Co-directing Agent on Phase Transitions in a Nanostructure Silica/Surfactant Composite

Effect of benzyltrimethylammonium ion as a co directing agent in phase transition from hexagonal to cubic and lamellar mesophases was studied in the constant pH at 130 °C. This phase transformation was carried out in constant surface charge and pore size distribution (2 nm). Influence of BTMA+ ions between head and tail of surfactant and phase transformation were observed by using the XRD and elemental analysis

Knoevenagel condensation of isatins with malononitrile/ethyl cyanoacetate in the presence of sulfonic acid functionalized silica (SBA-Pr-SO3H) as a new nano-reactor

The Knoevenagel condensation between isatins and active methylene compounds like malononitrile and ethyl cyanoacetate to prepare 2-oxoindolin-3-ylidene malononitrile/ cyanoacetates is described. The reactions occur in the presence of sulfonic acid functionalized silica SBA-15 (SBA-Pr-SO3H) in an aqueous medium giving excellent yields of the products in short reaction times. SBA-Pr-SO3H with a pore size of 6 nm is found to be an efficient and environmentally benign catalyst for this reaction